A Revolution in Structural Engineering: The Rise of The Pure Tension Tower
Author: Christophe Pochari, Christophe Pochari Energietechnik, Bodega Bay California.
The earth’s polar equator thermal gradient is a powerful heat engine that is a free and unlimited source of mechanical power. While there are challenges associated with its effective capture, it would be silly to ignore its vast potential just because we have more convenient sources of combustible fuels at the moment.
The boundary layer for wind traveling along the surface of the earth is up to 350 meters in height even on relatively smooth grass surfaces. This frictional resistance considerably reduces the available kinetic energy in the wind, constraining the potential power that existing wind turbines can extract. If a method existed to build wind turbines up to 350 meters tall, their power output would increase by 3.4x from a height of 50 meters (hub height for the Enercon E-44), without making any changes to the basic design and aerodynamics of the turbine, which has already reached a physical limit. Wind speed for a hypothetical location in Nebraska USA increases from 8.39 m/s at 50 m to 12.64 m/s at 350 meters as predicted by the power law using an exponent of 0.15-0.16 for grassy surfaces. Since the energy yield from wind is the cube of velocity, a 1.5 increase in wind speed translates into a much larger 3.4x increase in power. A near quadruplicating of the power density of a wind turbine is a very significant thing, allowing it to produce electricity for less than third of the current cost. Unfortunately, such an ultra-tall tower is simply not feasible with current engineering. Existing wind turbine towers make use of cantilevered masts, generating immense bending stress at their mounting point, requiring very thick steel construction, which results in high fabrication and material costs.
A better solution is desired so that the higher kinetic energy of higher altitude winds beyond the boundary layer can be tapped into economically.
Existing tall and slender structures are limited by the elastic deformation of the plastic material, primarily metal, used in their construction. Elastic deformation is a major constraint on the structural efficiency of metallic structures. An ideal structure would be constructed using only tension-loaded components, such as cables and pressure vessels, so that each structural element could be loaded just below the yield point without any structurally compromising deformation. To create a truly high-altitude structure, a means is sought whereupon the elastic deformation can occur only via the circumferential stretching of a cylinder which does not compromise the integrity of the tower. If the tower is made out of thin-wall metal but with a large diameter to evade Euler buckling, it will merely fail by crumpling or what’s called “flexural buckling”, so this is not a solution.
A classic way to increase the lateral stiffness of a tower is by fastening guy cables to transfer the lateral bending moment into vertical compression. Unfortunately, such a scheme does not increase the load capacity of a slender-column tower, since it simply discretizes the compression forces between the guy-cable mounting points. Guy cables therefore only impart an improvement in the stiffness of the tower, but they do not increase the load capacity, they are not in themselves a source of strength. A wind turbine is heavy and generates strong torsional loads, which cannot be born by a thin-wall tubular or lattice tower, regardless of whether it is laterally stabilized by guy cables. In order for an ultra-tall tower to work for a wind turbine, it must be very stiff and able to carry tens of tons of both static dead-weight and occasional gust loads which generate strong bending and subsequent compressive forces.
An elegant and perhaps genius solution is to employ the power of pneumatics to create a continuously pressurized gas cylinder acting as a tower to absorb the entirety of the compressive loads. Upon first examination, this idea appears obvious and seems to solve virtually every problem faced by the designer of a tall tower. Surprisingly, such an idea has never hitherto been proposed.
A the end of this cylinder a sliding piston would be placed to carry the loads acting on the tower. A method to seal the pressurized gas would be devised. In such a scheme, the lateral loads are transferred to compression along with any dead weight placed on the tower, which is then converted to hoop stress in the cylinder by pushing against the piston. But since the cylinder is filled with pressurized gas, the downward force is resisted by the force acting on the piston by the compressed air, which is at a steady-state pressure generating mild hoop stresses on the cylinder wall. A 750mm diameter constant diameter tube could generate 150 tons of force or equal load bearing capacity before displacement using only 4 MPa of gas pressure, requiring only 8mm in wall thickness to keep hoop stress under 160 MPa. This simply an unparalleled degree of structural efficiency, the ability of a light-weight thin-wall tube to carry 150 tons can only be realized using the power of pneumatics. The weight of this tube would only be 55 kg/m, or 19 tons for the entire tower! In this scheme, we have completely eliminated elastic deformation of the tower’s main structural member, and we are now able to generate a tower as tall as 350 meters using lightweight aluminum pipes filled with compressed air and stayed with cables connecting to the piston at the apex of the tower. The designer is no longer required to use thick gauge material to generate the required stiffness and strength to bear compressive loads since cables can produce all the needed stiffness by transferring their bending moment into the upwardly forced piston, and the walls of the cylinder can carry this compression force via gas pressure. This scheme is extraordinarily elegant since it optimizes the distribution of forces to minimize loading in ways that utilizes a plastic materials greatest asset: its strength in tension, while minimizing its greatest weakness: its susceptibility to deformation, itself a corollary of the very ductility we want for such a structure.
A series of cables can then be spanned vertically connecting intermediate guy cables to stabilize the thin-wall tube. A 0.75-1 meter diameter thin-wall aluminum cylinder/tube can be braced by cables every 25-40 meters, allowing an otherwise infinitely slender tubular column to be broken up into discrete rigid sections. Such a structure would be unique in the world of structures in that strictly speaking, it has no compression-loaded structural members other than its foundation. The guy cables experience only tension, and the thin-wall pressure-bearing column experiences circumferential and longitudinal tension. It should be noted that pressure vessels can be constructed out of materials with no intrinsic compressive strength or stiffness, such as aramid fiber (Kevlar) widely used to construct ultra-lightweight pressure vessels for space vehicles, so a pressure vessel is a solely tension-loaded structure. In order for such a structure to maintain long term structural integrity, redundant air compressors can be placed at the base of the tower to counter any leaks that could develop along the piston seal. A number of additional design considerations are discussed in a more extensive description that can be found in the following text.
Christophe Pochari Energietechnik is the first company in the world to devise an entirely tension-loaded structure in the category of high-altitude guyed towers. When we mention “hydraulic or pneumatic” with reference to a tower, people assume it is some form of self-erecting mechanism, which is of course not new at all. We are not claiming novelty or that self-erection by itself is revolutionary, it is not, but we are claiming novelty to devising a method to build a structure who’s load capacity is unparalleled by conventional means. As long as the structure must bear weight with the material’s longitudinal stiffness, the tower is still limited like any slender structure: by buckling.
A “pressurized gas filled tubular guyed-tower” is a sui generis structure, in that it has no components other than a foundation, loaded in compression! Under the premise of ordinary structural engineering, much like one cannot design around the law of thermodynamics, it is strictly impossible to construct a conventional structure, that is one that relies on stiff members for load transfer, purely in tension. Such a scheme would be seen as violating basic mechanics, as it contains a discontinuous load path continuum. To truly “erase” compression, one must use hydrostatics. It will become immediately obvious upon further elucidation that a pressurized structure is extremely fascinating in this respect. Even in Buckminster Fuller’s famous “tensegrity”, there is always a lowly compression member, that might not catch the eye of the beholder, but that surely carries the tension of the string and transfers it right back into compression. One cannot escape the need for compression, because, by definition, compression is the reciprocal of tension, like a magnetic field is to an electric field or cold is to heat. A hydrostatic structure, being pressurized and loaded in hoop stress, does not actually possess any compression-loaded parts. One could say that the use of gas provides a “loophole” or a cheat that allows a violation of the conventional structural engineering logic that dictates that for every tension-loaded member, a member must ultimately bear compression in order to maintain a continuum. Since we can exclude the foundation pad as a compression member because it falls outside of the domain of the “above ground” structure, if we restrict ourselves to examining the portion of the structure that actually performs the critical load transfer, we find not a single component loaded in compression. Naturally, in light of this fascinating property, we have decided to name the technology a “pure tension tower”: (PTT). A pure tension tower in this case is merely a type of pure tension structure, the broader category refers to any structure, such as an inflatable dome or any pressurized structure that effectively transfer all their otherwise compressive forces isostatically to produce compression forces, but compression forces which do not necessary possess a load-path distribution parallel or coincident to the structure’s vertical plane. A pure tension tower thus produces compression, but only in the X and Y coordinate of the Cartesian plane. It therefor is able to violate this structural engineering dictum by cleverly orientating the compression in a manner that does not elastically deform the tower’s inherently slender shape. This term isostatic is important, because it perfectly describes the behavior of gas or liquid under pressure, they do not hold any preference, spreading their force homogenously across the entirety of the load-bearing surface. One cannot create points of force concentration or dispersal with a gas or liquid, it will find every crevice and impart its constant pressure towards it. The inherent tendency of pressurized fluids or liquids to produce uniform forces is termed Pascal’s law. The conclusion of this review is to the need to stress the role of the gas’s ability to impart isostatic force, this is the only conceivable way to generate a state of pure tension and what allows us to bypass this fundamentally structural axiom.
Christophe Pochari Energietechnik has employed rudimentary logic according to first principles to the field of structural engineering to improve the structural efficiency of high-altitude structures in order to improve the energetic yield of wind generators. In order to do this, we designed a tower that could reach heights of 350 meters to increase the power output by 3.5 fold over a base height of 50 meters. In order to reduce the weight of this otherwise massively heavy tower, we have made use of a technology using internally pressurized thin-wall tower sections that are held in place laterally by tensioned guy cables. The weight of the wind turbine is born by the pressure inside these thin wall columns which push a piston that freely reciprocates within the cylindrical tower. The entire structure is made stiff and rigid by tightening guy cables to this piston at the top of the tower. The confluence of the higher wind speed and reduced mass needed to build the tower affords a marked reduction in the levelized cost of energy, since more energy is yielded from the same mass of material, yet even less weight is needed to construct it for the same power output. Further details of the technology are provided in the text below. Images and schematics which readily illustrate the working principle of the invention are provided below as well as priority patents which have alluded to similar concepts before. To summarize as simply as humanly possible, the tower uses the pressure of gas to exert force on a piston which bears the weight of the wind turbine as well as tensions a series of guy cables which prevents the structure from toppling over. The basic rationale is that thin and tall columns are suspectable to buckling due to elastic deformation, by pressurizing them, no force is exerted on the column as it merely serves as a way to keep the gas from escaping.
Note this load-path and force distribution diagram. As weight is exerted on the piston, since there is zero physical contact between the floating piston and the tube’s wall, all force must be transferred to pressure in the liquid or gas, resulting in isostatic force transfer directly into hoop stress on the walls of the tower. This principle does not mean the structure has infinite load capacity, if more weight is placed on the piston than is tolerable as pressure in the tube, the tube will burst and the structure will then have zero load capacity. The structures “Achilles’ heel” is the need to eliminate 100% of the force or load transfer between the free-floating piston and pressure tube wall, this can be accomplished by a clever method explained in further detail. The invention is so simple it can be grasped by a child. But the diesel engine too is a simple invention (squeeze air to ignite viscous fuels), but it took a man of great intellect to invent it! Note that the image above was made with the assumption synthetic cables could be used prior to the realization that materials like Dyneema are subject to creep upon subject to a continuous load. The cables used would be ultra high strength steel cables from the tire industry. The invention effectively pertains to a column of compressed media that acts as loading bearing platform. As long as the fluid is contained and sealed within the cylindrical container, the structure has an “upward impulse” that keeps it aloft. Note that the article below is poorly organized as it was written very quickly and frequently edited with new information added. Christophe Pochari Energietechnik is a one-man operation and therefore lacks a full-time editor. Some parts of this text are unrelated strictly to the technology in question and there are entire sections of text with no bearing to the technology in question. We are in the processing of cleaning up the article and removing these sections. The choice of a rather long and discursive article was not to bother the reader, but to highlight important points we believe were worth covering. Those who are not interested are encouraged to skim over and focus their attention on the technical schematics or short YouTube video. The article covers disparate topics such as manufacturing and material selection. The crux of the matter should be summarized in a manner as condensed as possible. This has been provided by a very brief and parsimonious introductory text above.
The image below is Christophe Pochari Energietechnik‘ “Hydrostatus” 750 kW 350-meter tall high power density wind generator. The turbine’s nacelle is constructed from a iso-grid aluminum truss-frame structure and clad with thin-gauge aluminum walls. The flat quad-pattern rectangular structure spanning outward is constructed from the same aluminum iso-grid, these members are used to fasten the vertical stabilizing guy cables, preventing the turbine’s nacelle from pivoting back and forth during strong winds. They also act as a torsion-prevention member, allowing lateral guy cables to prevent the nacelle from twisting along the tower during fierce winds. Christophe Pochari Energietechnik‘ 750 kW turbine uses only 35,000 kg of aluminum to construct, costing only $100,000-$150,000 to manufacture using our novel iso-grid machined aluminum frame assembly. The LCOE of the turbine installed in Nebraska Sandhills would be a record breaking 0.10¢/kWh, 46 times cheaper than natural gas power generation. If the reader is not interested in reading our extremely detailed article, skip over and watch the video linked below to understand the working principle of the hydrostatic tower.
The novel dual-cable torsion prevention design. Two sets of quad-cables at 55 degree angles cancel even the slightest pivoting action of the cantilevered vertical offset of the turbine mounting platform. If the turbine experiences a powerful gust pushing to one side, the untethered mast will bend generating a sharp torsion force at the main guy cable mounting points shown above. The cable on the top left cable cannot prevent the mast from twisting in a clockwise direction, but the bottom right cable cancels this clockwise twisting, since the piston is vertically rigid. A clockwise rotation would require the bottom right cable to pivot the left, forcing the piston down. Torqueing of the turbine relative to the main pressure-bearing tube is prevented by the eight cables, there is simply too much tension to allow but a slight degree of torqueing.
A CAD model of the 44-meter 750 kW high-altitude wind turbine showing the aluminum iso-grid frame, gear set, hydraulic struts, and monolith-spar blades.
Since lateral stiffness is of no use to the structure, the thickness of the tube need only be sufficient to prevent bending between guy-fasten points. There is no need for a bulky large diameter column if it is not subject to horizontal swaying motion from the mass at the top. A conventional cantilevered tower is a structural abomination, by concentrating all the swaying motion of the heavy nacelle at the bottom of the mounting flange, a massive stress concentration occurs requiring a huge over-use of material. A pure tension tower is unparalleled in its structural efficiency due to a harmonious load path distribution and the widespread exploitation of isostatic loading.
Below is a video showing an example of a small scaled prototype of the fundamental principle of a compressed medium column.
The basic working principle of the technology is the use of a pressurized medium, a gas in our case, to continuously press upon a receiving piston that is used to carry both structural and dynamic loads and generate tension by pulling on ground-mounted high taught guy cables. A slender cylindrical column spans the height of the tower and is laterally stabilized by guy cables, this tower carries in it the pressurized fluid that is prevented from expanding at its base, but allowed to expand on a free-floating piston. This piston, when experiencing the isostatic force of the fluid or gas, has the urge to move upward, increasing its height. If cables are placed to restrain this piston from moving along the Z coordinate, tension is naturally generated as long as the cable’s mounting pads are firmly seated in the ground. Once tension is generated, stiffness is available that can be used to generate a laterally stable structure. The structure can be simply thought of as an incompressible column braced by tensioned cables, in that there is no fundamental difference between a solid concrete column and one whose equivalent incompressibility derives from pressurized media. Although this accuracy of this statement from a strictly mechanics perspective is questionable. Since the pressure column expands up to its elastic modulus upon being filled, and any force on the piston that does not exceed the net pressure load acting beneath it, will result in zero downward deflection. All structures require both tension and compression-loaded members, this structure simply uses pressure to generate compression and cables for tension.
A hydrostatic tower, hydraulic column, pneumatic column, isostatic structure, pressure-filled tubular load-bearing member, pressurized cylinder tower, defined hereinafter as a pure tension tower, works by imparting molecular energy from a compressed gas or liquid onto a piston and using that energy to bear loads, through the use of a friction-free piston free-floating above the pressurized media in a sealed container. Since the walls of the sealed container are unable to expand beyond a slight initial elastic deformation, the pressurized gas takes the path of least resistance and travels upwards to the free-floating piston and down-ward on the same piston but installed on a concrete footing. Since the free-floating piston has no resistance, it is freely pressed by the fluid and is subject to the sum of the force of the pressurized media. The force of the free-floating piston at the top of the tower can then be used to carry nearly unlimited loads without transferring these loads to the containment pressure tube. This simple but powerful statement is critical to understand the working principle underlying this invention. If the piston were to have friction between it and the cylinder wall, any load placed on the piston would be transferred as a downward compressive force which could buckle the thin walled column.
The critical fact to understand is that once fully pressurized, the cylinder is unable to move down unless a force greater than the force acting upon it is produced, in other words, the load would need to exceed the pressure inside the column for the tower to sag under a load. Since the sealing mechanism (discussed in further detail further along the page), is unable to transfer even a few kg of force to the walls of the tube, the load is always and everywhere borne solely by the pressure media. In short, the structure derives its load-bearing capacity by using a portion of the upward force produced that would otherwise have to be carried by the restraining cables by placing and carrying a weight on the piston. If a load that comes very close to the hydrostatic force is placed on the piston, the piston is able to reciprocate by slowly compressing the medium below, but by definition, a force cannot move the piston unless its sum is greater than the pressure acting on it. Since the target application for this novel type of tower is wind energy, the piston would then carry the dead weight of the nacelle, blades, plus any lateral exogenous forces resulting from static wind pressure acting on the turbine blades, nacelle, counterweight, in addition to the lateral loads acting on the tube. Using highly intuitive Newtonian mechanics, it can be readily illustrated that the structure’s load-bearing capacity is thus equal to the area times the pressure using the formula: pressure equals force divided by area written as: P = F/A. There is sometimes confusion about the nature of force produced by compressible gases, since conventional pneumatic structures (inflatable domes) are viewed as “spongy” and infinitely flexible, some have difficulty understanding how a pneumatic structure can possibly possess rigidity. The answer is that to compress a gas, a given amount of energy or force is needed, and the force is proportional to the pressure, thus as the intermolecular distance of the gas molecules decreases, electrostatic repulsion increases, and proportionally more energy is required to displace them. So while it is true that pneumatic structures are “spongy”, this is only the case at very low pressures where the structure’s loads can often momentarily exceed the outward force from the gas, serving to temporarily compress the gases inside the containment canvas. While it is correct to state that gases are theoretically almost infinitely compressible (in reality they are not once a high pressure is reached), and if enough force is available, they can be continuously squeezed until the gases would eventually turn to a solid. A gas effectively behaves as a solid if its pressure is well above the surrounding forces. A compressed is gas thus a wall of incompressibility provided there is less force applied than the gas contains from its compression.
The pure tension tower structure works by ensuring that the structure’s payload is always less than the force needed to compress the gas, even at peak loading regimes such as during freak storms. As already stated, a load cannot move a compressible medium if the compressible media contains within it an energy level that yields a force that exceeds the force applied, no matter how compressible the medium is. Gas is highly compressible, yet one cannot stop a pneumatic cylinder from retracting with their hand nor an internal combustion deriving its torque from expanding hot nitrogen gas, even though the gas residing within these devices can be squeezed. It is important to realize that all heat engines are “pneumatic” in principle insofar that they rely on the force of gases under pressure to produce work. A pure tension tower is thus a stationary pneumatic engine, rather than extracting work by creating motion, it extracts a static or idle force to counter a lesser static load. In the pure tension tower, the pressure bearing component is constructed from a cylindrical pipe that spans the height of the structure, which can approach 350 meters. The pressure-bearing tube, while not subject to the gravimetric load of the nacelle, is nonetheless still subject to the static force of the wind which causes it to bend. This bending motion is prevented from occurring with the guy wires that ultimately transfer this lateral wind load onto the piston which is prevented from displacing down by the fluid pressure acting on it, thereby allowing the lateral guy wires to prevent any deflection of the pressure column. The upward force of the piston allows the column to be tensioned thereby reducing the compressive loads it must withstand to zero. In a classic guyed tower, the tower section wants to bend from the force of the wind, and while the guy cables may prevent this, this lateral force is simply transferred or converted directly into compressive loading. A classic guy tower thus fails in both compression and buckling, since by definition any force withstood successfully by the guy cables is always transferred to downward force on the tower since the guy cable can only pivot and cannot stretch. As the tower wants to bend, the cables must pivot since they cannot stretch, as a result, the only way for lateral movement to occur is by shortening the tower, that is for the tower to sag and droop under a load, even though the direction of this load is not vertical. This places very strong compressive loads on the lattice structure of the conventional guyed tower. In the pressurized media tower, this is completely obviated by running a series of cables vertically from the piston down to the intermediate tube stabilizing guy cables which are placed every 15-25 meters depending on the thickness of the tube. The diameter of the tube is determined by the maximum expected wind load, for a 750mm diameter tube, a wind speed of 67 meters per second would cause a deflection of approximately 4 to 5 mm for a span of 25 meters. In a guyed tower, regardless of whether it is a hydrostatic one or a classic one, the tower sections are treated as discrete members rigidly connected at their fastening points which correspond to the mooring points of the intermediate guying anchors. With the pure tension tower, as the tube wants to bend from the wind, the lateral guy prevents it by attempting to compress the tube, but rather than this compressive load being transferred to the tube, it is transferred to the piston by the vertical cables. The tube is encased within a series of helicopter swashplate-like brackets that are not rigidly attached to the tube, allowing the tube to move ever so slightly within them by pressing against a rubber diaphragm. These swashplate-like brackets fasten to the four vertical cables spanning the height of the tower and then fasten to the lateral cables. Since the lateral cables are rigidly connected to the vertical cables which connect to the top-piston, pivoting action is canceled maintaining a straight and rigid pressure column regardless of height. Of course there are limits to the allowable height due to the accumulation of peak wind gusts on the tubular tower section. Therefore, one can say that the tube itself is simply standing there virtually “idle”, indifferent to the prevailing loading regime, needing only to perform its job as a pressure container, with the entirety of the exogenous structural loads carried by the piston which is then carried by the force of the “desirous-to-expand” fluid, and ultimately, all of which is born by the tensioned cables and transferred to the foundation on the ground. It can be said that a pressurized media tower’s raison d’etre is its unique and elegant ability to entirely bypass classical Euler buckling, flexural buckling, or compressive failure no matter how tall, slender, and thin the column is. As long as the lateral guy cables are placed frequently enough to minimize column bending during fierce winds, the structure is unable to move unless the loads exceed the yield strength of the steel cables. In fact, since the 1-meter pressure column spans around 20-25 meters between guy mounts, it therefore actually features a lower slenderness ratio than most untethered wind turbine towers! The tower section is in fact far more rigid since it functions as a discretized member at all times. In other words, the tower is not 350 meters, but rather 25 meters or whatever is chosen as the guy interval, which means its actual slenderness ratio is actually very low. Conventional wind turbine towers or masts are rather slender cantilevered structures which are free to bend and sway often quite severely in the wind. This can potentially although rarely cause resonance if the blade rotational speed syncs in phase with the cantilevered tower’s natural frequency. A pure tension tower is so immensely stiffer than any cantilevered tower that it is not even remotely comparable. At first appearance, a guyed tower appears so slender and skinny that it almost defies structural engineering, but it bears repeating that a pure tension tower is never treated as a singular member, but rather a multitude of stacked and rigidly connected discretized members that span the height of the tower in increments between guy fasten points. Think of each lateral guy mount as a foundation, no different than a foundation pad holding a building’s column in place, the only difference is rather than the connection being facilitated by the torsional resistance of the footings, it is withstood by maintaining a maximum load less than the force needed to stretch the restraining cable. Each cable is tensioned to the point that the average force acting on the column is far less than what is needed for the cable to plastically elongate let alone yield.
The essential point to understand is that the pure tension tower works by exploiting the properties of the plastic column material by transferring a directional compressive load into uniform hoop stress or internal pressure, distributed evenly along the interior surface of the cylindrical tubular containment structure, which remains loaded only in tension the entire time, regardless of the force acting on the piston. The pure tension tower thus converts compressive load into tension, which is a unique feat among structural systems. Most structures, including structures that use tension-loaded cables such as cable-stayed bridges, still nonetheless exploit the compressive load capacity of the concrete columns. In fact, no structure in existence can operate without at least one member being compressively loaded, the famous “tensegrity comes to mind.
The tensegrity, coined by Buckminster Fuller, is not really that genius after all, since it still places compression on the upward facing wooden strut visible in the image above. The pure tension tower in contrast is truly a compression free structure. The word “tensegrity” is therefore a misnomer because the structure is equally compressively load as it is tension loaded.
A pure tension tower does not use a single compressively loaded structural member! In fact, if one excludes the footing, it has none. As long as the piston generates zero friction between itself and the cylinder around it, it is physically impossible to transfer any compressive load to the column, unless the lubricating medium between the piston surface and tube were to seize or solidify for some reason. Only the viscous friction within the thin layer of oil between the piston and cylinder can transfer loads from the piston to the tubular structure, but this force is negligible. Since all plastic materials (including metals) will not elastically deform prior to yielding in a structurally compromising manner in tension, a hydrostatic structure is able to increase the structural efficiency of the load-bearing members by an enormous factor. The technology is discussed in much greater detail below including how a truly friction-free piston is designed. In short, a friction free piston merely continuously routes a highly viscous oil between itself and the cylinder wall, preventing any pressure from pushing a piston ring against the cylinder and generating friction.
We are forced to mention that a pure tension tower as a structure has no inherent relationship with wind generators. Wind generators are a wholly disparate field of engineering with their own unique, and arguably more challenging design exigencies. The pure tension structure technology is itself a lone branch of structural engineering that can barely be encompassed within the category of pneumatic structures. Since it does not obey the peculiar characteristics of conventional pneumatic structures (infinite flexibility), it cannot be fully placed in this already amorphous category. Consequently, for the foreseeable future, the technology will have a difficult time being assigned a specific category of any widespread name recognition. The only reason there is an extensive overview of wind turbine technology is due to the fact that there is very little use for a pure tension tower other than cellular and radio masts, but these structures do not need much load-bearing capacity and hence can sufficiently with lattice structures, this is why this form of structure has not yet been invented
Schematic of the nacelle stabilizing structure. Since the column produces a constant upward pushing force, torsional forces are withstood by transferring them into compressive forces across four laterally projecting pressurized columns, the same pressurized column system as the main load bearing tower. Any torsional force produced is canceled by the pivoting gyro placed at the piston’s center to prevent the piston from rubbing against the cylinder wall and generating friction.
Small reference model of a short pure tension tower. Note that a pure tension tower is “height-invariant” in that it is a discretized tower, not a singular cantilevered tower. By breaking up the tower between guy fasten points, we can treat it as a series of stacked small towers, which is why they can boast such high slenderness ratios which defy the imagination yet possess an even stiffer facility than any cantilevered tower.
The basic schematic below of the pure tension tower. The load-bearing piston, which carries all the load of the payload placed atop the tower, plus any wind force on the tube, cables, or payload, is never in any way adhered or adherable to the tube’s wall, so the pressure column is an unloaded component excluding the internal pressure and wind loads. The critical failure mode of the thin wall pressure column is flexural buckling or crumpling, no such event can occur since the tube is constantly tensioned as it floats on the bottom-mount piston on the foundation pad. Since pressure is a uniform force, pressure cannot cause a directional movement of the member unless there is an unequal surface area distribution. In other words, pressure acts to move bodies only if they are not submersed in the media, otherwise, the force of the pressure on the other side of the surface cancels it, it then becomes an “atmosphere”. The pure tension tower thus uses the weight of the dead-load to cancel the upward force of the pressure below a certain margin.
A technical schematic of the basic pressurized media tower components.
Before we go into more detail on the design, workings, and engineering factors that go into the pure tension tower, it is necessary to provide an overview of the motivation behind the technology’s development. Since a pure tension tower have a single point of failure, their use makes the most sense for cost-sensitive applications where the safety of humans is not dependent on the structure’s reliability. Despite the structure’s stellar mass to payload ratio (structural efficiency), like all technologies, it is not perfect. It possesses several weak points, an “Achilles heel”, if you will. This is unavoidable and comes with any complex system. An airplane cannot fly without an engine or a working hydraulic system, nor can an aerial tramway function without effective breaks and strong cable attachment points. The so called O-ring theory effectively states that regardless of how over-engineered the machine might be, there will always be failure modes unreceptive to over-engineering that ultimately limit how much one can engineer in redundancy. The principal weakness for the pure tension tower is the ability for a leak to eventuate in complete structural failure. Since without internal pressure, the structure has no load-bearing capacity whatsoever, a major leak caused by a failure in the sealing mechanism or a puncture in the tube walls will inevitably result in the structure’s complete collapse. Thankfully, engineering and material selection can mitigate this and make it rare enough to be accepted as a non-human carrying structure. It should be noted that we are by no means the only technology that is dependent on the absence of leaks for system integrity, a number of high-pressure systems are found in engineering where severe leaks can result in major failure or hazard, notable in cases where toxic or flammable compounds are being stored such as in oil refineries and olefin polymerization plants. Even though hydraulic and pneumatic sealing mechanisms (discussed extensively further down), can be made extremely reliable, and while they could find immense use for civilian structures and building construction, it is anticipated the PTT’s prime application will be in wind energy, therefore a relatively extensive discussion of the salient facts pertaining to the energy landscape is performed.
Motivation behind the invention
It has become almost trite to say energy is by far the most valuable asset after human capital for a nation. The entirety of modern industrial civilization is predicated on the continued flow of power dense streams of calorific compounds, without which no modern technological society could sustain itself for more than mere months. Unfortunately, the planet contains only small quantities of highly concentrated energy, most of the energy available on earth is in a diffuse form, highly dispersed across its surface as downstream solar energy. In this vein, it must be stated that there is presently no evidence of a genuine “shortage” of energy, there are massive supplies of coal, natural gas and petroleum readily extracted with century-old technology that will likely be available for centuries to come. In spite of this rather auspicious predicament, headlines are chocked with news stories of an impending “energy crisis” about to send industrial civilization back to the stone age. One has only to make a little effort and search historical newspapers, books, and articles, of which there is no scarcity, for predictions of looming droughts of oil or virtually every other precious resource. There is very little geological and technological evidence and veracity behind any of these sensational claims, historical or modern. Those who claim energy is in short supply are conflating risk premiums with supply-driven price escalation. Risk premiums are often ignored in the energy debate, with consumers conflating genuine scarcity with monopolistic supplier behavior. A perfect illustration of this phenomenon is the recent escalation in the price of natural gas in Europe. Natural gas in Russia is more abundant and cheaper to produce than ever, after all, drilling technologies, pipelines, and storage continues to improve in efficiency and cost effectiveness. But instead, unwise politicians imposed sanctions which resulted in retaliatory behavior on the part of Russia, driving the price of an otherwise incredibly cheap resource to absurd highs. In light of these facts, there is still nonetheless tremendous demand for energy, often expected to be made available at a market price below what is currently available. In this regard, wind has a number of attributes. Wind is a manifestation of the angle of incidence of solar insolation increasing with distance from the equator, creating permanently frozen zones called the poles. The past 50 million years, since the Eocene thermal maximum, has witnessed tremendous cooling imputable to declining atmospheric density, resulting in a sharper pole-equator thermal gradient, generating more powerful winds. When the earth’s atmosphere is thicker, as it was during the Mesozoic, more of the earth’s energy budget was derived from adiabatic heating of the atmosphere through the gravito-thermal effect, causing a more uniform temperature distribution. As the atmosphere has thinned, cooling has been the norm. The earth is expected to continue to cool until its atmosphere is eventually stripped away when its internal dynamo shuts down as the core cools and solidifies. But this represents the long term cause of climate variation, the short terms temporal variations we have witnessed are imputable almost exclusively to a complex interplay between sunspot activity, cosmic ray flux, and cloud formation, called “cosmoclimatology”, coined by Henrik Svensmark who first proposed the mechanism.
The current climate on earth is in a warming cycle, caused by a reduction in cosmic ray activity due to a high sunspot count which started at the end of the “little ice age” in the mid 19th century. When the sun’s volatile magnetic fields are dormant, more energetic particles escape the photosphere and make their way to earth. When they strike the atmosphere, they ionize aerosols such as sulfuric acid and generate cloud condensation nucleons, which act as seeds for clouds to form, blocking more of the visible and ultraviolet spectrum from striking the surface of the earth. The concentration of beryllium 10, chlorine-36, or carbon-14 serve as proxies for historical cosmic ray intensity and subsequent sunspot activity. There is a major misconception that carbon dioxide acts as a “climate knob”, this is one the greatest myths of the current era. The current “modern warm period” is anticipated to reverse some time this century, sending temperatures falling back to substantially below the current “modern warm period”. This will create a sharper polar-equator thermal gradient and increase global wind speeds, making wind energy a very attractive energy source. When sunspot activity begins to decrease, temperatures will likely a full degree in a century, reversing the entire 0.8 degree of modern warming, causing wind speeds to increase by at least 10% globally. Wind power is the cube of velocity, which means a 10% increase generates a 35% increase in extractable energy. Solar irradiance varies only around two-fold between a very sunny region such as the Sahara Desert and a low irradiance climate such as England and Whales. In contrast, wind speeds may very from three meters per second in the tropics to 15 meters per second in the Ice sheets of Greenland, a difference of 5 times. This means wind is 2.5 times more variable than solar energy, which has a unique advantage for power generation. While the average power density of wind and solar energy is quite close, the potential to harvest the extreme ends of the distribution is greater with wind, this is a unique way to exploit a statistical phenomena manifested as polymorphous energy fluxes. Two phenomena that are normally distributed along a Gaussian curve with the same mean can produce different extreme values with a difference in only their standard deviation.
Returning to the subject of energy, while we have a number of options on the table, not all are as easily deployed. The caloric value from the heat of decaying radioisotopes and residual mantle heat is extremely weak at depths available to present drilling technology, placing a cap on the availability of geothermal energy. The highly concentrated energy, and the one we rely on for the bulk of our caloric needs, is principally in the form of gaseous and solid carbon-hydrogen compounds, with oils forming only a small percentage of the total array of carbonaceous hydrogen bonding compounds. Of all the calorie-emitting compounds in the crust, virtually all of them are in the form of carbon and hydrogen, there are no other heat-emitting molecules that we have access to for energy, silicon or other metal hydrides have not been found in the crust. While most earth abundant metals, iron, aluminum and magnesium, in their reduced form can be burned to liberate considerable heat, they exist only in their oxidized states, and hence do not contain any net surplus of energy. It needs to be stress that hydrocarbons are the only “pre-reduced” compounds we know of, virtually everything around is is already highly oxidized, hydrogen are thus quite precious and outright anomalous. Hydrocarbons are thus a unique case of highly reduced compounds that have remained free from the ravages of our oxidizing atmosphere. Russian physicist Vladimir Larin proposed a unique theory that the mantle and core is comprised principally of metallic hydrides which over time degas into the atmosphere, accounting for the occurrence of hydrogen in the exosphere and potentially even abiotic hydrocarbons. Abiotic hydrocarbons may be quite dispersed in the crystalline crust, but remain inaccessible due to the high cost of drilling. Larin proposed a very novel theory in the 1980s and went on to write a book titled: “Hydridic Earth: The New Geology of Our Primordially Hydrogen Rich Planet”. A documentary was made about the theory in Soviet Russia that can be viewed on Youtube.
Larin’s basic theory was during earth’s formation, the protoplanetary disk that emerged after the after the collapse of the molecular cloud sent a stream of particles particles toward its outer edge that eventually formed into the earth. Elements with low ionization potentials, low voltages needed to to ionize, were captured and retained by the sun’s magnetic field, while elements with high potentials, hydrogen for example, which requires a high 13 electron-volts to ionize, could escape the sun’s magnetic field and make their way to earth. His thesis is corroborated by the correlation between the ionization potential of the elements and their distribution on earth. Larin’s theory predicts earth contains 1500 times more hydrogen than is commonly assumed, 4.5% vs 0.003% by mass. Larin’s theory has important implications for the abiogenic hydrocarbon origin theory since we now have a mechanism that can produce a continuous supply of hydrogen. Larin believes that rather than pure metallic iron or nickel in the core and mantle, there exists considerable quantities of hydridic compounds, such as nickel hydride or iron hydride. The polymerization of hydrocarbons takes place in the temperature range 600-1500°C and at a pressure range of 20-70 kbar. These conditions prevail deep in the Earth at depths of 70-250 km beyond the lithosphere and well into the asthenosphere. The carbon found in the carbonate rocks (Calcium carbonate) fuses with H2O in small crevices and slowly peculates to above under high pressure. These incredible pressures allow the formation of longer chain hydrocarbons like oil, while at more moderate conditions, simple molecules like methane and butane form. In the Russian geological community, this process is called “deep abiogenic”. A strong reason to believe in the unorthodox abiogenic theory is that fossils have not been at depths greater than 16,000 feet, while natural gas is drilled as deep as 39,000 feet. The well in Eastern Russia in the region of Sakhalin known as Z-44 Chayvo, reaches a depth of 40,000 ft (12 km) into the ground. How decomposing organic matter could have reached such a depth is presently unknown, subduction is likely not a satisfactory explanation. Secondly, no fossil has been found at these depths. L. Fletcher Prouty, a general and business executive, became a staunch proponent of the abiogenic theory. There have been numerous experiences in Russia where an oil or gas well is depleted, left to sit for a few years, and then is refilled somehow. With that said, even if oil is a renewable resource, that does not mean it cannot be depleted. It’s probable that the natural production rate of hydrocarbons in the asthenosphere is substantially below the rate of extant human consumption. Therefore, it makes little difference is hydrocarbons are a fossil or not, they will be depleted, it is inexorable. Lastly, biotic molecules, organic carbon-hydrogen oxygen molecules like β-Carotene, Vitamin D etc are highly oxidized with very low chemical potential. A large sum of energy was needed to reduce them to the highly reduced state of energetic hydrocarbons of high chemical potential. This energy could only have come from the mantle from the buried hydrides. Vladimir Larin estimates as much as 500 billion tons of hydrogen are being degassed into the atmosphere, which explains the high concentration of hydrogen in the exosphere. If only a small fraction of this degassed hydrogen picks up a carbon atom from a carbon bearing rock this is enough to generate all the hydrocarbons we see today. Since carbon has a lower ionization potential, more of it would have stayed in the protoplanetary sun than could have reached earth, so this explains the relative scarcity of carbon on earth. Larin does not estimate the carbon content of his earth model as any higher than the conventional estimate. Larin’s theory predicts that the earth must be expanding since its density must decrease as a consequence of the hydrogen degassing.
Carbon is found in the upper crust at a concentration of roughly 0.02%, only 2.38 times higher than the concentration of nickel, an expensive metal, and 4.75 times less abundant than manganese, a moderately expensive industrial metal. Carbon is also rarer than strontium and barium, hardly elements abundant enough to burn ad libitum. Most of the carbon in the crust is in the form of carbonate rock, limestone, and dolomite, highly oxidized states with no caloric value to speak of. It’s estimated that of all the organic carbon on earth, only 0.01% is in the form of hydrocarbons within the sedimentary rocks. While the theoretical quantity of hydrocarbon is massive and represents thousands of years of present consumption, the tiny fraction that is amenable to extraction renders an initial huge number a far more meager one. Man consumes around 4.5 billion tons of oil annually, 3.8 trillion cubic meters (2.6 billion tons) of natural gas (methane), and 8.6 billion tons of coal, for a total of nearly 16 billion tons of hydrocarbon annually, or 1000 years of present consumption if we take the estimate of 2 × 10^13 tons of hydrocarbon as the theoretical reserve. Most of the crustal carbon is in an oxidized state bound up with oxygen, offering no energetic value to speak of. A small fraction of this 0.02% carbon concentration is in the form of energetic and highly reduced molecules: the valuable carbon hydrides that man profusely mines for. Prosini et al estimates the total reserves of hydrocarbon to be nineteen quadrillion, but of course, these estimates are silly and for intellectual curiosity only, since current drilling technology limitations makes most of this theoretical reverse inaccessible. The estimated reserves of methane hydrates in the arctic seabed are immense, numbering thousands of years, no present extraction scheme has been proposed. The U.S. Geological Survey estimates that methane hydrates could contain between 10,000 trillion cubic feet to more than 100,000 trillion cubic feet of “natural gas”, an American industry term for methane and ethane. The world uses 30 trillion cubic feet annually, thus, the theoretical reserves assuming 100% extraction efficacy (far from possible) would amount to more than 1600 years. In a book by Michael D. Max, Arthur H. Johnson, William P. Dillon titled: “Natural Gas Hydrate: Arctic Ocean Deepwater Resource Potential”, they estimate the total global resource potential for high-grade natural gas hydrate sands may hold up to 43,300 trillion cubic feet of which 50% is technically recoverable. Other estimates place the number at 1.5 x 10^16 m3 (Makogon et al., 2007) to 3×10^18 m3. In contrast, total reserve estimates for coalbed methane is 9,000 TCF, shale gas of 16,000 TCF, and tight gas of 7,400 TCF. Turbidite-related sands of the Terrebonne Basin have been estimated to possess a natural gas density of 1.183 × 109 m3/km2 while so-called delineated sand reservoirs are thought to be around 0.32 × 109 m3/km2. Max, M. D., Johnson, A. H., & Dillon, W. P. (2013). Natural Gas Hydrate – Arctic Ocean Deepwater Resource Potential. The International Energy Agency (IEA) estimates that if efficient methods and processes are developed, natural gas produced from methane hydrates will cost between $4.70 and $8.60/MBTU. This places the generation cost at 4¢/kWh.
While at the present moment there is ample hydrocarbon available, one must not forget that hydrocarbons are by no means inexpensive anymore, and many small scale users of energy would greatly benefit from a lower cost non-consuming energy source. This is not because technically illiterate politicians call for it, but because the LCOE from photovoltaic and existing wind turbines is often substantially below combusting a hydrocarbon at retail value in a heat engine. While it is true “renewables” (natural harvesters) are “unreliable” and geographically limited, there is almost invariably a trade-off in any physical system between two extremes. In this case, the two extremes are energy density and diffusiveness. It is logical to assume diffusiveness should be inversely related to energy density, since the bulk of energy is in a diffuse state while concentrated states occur rarely due to eventual entropy, oxidation, and degradation. It therefore follows that if we choose abundance we should sacrifice power density. An extreme case study is nuclear, the most power dense energy source presently known, but one which is reliant on an exceedingly scarce element. If an input of fuel is not required, certainly, we must accept some disadvantages. Critics of alternative energy often adduce the cost advantage of natural gas or coal over photovoltaic or wind generators, but the reality is quite a bit more complex and case-specific, especially when grid connection and the non-baseload nature of the energy are taken into account.
If we take the current spot price of natural gas, which in the U.S hovers between $6-8/million MBTU at the time of this writing, it becomes immediately obvious that the notion that “natural gas” is a “cheap” source of power is largely relative. There are 293 kWh in a million BTU, so the price of natural gas on a raw heat basis is 2.3¢/kWh. Since the average efficiency of a dual-fuel gas fueled diesel engine with pilot fuel injection is 40%, a medium-sized gas turbine is 35%, and a spark ignited Otto cycle gaseous reciprocating generator is only 30%, the cost per kWh electrical is around 2.5 to three times more than the raw value of the material. While very large industrial gas turbines such as the GE-7HA can approach 60% efficiency, this technology is not accessible to the small user, our target customer is the mid-size consumer of industrial energy, so we must remain scale conscious. Thermal powerplants are highly scale-dependent due to heat transfer and aerodynamic reasons. Since gas turbines are rarely above 30% efficient at the sub-megawatt scale, we can use a pilot-injected diesel engine instead for our comparison. Such an engine approaches 40% brake thermal efficiency, so if our natural gas price is $7/MBTU, we generate 117 kW of net brake power, since our generator is 97% efficient, we are left with 113.68 kWh, or an LCOE of 6.15¢/kWh. This number might seem like a low number for consumers who are price-gouged and must shell out over 30¢/kWh in Europe, but this price is hardly cheap compared to hydropower or nuclear fission, let alone contemporary photovoltaic which can reach 1.5¢/kWh in deserts. Obviously, we would be silly to use the price of European natural gas, which is artificially high compared to production costs due to a risk premium. In Russia in 2021, natural gas (methane) was sold to businesses and consumers at a price $0.009 and $0.01/kWh respectively, assuming 40% conversion efficiency, a bitcoin miner in Russia could realistically access power for 2.5¢/kWh, but not much less.
Of course, we could have cited the efficiency numbers of a General Electric 7HA, but this turbine is only available to grid operators since it costs over $50 million. Christophe Pochari Energietechnik has been interested in developing the concept of slightly smaller scale systems, more accessible to small-scale players in need of affordable energy, that is we are interested in overturning the paradigm of grid dependence, where public utility monopolies sell overpriced energy to consumers with no alternative options. Christophe Pochari Energietechnik has also been actively developing a very low cost power generator for bitcoin mining, so far no such technology exists except for hydropower dams, which are inaccessible to individual miners. In the later part of this text, a discussion on the possible LCOE regimes attainable is provided. It is possible for power as cheap as 0.083¢/kWh (yes 0.083¢!) is attainable in high wind regimes.
In the case of coal, the energetic cost-effectiveness is typically inferior to natural gas (methane) since the thermodynamic efficiency of the Rankine generator is poorer than the Brayton gas turbine. Newcastle coal futures have historically traded at $100-150/ton, historically speaking referring to the past decade. In recent months, coal futures have jumped to over $400/ton due to a convergence of circumstances, but principally growing electricity demand caused by increasing air conditioning demand and rebounding industrial production in China after Covid lockdowns. Unfortunately with coal, highly efficient Brayton and Diesel cycles cannot be exploited, leaving marginally efficient Rankine cycles as the only option. Most steam turbines are under 30% efficient unless in the supercritical class, where CAPEX becomes an increasingly dominant factor. Additionally, the cost of the steam turbine and boiler per kW is far higher than a gas turbine due to its much lower power density, hence a greater material intensity.
Since carbon comprises 90% of typical anthracite coal by mass and carbon possesses a heat of formation of 32 MJ/kg, we are left with 8.86 kWh/kg. At €150/ton, the levelized generation cost is therefore 5.6¢ excluding boiler, turbine, and condenser CAPEX. Since coal is not always 90% carbon, a more conservative estimate of 20 MJ/kg is used, most “steam” coals possess between 20 and 25 MJ/kg, or just under 7 kWh, yielding an LCOE of 7.5¢ at $150 per ton with a 30% efficient turbine. The reason that “steam coals” or any coal in reality possesses a lower heating value than the theoretical heat of formation of carbon alone is due to the presence of moisture in the coal, sapping the energy during its evaporation. Steam turbine price estimates can be sourced from online marketplaces like Alibaba, which are usually very accurate estimates of real-world wholesale market prices. Dongturbo Electric Ltd retails a 1000 kW condensing steam turbine for around $250,000-300,000. These medium-sized condensing turbines consume between 5-6 kg of steam per kWh. The inlet pressure is 2.1 MPa and the inlet temperature is 300°C. The CAPEX of the attendant coal boiler is approximately $50,000. Since we are comparing to a wind turbine, we can exclude the cost of the synchronous generator, since a steam turbine would require a synchronous generator as well. The cost per kW for a small scale 1000 kW coal powerplant so far is around €300, which seems low, but one must remember that with thermal powerplants, the CAPEX is almost always a tiny contributor since hydrocarbons have tremendous mobility, their value is far higher than stranded renewable electricity, rather the lifetime fuel costs dwarf the initial purchase price, by thousands of times. A steam turbine can expect last over 250,000 hours, but a realistic amortization is 150,000 hours before a major overhaul is needed. Using this number, a negligible additional 0.2¢ is added per kWh, highlighting the disproportionate fuel share of LCOE. But it is interesting to note that the LCOE is still higher than the total LCOE of the high altitude turbine, which places it in a league of its own.
The conclusion of this brief analysis of the state-of-the-art thermal hydrocarbon powerplants suggests a lower limit of 5 to 8¢/kWh is achievable. Coal is unlikely to fall below $150 per ton in the foreseeable future as electricity demand from countries like India which are under pressure to provide growing power for urban air conditioning, therefore. It is thus expected that wind-generated electricity will become more competitive in cost, since the price of aluminum is the #1 cost contributor of the high-altitude wind turbine, and aluminum’s cost is principally bound in the electricity needed to liberate it from its oxide. Aluminum is 400x more abundant than carbon in the crust, 8% vs 0.02%, therefore, civilization will always have a surplus of aluminum. Since a wind turbine effectively harvests energy for free from a stream of air, it effectively generates energy from the metal alone, there are no inputs, consumables, or resources which must be expended to maintain the machine. When the machine reaches its useful life, the aluminum is melted down and recycled. In contrast, natural gas, since it is a clean burning fuel and very convenient for producing hydrogen for nitrogen fertilizers, will likely grow in cost as time passes.
In conclusion, until someone successfully overturns the 1st or 2nd law of thermodynamics, man is forced to scavenge tirelessly with his various contraptions to harvest the biosphere for every vestige of energy, whether low grade or high grade. As civilization advances and spreads, the demand for caloric value increases strongly, and if this caloric value cannot be met, a lower standard of living has to be accepted which may result in the collapse of many governments, whose rule is tolerated only because of the prosperity they guarantee. Energy can thus be said to have immense political and geopolitical reverberations, and if the hydrocarbon era is to end without a collapse in living standards, a very heavy burden is placed on the shoulders of alternative energy designers.
The 21st century can be characterized as a perfect storm that is brewing between runaway hydrocarbon demand and concomitant downstream reverberations from their combustion beginning to be widely felt. Hydrocarbon combustion emit nitrogen-oxygen compounds, which react with volatile organic compounds, isoprenes, terpenes, and form ozone (trioxide) forming photochemical smog. Solid hydrocarbons or any hydrocarbon with a carbon-carbon bonds releases soot, so called “carbon black”, which is effectively pure carbon dust which is harmful to human lungs. Despite these drawbacks, we find few saleable alternatives to these dirty molecules. Hydrocarbons, being the most convenient form of energy, will remain the mainstay of our energy budget for centuries to come, despite their likely escalating future cost. But for certain specialized applications where energy cost is critical, but power density is not, natural harvesters, photovoltaic, high-altitude wind, and hydropower, will provide these niche sources with the energy they need and enable an increase in the profitability of producing electricity-intensive commodities. We should develop and improve all energy technologies regardless of what politicians tell us. If a wind turbine or photovoltaic panel can produce electricity for less than the cost of buying natural gas and burning it in a gas turbine, why should we not use these technologies? We have been conditioned to think in this oversimplistic binary framework of “green” equals: “trying to save the planet” and “fossil fuel: = low-cost and reliable”. One cannot use non-hydrocarbon energy to “save the planet” but one can certainly supplement our current energy budget with additional disparate sources, without one one hand making false claims about some “renewable panacea”. Quite surprisingly, hydrocarbons are not always the go-to source for applications that require “ultra-cheap” energy. For example, rarely finds the owners of Hall-Heroult plants burning natural gas to power their electrodes, instead, they are more likely to be found nestled in the Fjords of Norway harvesting the hydraulic manifestation of gravity. Are they doing this to save the planet? far from it, they are doing it because hydropower presently is the cheapest source of energy, even though it has very low power density. In China, the government has constructed thousands of dams with several hundred of them being in the multi-megawatt and even multi gigawatt scale. The cost to construct these dams is the price of the labor to excavate the rock and pour the concrete, and the cost of the rebar, concrete, machinery, and Pelton turbines that go into the system. In the West, environmental regulations have effectively halted any type of hydropower construction, but in the “developing” world, it is likely we will continue to see dams being constructed, regardless of the costs to upstream populations or negative agricultural or irrigation reverberations.
Highlighting the very competitive LCOE of Chinese hydropower, one book estimates the average cost of dam construction amounted to just under 1 RMB/kWh, so for the per kW of power output capacity, the cost would be €1180. If the dam lasts 60 years, a more realistic life is at least 70 years, if constructed properly, a dam can last upwards of a century assuming no geological perturbations, earthquakes, or erosion. Realistically, an anti-gravity dam is almost immune to destruction, but many Chinese dams are concrete rock-fill dams, which are more erosion prone, since an anti-gravity dam is nestled in solid rock, whereas embankment dams can in theory more easily move, although this does not really occur. The lifetime levelized cost of energy for these Chinese embankment dams is around 0.22¢/kWh, since maintenance is exclusive to the Pelton turbine as it forms the only moving part in the system. Unfortunately, as cheap as hydropower is, it is not accessible to everyone, one must own property with a river on it and gain approval from the relevant authorities to construct it. Dams are the job of a central government, not a company or individual. No one really owns a river, it is used by almost everyone that lives along it. Those who rely on fisheries and irrigation might not be terribly excited about the prospects of their river drying up to a tiny fraction of its former flow, nor do villagers upstream take lightly to the prospects of seeing their village turn into an underwater artifact. In a Western country, where the voice of the weak is heard, if farmers or villagers are flooded, the dam will likely never be constructed, whereas in a benevolent dictatorship like in China where the collective interests trump the individual, the value of pollution-free power far outweighs the cost of few thousand villagers that need to say goodbye to their ancestral home. In short, hydropower has tremendous value, but there is nothing to say about it, since it depends on whether governments are willing to build it, since we are not Chinese citizens, there is little hope to have access to this potentially near-free energy. The profits generated from this cheap power belong to its owners, so hydropower is much like nuclear energy, potentially very attractive, but out of reach for most users. This is what makes hydrocarbons so attractive, with most energy sources, you have to locate yourself where it flows, with hydrocarbons, one can transport them where you consume them even if they are extracted at a select few locations. This is what has made photovoltaics appear like the “dream” energy source, the utopia where everyone owns a photovoltaic panel and services all their energy needs seems almost too good to be true. But it is not too good to be true, since we know the technology is very mature, a photovoltaic system is the closest we have to ultra-low-cost energy. A photovoltaic module costs around €350-380/kW excluding installation and land costs. The bare panels or modules cost only €200-250/kW, and their direct production cost is as little as €150/kW, we know this because in 2021 the average polycrystalline module price was as low as 16¢/watt. Assuming an irradiance of 1850 kWh/kWp, which would effectively place one in the desert, the LCOE of the photovoltaic panel over its 20-25 year life is 0.85¢/kWh. But this number is by no means the floor for natural energy harvesting. A wind turbine mounted on a high altitude can exceed the photovoltaic panel by many fold, and better yet, it occupies no land. In fact, any skepticism towards our high power density high-altitude turbine can be countered by the simple fact that a photovoltaic array can generate energy for less than 1¢/kWh, but since wind speed is more variable, if we place the high-altitude turbine generator at the tail end of this curve, the power density will be higher than the highest available insolation. Furthermore, an high-altitude turbine is constructed only out of aluminum with some alloy steel, mainly for gearing, where the bulk of is photovoltaic panel’s cost is related to the purification of the polysilicon.
What is the cheapest source of energy today besides hydropower?
The cheapest source of energy that is not hydropower is either domestically produced Russian natural gas or Saudi Arabian oil, but Qatar or Iran’s natural gas is probably pretty close. In Iran and Venezuela, diesel fuel is subsidized by the government and costs only $0.011 and $0.022 per liter! Imagine if Germans knew this! Russian natural gas goes on record as the single cheapest source of energy after hydropower. The average direct untaxed production cost for Gazprom is only $0.4/MBTU, or 0.34¢/kWh. The net total cost is around $1/MBTU, but the Russian government mineral and energy resource tax adds another 40 cents. Of course, this tax has to be paid, but it does not reflect the actual cost of extraction. But since the most valuable gas and oil wells are rarely privately owned since they are of such immense strategic value, there is little to no opportunity for private investors to tap into this source of ultra low cost energy.
At this price, one could make a fortune mining bitcoin, but again, this fuel is only available to the citizens of these vibrant nations, so bitcoin miners will have to look elsewhere. It’s been estimated by independent “analysts” (you should take them with a grain of salt) that Saudi Aramco spends only $3-5/barrel to extract its crude. Since one barrel of oil contains 136 kg, and the caloric value of crude is 45 MJ/kg, the energy content of crude oil is around 12.4 kWh/kg. Since it would be a waste to burn the oil directly in a boiler and generate steam for a condensing turbine, we would be wise to distill the oil using thermal cracking to convert it into diesel fuel which can be converted to electricity much more efficiently. To turn crude oil into diesel fuel, we must heat it to 300°C. The heat capacity of crude oil is around 1700 J/kg-K, so we must expend around 146 kWh per ton of oil to raise its temperature by 280 degrees. Since the cost of thermal cracking is negligible, one barrel of oil thus allows us to generate 667 kWh per barrel using a 40% efficient diesel generator, with a net electrical output of 646 kWh since or generator is only 97% efficient. Since the cost to produce this barrel if we were Saudi Aramco is only $4/, the cost per kWh is 0.61.9¢/kWh. But of course, this comparison is meaningless because only the owners of the oil fields can pay this price, the market price is 22 times higher since the international demand is so great for this precious commodity. Regardless, what is true is that it does not cost anywhere close to $90 per barrel to produce oil in these highly productive fields like Ghawar, Safaniya Shaybah, etc. This is why Peter Zheihan is simply so wrong, because he falsely claims fracking is some panacea when in reality it costs ten times more (around $45/bbl) to produce oil in the “Permian basin” than in the deserts of Arabia or in the Yamal peninsula. Most of the highly productive Russian fields in Siberia cost around $10/barrel, and Iranian oil is estimated to be around $10 as well. It should be remembered that these are just rough estimates, we do not truly know what Saudi Aramco actually spends, it is a top state secret along with its reserves. Since it’s a publicly traded corporation now, we can make rough estimates based on its stated spending. Since all of Saudi Arabia’s oil is produced by Aramco, we could theoretically divide its annual spending by the oil production to arrive at a reasonably accurate estimate. In 2022, Saudi Aramco listed an operating expense of $42.8 billion, since Saudi Arabia produced 10.6 million barrels per day, 3.86 billion annually, or $11.08/barrel, so perhaps the $5 per barrel estimate is wrong. But since Saudi Aramco makes investments unrelated to direct oil extraction, such as refining, exploration, research and development, maintenance, etc, the $5 per barrel number still stands. Now the question is how does our high altitude wind generator stack up to the cost of extracting oil in Saudi Arabia? Since we concluded the cost per kW is 0.65 cents, and we estimate the levelized cost of energy for the high altitude wind turbine tower is only 0.08 cents, we are still considerably cheaper than the most plentiful hydrocarbon reserves on earth, but albeit not scalable.
A few points we believe are important to highlight
#1: The impetus for developing hydrocarbon substitutes should be motivated by a combination of resource and not atmospheric/climatic concerns, which are based on unphysical assumptions of the “greenhouse effect”. The fact is hydrocarbons are naturally becoming scarcer and costlier, and with enough time, will be depleted. Just because past predictions of “peak oil” have proven premature, does not mean that the underlying geological arguments made are false. Besides, current oil and gas production is arguably at close to maximum capacity, so any additional energy, especially in a decentralized context, may not realistically be fueled with hydrocarbons.
Energy development should not necessarily be driven entirely by policy alone, which may not perform the necessary selection for performance and financial viability, development rather should be based on a combination of market forces and externality concerns that should compel the adoption of more competitive technologies. High-altitude terrestrial wind, or any alternative energy technology, must succeed on its own, without subsidies, promotion, or favorable treatment. The technology should succeed and proliferate based on its intrinsic attributes, and these attributes should in part suggest an innate superiority, whether in cost-effectiveness or longevity, or environmental cleanliness over contemporary hydrocarbon technologies. If these attributes are not met, there is no rationale for their deployment, regardless of their social attractiveness on non “hard” metrics. In other words, we should not develop technologies that are less effective than hydrocarbons, unless they possess other attributes that compensate for their relative deficit. We are making the argument that high-altitude terrestrial wind is a superior form of power generation even compared to thermal technologies, in a non-grid scenario. We must accentuate the fact that in no way are we claiming that high-altitude terrestrial wind generation somehow possesses even close to the power density or scalability of hydrocarbon, but in a purely economic sense, in terms of cents per joule of energy, this technology is no slouch. The arrow of technology has pointed in a single direction in the history of civilized man, and this direction is towards ever exalted forms, more potent forms, and more intensive and expansive forms. Technology rarely if ever regresses backward, and such a condition would be greatly lamentable.
#2: The term “renewable energy” should be dispensed with and replaced with the term “natural energy harvesting”, since no technology is renewable according to the strict definition of the word. While it is true that the aluminum and copper used in this wind generator can in theory be recycled indefinitely, there are still nevertheless certain limitations that cap the scalability of all human technologies. Firstly, the technology is perhaps renewable but not infinitely scalable, since there is a limit on the available land in which wind speeds are high and populations densities permit construction of the devices. In the case of the high altitude wind generator, it is not metallurgical limitations as in the case of lithium-ion batteries or platinum fuel cells, but a rather a limit on the number of onshore sites that can be exploited. While the theoretical scalability is immense, likely equal to 10 times current global energy consumption, this would entail turning the entirety of North Africa, the North American Mid West, and Southern Argentina into a wind farm, which clearly faces immense technological and infrastructural limitations, notwithstanding the probable decrease in wind speed that would occur from the high density layout. Just as with a geothermal well, a high density wind farm layout could in theory slow down slightly the mean wind speed around the vicinity in the farm while free to flow areas would remain undisturbed. A high density layout with 8 times diameter longitudinal spacing will yield around 30 MW per square kilometer in a 12 m/s wind regime. To power the continental U.S, 15,000 square kilometers, or 7.5% of the state of Nebraska, would be required. While technically possible, we do not envisage such a scenario due to a lack of political will, lack of government centralization, lack of competence in government, and a deficit in the necessary vision and ingenuity needed to incorporate the infrastructure to utilize the energy generated. We therefore envisage the technology being used in concentrated forms in highly propitious geographies to mine bitcoin, produce ammonia, and electrolyze aluminum and a cost far below current power technologies. We expect investors to realize the high return on capital realizable with this setup and this alone will provide the necessary impetus for development.
Returning to our list of suggestion to increase the level of clarity in the debate pertaining to the energy domain.
#3: We must be willing to diverge from the design dogma in the present industry, such as the emphasis on the use of glass fiber over metallic blades, or the use of multi-megawatt scale as opposed to high densities of single mega-watt scale units.
#4: We must stop futilely trying to force wind energy or any spasmodic source to be merged into the power grid. This is perhaps the single most critical factor to highlight. Present-day electrical girds are designed for a variable but predetermined controllable flow of current, not a stochastic and uncontrollable flow. Current is modulated only above the so-called “base-load” using variable output thermal engines throttled according to temporal demand conditions. Furthermore, unless the wind turbines converts its energy to DC and back to AC, a fluctuating waveform will be emitted. AC grids require a constant frequency of 50 or 60 cycles per second depending on the country, otherwise critical machinery drawing power can be damaged. Additionally, when the turbine yields more current than can be consumed by the grid, energy is shunted and lost forever. Since power consumption drops considerably during the night, but the wind turbine keeps spinning away all night long, if storage is not available, any energy surplus is wasted. Since it is unlikely we can meet these stringent exigencies imposed by the AC grid, we should look for other options. Rather than force grid integration which strikes the intelligent engineer as a fool’s errand, these spasmodic wind sources should be deployed where a certain degree of variability can be more easily tolerated. For example, if we install these spasmodic wind generators in a rural site we can use them not to power the mains, but rather to cut present hydrocarbon consumption by producing hydrocarbon-intensive chemicals, such as hydrogen for ammonia, methanol production, hydrocracking, and electricity intensive processes, such as caustic soda production, aluminum electrolysis, electroplating, silicon reduction, titanium production, and steel recycling using electric arcs, and many other electricity-intensive or hydrogen intensive processes. What distinguishes these crude industrial processes is their ability to absorb variable power by using modularization, where banks are selectively switched on and off consecutively according to the available current. In contrast to the grid, these processes, while they may suffer a slight efficiency penalty caused by cycling, they can still nonetheless absorb isochronous power, while grids struggle to absorb isochronous current without massive storage banks. It should be remembered that every joule of energy saved by avoiding hydrocarbon consumption in these sectors is more energy available elsewhere, or a reduction in emissions. Politicians and “climate activists” seem to believe that only cars and household appliances consume energy, but this couldn’t be further from the truth. Cars barely consume 10% of global energy, and the entire power grid represents only 22% of total primary energy consumption, https://www.iea.org/data-and-statistics/charts/share-of-oecd-total-final-consumption-by-source-2019. Even if the entire grid was made hydrocarbon-free, 80% of the world’s energy would still remain untouched. This is quite a bold factual statement, because people somehow assume that the global energy budget is merely automotive and electrical because they do not personally see with their own eyes the legion of old and dirty industrial facilities consuming gobs of of heat energy. A key competitive advantage afforded by any spasmodic power source is its ability to produce storable, energetic compounds that are conducive to transportation and storage and on-demand reversibility into calorific value.
What renewable energy is and what it’s not
Photovoltaic and wind energy is for the small rural user of energy, it’s not for powering the greater Tokyo metropolitan region. Global primary energy consumption, which is the complete sum of all joules released by man, whether by water wheels or burning peat, amounts to 177,000 terawatt hours, or 1.77 × 10^14 (one hundred seventy-seven trillion kWh). Those who claim this number can be fulfilled without the combustion of carbonaceous fuels are ignorant. But that is not to say that out of these 170 trillion kilowatts, many scenarios cannot make use of unconventional sources of energy, especially if these use-case scenarios involve significant geographic distance from major centers of consumption. High-altitude wind turbines were invented and are marketed for customers that need a reliable, low-cost, and localized source of energy and who do not want to continuously transport and refill their energy needs. It is especially attractive to small factories that need to power electricity or heat-intensive industries (through the combustion of electrolytic hydrogen). It is designed as a more economical solution to diesel generators, paired with advanced thermal energy storage, it is able to generate a base-load source of energy at a price of less than 1 cent per kWh. The high-altitude turbine is a lower cost, simpler, and less space-intensive solution than photovoltaic. It is a niche technology, but that need not mean it is not extraordinarily useful. A helicopter is a niche technology, with annual production capacities for civilian helicopters not exceeding the hundreds, but the usefulness of this technology is not in dispute. The high-altitude self-erecting wind generator is projected to have a relatively small market size of a few hundred million per year or around 1200 units annually. Unfortunately, this rather obvious statement has to be accentuated because of a recent trend by uneducated politicians to use these “natural harvesters” of wind or solar energy to power entire electrical grids, causing myriad problems and giving these otherwise strong technologies a bad image. Wind turbines have been powering well pumps on American farms for over a century and a half. Many facilities, especially in high-wind regions, produce a surplus of power to cover most of their electrical needs with a single wind turbine. Photovoltaic panels were originally developed to power spacecraft, and their first terrestrial applications were lighting buoys and offshore oil and gas platforms. Other early niche applications include powering cathodic protection circuits in oil and gas casings and well caps. Powering Tokyo was never the intention of these formidable, yet tiny cells.
The Role of Natural Energy Harvesters
Christophe Pochari Energietechnik has designed a novel lightning-proof gearbox and generator module sealed within an anoxic atmosphere always under a slight positive pressure. This design makes it effectively impossible for the gearbox oil to catch fire. The generator module itself contains no flammable material, the generator is made of metal. The fire risk on the gearbox emanates exclusively from the gearbox oil which is submerged in an oxygen atmosphere. Denied oxygen, the gearbox oil cannot burn from a lightning strike. We believe that hydrocarbons, being the most convenient form of energy, will be the mainstay of our energy budget for centuries to come. But for certain specialized applications where energy cost is critical, natural harvesters, photovoltaic, high-altitude wind, and hydropower, will provide these niche sources and enable an increase in the profitability of producing electricity-intensive commodities.
Background and motivation
Since our invention pertains to wind generation, it would be foolish to ignore the crucial design variables and technical realities of wind turbine design. Wind turbines, much like water wheels, are perhaps the oldest cases of natural energy harvesting schemes, providing man with the first “augmentative” power source beyond muscle and animals. It is noteworthy to mention that wind energy attracted interest in Germany in the 1930s, hardly a country and era interested in gimmicky ideas! A German named Hermann Honnef proposed a tri-turbine mounted atop a 500 meter lattice tall to generate 20 megawatts of power at 15 meters per second, the speed he anticipate at such an altitude.
Honnef was the first to propose using hydrogen as a way to overcome the intermittency of wind. He was also the first to propose constructing towers offshore and to build much taller towers than had previously been constructed. Honnef’s ideas ultimately failed to be realized due to the extremely low cost of hydrocarbons across much of the 20th century, arguably the “fossil fuel” century. But enter the 21st century, and his ideas, albeit much improved, will undoubtedly see the light of day. Honnef’s plans were ambitious, arguably more a matter of structural engineering than wind engineering. Interestingly, we find ourselves in the same predicament, we are structure limited, not wind limited. In other words, we could conceivably build 1000 meter tall towers and tap into wind speeds well in excess of 15 meters per second, but at these heights, wind loads begin to overwhelm the structure’s ability to absorb the forces generated by the static pressure of the wind against the structure’s exposed surfaces, resulting in reduced structural efficiency and increased material intensity. The practical upper limit on height of the tower is 400 meters for the pure-tension tower using a 1 meter diameter tube with high strength steel cables.
Wind harvesting technology has remained almost entirely unchanged since the days of the German Growian, American MOD series, Danish Nibe A, and Italian Gamma 60, among others. Harvesting power from the wind is not a “boondoggle” by any means as often claimed by “Green critics”. If engineered properly, if geographic optimization is appreciated and respected, if grid connection and frequency modulation is circumvented, and if structural efficiency is optimized, wind generation can absolutely be an extremely low cost form of power generation, but like any technology, it has limitations, it will struggle to scale to global energy demand, but it can offer a number of operators very low cost power for critical industrial processes. At an equivalent altitude of 10+ meters per second, more acreage is available onshore only than the world’s total energy consumption by many-fold, but as already mentioned, it is unlikely such a deployment will happen.
The above is a wind velocity map of Europe. Below is the estimated land usage if high altitude turbines were placed in the 10 m/s velocity regions. Germany has 357,000 square kilometers, the total land needed for turbines placed at 350 meters is around 3000-4000 km2 to cover the entire power grid. Of course, this still doesn’t address the “baseload” problem, but one should remember that wind is much fiercer at higher altitudes and less variable, so the temporal variation is reduced. Of course, this temporal variation is not reduced to zero and storage is still necessary. For energy storage, we have already proposed effectively the only viable option and this is a helium Brayton cycle driven by banks of high-temperature aluminum oxide brick.
Judging from this map it is clear there is absolutely no need to bother building turbines in the corrosive ocean with all the attendant foundation, electrical cabling, and installation challenges. It is our opinion that offshore wind is completely ridiculous in light of high-altitude terrestrial technology, since after all, the whole idea of offshore wind is to tap into high-velocity regimes, but since we can get those same speeds on land by simply going up a few hundred extra meters, one has to seriously wonder anyone would even attempt to subject themselves to the ferocity of mother nature’s oceans when you can take to the safety of land. In fact, there is more land available for turbine installation than there is of suitable shallow waters where foundations can be practically constructed, the total area of waters where the depth is less than 100 meters, which is the practical limit for foundation installation, is relatively small. Additionally, fishing vessels risk colliding into the turbines at night during storms and an overall navigational pollution of coastal waterways is a significant risk. A tractor can easily bypass a mooring anchor for an onshore turbine, but a large slow moving vessel has difficulty turning on a dime to avoid colliding with a turbine mooring anchor. The constant bombardment of chloride-containing water produces a highly antagonistic environment for metal structures and shortens the lifespan of the unit significantly. Stress corrosion cracking caused by the presence of sodium chloride can induce premature structural failure, sometimes catastrophic. Steel, especially high-strength alloys, are highly prone to stress corrosion cracking in the presence of chlorides and general oxidative corrosion. Add in microbial corrosion, a number of bacterial oxidize iron as their food, and one has to wonder why anyone in their right mind would construct large permanent metallic structures in the ocean. Oceans are also much colder, since the heat capacity of water is greater than rock and soil, so blade icing is of greater concern offshore and such an increase in air density by the cold air will not compensate for the greater icing losses.
A guyed wind turbine takes up virtually no precious farmland unlike conventional wind turbines which have a large diameter tower, some as wide as 5 meters, since the tower base is much narrow and the silo is placed entirely underground. The guy cables that exit the earth at a 55-degree angle do not impede operation at a farm since their spacing is very far apart allowing harvesting vehicles to pass freely through. High altitude terrestrial self-erecting turbine technology makes expensive offshore installation redundant and obsolete.
A brief history of modern conventional wind turbines
The oil crisis of the 1970s prompted the advanced nations of the world to embark on a path of alternative energy development, probing into the technical feasibility of large-scale wind installations, concentrated solar, and photovoltaic. This was amidst a growing disillusionment toward nuclear fission, a combination of growing environmental fears and cost-overruns served to kill most of the “Panglossian” predictions made during the 1950s about the future of nuclear. This concerted effort to identify a viable alternative to hydrocarbon has only recently been surpassed in recent years over fears of “greenhouse gases” (which don’t exist), rather than resource depletion.
In 1974, the DOE commissioned the “Project Independence” report which studied a multitude of different wind turbine configurations, including a two-bladed turbine with a mast as high as 300 meters. In 1975, NASA contracted out blade manufacturing to Lockheed and installed a large turbine in Sandusky Ohio. In 1978 Boeing was contracted to scale up the Mod-O with the Mod-1 and Mod-2 in Wyoming. In 1976, Germany under the Federal Ministry of Education and Research tasked MAN SE with building a megawatt-scale wind generator called the Growian 1 and 2. In Denmark, extensive research and development was taking place with the ELSAM Nibe series of turbines in Denmark. Similar programs operated in Italy and Holland, but by far the most ambitious was in Denmark, with Danish firms such as Vestas that continue to dominate the industry to this day.
While the overall architecture has remained remarkably consistent, a few distinctions do appear. What made the 1970s generation of wind turbines stand out was their use of metallic blades in place of glass fiber. Glass fiber technology had not yet reached the level of maturity that it did in the 1990s, and despite the heavier metallic blades, their performance and longevity would be superior to today’s fiberglass. Steel blades can be designed to be thinner, afforded by their higher tensile strength, a more aerodynamically optimally geometry can be achieved. For example, 4140 steel can be cycled ten billion times if the stress amplitude does not exceed 500 MPa. If aluminum is used, such as 7075 T6, the cycle life is can exceed 10^10 cycles if the stress is kept below 200 MPa.
The case for aluminum and the counterintuitive weakness of steel
Aluminum 7068 (AlZn7.5Mg2.5Cu2), an ultra-high strength zinc aluminum alloy originally developed for ordnance applications, offers the highest specific strength of any metal alloy known. There exists very little data for this alloy on the internet and it is not commercially available, but at its core, it’s simply 7075 with more zinc. On a density-adjusted basis, it has equivalent strength to maraging steel, or 1928 MPa! This means thicker and more solid parts can be constructed, in contrast to a steel structure, where the material’s high density forces the designer to employ very thin-walled components. Its low melting point makes recycling chips generated from machining convenient, the low melting point also lowers the cost of degassing, essential for high purity and low inclusion count. But by far the single biggest asset afforded by this abundant metal is its softness, making machining very easy and rapid, allowing for the construction of “monolith” parts, free of bolted connections, welds, or adhesives. Christophe Pochari Energietechnik has designed a highly novel monolith-solid spar blade design where the entire blade spar is machined from a solid billet of aluminum, generating a weld-free structure for high fatigue life.
Material properties specifications for aluminum 7068 (AlZn7.5Mg2.5Cu2).
Tensile and yield strength for aluminum 7068 (AlZn7.5Mg2.5Cu2) as a function of aging time.
Breakeven cost for commercially pure titanium vs aluminum 7068 and 4140/4340 steel.
The material selection challenge for the high-altitude wind generator is by no means a trivial endeavor. It’s far more complicated than simply look at an “Ashby” plot and picking a “strong” material. The first thing we can say most if not all the so-called “composites” (which are really just fibers bonded with resin) are immediately ruled out, their complex fabrication methods and high cost will render them The high altitude wind generator require an elastic, ductile, energy absorbing, easily machined and low cost metallic main construction material.
If we look at the periodic tables, surprisingly few elements can meet these strict requirements. If there is a creator, he had mankind in mind when he deposited the elements on earth. With the exception of beryllium copper and titanium, few non-ferrous metals have structurally attractive specific strengths. Non-ferrous Alloys of chromium cobalt and nickel have high toughness and ductility, but do not possess any degree of superiority in tensile strength. If we go up further along the atomic scale, we arrive at tungsten, and while pure W possesses an ultimate tensile strength of 980 MPa, it is quite brittle, and adjusted for density, it is barely stronger than pure aluminum.
If we compare both the fracture toughness and the Young’s modulus (stiffness) of high-strength low alloy steels, 4140, 4340, etc, and 7068 Al, we find identical density-adjusted values. 7068 Al (AlZn7.5Mg2.5Cu2) has a young’s modulus of 73 GPa, but adjusted for density, it’s 201 GPa. For fracture toughness, the transverse and longitudinal, the average value for 7068 is 20 megapascal square root meter, or equal to 55 on a density-adjusted basis. These values place it in a competitive league with alloy steels.
On a purely “cost per MPa” basis, nothing can compete with ferrous alloys, even containing small nickel molybdenum and chromium content, such as the low-alloy steels. But a cost per unit strength metric insufficiently captures a number of other disparate properties which are propitious. Density is perhaps one of the most prized attributes of a metal, aluminum is simply unparalleled in this regard. A high-altitude wind turbine is not like a house, whose weight can all be born by a concrete pad and transferred directly onto the soil. A high-altitude wind turbine must transfer its mass to pressure, and this pressure must be born by hoop stress. The mass of the entire structure is directly proportional to the specific strength of the material used. Titanium alloys are entirely uncompetitive, relying on vanadium to achieve high tensile strength, unalloyed titanium possesses no attribute that warrants its use over aluminum. But while these steels boast superlative tensile strength and toughness, they possess intrinsically high hardness, and for them to be machined, must be before they are heat treated. This complexifies these fabrication processes. But even if machining is performed prior to heat treatment, most of the 4140-4340 grades will still have a hardness of over 30 HRC (285 Vickers) even if tempering is kept at over 700℃. In contrast, aluminum, even allowed with up to 8% zinc, maintains its softness allowing it to be machined with high-speed steels, carbides are really redundant for machining aluminum, but can still be used. A Vickers hardness of 285 is an absolute hardness of 93 kg/mm2. 7068 aluminum has a Vickers hardness of 186, or an absolute hardness of 61 kg/mm2. This difference may not seem that significant, but it has deeper implications for their respective machinability. A small difference in hardness can translate to a much larger difference in insert life, reducing machining costs. The absence of carbon in the material also contributes to easier machinability. Moreover, a small reduction in hardness can allow a larger increase in machining speed, increasing the volumetric removal rate. Aerospace aluminum parts are routinely machined at MRRs of between 2000 and 6000 cm3/min using 20-25,000 r/min spindles using up to 120 kW. Ultra-high-speed machining of this kind can allow the blade to be machined into a monolith iso-grid type structure from a solid forged aluminum billet using a gantry CNC, eliminating virtually all the labor in the blade assembly. The 44-meter 800 kW blade unit, machined from a solid billet of aluminum weighing 36 tons, would require removing only 4.6 cubic meters yielding a solid monolith blade spar weighing only 1.4 tons. The total time to machine the blade at an MRR of 4000 cm3/min is 19 hours per blade, or 60 hours total. Assuming an hourly operating cost of $50/hr, the cost is only $2,850 for a full set of blades. A steel blade would need to be constructed from multiple built-up parts, requiring welding, adhesives, or bolting/riveting to hold these parts together. The spar would need to be mechanically fastened to the skin element, generating fatigue stress concentrations. Any time a bolt, rivet, weld, or adhesive joint is generated, the stock fatigue strength of the material is reduced by at least 75%. Aluminum 7075 specimens have demonstrated gigabyte fatigue strengths of 177 MPa at 10^9 cycles. The maximum stress amplitude for the gravitational acceleration of the blade generated by its own mass is 40 MPa. Over a period of 30 years, the blade spar has incurred 394 million cycles, where the stress amplitude is 200 MPa.
In short, Christophe Pochari Energietechnik‘s solid-spar monolith blade technology generates the strongest possible blade design achievable with current materials and methods. It is orders of magnitude stronger than existing epoxy resin-bonded fiberglass blades, which have miserable fatigue cycle life. Compared to a welded steel blade, its fatigue performance is simply beyond comparison. By vacuum melting and degassing the aluminum before forging the machining ingot, inclusion can be minimized to maximum fatigue life.
Returning to a specific strength, if we examine high zinc-aluminum (7068), with a tensile strength of just under 700 MPa (680 as a more conservative number, larger specimens for all metals will have lower strength due to inclusions), we find that for steel to have the same specific strength as 7068, it would need a tensile strength of close to 2000 MPa. Clearly, this is almost impossible to achieve without resorting to maraging steel, which is not scalable due to constraints on cobalt and molybdenum mining. One could argue the central attribute of high-strength aluminum is its reliance on zinc as its chief alloying element. Zinc reserves are estimated to tally up to nearly 2 billion tons, with a low cost of $2500-3000/ton and a global production of 13 million tons, this is hardly a metal worth fretting about. Zinc has almost no use outside of the galvanization of steel, and the primary determinant of the price of zinc is steel demand in China, which is slowing drastically. Zinc is not one of these “green metals”, such as nickel or cobalt that are attracting attention among decarbonization advocates. Aside from zinc, only trace amounts of other metals are needed, principally copper, with concentrations of less than 2.4%, unlike high-strength steels which require non-trivial amounts of molybdenum, a metal in scarce supply.
4140 steel costs around $800/ton, with the bulk of the cost difference over ordinary steel due to the molybdenum and chromium. Since 4140 steel with moderate hardness and satisfactory toughness is around 950 MPa, this translates to 121 MPa/g. In contrast, pure titanium at 700 MPa with 0.45-5% oxygen is 4.45 g/cm3, or 157 MPa/g. In the case of aluminum, with a density of 2.81 g/cm3, 7075 has a specific strength of 203 MPa/g. Aluminum 7068 has a fracture toughness of only 18-29 MPa-m½. If the benchmark is 4140 steel, in order to meet this requirement we must produce titanium for equal to or lower than $0.00084/MPa, or $0.59/kg. Clearly, the production cost of titanium via a non-Kroll process using calcium electrolysis, while considerably lower, it still somewhat above $1.5/kg. The current price of aluminum is $2.4/kg, or $0.0041/MPa.
Aluminum production cost from acid-leached orthoclase feldspar (K2O-Al2O3-6SiO2), the feldspar family of minerals makes up 70% of the crust.
There is no need to purchase bauxite, the rock beneath your feet can be effectively leached for aluminum oxide using regenerated acids for far less than the cost of buying bauxite.
Feldspar aluminum content: 9.7% mass Al: 91 kg/ton
Raymond mill (fine crushing) 45 microns: $0.08/ton-feldspar
Large Mill: 150mm-25mm: $0.0025/ton-feldspar
Total comminution energy ball mill: 30 kWh/ton-feldspar
Comminution energy jaw crusher: 0.29 kWh/ton-feldspar
Transport via trolly to comminutor: $0.02/ton-feldspar
Acid regeneration: (Sulfur dioxide passed over V2O5 catalyst to recover HCL. Catalyst consumption is around 0.26 kg V2O5/ton-H2SO4/yr): Negligible cost per ton of aluminum
Leaching reactor: ($2500/m3, 8-hour leaching time, 9% Al content, 1500 kg/m3 slurry density): $0.017/kg-Al
Total processing: $0.025/kg-Al
Carbon consumption: 420 kg-ton-Al (LWG graphitization from MSW): $100/ton-Al
Primary electrode current consumption with electricity from photovoltaic or high-altitude wind (1.5¢/kWh): 13 kWh/kg $0.195/kg
Electrolysis plant CAPEX: $0.25/kg ($9000/TPY 1979 estimate, 544 million for 75,000 TPY 2018, $7200/TPY, over 30 yr amortization, reduction factor for small-scale COTS part use)
Copper and zinc costs (assuming a zinc price of $2500/ton and a copper price of $8000/ton: $0.28/kg
Note, no cost reduction is attributable to any technological changes, the use of graphite produced from MSW and the use of low-cost electricity from high-altitude turbines allows the aluminum to be produced for around 70 cents per kg.
Besides the standard techno-economic metrics, namely strength, density, and ultimately price, a more nuanced economic metric is “producibility” or a measure that captures how difficult it is to produce a given material. Producing carbon fibers will forever be difficult and not conducive to cost reduction assignable to the inherent complexity of the process. We, nor many credible people claim that a dramatic cost reduction is possible. An aluminum electrolysis cell is a big rectangular can lined with graphite blocks, it is a crude piece of equipment easily manufactured. In contrast, carbon fibers are 7 microns on average, handling fibers so small is inherently difficult. In a carbon fiber plant, a number of complex specialized components are required. The basic system consists of a carbonization furnace, consisting of two units operating at 1000 and 2000℃, and an oxidation unit operating at 300℃, But more importantly, the entire process is dependent on exacting controls of the major parameters, temperature, pressure, and trace concentrations of impurities. Worst yet, The feedstock, polyacrylonitrile, is already quite expensive, upwards of $5/kg. The final fiber may have widely different strengths depending on the relative balance of these parameters. This is why carbon fiber costs $25-50/kg and will likely not come down very much in the future. Note that despite claims carbon fiber can be produced for as low as $9/kg, no seller on commercial marketplaces like Alibaba or Baidu B2B offers CFRP yarn for less than $25/kg. One would be highly foolish to expect slightly cheaper electricity costs or higher volume manufacturing to bring this price down. In contrast, aluminum production is mainly dependent on the cost of electricity and graphite, the two major consumables. The electrolysis reactors are very crude devices, many look like they’re built by a DIYer, with patchy-looking construction. Dimensional tolerances are the least bit important in these reactors. The two major consumables are resources that are hardly scarce nor fixed in price, both are inherently variable depending on production methods and supply conditions. The actual metallic electrolysis tanks last for half a century and are constructed of low-cost materials. What actually “wears out” is the liner inside the cell made of graphite, this usually has to be replaced in less than 7 years. The cells have no moving parts, and unlike carbon fiber where precision-engineered yarn rolling devices are required, the electrolysis cell just sends massive amounts of current into a boiling liquid emulsion.
We are interested in a material whose production process is amenable to non-technological cost reduction, mainly through energy costs but also consumables, for example, imagine graphite were indigenously produced by the partial oxidation of solid waste, coal or low-cost biomass to produce charcoal or amorphous carbon, which can be graphitized with a lengthwise graphitization furnace. Graphitization takes 10-18 hours in lengthwise reactors with temperatures of between 2500℃-3500 ℃. Low-purity charcoal produced from MSW can be converted to coke through thermal distillation or pyrolysis, to generate a higher-purity amorphous carbon source for graphitization. Alternatively, the entire graphitization can be dispensed with by using a Fischer-Tropsche cycle where synthetic diesel fuel is produced from synthesis gas and pyrolytically decomposed liberated hydrogen and carbon black. The Kværner process, or the Kværner carbon black and hydrogen process (CB&H), is able to convert nearly 100% of the methane feedstock into hydrogen and carbon black using about 29 kWh/kg-carbon. But since hydrogen is generated as well, this can be burned to recover a substantial portion of the energy, around 4.5 kWh-kg-carbon assuming 45% efficiency. The high energy consumption of this process may not justify its advantage of producing higher-purity graphite.
The production of graphite requires only a source of carbon (biomass, MSW, coal, synthesis gas, etc), and electricity or heat. Carbon has a specific heat capacity of just over 2000 J/kg-K at 3000 K, so producing one ton of graphite requires just over 1550 kWh. Depending on the insulating value of the reactor, it may lose 50 kWh. Since it requires an average of 14 hours to fully convert the amorphous carbon into graphite, an additional 500 kWh is consumed, yielding a total of 2300 kWh/ton of graphite, or $35/ton at a price of 1.5 cents/kWh.
If we performed a techno-economic analysis of the major consumables, both energetic and material, we are led to conclude that the cost of producing aluminum is highly variable and the core fixed cost (the reactor construction), plays only a very small role.
The average electricity consumption is 12.5 kWh/kg, this alone in a region where electricity is dependent on coal or gas, such as in Europe or the U.S., electricity costs may exceed $870/ton alone. If we then look at graphite, if this graphite were purchased on the current market, with an average price of around $1000-1200 per ton on Alibaba, the cost of the electrode alone is $420/ton-Al. If both these consumables are substantially lowered through self-production, aluminum costs can easily be lowered to $1.5/kg without resorting to exotic or unproven technologies.
7075 T6 gigacycle fatigue.
There’s a common misconception that extant wind turbine blades are “optimized” beyond reasonable limits with the use of CFD, and that no major changes to improve their lift coefficient are possible. In reality, this could not be further from the truth. The Danish Nibe A, with its thinner metal blades, achieved a significantly higher power density, around 450 w/m2 at 12 meters per second, while most modern fiberglass bladed turbines with their whale-shaped bulbous blades barely achieve 300 w/m2. The Enercon series of wind turbines is one such exception, boasting the highest power coefficient of any turbines on the market. But upon closer examination, one can easily infer that their blades resemble the older metal designs, with a slimmer geometry that looks quite different from the standard extant design featuring a bulbous root section that extends out a considerable amount. Since current wind turbines use fiberglass that has very low stiffness, the blades must have a very deep spar to prevent excessive bending, which can severely compromise aerodynamic efficiency by lowing the lift to drag coefficient. A slender metal and stayed blade can achieve a significantly higher lift-to-drag ratio which improves the power coefficient, translating to higher power densities. The Enercon E-44 achieves a power density of 460 W/m2 at 12 m/s at a power coefficient of 0.44, while the E-70 achieves a power density of 0.48 kW/m2 at 12 m/s at a power coefficient of 0.45. With guyed metallic blades, a higher power coefficient can be stemming from the ability to reduce the chord thickness of the blade.
Power curves for the Nibe A (below), Enercon E-44 and Enercon E-70. The power densities at 12 meters per second are 0.434, 0.46 kW/m2, and 0.48 kW/m2, respectively. It should be noted that the Enercon turbines, as well as many other turbine models, actually produce far more power than advertised since the power curve lies on the outer parameter of the power band distribution, in other words, the published power curve is the minimum power the turbine is guaranteed to produce under a given wind speed.
The Nibe A and E-44 are substantially more efficient than the mean wind turbine in use today, this is attributable to an optimally slender blade geometry. The Enercon E-70 currently boasts the absolute highest power density of any wind turbine existence thanks to its unparalleled CP of 0.45 at 12 meters per second, the E-44 has a CP of 0.44 at 12 m/s. The unique airfoil shape, which is readily observable with its highly cambered geometry, accounts for its high CP. The reason other manufacturers do not appropriate the airfoil design is unkown, since Enercon Gmbh does not maintain any patents in the Google patent archive or the European patent Espacenet search engine.
Power curve of two E-44s installed in Iceland, showing up to 20% overproduction.
This chart suggests that there is no anomaly but rather that Enercon merely simply measures the minimum production and cuts off anything above the minimum, but since there is considerable variability in the local aerodynamic efficiency of the blade caused by changes in air density, particles, moisture, etc, this means there is quite a wide band of potential power outputs. If we take the midpoint of that green scatter plot they construct, the power density is nearly 600 watts/m2. This curve, although considerably more power dense than most models, is perfectly compatible with wind turbine physics and the Betz limit. The DTU wind map estimates the power density of a 12 m/s wind regime at 1.67 kW/m2, if the CP is 0.44 then the power density would be 0.73, so the CP is likely only 0.32.
The Enercon E-44’s overproduction and the power law.
Ragnarsson et all performed a study on two Enercon E-44s installed near the Búrfell volcano in Iceland and found a dramatic overproduction compared to the power curve predicated by Enercon. They concluded that either Enercon underestimated the true power output to be conservative or that the particular site which featured an 8.7 m/s mean wind speed and a standard deviation of 5 m/s featured substantially more storm speeds in the 25-34 m/s range which could account for the higher power output. The authors concluded that it was likely that both factors accounted for the substantial overproduction, which of course is excellent for the wind turbine owner. Either way, the turbine produced about 17-20% more power at 12 m/s than the rated curve predicts, yielding a power density of 0.545 kW/m2, or on average producing over 850 kW at 12 meters per second. Since the Icelandic site is located in a class 3 Ice zone, one can assume at least a 5% power loss to icing, making its real power density perhaps as high as 0.57 kW/m2.
We can now turn to the power law of vertical wind shear profile. The entire modus operandi of our tower is to tap into faster wind speeds. The reason wind speed decays is because of surface roughness, which has a diminishing effect as height increases. Over oceans, wind speed does not decay as severely as over shrubs or forest, hence the higher speeds found over oceans. It is not that wind travels inherently faster over the oceans, it’s that more of its kinetic energy is preserved allowing it to maintain its momentum. For offshore installations, there is less incentive to increase height.
A number of formulas exist for calculating wind speeds at elevated heights, but the most common wind is the so-called power law, widely used by skyscraper designers to estimate wind loads. To utilize the power law, an accurate estimate of the surface roughness is needed. The power law uses an exponent which is a function of the roughness, which varies from 0.10 for oceans and over 0.2 for urban areas. One thing is to be noted, either the DTU wind map overestimates the vertical wind profile, or the power law underestimates it, because if one uses the power law with an exponent of 0.15 (typical for short prairie grass) the increase in wind speed from 50 meters to 200 meters is substantially less than the DTU estimate, which has likely been verified experimentally with SODAR data.
In the 1970s, the aforementioned Department of Energy “Project Independence” investigated designing a 300-meter tall tower to capture high-speed winds in Caspar Wyoming, they estimated a 1.093x wind speed increase from 182 meters to 300 meters, Caspar Wyoming is primarily short prairie grass. The Dutch offshore wind atlas measured a 1.075x increase from 200 to 300 meters over the Dutch countryside, which is mainly pasture with low tree density, but a higher density of buildings than the Argentinian prairie or the Nebraska sandhills. Assuming a wind speed exponent of 0.15, between 0.14 and 0.16 is realistic, then if we increase the height from 200 meters where we know the wind is 11.5 meters per second from the DTU map, we can then get a speed of 11.7 m/s at 300 meters. But this number is likely underestimating the true speed exponent, because if we compare it to the Global Wind Atlas, to match the speed increment from 50 to 200 on the Atlas, an exponent of 0.225 is needed, which suggests the mathematical formula is ill-equipped to calculate the true wind speed at elevated heights unless the DTU wind atlas is completely inaccurate, which seems unlikely. For example, in one selected coordinate, Magallanes, Santa Cruz Province, Argentina, the mean wind speed at 50 meters is 9.24 m/s but increases to 12.55 m/s at 200 meters, but the power law predicts only 11.38 m/s at 200 meters, a full 1.17 meters per second slower than wind atlas.
What is the true number?
The “true” number (which of course requires an anemometer to be placed at the altitude and coordinates in question for 100% confidence) is likely closer to the DOE estimate and the Wind Atlas, after all, they would be very careful to validate the exponent they used since they were making financial estimates based on the wind velocities. Without renting a SODAR or placing an anemometer on a tower at the site, it is impossible to say with 100% accuracy, the question is can we achieve a reasonably close approximation? the answer is a sound yes. A sight with a wind speed of 10.9 meters per second at 200 meters, which is much of the Nebraska Sandhills, at 350 meters, the speed should be very close to 12 meters per second.
The issue of gearsets
The single biggest limitation in wind turbine technology after the heavy tower is the need for a speed-increasing gearbox. The rotational speed of the shaft from the hub is only about 25 r/min for a 750 kW 44-meter diameter turbine. The weight and cost of a 25 r/min dynamo would be exceedingly prohibitive. The way the direct drive systems work is by increasing the diameter to increase the velocity of the stator and rotor, so the actual velocity of the magnetic flux is close to a smaller diameter high-speed device. But these large diameter dynamos occupy a large amount of space and feature a large frontal area which places a heavy bending load on the tower from the drag it generates, the nacelle also adds significant weight. The mass of a 1500-1800 r/min synchronous generator is already nearly 3 tons, while if the speed is increased to 20,000 r/min, the mass declines to barely 150 kg, very close to a linear decrease. The average copper winding intensity of a 90 kW induction motor at 1500 r/min is approximately 0.47 kg/kW, no data is available for synchronous generators, but the numbers are expected to be close. This winding intensity translates into a direct cost of €4500/MW at present spot prices, or approximately 40% of the cost of the typical 1 MW synchronous generator, the rest being assembly labor, which makes perfect sense. In contrast, by adding only two additional epicyclic gears, we can increase the r/min from 1500 to 20,000 with only an extra few tens of kg of 40Ni2Cr1Mo28 (AISI 4340) steel, which is one-eighth the cost of copper. This is a very intelligent design trade-off, namely using slightly more of a cheaper material to reduce the amount of expensive material by a large amount. For a 20,000 r/min synchronous generator, the amount of copper needed is barely 100 kg, or €800. Christophe Pochari Energietechnik is actively considering a generator-less configuration where small diameter low torque drive shafts are inserted on the exterior of the column to drive a generator on the ground. Such a configuration would eliminate one of the only major hazards faced by wind turbines: electrical fires: Perhaps surprisingly, fires are one of the leading causes of wind turbine failure, by removing electrical components, it is difficult to generate the necessary sparks to ignite flammable material. Christophe Pochari Energietechnik is also investigating the use of non-flammable ionic liquids for gearbox lubrication. Many ionic liquids have viscosities as high as standard motor oil (50 centipoises) and possess superior tribological properties, also this is highly tentative and no present modeling is based upon the use of ionic liquids. Christophe Pochari Energietechnik has designed a novel lightning-proof gearbox and generator module sealed within an anoxic atmosphere always under a slight positive pressure. This design makes it effectively impossible for the gearbox oil to catch fire. The generator module itself contains no flammable material, the generator is made of metal. The fire risk on the gearbox emanates exclusively from the gearbox oil which is submerged in an oxygen atmosphere. Denied oxygen, the gearbox oil cannot burn from a lightning strike.
A 1 megawatt 1500 r/min synchronous generator juxtaposed with a 20,000 r/min version. The amount of copper saved easily pays for the added gearbox stages. It should be noted that once the initial high torque reduction is performed, gearboxes last much longer at the higher speed section since torque is dramatically reduced even though friction and heat are somewhat higher.
Some may object to the added gearbox challenges associated with operating at elevated speeds, namely increased friction, heat, and subsequent lubrication degradation. But such concerns are trivial compared to the cost savings that can be had from the smaller electrical machine.
Without such speed intensifying gearbox, heavy low-speed generators that need permanent magnets, usually made from neodymium, must be employed, at a significant cost and weight penalty. These slow-speed permanent magnet alternators make additional use of praseodymium to increase the flux density at low speeds, and are usually ten or more times more expensive than high-speed synchronous generators or induction generators. Beyond a mere cost disadvantage, the weight of the generators even after adjusting for the weight of the gearbox makes it an unattractive option as it adds nacelle volume which contributes to greater drag that has to be borne by the tower structure, be it conventional or hydrostatic. Despite the high cost of permanent magnet dynamos, neodymium, and especially praseodymium, contrary to popular belief, most of these lanthanides are not “rare” at all. Neodymium reserves do not actually limit the scalability of wind power unlike platinum group metals limit the scalability of fuel cells.
Technology is ultimately subordinate to the elemental and the material substrate it can be constructed from, and their techno-geological attributes. In the realm of structural engineering, man enjoys a privileged vantage point, since there exists only one non-ferrous alloy with a tensile strength of close to 1000 MPa, that is beryllium copper. Excluding titanium, virtually all of the high-strength metals available are ferrous. Beryllium copper is an ideal choice for extreme applications, its application include drill string collars, marine fiber-optic connectors, and spark-less tools. But since reserves of beryllium, primarily mined from pegmatite, total only 80,000 tons, and typical beryllium copper contains 2.5% Be, theoretical production is only 3.2 million tons of the alloy.
Man has not been kindly enough bequeathed with the more exotic of the elements, the most abundant elements he has access to are rather bland elements, that may shine in structural applications, but have limited electrically attractive properties, such as high conductivity or unique optical properties due to their electron orbital shapes. Iron is the most abundant metal after aluminum, and while solute strengthening, precipitation hardened, and plastic deformation can be performed to produce the strongest metal known to man, it has rather unextraordinary properties needed for certain highly specialized applications, such as catalysis or electronics. For any technology to be viable, its material constituent has to be scalable with the demand for said technology. A technology that cannot scale for reasons of elemental scarcity, is a useless technology no matter how impressive it may look. PEM fuel cells, and lithium-ion nickel-cobalt manganese batteries both cannot scale to worldwide levels of deployment, even though many technologies that use exceedingly scarce elements, for example, catalytic converters, have been scaled, but that is thankfully because they use such minute quantities.
A low-speed permanent magnet generator uses an average of 650 kg of magnet per MW, and of that, 22% is neodymium and 0.76% praseodymium by mass, although some estimates suggest as much as 4 to 6% praseodymium is used. For medium-speed permanent magnet motors, the magnet loading is 160 kg, for high speed, it drops to 80 kg. Since the whole point of using a permanent magnet is to dispense with the gearbox entirely, we will choose the 650 kg/MW for our scalability analysis. The benchmark for all our scalability studies is the U.S or European power, which are both around 3-4 billion megawatt-hours a year. We would need 450,000 MW of installed capacity to power these big grids or close to 90,000 tons of neodymium and 3,000 tons of praseodymium. The estimated reserves of neodymium are massive, estimated to be 20 million tons, and praseodymium is estimated to be 2 million strong, so the scarcity of neodymium nor praseodymium is not a concern, but rather their added cost, weight, and volume occupied compared to a high-speed unit. An electrical machine’s power density is a linear function of its rotational velocity, so the worst possible thing we could do is operate the generator at low speed. A speed modulation system is far more elegant than squandering materials and manpower into constructing inordinately heavy low-speed machines.
Elemental composition of NdFeB magnets.
Since our turbine operates for simplicity at 100% “capacity factor”, our annual power output is its hourly output times 8760 hours minus 3-5% maintenance downtime.
While direct drive turbines suffer from numerous electrical machine limitations, gearboxes are not exactly perfect either. Wind turbine gearboxes have historically suffered from far from ideal failure frequency, caused mainly by cyclical torque loads caused by varying wind speeds. Unlike a gearbox used in industrial machinery operating at a constant speed, a wind turbine gearbox is subjected to isochronous loads, which cause a sudden introduction of torque placing dynamic loads in the gear teeth and prematurely wearing them out. The term “hydrostatic” when invoked with reference to wind turbine technology has almost always insinuated the use of some form of gearbox system for power transmission, namely to up the r/min to suitable generation speeds. Hydraulic fluid is incredibly convenient for designing an infinite-speed variator, but the losses have served to thwart this technology application. The use of ionic liquids, combined with short path flow circuits and low leakage seals, may open up the possibility of infinite speed hydrostatic speed-up variators, finally ridding the annoying gearbox from the wind turbine. While conventional hydraulic drivetrains as aforementioned suffer from an efficiency penalty relative to gearboxes, ionic liquids with their almost zero compressibility offer the drivetrain designer the ability to contrive a close to lossless pure hydrostatic speed variator. Ionic liquids boast a bulk modulus (a measure of incompressibility) of almost 3.6 gigapascals at 400 bar, while traditional hydraulic oils are around 2.2. This difference may appear insignificant, but for a hydraulic system, it makes a substantial difference in the net efficiency. The less energy is absorbed compressing the fluid, the more leftover for performing useful work. The second major cause of energetic losses in a hydraulic circuit is viscous drag and the concomitant pressure drop as the fluid is pumped at high flow rates in a long hosing circuit. Fluid loses momentum as it incurs viscous drag along the hosing wall and pump and motor surface area, since any given volume of hydraulic media contains only so much energy, the amount of viscous induced momentum loss is significant. An ideal hydrostatic power transmission circuit would minimize viscous losses to the greatest extent possible, this would be achievable by minimizing circuit distance, but there is limit to how small a circuit can be achieved. In summary, it is unlikely an alternative to the gearbox will ever be designed, a better solution is to try to reduce gearbox manufacturing cost through innovative fabrication and assembly.
It would make little sense to design a transformative and innovative tower technology without making at least some minor improvements to the main turbine module. A wind turbine, ours for that matter, that uses a high-speed generator, makes use of no scarce elements.
Archimedes’ lever in reverse
It is possible through intelligent engineering to minimize the force acting on the gear teeth to keep the material well within the fatigue limit of common gear steels such as 40Ni2Cr1Mo28 (AISI 4340) and 18CrNiMo7-6. Since the tangential force of a rotating object is proportional to the distance from the axis of rotation, a larger diameter sun gear experiences a reduced load at the contact points. It should be noted that gears are very rarely a fatigue-limited system, but rather an abrasion and wear-limited system. The single largest contributor of gear wear rates is lubricant viscosity. Using high viscosity lubricants, with dynamic viscosity as high as 6,800 cP, very high film thickness can be maintained affording gear lifespan of over 100,000 hours. Wear rates are linearly related to lubricant viscosity and film thickness. Lubricants become more viscous when compressed, when the oil film is compressed between the gear teeth, the pressure may be in the gigapascal range, and viscosity increases according to the Barus and Roelands equation. Once the initial bulk of speed reduction is provided for, the torque drops dramatically and the gears can be designed to be much lighter. One of the best things the gearbox designer can do is install an oil cooler to as quicky as possible removal heat generated from mechanical losses to keep the oil as cool as possible maintain the highest viscosity. For the 750 kW 44-meter turbine in question, the blade tip speed ratio is around 6.5 resulting in a rotational speed of 30 r/min producing 238,000 N⋅m of torque. With the main low speed gear diameter of 600mm, the maximum tangential force generated is 79,000 kgf. The peak stress on the gear tooth is 140 MPa.
The three stage 6.6:1 speed-increasing gearbox. Approximate gear set weight: 135 kg.
The gear pictured above takes the highest torque low speed 30 r/min produced initially by the turbine and increases to 198 r/min, dropping the torque from 238,900 N⋅m to 36,000 N⋅m. The second gear set increases the speed from 198 r/min to 1306 r/min, further reducing the torque to 5,500 N⋅m. The last gear ups the speed to 8,600 r/min with a miniscule remaining torque of 860 N⋅m. The 8,600 r/min synchronous generator is almost 9x times more compact than a 1,000 r/min generator. Modern gearbox technology is incredibly efficient. For example, the main speed-reducing main rotor gearbox on the Bell OH-58 Helicopter maintains a mechanical efficiency of 98.4% at maximum torque, dropping to 95% at fraction of its peak torque. Since higher altitude wind features less variability, a higher gearbox efficiency is achieved, yet another advantage of the high-altitude wind generator system. It should be noted that dynamo efficiency also increases sharply with load, a clever solution is a dual generator system, where each generator is run at 100% load constantly and when the wind speed falls below the load threshold, one generator is switched off, placing 100% of the load on the other generator. This can be achieved with very simple centrifugal clutch technology.
Magnetic and Hydrostatic bearings
Wind turbines are subject to very large axial and radial loads. The 44-meter turbine has blades that weigh has 1,600 kg/ea and a hub weighing 600 kg. The radial loads not only emanate from the dead weight of the rotating equipment, but also from the wind force acting on the blades laterally. An additional ten more tons may be generated by strong gusts acting on the side of the blades. Therefore, a wind turbine bearing must have very strong lateral load capacity as well as gravitate vertical load capacity. Since the parasitic power loss is proportional to the bearing friction, and friction is proportional to the force applied, a heavy shaft spinning even at low speeds incurs a small power loss, which of course would need to be larger than the power required by the hydrostatic or magnetic bearings. This is where the crux of the matter is, as all alternative bearing technologies actually have greater parasitic losses than ball bearings, their improved lifespan and reduced maintenance cost must offset their greater parasitic power. In some cases, this may not be fully compensated by their superior longevity. An axial ball bearing with a typical friction coefficient of 0.005 will incur a power loss of 320 watts, or 500 N for an 800mm diameter shaft spinning at 20 r/min, or approximately 0.00053% of the output power. This is truly a testament to the efficacy of contact-bearing technology!
Magnetic bearings rely on the repulsive and attractive force of an electromagnet to produce the levitating force necessary. The achievable zero-gap forces are between 50,000 and over 70,000 kg/m2 for electromagnets, but at a gap distance of 1 millimeter, this would decrease by about 17%. At 2.5 mm of gap, the force declines 30%. Magnetic field intensity declines as the inverse cube of the distance, so it is desirable to maintain as small a gap as possible, but there exists a clear limit on how close they can come, since the bearing has some degree of movement within the magnetic confinement.
The power requires by an electromagnet varies from 3 mW/kg to 10 mW/kg, depending on the flux intensity, more current running through less winding generates more heat and eddy current losses. The average power consumption is around 10 mW/kg for a magnetic pressure of 60,000 kg/m2. For a conservative estimate, we will use 12 mW/kg, thus for a 10 radial load-bearing, we will consume 1 kW, or three times more than a friction roller bearing. At first glance, this would seem like the ideal magnet design, but upon further examination, there are some notable issues that have served to keep this technology from reaching mainstream use. A central issue has been the relative bulkiness and cost of the copper winding, the second has been the need for precise balancing of the shaft inside the electromagnet coil array. Precise gap sensors operating at high frequencies feeding into a digital controller are necessary for stable operation, this has served to dissuade designers from incorporating magnetic bearing in all but the highest speed and critical applications. The other issue is lack of redundancy, all magnetic bearing systems require an auxiliary friction bearing that must be capable of relieving its load before the magnetic bearing is turned on during startup. Moreover, if the magnetic bearing fails, catastrophic failure would occur without the ability to carry the shaft’s load on an auxiliary bearing. The amount of volume needed is substantial since the relative magnetic pressure is very low compared to hydrostatic bearings or conventional friction bearings.
In contrast, an externally pressurized hydrostatic bearing would generate a pressure of 700,000 kg/m2, allowing for a much more compact bearing package. Using pressure drop as our flow rate determinant, we can calculate the pumping power of the bearing. For an oil film thickness of 50 microns, which is typical for a hydrostatic bearing, if the diameter is 800mm with a length 350mm, assuming a steel surface, a flow rate of 20 liters per minute generates a pressure drop of 100 bar. The pumping power is thus 6000 watts, or sixteen times more than a friction bearing. If reducing friction ends up increasing the power lost in the system, one has to ask whether this is a sound engineering decision.
In conclusion, there is little reason to believe bearing technology is receptive to significant improvement effort, leaving other systems as prospective candidates for process intensification and betterment.
What is needed rather than sundry marginal micro-innovations, whether in speeding modulation, bearing technology, or even blade aerodynamics, is precisely the antonym of a micro-innovation: a macro-innovation. A departure from the world of incrementalism and minor tweaking is needed, a radical leap onto a higher plane of technology is called for. A Kuhnian paradigm shift and revolution in the way structures are constructed, away from Euler columns towards hydrostatic columns, is wind energy’s new calling. This paradigm change in the way we support wind turbines, an “aerial platform”, that allows the designer to place the state-of-the-art windmill in the fiercest wind regimes in existence, all while staying within the safety and comfort of the solid ground, culminates in a unique technological optimum. This technology allows this designer to capture wind speeds equal to the best offshore wind farms without the corrosion and foundation penalties encountered by the oceans.
Structural dynamics and the unique properties of the pure-tension tower
The following text is meant to be a brief exposition on this new type of technology, one that can greatly potentiate the power of wind energy.
A cable-stayed bridge in China. Cable-stayed bridges are among the few terrestrial structures that make extensive use of cabling to derive their structural integrity and distribute loads.
Christophe Pochari Energietechnik invented this technology in February 2022, after many months of studying how to improve wind energy by increasing turbine operating altitude. A fascinatingly novel structure, that defies the norms of structural engineering, arose out of this effort. The technology is so novel that an entirely new vocabulary must be developed, entirely new concepts have to be normalized and contemporary literature must be updated accordingly. This new type of pure tension tower is ready to be exploited with zero research and development required, using only contemporary materials procurable from commercial supplies, and using the current knowledge of gas sealing, compression, ferrous metal fabrication, and cold-drawn metal wire rope manufacturing. The technology’s compatibility with extant material and know-how means that it boasts a technological readiness level at stage 8 or even 9. Initially, it is expected that only minor logistical and erection challenges will be faced. Although a number of effective and reliable systems must be developed to make the self-erecting system (discussed at the bottom of the article) to reach a level of predictability and reliability needed for widespread commercial use.
In consequence of the vast power of hydrostatic force merged with structural engineering, a tower can be designed to reach heights of 1150 feet or 350 meters permitting wind developers to tap into inexhaustible amounts of high-velocity wind energy previously squandered out of a lack of suitable options. The use of the term “self-tensioning” highlights the structure’s ability to generate autogenous rigidity from the upward force of the desirous to expand hydrostatic media (liquid or gas), as well as to stabilize itself through the tensioning of guy cables. A third feature is the structure’s ability to elevate itself using a sequential tube-extension mechanism, what we have termed “autogenous erection”, which obviates the need for costly and bulky cranes for erection and their attendant transportation. This feature alone saves several tens of thousands of dollars on each turbine erection, further minimizing the LCOE.
The basic concept of using pressure to generate rigidity is itself not new, inflatable domes make use of it, but offer only rudimentary spherical structures with limited use. Despite no commercial application and the high degree of novelty surrounding this hydrostatic structural technology, it would be fair to say virtually every conceivable humanly possible idea has been patented in some variation or another, even if not exactly homologous, it’s hard to not to find a remote conceptual cousin in the patent literature, who for unknown reasons, floundered commercially. It would be hard to believe no one had imagined using the force of hydrostatic or pneumatic fluid to carry heavy loads in structural applications, low and behold a tiny number of people have, but the literature remains completely obscure nonetheless and this patent literature has not spilled over into textbook literature. The first person to seriously investigate and publish a technical article on the possibilities of pneumatically supported structures was Jens G Pohl at the California Polytechnic Institute in San Louis Obispo. It should be noted that the concept of a “pneumatic structure” is nothing new, but when the term is used, most people think of air domes, hardly a stiff and strong structure. Our inquiry into pneumatic or fluid-filled structures is strictly with the aim of achieving unparalleled stiffness, equal to or greater than conventional metallic structures which rely on the material’s elasticity modulus for stiffness. In 1967, Jens Pohl published a paper titled “A Preliminary Investigation into the Load-Bearing Capacity of Open-Ended Cylindrical Columns Subjected to Internal Pressure” at the Proceedings for the International Colloquium on Pneumatic Structures in Stuttgart, West Germany. Jens Pohl maintains an active website and authored a book on pneumatic structures, but makes little to no mention of the rigid pressurized column, but instead focuses on his concept for a pneumatic high-rise building using flexible membranes for pressure containment. Pohl constructed a small inflatable polyethylene bag using pressure to carry load, but due to the fact that the plastic piston readily transferred friction to the edges of the flexible plastic tube, it did not perform as a true pure tension tower. The “Pneumatic structures Colloquium” in Stuttgart is no longer held, pneumatic structures have found no widespread use due to their inability to be configured into a geometry that achieves high stiffness. Pohl’s 1967 paper on pressurized columns is not available to read, but judging from the title, it appears as if his intention was almost entirely homologous with ours, but it seems he has moved on to more flexible designs in recent times. Despite Pohl being the first, he is not the one that can be credited with the idea for designing a truly rigid and hydrostatic structure, that title belongs to Milton Meckler. Meckler is still active as a consultant, but has made little inroad in developing his ideas in hydrostatic building technology, not due to the merit of the technology, but entirely imputable to incorrigible industry dogmatism. In November 1970 Milton Meckler patented a design for using hydraulic fluid inside tubular members for mid-rise building construction, he went on to patent two other variations of the initial design, none have seen any commercial use. The concept was to use circumferential tension or “hoop stress” to absorb the otherwise compression and bending loads in ordinarily loaded structural members. Using compression to carry tensile loads is by no means a novel or unproven concept, worldwide, cable-stayed bridges experience superlative performance by transferring their loads to compression in concrete or steel columns. These bridges perform superbly in high winds, cable drag or vortex shedding surprisingly proves to be of little liability.
Meckler, as in our designs, does employ a free-floating piston at the ends of the hollow tubes, each of these pistons is then connected to an intermediate member which connects the tubular-truss configured members as highlighted in the image below. In 1981, Meckler published a book titled “Energy Conservation in Buildings and Industrial Plants” where his concept for fluid-filled tubular members was cited, but not discussed in detail, but the idea was never cited in successive literature.
Meckler’s hydraulic building system.
After Meckler, the closest anyone has come to developing a true hydrostatic structure is computer graphics developer Melvin Prueitt, who conceived of an inflatable flexible fiber composite multi-story structure over a decade ago. In 2009, Melvin L. Prueitt patented an inflatable structure drawing its rigidity from compressed air using low compressive strength fibers. Prueitt called his invention a “Compressed-Air Rigid Building Block”. Prueitt’s design employs pneumatics, and uses Vectran fiber “pockets” stacked to form a rigid tower. Prueitt, like Meckler, has found no takers, again evidence of a chronic poverty of imagination in the building and structure community.
Prueitt’s pneumatic tower using Vectran “blocks”.
Prueitt comes arrived at the concept of using lateral guys, using pressure as a source of rigidity, and loading is material in tension only, but unlike the following patent, failed to make the connection with free-floating reciprocation of a piston.
As can be seen from this quite diverse prior art, Christophe Pochari Energietechnik is not alone in our inquiry into a new class of structure, but we are alone in seeing their newfound potential, and we are responsible for the final design refinement which we will mention later. In 1984, Jack G Bitterly patented a hoop-stress-loaded hydraulic column to bear vertical loads. Bitterly’s design comes very close to ours, and is effectively our design except the only difference is that in ours the guy cables are oriented laterally. But even Bitterly’s design is not certain to be a full pure tension structure, since the piston ring sealing mechanism can still transfer compression to the walls.
Bitterly’s hydraulic “Euler buckling free” slender column patent drawings.
The following is from Bitterly’s patent description: “The pressure tube is mounted such that it can move axially with respect to the cable or the outer tube. When the tube is pressurized, some of the force is absorbed in hoop stress in the tube, and some of the force is directed to the ends of the pressure tube and to the cable or the outer member either through a piston arrangement or otherwise. When compressive loads are placed on the system, it can support force up to the preload without exhibiting Euler buckling. The system is useful for long, thin columns and for long beams where rigidity is important. The pressure tube is not subject to compressive loading because its ends are free to move axially without compressing the tube. The pressure tube may be wrapped in high tensile strength unidirectional fiber material to withstand higher hoop stress”.
By no chronological order, below is a list of homologous hydraulic or pneumatic structures that individuals have patented throughout the years. It is interesting to note that this is what we see in the patent archive, it is reasonable to expect there are private documents within corporations or government bodies that have not been published that allude to similar concepts.
In 1951, Archibald Milne Hamilton patented a design for a pneumatically supported tower structure, which according to the patent description, would use air at 80-100 PSI to generate rigidity, but he does not employ the use of a free-floating piston, so he cannot perform the feat of self-tensioning. Below is the patent drawing for Hamilton’s pneumatically rigidified structure.
In 2001, William E Drake patented a pneumatic column structure titled “Column structures and methods for supporting compressive loads”. In the patent, he describes the use of a hoop-stress-loaded composite fiber column filled with gaseous mediums to be used in supporting compressive loads. But unlike Bitterly, he does not use a free-floating piston.
In 2008, Michael Regan patented a pneumatic column entitled: “Fluid pressurized structural components”. The design is a constant volume containment unit.
In 1993, Raul A. I. Schoo patented a design for a hydraulic load-bearing column titled: “Tubular column of high resistance to buckling” with intended use with hydraulic or pneumatic media.
In 2010, Elberto Berdut Teruel patented another design for a hydrostatic column member titled: “Compressed fluid building structures”, the design seems to be very similar to Drake’s patent. Despite Teruel’s patent being accepted by the U.S patent office, Teruel promotes quacky free-energy gimmicks on his website, which is often the downside of creativity.
In 2010, Charles R. Welch et al patented a hydrostatic structure they named “Hydrostatically Enabled Structure Element (HESE)”, this design also appears virtually identical.
In 2004, Roland B. Heath patented yet another hydraulic column titled: “Load-bearing pressurized liquid column”. This patent again appears virtually indistinguishable from the above designs. Below are sundry images from the above patents. As can be evidently seen, they seem to follow a pattern: they are rudimentary cylinders that use hydraulic fluid to carry loading in a column-like regime, but none went to the next logical step which is to generate autogenous tension in the guy cables.
Below are sundry images of the above-mentioned patents in no particular order. The following patents can be studied in further detail in the source section at the bottom of this page.
Prueitt and sundry patents do not make full use of freely floating reciprocating pistons, nor do they make use of guy cables fastened in a lateral orientation, but what they do have in common, and hence their citation in this exposition, is that they all use the pressure of some form of hydrostatic media to generate stiffness. A pressurized fluid-filled system can either be in the form of fixed or variable volume containment structure to generate their rigidity and bypass Euler buckling via hoop-loading, of which they otherwise possess very little, if not none as in the case of Prueitt’s compressed air rigid building block which uses Velcran fibers. An important distinction to make and in fact the main distinguishing feature that allows us to separate and categorize these respective hydraulic and pneumatic structures is the difference between a fixed and variable volume system. The two main architectures of a hydrostatic structure regardless of its material composition, geometric orientation, or hydrostatic media. A fixed volume hydrostatic structure will of course pressurize its surrounding walls, and it will generate tension in its longitudinal direction, but because it is of a relatively fixed volume, it cannot perform the act of external self-tensioning. What all of these patents excluding Bitterly’s have in common is their use of a fixed volume column. A variable volume hydrostatic structure is where the free-floating piston is free to move longitudinally to the extent that the restraining guy cables permit it to. This affords the potential to generate longitudinal tension externally and subsequently permits the bearing of lateral loading such as wind shear loads, this is an exigency for wind turbine towers, whose static wind load can often exceed the weight of the actual turbine itself. It is only Bitterly’s design, which is most homologous to ours, that performs the stroke of genius to employ the free-floating piston which generates a variable volume chamber. Bitterly cleverly uses a high tensile cable fastened inside the tube submerged within the fluid to retain the pistons at both ends of the tube. Despite this extensive but overlooked patent literature, hydrostatic structures remain an anomaly and arouse strange looks among even educated structural engineers. The relatively extensive patent literature serves as corroboration to those who are skeptical of the technology’s feasibility, since after all, each patent is examined by a qualified examiner, so almost everything in the patent literature must be somewhat technically feasible to be approved as a useful invention. Interestingly enough though, according to U.S patent law, a technology does not necessarily have to be compatible with the present “laws of physics” to be approved, hence there can be found patents pertaining to electrogravitics or other yet-to-be-demonstrated phenomena. Of course, patents alone cannot be used to evaluate any technology, since there are invariably a significant number of patents that make it through despite having dubious technological feasibility. A technology can be only evaluated by a methodological and holistic analysis of its working principles and methods to attain such working principles. In light of this rich “prior art”, it is surprising there has been no effort to harness the immense force and rigidity generation of hydrostatics for structural applications. Despite the huge upside, there is not a single terrestrial structure that uses this brilliantly novel concept of bearing a load using the internal pressure of a cylindrical pressure vessel as opposed to transferring it into the wall of the structure via compression.
There’s an inherent paradox in the science of invention. This paradox arises because the inventor actually wants both novelty and a degree of familiarity to make said invention readily understood and compatible with known physical principles and science. Since constructing a prototype often requires considerable sums of capital to be raised from investors, ultimately, the inventor must be quite confident the invention is viable prior to its demonstration. This is why the argument “build a prototype” or else we cannot evaluate your idea is flawed, most inventions in history started off as drawings and went on to inspire so much excitement and confidence that businessmen poured money on them in the hope of a huge payoff. Because society and nations are always operating within a competitive dynamic, everyone is trying to out do each other, so no invention goes unnoticed for long because of the commercial upside potential. This competitive dynamic is especially pronounced in military affairs, since a smaller army or nation can win against a more powerful opponent by perusing a better technological accouterment. For example, the origin of canned food dates back to Napoleonic times when armies became so big as to outstrip the available local food supply they could gather from nearby farms. The food problem was so acute that Napoleon tasked a commission to study the possibility of preserving food. One of the first attempts was to place food in a glass bottle and heat it to sterilize it, glass was used by the French for lack of tin, while the British used tin thanks to their productive tin mines dating back centuries.
There is thus this antinomy that the inventor subconsciously desires both novelty, as to make his invention truly an invention, but also guaranteeing a minimum degree of certitude and familiarity. Yet another paradox is that the more “inventive” the innovation is, the more it befuddles the best minds, making it more difficult for a critical analysis to be performed. For example, Rudolf Diesel sent his manuscript “Theory and construction of a rational heat motor with the purpose of replacing the steam engine and the internal combustion engines known today” to Lord Kelvin who readily praised it because it made perfect sense to his thermodynamic mind. In contrast, many modern innovations are so difficult to comprehend, say in DNA sequencing or nanotechnology, as to make them extremely difficult for a moderately technically skilled person to evaluate. This may explain the prevalence of very dubious startups pitching gimmicks who are spun as “groundbreaking” as to even befuddle the experts. There is yet another pernicious myth and that is the notion that technologies have been suppressed throughout history and that inventors were persecuted. This argument has been used to justify scams including Theranos. Elizabeth Holmes repeatedly made this statement in her defense. Cases of ridiculed inventors include Richard Trevithick who was called a “madman” by James Watt, his steam train earned the title of “puffing devil” by local onlookers. Early airplanes were believed to be unable to carry guns onboard as the recoil energy would cause them to “capsize” in air. There was also a believe that early airplanes could never scale above a certain size as the wings would become heavier than the available lift. Yet another belief was that if two engines were installed on the airplane that it would become too unstable to pilot. In 1911, a prominent engineer wrote in an electrical journal that the gas turbine would be “impossible” and the British society of mechanical engineers discouraged people from pursuing the idea. It is perfectly fair to argue that most people failed to anticipate the groundbreaking innovations that occurred throughout history, but no one suppressed them. It is perfectly true that simple people scoffed at brilliant ideas, but there is simply no evidence that anyone had sufficient power to suppress them. It is likely that rather than suppression and or persecution of inventors, the general public and society in general are often simply too ignorant and shortsighted to appreciate them and henceforth we have this modern legend of the persecuted lone inventor. It is also the case that invention is rarely a spontaneous lone event without a considerable trail of prior art serving as inspiration. The inventors of the steam engine were not without intellectual precedent, Papin, Giovanni Branca, and John Wilkins, not to mention Hero of Alexandria’s Aeolipile a millennia before. The principle of using expanding gas to drive something was known to men of learning prior to Savery. It would be a mischaracterization of history to claim that most inventions were without precedent or hardly understood by learned men of the time. Take for example the principle of magnetism, it was understood centuries before any technologies made use of it. Lodestone was a curiosity across the ages and it was known to the Greeks that metal objects could be attracted to these strange rocks. One did not necessarily have to understand the geometric pattern or field intensity of the magnet to utilize it for a compass.
Those who are skeptical should look towards existing technologies that are at least remotely homologous to ours. One such example are cable-stayed bridges, while not employing pressure for load bearing capacity, they do nonetheless rely on cables for stiffness. Structurally, there is no difference between a guyed tower and a cable-stayed bridge, the only difference is that a guy tower is elastic, it is vertically compressible, and hence laterally flexible, while a cable-stayed bridge is much less elastic since the dead weight of the deck serves to constantly tension the cables. Unlike the classic guy tower’s flimsy hollow tubular lattice tower, the cable-stayed bridge employs heavy duty reinforced concrete columns that are extremely stiff vertically, although not necessarily laterally rigid. Despite the weight of the deck maintaining a relative degree of rigidity, the deck is still not entirely stiff, in fact, it is free to flap in the wind if the load is sufficiently high, although since the Tacoma bridge, most designers have maintained a minimum degree of deck deadweight to prevent aeroelastic flutter. A common perception is that Tacoma bridge collapsed due to a resonance effect where the wind oscillations matched the deck’s natural frequency, this is a major misconception, the wind load was constant and not cyclical and did not come even close to the natural frequencies of the bridge deck. The failure of the Tacoma bridge was simply caused by the low weight of the deck which was effectively turned into an airfoil by the wind, so called aeroelastic flutter. Early aircraft wings experienced this fluttering phenomenon when designers did understand that they needed to insure the wing had to be extremely stiff and not excessively supple.
The key to understand a stayed structure, regardless of whether it is a pressure derived or conventional one, is that tensioned cables that are prevented from elongated can only pivot around a fixed axis. This allows one to generate a very stiff structure if this pivoting action is canceled fully. Intuitively, it is obvious that the only way to perform this is by preventing vertical descent, since pivoting in the downward direction results in a reduction in height. A cable of fixed length cannot pivot laterally unless it follows its height-dependent angle. As a cable pivots, it follows a circular path that revolves around its fixed pivot point at the start of the cable, to move just a few degrees, it must move downward a significant distance, unless this can be facilitated by a height reduction in the column, a structure can be laterally as rigid as the force acting upward. This lack of any force pushing the tower up allows it to bend in the wind, whereas a pure tension structure is constantly being “pulled” or pushed up, whichever analogy one prefers, ultimately this is the same action. It is as if a gigantic crane were suspending and pulling the whole thing from the air, keeping the cables taught and preventing any sagging of the column. This is the key concept to understand and why one can never compare a pure tension tower with a classic guyed tower. A classic guy tower has nothing but the stiffness of its flimsy lattice structure to keep it aloft, a pure tension tower has hundreds of tons of force trying to snap its restraint cables, it is a completely different beast. Furthermore, the entire pressure column, the hollow tube which retains the fluid, does not bear its own weight, the column is actually always levitating, its deadweight carried by the force of the piston since the bottom of the tower is free to reciprocate as well on a separate foundation-mounted piston, which rather than pushing up, pushes down on the pad foundation and ultimately is born by the bedrock or soil. The only compression bearing component is of course the foundation, fundamental physics and mechanics forbid us from entirely eliminating compression, such a proposition would entail levitation.
This image readily illustrates this pushing force. Since the column is kept perfectly level by the four lateral restraint cables being the exact same length, the piston cannot swivel in its cylinder or bend the column. The piston remains vertically level and pushes tightly on the four vertical and lateral restrain cables. This means that even if the wind does want to bend the tube side to side, the tube is still being stiffened by the force of the vertical restrain cables pulling on the tube stabilization cables pictured at the midpoint of the tower. One analogy is a vertically upright cannon, firing a projectile into the air, imagine the projectile was somehow restrained and could produce thrust indefinitely, such a strange configuration would result in the same principle: permanent stiffness from tension and pressure.
The nature of structural loads
Structural loads can be broken down into two basic categories, uniform, that is isostatic loads, and directional, heterogeneous or “multiform” loads. The force acting on a slender (assumed to be solid) column is both compressive and torsional, that is deformative, in that it subjects a plastic material to deformation. The reason for this is very intuitive. Metals are comprised of a crystalline lattice structure of atoms, these atoms can slide with respect to each other. Imagine taking a long row of marbles, stacking them up perfectly, and applying a force between both ends, one of the marbles within this row will invariably be ejected from the row and pushed out orthogonally. The only difference between the marble analogy and the metallic crystalline lattice is that the atoms are “sticky”, they are prevented from sliding excessively which is what makes metals stiff, they cannot merely fly out like our marble, but they can deflect ever so slightly. This deflection is what gives every metal its elastic modulus. If we multiply each atom by the distance and number, we arrive at a huge potential deflection moment by applying even a small compressive load to a narrow member. For a slender column, this failure mode is the well-known “Euler buckling”. This buckling dynamic will occur above a certain slenderness ratio, usually around 30. Euler buckling occurs far before yield is reached, the buckling is entirely facilitated by the material’s modulus of elasticity, all plastic materials are somewhat elastic and can elastically deform somewhat before permanently yielding. In contrast, flexural buckling or crumpling, such as in the case of a soda can, occurs when the thin wall materials elastically deforms and then yields. The last form of of buckling is pure compression failure where the material reaches its maximum compressive strength. Most steel columns will fail via either Euler buckling if they are very thin, or flexural buckling if they are wide but possess thin easily crumpled walls. The Pure Tension Tower (PTT) is loaded exclusively in tension (for the main cables) and hoop stress for the pressure column. Hoop stress can be easily calculated with the formula below, which has been empirically derived and remains very accurate assuming the seam strength is close to the material strength. While it’s easy to calculate manually, we have corroborated our calculations with the calculator below. It should be noted that the stress produced by this equation is around 5% less than predicted by Altair Simsolid. The formula for hoop stress is: σh = p * d / (2 * t). Where p is pressure, d is diameter, and t is thickness, σh is stress in MPa. Our optimal media column is 750mm in diameter for minimum drag load, with a pressure of 3.4 MPa, generating 150 metric tons of force. The weight of the tube-section is 68 kg/m with a wall thickness of 12mm. The total hoop stress on the cylinder is only 127 MPa, with 63 MPa of longitudinal stress. The elastic expansion of the cylinder is 0.72mm in diameter and a 0.2% increase in volume.
There is no free lunch in structural engineering, you may escape classic Euler buckling by increasing the diameter of the column, but then you will simply move the failure mode to another kind, namely flexural buckling and crumpling. Slender or thin-walled columns have very limited compressive load capacities, and hence high altitude towers are effectively impossible without the use of inordinately heavy thick-walled steel towers.
But before elucidating the working principle, it would be useful to highlight the difference between a pressurized or “energetic substance” and a placid but highly firm material. Ultimately, the force from a compressed gas or liquid derives from intermolecular repulsion, which is electrostatic in nature. Gases possess very high average molecular velocity, this combined with their neutral charge prevents them from agglutinating into heavier compounds. The force that causes air molecules to repel each other is ultimately the same force that causes metal atoms to solidify tightly together, resisting intra-crystal sliding and generating a hard substance we can use for structural purposes. The difference is the energy levels of the metal is at equilibrium, there has been so external application of force, while for our liquid or gaseous medium, the energy levels are excited, in an unnatural state. In the case of a metal or solid, say stone, the atoms may solidify strongly, but they do not contain any releasable energy that desires to take the path of least resistance, they are stable systems in harmony with their surroundings. A gas in a compressed state is highly unnatural, just like a highly reduced metal, that wants to go back to its oxide state. Therefore, a dam carrying meters of water or a pressure vessel in a CNG car, are both systems that desire to release energy in a sudden burst, while metal experiences no such urge, yet both states have the potential to generate the same result: a rigid state. The reason a comparison is of value is that both aggregate states have the potential to generate rigidity or a firm surface, so we can now do something intuitively strange, compare an elastic, buoyant, compressible, and otherwise formless gas to a hard, solid material like metal. The difference is simply that to generate a firm condition with a compressed otherwise very elastic and buoyant substance we must put energy into them, but never allow the energy to be released, the energy is effectively levitating or hovering but never being allowed to flow to its natural diffused state. In this case, we are but a “receptacle’ for the energy of the contained pressure media, always exploiting its force, but never depleting it. It should be also noted that no structure, no matter how rigid the material may appear, be it steel or concrete, does not generate an equal opposite forcing countering the force acting upon it. A hydrostatic structured always produces a force greater than its rated load, meaning that deflection is actually impossible, just as it would be impossible for a man to pull a semi trucking driving down the road with a rope as it’s accelerating. Every load that does not exceed the hydrostatic force is countered by the structure’s momentum, a steel or concrete structure has no impulse or dynamic tendency, in fact a steel beam can be deflected ever so slightly even if the load is insignificant since the material by nature is elastic and there’s nothing acting to counter the force other than the material’s modulus of elasticity. While steel has an immense modulus of elasticity, around 200 gigapascal, 200,000 MPa, a force close to the yield strength for a relatively slender member can cause a substantial amount of pre-yield deformation. Since the pressure in the vessel is constant, it is not possible for the piston to be pushed down by the load and compress the gas inside, even micron-sized deflection is impossible. In other words, since the structure is always overloaded, that is the hydrostatic force is greater than the sum of all forces acting on it, it can never deflect downward, even minute quantities, unless there was a depressurization and subsequent structural failure. For deflection to occur a force greater than the hydrostatic force is necessary which would not occur during the structure’s lifetime. If this overloading were to occur, the pressure column would slightly expand laterally according to the newly increased pressure and accommodate the added pressure, but the piston would still not deflect downward any considerable degree since the added pressure would be merely absorbed by the tube, but it would not cancel the previous pressure or reduce it unless the tube reached its yield strength. Ultimately, this gambit of generating “free rigidity” from pressurized gas still of course requires a stiff material, otherwise it would merely act like a balloon when inflated, growing as its being inflated. A rigid material, be it metal or a fiber composite loaded in tension, there is no free lunch, we need material to bear the pressure, the crux of the matter is the nature of the loading regime. It just so happens that geometry makes an immense difference in how the same material reacts to a load, especially an isostatic load, and so one can interpret this technology as a geometric loophole that we are free to exploit: plastic materials perform much better in tension when they are free from non-uniform deformation, merely stretching in unison. Even if we still have to bear the force of the energized gas, hoop-loading is still far more structurally efficient, it is how we load the material that matters, not how much we load the material, since by definition there can no be no “free strength”, loading the column by pressurizing produces the same amount of stress as placing a vertical load on it in theory, but the behavior of the member under this equal loading regimes is hugely different. The same material, be it metal or fiber, may perform spectacularly when in a hoop-mode, but fail miserably when placed under a compressive load. The same aggregate amount of force is ultimately present in the system, in the same force density or stress, but the direction of this force is pushing out on the member (pressure column) which prevents it from elastically deforming, while in a vertical compressive regime (compressive loading of the tower), the force readily exploits the material’s elastic tendency. One can use a crude analogy of swimming up a river, the water bears our weight, but works against us, while if we swim downstream the water’s still bearing our weight as effectively, but stops pushing against us. It can thus be said, according to strict scientific exactness, that a pure tension tower is a structure where all load bearing components are loaded in tension! Since pressure vessels can be built of Kevlar which has no compressive strength to speak of (how many beams are made of kevlar?), we can conclude a pressure vessel is a tension only structure. Even in the axial stresses alongside the vessel’s longitudinal direction are tension forces.
A NASA aramid fiber pressure vessel. Aramid fiber pressure vessels have been studied by NASA since the 1970s and have been used on the Space Shuttle. Aramid fiber possesses very low compressive strength in a resin reinforced composite, around 117 MPa. Steel possesses 100% of its tensile strength in compression.
Returning to the working principle, it is necessary to highlight the nature of the load distribution and how this accounts for the structure’s core competitive advantage. This crucial point is the nature of the “loading regime” and its effect on a material’s behavior. Plastic materials are naturally just that: plastic, they are easily deformed and this is what gives them their tremendous ductility. But this deform-prone characteristic also generates a unique vulnerability: buckling. As mentioned before, buckling occurs when the material modulus of elasticity is reached and the material is then yielded as the thin wall member is stretched and then crumpled. A metal rope is readily flexed, folded, and bent without ever reaching its yield strength (the point where it permanently deforms). The rope’s ability to bend easily is due not to any mysterious properties possessed by the cable compared to a steel beam, but to its relative geometric configuration, which allows the loading regime to exploit its elasticity. The modulus of elasticity is a measure of the force over an area, defined as a multiple of a pascal (1 newton per square meter) required to non-permanently deform the material a given amount.
This provides a brief overview of the technology, applications include not only wind power, but pile drivers, novel high elevation structures for human habitation, communication towers, cell, radio etc, and potentially stationary gantry cranes.
Manufacturing of the pressure column. The ideal diameter of the column is approximately 1 meter, this allows a single column member to span 25 meters while experiencing only 5 mm of deflection during a severe storm, and during the routine wind loads, barely a fraction of a millimeter.
The tubes under ideal circumstances would forged into seamless pipes and then machined for smoothness and according to the tolerance required using a lathe. Christophe Pochari Energietechnik plans on manufacturing the tubes into 10-meter sections (necessary for them to fit in the self-erection solo) and connecting them using threaded fitting. The 750mm wide ingots would be vacuum melted from aluminum 7068 for maximum fatigue strength by minimizing non-metallic inclusions such as hydrogen, nitrogen, or oxygen. Vacuum induction melting is not an inherently more expensive process, the reason most metals are not cast using vacuum melting is that it is difficult to scale to huge volumes, but our production volumes would be relatively small, less than 100 turbines a year. A vacuum induction furnace simply consists of an ordinary induction coil that passes high-frequency AC to heat the metal to its melting point encapsulated within a vacuum chamber. To purge the gases released when melting the metal, high flow rate diffusion pumps are used. The cost of a 12000 liter/second diffusion pump is only €2,100. The vacuum of this pump is 0.00005 Pa and the power usage for vaporizing the fluid is only 8 kW.
At a drag coefficient of 0.35, each tube section experiences 14,400 N of drag, which is well within the member’s load capacity, generating stress of only 8 MPa and a deflection of below 2 mm, far below the stress amplitude needed to cause failure at 10^9 cycles. The drag can easily be calculated using the drag equation below. Note that for cylinders it is not the wetted area that serves as the reference point but rather the projected area, equal to 31.3% of the wetted area:
Fd = 1/2 * ρ * u² * A * Cd
- Fd is the drag force.
- ρ is the liquid’s density,
- u is the relative velocity,
- A is the reference area,
- Cd is the drag coefficient.
The tube experiences around 720 N of drag per meter of length at the maximum lifetime wind speed of 67 m/s. The total drag on each 20 meter section is thus 14,400 N. The stress generated is just under 9 MPa and the total deflection is only 1.5mm. The total drag load on the entire tower is thus since there are a total of 16.5 tube sections is 25,228 kg. But it should be remembered that this force may never actually occur during the structure’s lifetime, the odds of a 67 meter per second storm are mathematically predicted to be near infinity. The average load on the tower during operation is only 1115 kg-force.
The use of a ballistic liner, manufactured from thin high molecular weight polyethylene sheets is chosen for areas where security is poor and the risk of vandalism is high. The sites where the unit will be located would not be considered high-risk sites for vandalism, so this would only need to be considered in insecure areas. One of the only weaknesses of our ultra-high power density high altitude wind turbine is the ability for a committed saboteur to destroy the tower by firing high-powered rifle rounds into the pressure-bearing columns. But thankfully, a number of engineering options exist to counterpoise these concerns. At fifteen meters, only 18mm worth of UHMWPE can stop a 7.62×51 NATO. UHMWPE powder can be bought in bulk for €2.5-3.5/kg, but the cost does not include the extruding machine needed to turn the bulk powder into very fine yarn and then the weaving machine needed to turn that yarn into a textile-like layer. While a ballistic liner is technically feasible, it nearly doubles the cost of the tube section since UHMWPE is rather expensive. Even though UHMWPE is cheaper than steel on a mass basis, the additional mass of an 18-23mm liner is significant. Only in areas with extremely high vandalism risk is the cost justified. In areas that are low risk, such as in Europe, Argentina, North America, the risk of sabotage via firearm is extremely remote making the use of a ballistic liner redundant. Operators of a large wind farm using these towers would be wise to hire a security firm to patrol the peripheries of the property to ensure no saboteurs sneak onto the property. Drones and security cameras can be used to preemptively detect trespassers. It should be emphasized that our tower is not uniquely pregnable to sabotage, one should consider that existing wind turbines can be severely damaged by firing high-powered rifle rounds at the blades or nacelle possibly causing a fire in the generator, transformer, and electrical box on the ground, destroying the unit within minutes since firefighters would take at least half an hour or more to arrive. Thankfully, vandalism against wind turbines has been rare because most people have better things to do.
It should be remembered that the pressurized media tower differs greatly from conventional guy towers not merely in load capacity, but in critical structural dynamics. Because the upward force acting on the piston always exceeds the loads placed on it, the piston is unable to deflect down a few mm, rendering the structure completely rigid vertically. With the tension-loaded members then transfer vertical rigidity into lateral rigidity. This contrasts starkly with the classic guyed mast, which is a highly elastic and hence a uniquely resonance-prone structure. Because the wind loads can cause the mast to bend hence changing its height, the structure can sway back and forth until the elastic limit of the lattice is reached. An attractive option is to employ a small diameter but high-pressure high-altitude wind generator column and wrap this column with Dyneema fiber, and then place this narrow pressure inside a larger thin wall column for lateral stiffness. Such a design is illustrated above.
Resonance has caused a number of structural failures, but high speed dynamic structures are more easily affected than relatively stiff static structures. The Saturn V launch vehicle experienced catastrophic “pogo oscillation” when the fuel lines would delivery a pulsating pressure fuel supply to the engine matching the fuselages’ natural frequency. A number of high-rise buildings are fitted with dampers, either tuned mass dampers or hydraulic dampers to absorb any potential wind forces from becoming in phase with the structure. The classic guy structure is henceforth somewhat susceptible to resonance-induced structural failure caused by the runaway amplification of loads that occurs if the natural frequency of the structure is in phase with a dynamic inertial loading regime, such as cyclical wind loads or cable oscillation caused by vortex shedding. Additionally, were the vortex shedding frequency to match the rotor speed of the turbine, resonance could occur. Resonance could also occur if the wind loads were to agitate the cables at the same frequency as the lattice mast’s natural frequency, or any structures vibrating at the same frequency as a natural loading regime can lead to resonance. Resonance-induced structural failure occurs only when a cyclical load happens to correspond very close to or exactly with the structure’s natural frequency, for highly rigid or stiff structures, the natural frequency is very high, whereas the cables even highly tension have a natural frequency of far below 1 Hz, around 0.16 Hz for the main lateral guy cables. Cables on cable-stayed bridges experience what is called “vortex shedding” where vortices existing on the rear of a relatively blunt surface periodically alternate their direction of propagation, generating an isochronous force perpendicular to the wind direction. Vortex shedding can cause cables to vibrate at certain Reynolds numbers, usually when the wind speeds are relatively high. For rigid columns such as cable-stayed bridges, vortex shedding is of little concern, but for a guyed tower where the mast is elastic, if vortex shedding is severe enough collapse could occur, although no documented cases exist since dampers are almost always employed and rarely fail. Vortex shedding is mitigated on classic guyed towers using Stockbridge dampers. Since classical guy lattice towers have a limited compressive load capacity, the cables cannot be tensioned to a high degree, contributing to a vulnerability to aeroelastic flutter or “galloping”, where the cables flap up and down in the wind. In a high-altitude wind generator, the force on the piston is much greater than the load placed atop that a significant cable tension exists, preventing aeroelastic flutter of the cables.
As we’ve explained, resonance occurs if the forcing frequencies occurs very close to the natural frequency of the structure, in the case of a high altitude guyed structure, this is the vortex shedding frequency of the cables and main tube and the rotation of the main rotors. A dynamic amplification curve such as the ones below show how much load amplification there occurs a function of the frequency ratio, the ratio between the structure’s natural frequency and the forcing frequency. Severe resonance or that which can cause structural damage occur if the frequencies are nearly in phase. The charts below illustrate how close the two frequencies have to be, which is obvious since resonance merely refers to a process where two co-occurring load paths concentrate themselves to produce a force that exceeds the sum of their constituent forces, such as a rogue wave in the ocean, palm tree in the wind or a piano string.
The damping coefficient refers to the frequency offset needed to cancel out a given amount of resonance.
In the case of the turbine and structure’s frequency, there is little risk of resonance since the blade rotational speed is 30 r/min (0.5 Hertz) during steady-state operation, while the natural frequency of the 15mm 1.36 kg/m guy cables tensioned to 248,000 N each is 0.16 Hertz, dampeners can be easily installed if the turbine is to operate at a lower speed. The catenary sag is about 1 meter. All the other frequencies, be they vortex shedding or in the nacelle truss frame and turbine components, are much higher than these, all of them in the multi-hertz range, with the lowest frequency being the 1-meter wide main pressure column. Of all the different frequencies, the one that is closest is the cable’s natural frequency and the wind turbine’s rotational frequency, but this difference is still over 4.5 times the lowest frequency, which is the natural frequency of the tensioned cables, with no overlap possible unless the turbine is operated at very low speeds. Vortex shedding occurs at a frequency far higher than what is required to potentially produce frequencies in phase with the cable’s natural frequency. The Strouhal number for a 40-millimeter cable at a Reynolds number of 6000 (corresponding to the mean wind speed) is 0.199333, giving us a frequency of 59 hertz. The frequency of the nacelle is not remotely close, suggesting there is little opportunity for these three disparate frequencies to sync in phase-producing resonance. When the cable experiences wind speeds at its design maximum of 67 meters per second, its frequency increases to 335 hertz. For the main pressure column with a diameter of 1000mm, the Reynolds number at the average wind speed is 212155 (characteristic linear dimension of 0.25 meters), producing a vortex shedding frequency of 2.399772 hertz, when the speed increases to its rated maximum, the Reynolds number grows to 1184530 and the frequency goes up to 13.3998 Hertz at a Strouhal number of 0.199997. The force acting on the 1-meter column section during the average 12 m/s wind speed is only 82 kg force, barely enough to budge it 0.05mm and generate 0.20 MPa. The tube’s natural frequency at a significant mass participation factor is 0.001 Hz. If we plot the four disparate structural frequencies, we do find any significant overlap. The only potential for natural frequencies and the forces of outside forces to overlap is when the main rotor speed slows down. If the main rotor operated continuously at 10 r/min, it would match the natural frequency of the guy cables, but not the vortex shedding, which cancels the natural frequency of the cables, there is little reason to expect the rotor speed to sync with the cable’s fundamental frequency. As cable slack decreases as weight is placed on the tower, the natural frequency decreases as the tension drops. The actual tension on the cable is somewhat lower than the initial tension, allowing the turbine a safe margin to drop down to low speed without fear of being in phase with the cable.
In some structures, such as skyscrapers, the geometry produces a structure whose natural elastic frequency matches nearly perfectly with prevailing vortex shedding frequencies. Even if parts of our structure had a frequency that was close to vortex shedding frequency, active dampening is more than capable of counterpoising any resonance. For the 9mm cables, the vortex shedding frequency is 265 and 1498 hertz at 12 and 67 meters per second respectively, the Strouhal number for the lateral cables is 0.199556 for a Reynolds number of 9000 and 0.1975 for a Reynolds number of 1600, corresponding to 12 and 67 meters per second. The vortex shedding frequency is easily calculated by multiplying the free stream velocity by the Strouhal number and dividing by the cylinder’s diameter. The Strouhal can be roughly inferred by the Reynolds number. The calculation is often performed backward, where the Strouhal number is derived from the frequency and the freestream velocity.
Strouhal number vs Reynolds number.
In the video below, the relative laxity of the cables is readily illustrated. In a pressurized media tower, the cables are highly tensioned, since after all, they are continuously carrying the load of the piston minus the force acting on it. The more weight is placed on the tower, the less tension the cables experience. Even in a cable-stayed bridge, the bridge deck is still an elastic structure, whose rigidity is a direct function of its dead weight and lateral and torsional stiffness. Bridge decks are designed to move slightly, hence a cable-stayed bridge, like a guyed mast, is a somewhat elastic structure. A hydrostatic column is not an elastic structure, since the upward force produced by the pressure acting on the piston serves to apply a constant tension, absorbing all forces applied to the structure. Applying tension dramatically reduces galloping, since a tensioned cable requires considerable force to stretch, wind loads lack this force hence the cables find a natural spot where they remain undisturbed. Classic guy towers use Stockbridge dampers to control low amplitude high-frequency vibrations, for high amplitude low-frequency vibration, hydraulic cylinders are used on cable-stayed bridges that connect orthogonally to the cable, but conventional guy towers make no use of high amplitude dampening technology since they do not find any issue with excitation and resonance. Of all the documented cases of catastrophic guy tower failure, most are attributable to bolt failures, anchor failures, or metal fatigue, but no cases of resonance-induced failure have been documented. Virtually all failures that are not caused by anchoring failure are caused by excessive static wind loads exceeding the bending strength of the tubular lattice inducing a progressive torsional collapse of the lattice.
Since cables are elastic members (they are only rigid in longitudinal tension), they have unlimited degrees of freedom perpendicular to their span. For a 120,000 kg ultimate breaking strength cable, the sag will be about 2.43 meters for a flat span, since the cable is at a 59-degree angle, the vertical sag is only 1.52 meters tangent to the cable The prevailing wind loads are far too small to move the cable back from its natural sag state, only when the wind loads approach the rated limit does the cable have the ability to flutter significantly. To cancel the transmission of cable flutter and vibration, lateral dampers can be fitted on the tower apex structure, allowing the cable to move perpendicular to its longitudinal orientation, while retaining its lengthwise tension. At the cable base mooring point where the winches are placed, each winch can be attached to a hydraulic damper which provides widthwise degrees of freedom, absorbing any cable fluttering energy, canceling any potential vibrational transfer to the rotating turbine. The level of tension on the cables, unlike a guyed tower where the tension is relatively minor, prevents excessive cable movement, tension does naturally increase the fundamental frequency of vibration since the degrees of freedom are restricted, hence reducing its amplitude and reducing the time to needed to complete a full movement from its maximum and minimum degrees of freedom.
In summary, even if the blade speed drop down to the fundamental frequency of the cable, vortex shedding is likely to cancel the cable’s fundamental frequency and serve as the determining vibrational amplitude, making it difficult to impossible for the turbine’s rotational frequency to fall in phase with the cable vibration. The rest of the vibration ranges are far outside the range of the 30 r/min turbine, so there is little cause for concern. If a different size turbine is desired, such as a very large low-speed system, the cable mass would increase proportionally serving to maintain the same difference in frequency as a smaller turbine. If we find that Vortex shedding is not congruent with the theoretical calculations (highly unlikely) and main tube vortex shedding or cable vortex shedding does indeed fall in phase with the turbine’s spinning frequency, actively tuned electro-dampers can be fitted to mitigate any chance of resonance.
The principle rationale of the invention is premised on the idea of structural efficiency, a measure of the ratio between the weight of a structure and its load capacity holding material density constant.
Structural efficiency is paramount in mass-sensitive engineering disciplines, such as heavier than air aircraft. Modern wide-body aircraft have superlative structural efficiency, but most aircraft structural components are not slender enough to experience pre-mature plastic deformation such as Euler buckling. For example, the mass of the main-wing module of a Boeing 747 is 45,000 kg, while its takeoff weight can approach 400,000 kg, which yields a weight-load ratio of 10:1. This is with aluminum 7075 or 2024, which has a yield strength of around 400 to 500 MPa.
In the case of the pressurized media tower, the structural efficiency is lower since the tower safety is far higher than the 1.5 commonly used in aviation. The 350-meter tall main pressure tube weighs 66,500 kg but produces a load-bearing capacity at its piston of 338 tons, yielding a structural efficiency of 5:1, which is very impressive considering the main pressure vessel possesses a safety factor to yield of over 4.7 times, a highly conservative design which is frankly unnecessary except for reasons engineering jingoism. In contrast to this superlative structural efficiency afforded by the technology’s optimization of loading regimes, a conventional tower will usually feature a negative structural efficiency, meaning it will be heavier than its supported load. This is a sign of a highly inefficient structure, suggesting the nature of its loading regime is not optimized for the structure’s geometry, forcing the designer to heavily overbuild the structure for reasons of stiffness, not stress. In other words, conventional cantilevered wind towers are inherently prone to bending under severe wind gusts placing immense stresses at the root of the tower. Moreover, the foundation pad must be extremely wide to distribute these bending forces and prevent it from being “uprooted” and falling over. In contrast, the main foundation on a pure tension tower experiences only compressive load, pressing the concrete into the soil or rock. The lateral stabilizing cables are restrained by the weight of cast-iron-filled weights that suspend inside an excavated rectangular space. The gravitational force acting on the suspending mass pull on the cable which wraps around a coil free to rotate, placing no torsional stress on the foundation.
While hydrostatic force is not harnessed for structural engineering, many disciplines have made full use of it. The power of hydrostatic force is exploited in virtually all thermal engines, with the first British condensing steam engines using the hydrostatic force of the atmosphere to push the piston into a partial vacuum. A modern diesel engine uses immense hydrostatic force, often 200 bar at peaking firing pressure, to generate its power. A hydraulic ram on a stamping press can generate thousands of tons of force, not to mention the power generated from large streams of water in dams. The power of hydrostatic force is often overlooked and has rarely been applied to structural engineering. In some instances, structural engineering has been able to make use of pressurized mediums, such as inflatable domes, automobile tires, and basketballs, all of these structures make use of hydrostatic force to function and attain stiffness, but are very rudimentary and cannot be used to generate complex structures.
There are four main components that make up the self-erecting pressurized media tower
#1 Load-bearing piston and torsion cables: This module comprises the free-floating hermetic piston with closed-cycle constant flow hydraulic seals connected to the end of the pressure column. The load-bearing piston employs a novel hydraulic seal to prevent friction from transferring the piston’s force to the sidewall. The sealing mechanism is discussed in greater detail further along in the text.
#2 Pressure column: Hydrostatic containment structure, 750mm diameter diameter monolith-bored aluminum cylinders, 15mm diameter. The tubing sections span 25 meters from each guy cable fastening point. The tube is levitated by suspending from the apex piston and does not carry its dead weight as compression as it is prevented from bearing on the bottom foundation pad.
#3 Cables: Guy cables or stay assembly with winches, 2000-3500 MPa carbon steel with plastic sheathing and Spelter socket end termination. Cables feed into automatic electric winches with self-locking function and built-in hydraulic dampers.
#4 Ground anchors: Underground rectangular silos fitted with silica-filled steel weights suspending from a pulley maintaining a force greater than the maximum wind load carried by the lateral guy cables. Cables are initially tensioned to a load equal to 75% of the gravimetric force of the suspending mass.
#5 Foundation pad with underground erection silo. The silo accommodates the unique “constant diameter telescoping mast” which is lifted into place by inserting 10-meter tube sections and threading them together. The underground tube extension silo features a nitrogen compressor, and PSA unit, with a multi-function tube insertion, sealing, and partition mechanism that facilitates the continuous telescoping process. The ground pad features mounts that connect the vertical piston restraint and tube stabilizing cable connection points. There is no net upward force emanating from the cables since the force acting down on the foundation pad is equal to the force acting.
Further description of the working principle
During erection, as the open-ended cylinder is filled, the piston is pushed to the end of the cylinder until it exits the end. Guy cables are fastened to a bracket that rests above the piston, preventing the piston from exiting, thereby generating tension on the cables. The tube is placed vertically in the air, with the piston all the way at the top of the tube just near the end, the bottom of the tube is attached to a foundation pad, bearing the weight of the hydrostatic force as well as the weight of the tube. As said previously, The pressure-bearing cylinder is subject only to hoop stress, the cylinder bears none of the weight that can be placed atop the piston. This allows the tube to be designed as an ultra-slender member thanks to the fact we eliminated lateral and compressive loads. At the base of the column, a concrete pad bears the weight of the bottom section of the cylinder, since the apex piston is paralleled by a base piston, with the same frictionless sealing mechanism. The column is a slender cylinder, designed to withstand the internal pressure of the hydrostatic media only, the column derives its lateral stability from a series of guys, much like a classic guyed communication tower. At the end of the cylinder, the piston is able to reciprocate up and down freely, transferring one of its linear forces to the walls of the tube. As the column is filled with a pressurized medium, the piston is subject to a force equal to the pressure times the area. This force would result in the piston being lifted with great speed until it exits the end of the cylinder, the guy cables carry all of this force and transfer it to the foundation pads on the ground. One of the most elegant aspects of this structural technology is its exploitation of the inherent desire for materials, be they metals or composite fibers, to be loaded in a tensile regime. All plastic materials perform better in tension than compression since they are elastic.
Cabling material selection
The choice of cabling material is narrowed down to high-strength steel wire for reasons of low-creep, low elongation during initial loading, elasticity, abrasion resistance, manufacturability, low cost, and high specific strength. Synthetic fiber cables can of course be used, but a number of limitations exist that render them far less attractive and competitive than high-strength steel cables. Ultra-high molecular weight polyethylene could be used for example as it possesses extraordinary tensile strength, but excessive creep, as high as 5% per anum, limits its long-term use without frequent cable swapping. Aramid or Kevlar is another option, but its very poor abrasion resistance means it must be lined with a suitable housing or it will rapidly fray and degrade if winched back and forth frequently, this would serve to reduce the specific strength advantage of aramid fiber over steel. Kevlar does possess higher specific strength than steel, but unfortunately, the higher specific strength does not compensate for its higher cost, which is ordinarily around €25/kg on Chinese marketplaces such Baidu or Alibaba. For example, a 1960 MPa steel cable 35 mm in diameter has a breaking strength of 71,000 kg with a weight per meter of 4.28 kg, while the same breaking strength Aramid rope has a mass of 1.28 kg/m, a difference of only 3.34 times, while the cost is 25 times higher, or after specific strength, 7.5 times higher.
Considering its poor abrasion resistance, Aramid is not an attractive option. Since polyester, nylon, and polypropylene are either too weak or too creep prone, and Vectran, Twaron, Technora, or Zylon are too niche for widespread commercial use, the choice is narrowed down to ferrous metal, which enjoys widespread and extremely reliable use in cable-stayed bridge. The ultimate tensile strength of SWRH 82B carbon steel cable alloy ranges as high as 2100 MPa and SWRH 82A can reach 2200 MPa. SWRH 82B high-carbon hard wire rod is alloyed with 0.79-0.84% carbon, 0.15-0.35% silicon, 0.70-0.90% manganese, over 0.1% but usually less than 1.0% chromium and vanadium, 0.008% of aluminum, and 0.030% of phosphorous. The breaking strength of 82B wire 21mm in diameter is 57,000 kg. The weight per meter is approximately 2.4 kg, and a total of 3,000 kg of cabling is used for restraining the piston. The cost of carbon steel wire, which has extensive use in prestressed concrete, is typically below €1000/ton, while some extremely high-performance cables can exceed €1000/ton, even using the highest strength and price steel, the total cabling cost is negligible.
The superior strength of steel cabling over solid rods is attributable to the work hardening from the cold drawing of the wire. The plastic deformation that occurs creates a more robust and uniform grain structure at the parameter of the wire, which is why as the wire shrinks in diameter, its tensile strength increases. Constructing a steel cable out of multiple small diameter wires serves to produce a far stronger product than would otherwise be achieved by the carbon steel alloy in a beam or rod configuration. Additionally, since each wire is allowed to move relative to another adjacent wire, the loaded component is made more dynamic as loads can be distributed onto surrounding wires. Yet another reason steel wire rope is stronger is due to the elimination of a single failure point. A grain structure weak spot or “flaw” does not compromise the entire structure, since the load is distributed among dozens of small wires. During wire drawing, a defective wire typically fails to properly extrude and hence will be discarded, resulting in a virtually flawless grain structure of superlative strength. Steel wire is produced using a novel production technique called “patenting” where the wire pre-wire rod is heated to the austenite phase at 970 °C and then quenched in a bath of molten salt or lead at a temperature in the bainite phase region of around 550 C. The wire is squeezed through a conical nozzle and has its diameter reduced many fold ultimately producing a more “compressed” grain structure. The wire is then kept at this range for a period of time and then ultimately allowed to cool to ambient temperature. The final product is a sorbite crystal structure material, made up of thin layers of cementite and ferrite. The higher the carbon content, the higher the tensile strength, the maximum carbon content is limited by the minimum degree of ductility required. Individual wire strength can be as high as 4000 N per square millimeter of the cross-sectional area for wires below 0.8 mm in diameter, the strength drops to 2000 N/mm2 for thicker wires. “Patenting” is an informal name for “Iso-Thermal Phase Transitioning”. The elasticity module of carbon steel wire is usually between 150,000 and 200,000 N/mm2.
1960 MPa is by no means the limit for small diameter cold drawn eutectoid wire. The tire industry is constantly searching for mass-efficient reinforcing, rubber itself cannot withstand the tire pressures, rubber tires have made use of brass-coated steel reinforcing wires, usually less than 0.5mm in diameter and woven into a net-like pattern. The brass is present to maximize the adhesion of the rubber to the metal wire, brass strongly bonds with rubber whereas steel does not. The key metallurgical technique is to prevent the high carbon content from generating a brittle cementite grain structure, various elemental solutes serve to suppress this effect. It is not only the tire industry that generates demand for ultra-high strength wires, rubber hydraulic hoses are the second largest user of small-diameter steel cords.
Tire reinforcing chord had already reached a tensile strength of over 3000 MPa in the 1980s with recent developments approaching 4000 or more MPa. Tire cord, as well as piano wire to a lesser extent, are classified into four categories depending on their tensile strength.
- “High Tensile Strength Steel (HT): carbon steel with a tensile strength of at least 3400 MPa @ 0.20 mm filament diameter;
- “Super Tensile Strength Steel” (ST): carbon steel with a tensile strength of at least 3650 MPa @ 0.20 mm filament diameter;
- “Ultra Tensile Strength Steel” (UT): carbon steel with a tensile strength of at least 4000 MPa @0.20 mm filament diameter
- “Mega Tensile Strength Steel” (MT): carbon steel with a tensile strength of at least 4500 MPa @ 0.20 mm filament diameter.
As early as 1970 tire chord metallurgy reached the 3 gigapascal mark, by 1980, it increased to 3300 MPa, by 1990, 3600 MPa, and by the year 2000, the 4000 MPa threshold was crossed. 5000 MPa is possible with a wire size of 60 microns. Note that it is possible to simply braid the ultra-fine wires into any size wire rope needed, and unlike composites, they do not suffer from abrasive weakening. Hyperecutectoid steels are those with high carbon contents and an almost purely pearlite grain structure, composed of layers or “lamalars” of martensite and ferrite. If the carbon content is increased to 1.8%, the tensle strength could approach 5500 MPa. Presently, 4000 MPa tire wires are commercially available and manufactured by Kobelco, Nippon steel, Kawasaki Steel, Kobe Steel, Goodyear, Bekaert, Pohang Iron and Steel Company, among others. These respective companies have been commercially manufacturing and selling wires with tensile strengths over 3500 MPa for decades, the processes are rudimentary and merely involve plastic deformation and thermal modulation to attain optimal grain structures. Unlike exotic fiber manufacturing where highly complicated chemistry is involved, metallurgy is quite a bit simpler since the process of weaving is not nearly as delicate since the wires themselves are much thicker than synthetic fibers. Amit Prakash, who once worked for Goodyear, started a company called WireTough Cylinders aimed at commercializing the first wire-wrapped steel pressure vessel for hydrogen storage. The vessel has enjoyed success for stationary hydrogen storage. Exploiting the much higher tensile strength of wire and their low cost compared to carbon or kevlar, they can construct pressure vessels with equivalent pressure ratings of carbon fiber at a tiny fraction of the cost.
Goodyear filed a patent in 2002 for a 4500 MPa wire with a drawing diameter of 0.2 mm, the elemental composition of their alloy is as follows: 0.95% to 1.3% carbon, 0. 2% to 1.8% chromium, 0.2% to 0.8% manganese, 0.2% to 1.2% silicon, less than 2.2% cobalt, less than 0.1 niobium, and boron at between 0.006 and 0.0025 parts per million.
The strongest steals, such as bearing steels and ultra-high strength steels used in landing gear and bunker penetrating bombs, namely Maraging steel, Eglin steel, 300M, Aermet 100/310/340, USAF-96, M50, and Ferrium S53, among others, are high nickel and cobalt steels with tensile strengths of over 2000 MPa but high ductility and toughness, but are economically handicapped by the high cost of nickel and cobalt. Another reason these extremely strong alloys are not more widely used is their proneness to stress corrosion cracking.
All steels increase in brittleness as the tensile strength increases, placing a cap on the allowable tensile strength without compromising ductility which is required for any dynamic structure. When it comes to materials even stronger than metals, we are left principally with synthetic fibers, made by spinning liquid crystal polymers, aromatic polyamide, polyethylene in a high molecular weight form, or silica, alumina, carbon, or liquid-crystalline polyoxazole. These high-end fibers, despite possessing immense tensile strength, with the exception of carbon, have a very low modulus of elasticity, and hence find applications only in purely tension-loaded applications. But even in tension-loaded applications, namely cable and rope, these fibers still trail far behind steel. A further issue with using these fibers in even tensile applications such as rope and cabling is their loss of strength when the fibers are woven due to abrasion and friction. Carbon and glass fibers cannot be used in woven rope since they are so brittle, and even Aramid, Vectran, Technoran, Zylon, and Polyethylene, all lose at least 50% of their strength when woven due to intra-fiber abrasion, compression, binding, and shearing. The strength of fibers is tested on the basis of a single undisturbed fiber, not when woven in a cable configuration. For example, ultra-high molecular weight polyethylene has a tenacity of 40 grams per denier (1 gram fiber 9000 meters long), which translates to a breaking strength to weight ratio per 100 meters of 3600 times, but the actual ropes tested in the real world only achieve a breaking strength to weight ratio of 1475 times over a 100 meters. In the case of Aramid, the loss is less severe. Aramid fibers have a tenacity of about 25 grams per denier, or about 2270 times their mass over 100 meters, but Kevlar ropes tested only achieve 550 times their mass. In the case of Vectran, whose fibers possess a tenacity of 27 grams per denier, or 2450 times mass, the ropes achieve 1142 times strength, or a loss of about 50%. This loss may not be all that severe when one considers these fibers already possess specific strengths seven-fold higher than steel, but this five-fold advantage over steel wire drops to only 3.5 when the net strength of the actual cable is factored. One cannot use the theoretical tensile strength or tenacity since it does not take into account losses of strength due to abrasion. From a purely economic perspective, unless the application is simply extremely mass sensitive, all these fibers mentioned cost over €25/kg and that is from Chinese retailers, they are at least €50 per in the West. Since carbon steel wire can achieve 3500 MPa at a density of 8 grams a cubic meter, the difference in specific strength is now only 3.5 times, but the cost difference is 25 times, carbon steel produced using cold drawing is costs below €1000 per ton, so the net cost advantage of the steel is 7 times, even after adjusting for specific strength.
For example, the main load restraining cables on the 750 kW high-altitude wind generator using 3500 MPa tire chord steel are 24mm in diameter and weigh only 3.573 kg per meter yet can carry a load of 65,000 kg while possessing a 2.5 factor of safety based on breaking strength. The cables experience a maximum drag of 7000 kg max drag and weigh only 5002 kg in total.
The lateral tube stabilizing cables made from the same 3500 MPa Goodyear steel number 14 in total and are 5.9mm in diameter excluding the plastic corrosion prevention sheathing. Each tube stabilizing cable withstands a maximum wind load of 3900 kg load capacity at a conservative 2.5 safety factor, meaning a wind load of 2.5 times more than the 67 m/s speed is required for the cable to failure. The breaking load is 9670 kg breaking load. The drag on the cable is 1608 kg and the weight is 0.214 kg/m. A total length of 16750 meters is used for four sets of 14. The total weight comes in at a low 3585 kg.
The lateral restrain cables are 15mm in diameter and weigh 1.366 kg/m with a 4900 kg drag load and have a rated load capacity of 25,000 kg at 2.5 factor of safety. Their total weight is only 1600 kg:
Total cabling mass comes in at only 10,187 kg excluding end connectors, meaning that a material cost of only €10,000 is needed for the entire structure’s cabling system.
Returning to the issue of synthetic fibers, another factor that renders synthetic fibers less attractive than steel is their proneness to being cut, it is extremely difficult to cut a 30millimeter steel cable by hand, but a fiber cable can be snipped with ease with the exception of high-density polyethylene. But in the case of high molecular weight polyethylene, despite its low bulk cost of €2.5/kg, it has a tendency to infinitely creep, that is elongate until it reaches such a reduced diameter that it snaps after many years in service. As a consequence, high-density polyethylene cannot be used for constant load applications, despite its toughness.
While UHMWPE is subject to excessive creep to be suitable for constant load applications such as our pressurized media tower, Kevlar, Technora, or Vectran could all be used successfully were it not for their inordinate cost and it would possess a certain “cool” factor to use Aramid cabling, but coolness does not dictate material choice, economics and performance do.
A 2 kg/meter cable built up from 8000 0.2mm 3500 MPa tire chords can safely handle a load of 37,000 kg with a factor of safety of 2.4 times.
End termination is a challenge for all types of cables, regardless of material type, but fiber cables are more difficult to strongly splice or terminate without a strength loss. In steel cables, Spelter end termination achieves 100% termination efficiency by pouring molten zinc into the individual frayed unwound cables. The issue with this method is that with the higher strength wire, the joint will naturally be less efficient, since the wire’s increased strength does not automatically translate into more adhesion between the zinc and the wire’s surface. For the ultra-high strength wires proposed, it is foreseen that the best option is to construct the main cable out of multiple individual cables encased within a master sheathing and configure it so that it wraps around a relatively soft coil at the torsion platform. On the ground, the cable is ultimately bearing on the winches’ surface, since each woven cable section is sheathed with its own polyethylene to protect it against abrasion. The more gradual the bend around the circle, the less stress is placed in compression.
The aforementioned metallurgical characteristics of steel wire, namely its significant strength boosting afforded by downsizing the wire diameter through cold drawing are a further endorsement of the merit of tensile-loaded structures as it helps facilitate an ever superior specific structural efficiency.
The wire-rope carbon-steel cables experience some degree of stretching when loaded, at a load factor of 30% of breaking strength, they will stretch below 1%. It should be noted that the commonly stated load ratings in cable catalogs are usually 5-15% greater than the advertised number. This increased length is then retracted using a winch mounted on the guy mooring sites. Note that this elongation experienced is not plastic elongation, since by definition the loading regime is always safely below yield. Elongation in steel wire cable loaded below its yield threshold experiences two types of elongation, elastic and “constructional elongation”. In the case of “constructional elongation”, as the cable is loaded, the diameter of the individual wire strands shrinks as they also become more tightly packed, causing a constriction in its diameter and hence an increase in its length. Elastic elongation is exactly what the name implies, every metal has a fixed modulus of elasticity, and steel will experience a slight stretching even if loading is kept far below yield. Another cause of elongation is thermal expansion, for every one-degree °C increase in temperature, the cable will elongate 3.3 mm at its full distance of 346 meters. A winch carries any of this slack by unwinding the cable’s slack as pressure from the piston is allowed to tension the cable enough to minimize the slack while maintaining enough of a torque margin to allow the tower to climb during installation. The self-erection function is further explored later.
Ambient temperature and its effect on the column’s pressurized gas media
When the temperature is high during the day, the density of the liquid decreases slightly, and the volume it occupies increases, resulting in greater pressure. The converse happens when the temperature falls.
The main application of this tower, and its invention origin, is wind energy, while there are nonetheless other niche applications, terrestrial energy harvesting is its prime target and hence we are forced to undertake a brief inquisition into the nature of wind energy and its dynamics. It goes without saying that there is an ever-growing need for inexhaustible and clean energy, one such source is terrestrial wind power. In order to make existing wind turbine technology more competitive, reduce cost, and generate more energy, the ability to practically exploit higher velocity wind is desired. Since the energy from wind is the cube of the velocity, increasing the velocity only slightly has very significant effects on the annual power output of the turbine. Unfortunately, only a select few sites on land feature wind speeds over 9 meters per second. On the other hand, at a height of 300 or even 350 meters, many onshore sites around the world have wind speeds of up to or greater than 11.5-12 km/s where power densities of over 0.5 kW/m2 of swept area are realizable, allowing a 57-meter diameter turbine to produce 1.4 megawatts of power. For example, using a hypothetical site in the Nebraska sandhills, the average wind speed at 100 meters is 8.65 m/s, yet it increases to 10.66 at 200 meters. At 300 meters, the speed increases to around 11.65, or a factor of 1.10, the exact number was around 1.094. This is slightly more than the standard power-law prediction using surface roughness, this estimate was sourced from the USDE’s “Project Independence” from the 1970s which studied building wind turbines as high as 304 meters. They estimated the mean wind speed at 1000 feet in Caspar Wyoming to be approximately 1.092x times the speed at 182 meters. Using the Enercon E-44 turbine, the power output at 8.7 meters per second is around 340 kW, and the power output at 12 meters per second is close to a thousand kW. This difference in speed from 300 meters to 100 meters would yield an additional 5300-megawatt hours for this 40-meter diameter turbine. That is with an increase of only 3.3 meters per second, the power output nearly triples. This triples the potential revenue of the turbine and the concomitant return on investment. Beyond merely the velocity of the wind, another major benefit of increasing altitude is the reduction in variability encountered. The hourly variability of the wind speed at 200 meters estimated from the global wind atlas at the Nebraska location is only plus or minus 10% of the mean, allowing our turbine to produce grid-suitable power.
It’s worth spending a brief time understanding the somewhat nebulous concept of capacity factors when dealing with the power output of wind turbines. Because our technology increases the mean wind speed significantly, we are making the concept of a capacity factor less useful. The so-called “capacity factor” is an arbitrary concept and makes the turbine look less efficient than it really is, it’s an abstract concept that needs disbanding. The silly idea of a “capacity factor” probably originates from a clever but deceptive marketing gimmick contrived by the wind industry to sell models that appeared more powerful than they really are. A capacity factor would be like advertising a car engine of five liters of displacement being able to produce a thousand horsepower running on nitrous on a racetrack. If we had enough cylinder pressure, coolant flow, and oxidizer intake, we could easily produce a thousand horsepower with a tiny little car engine, but in the real world running on gasoline, it will never produce this much power, even though the piston and crankshaft have the theoretical strength and size to produce the claimed amount of power. A tiny wind turbine could produce megawatts if the average wind speed were 30 meters per second, but it would be completely useless to even measure it at such speeds, since a normally distributed wind gaussian curve will only produce such fast winds a tiny fraction of the time.
The capacity factor is a way for manufacturers to simply test the turbine in unrealistically fast winds and claim it produces “500 kW” while it would only produce 150 kW in the normal wind regime it would encounter on a day-to-day basis. Worst yet, the concept of capacity factor confuses people since it looks like the machine is producing less power than the average wind speed would predict when in reality this is only because the turbine’s generator is significantly or greatly oversized. Most wind turbines are “rated” at a certain wind speed, meaning they feature a generator whose size corresponds to an arbitrary power setting. This rated wind speed is usually an arbitrarily chosen velocity that is far higher than the mean wind speed of the site and even higher than the occasional peak winds of a typical site. For example, the Enercon E-44, one of the highest power density wind turbines on the market, is rated at an absurdly high mean wind speed of 16.5 meters per second, which is almost impossible to find even at 300 meters of altitude. So anytime this turbine installed at a typical site of say 7 or 8 meters per second which is typical for 50 meters of height, its “capacity factor” will be minuscule, say 20 or 30%, making it look as if it miserable. This is where the discrepancy between the turbine’s theoretical power and its annual yield emerges, which is often as high as a factor of 3, meaning the turbine produces only a third of its theoretical higher speed power potential. It’s not just the Enercon E-44 that’s rated at an unrealistic speed, the rated wind speed is often as high as 13-15 meters per second for many commercial turbines, which is obviously considerably higher than what can be found at a typical hub height of 50-100 meters. Of course, upon closer examination, this concept is flawed, since unlike a solar panel, which is rated for the most intense period of insolation possible, which always occurs by definition at a certain time of day, namely when the sun shines at peak hours, a wind turbine does not need to be measured at a higher than mean wind velocity, it can be sized very close to the mean speed and simply feathered when velocities exceed the generation capacity of the alternator. The sun always produces a peak irradiance a certain percent of the time, while in many geographies, the wind will nearly always blow at a mean speed of say 9 meters per second, but no one can say the sun shines at a “mean” irradiance of 1 kW, since by definition this only occurs a few hours of the day, but our panel requires this maximum capacity as to not squander this concentrated but small window of solar energy that occurs during peak day of which is used to size the panel and from which the 18% efficiency estimate or the kWh/kWp estimates derive from.
Of course, the designer would be still encouraged to somewhat oversize the generator, this is understandable since wind regimes can momentarily exceed the mean by a significant margin above-average temporality in rare instances, and since most power is captured at the higher end of the spectrum, it can be understood why most turbines are oversized as to not squander this higher than mean wind speed. But this is precisely where our design begins to modify the standard dogma, because low-altitude turbines are subject to more wind variability, there is a greater need to oversize the generator. The lower the wind speed, the greater the temporal variation, for example, in a 4.8 m/s wind regime at 50 meters, the variation daily ranges from 0.76 at 18 hours and 1.29 at 0 hours. In a higher altitude regime, where the hydrostatic turbine is installed, for example at 300 meters in Nebraska, the mean wind speed will be about 11.5-12 meters per second, with an hourly temporal variance of only +- 10%, which is far less than at 4 meters per second. This means our turbine will produce an annual power output nearly equal to the mean wind speed, since we can expect only a ten percent velocity drop off at any given hour, and this is compensated by a ten percent uptick at another time increment. The square-cube laws mean the bulk of the power is produced in the upper half of the median wind distribution, wind speed follows a normal distribution, but its usually measured as a “Weibull” distribution, where each speed incremented is measured as a percentage. A cubed relationship means the increase grows exponentially, so a drop in wind speeds produces a smaller corresponding drop in power than an equal uptick in wind speed. Either way, the capacity factor concept is misleading and should be abandoned. If our mean wind speed, especially at higher altitudes, shows little to no sharp variability, with only a 1.2 meter per second drop or uptick, the turbine will produce close to this number over the course of a year, it will produce no more or less than this.
A departure from fiber-glass blading
Abrasion and pitting of the blade surface is a notorious problem on fiberglass blades for obvious reasons, fiberglass is porous and has a heterogeneous surface, it is prone to flaking and pitting. Anyone who owns a fiberglass ladder will notice the rough flake-like surface morphology, which is far from aerodynamic. The biggest limitation with fiberglass is the weakness of the resin, epoxy resins are incredibly prone to UV-induced degradation, oxidation, mold, and chemical decomposition, since the fibers on their own possess no intrinsic rigidity, fiberglass is only as strong as its weakest link: resin. On the other hand, using steel blades where the maximum bending load is kept well below the fatigue limit, blades can remain highly smooth over time.
A 21.5 meter solid-monolith spar blade for a 44-meter 750 kW turbine. The final weight of the blade is 1460 kg, the maximum steady state stress generated during rotation at 32 r/min is under 40 MPa. Note that the picture above shows a single continuous member, the intended final design is a single pivoted bolted connection point in the center of the blade allowing the blade to absorb energy as well as making machining and transportation easier.
Metal blades also possess far superior dimensional uniformity and tolerances than fiberglass, which is very difficult to make uniform since cloth has to be manually cut and spliced. Fiberglass blades also require a massive mold the size of the single blade section which adds floor-space and contributes to an overall higher cost compared to metallic blades. Moreover, there is considerably more industrial experience borrowed from the aerospace industry with machined aluminum structural parts.
One has to depart from using density as a metric of evaluation and rather use specific strength. 7068 aluminum-zinc has a tensile strengths in excess of 650 MPa, while its density is below 3 grams/cm3. Fiberglass sheeting tends to possess lower tensile strength, as low as 160 MPa. In fact, Autodesk maintains a material property library in its CAD software, the GFRP is assigned a standard tensile strength of only 110 MPa in the software.
But material science is more complicated than mere tensile strength, there is a misconception that strength is the only thing that matters, if this were the case spider silk or bamboo could be used to make skyscrapers. While it would seem as if our glass fiber blade with its nearly 600 MPa tensile strength with a meager 1.8 gram/cm3 density would far outclass the metal blade on a specific strength basis, once we enter another variable in: the elasticity modulus (a measure of a material’s resistance to plastic deformation), fiberglass cannot hold a candle to metal. High strength zinc-aluminum has a modulus of elasticity of 73+ gigapascals, while GFRP is only 39. Since a blade is highly slender and must be extremely resistant to bending otherwise it will not generate any power since it will simply absorb the wind’s power through its own bending! One has to seriously wonder why an entire generation of designers have chosen a material with such poor stiffness for a component that must be as slender as possible to achieve a high lift coefficient! If we compare the Young’s modulus (a measure of deformation under a stretching regime lengthwise), fiberglass reinforced polymer is 14 GPa, while 7068 aluminum is 73 GPa. Tensile strength is a meaningless metric unless we compare the metrics that pertain to the rigidity and resistance to deformation, if these metrics are taken into account, there is no weight advantage at all to fiberglass, in fact, fiberglass would be heavier if the deformation rate is held constant. Christophe Pochari Energietechnik has designed the turbine to be entirely free from short-lived brittle glass fiber composites and constructs its blades from solid monoliths of aluminum. Fiberglass is a mediocre, short-lived, and labor-intensive material that should be dispensed with. From an environmental perspective, fiberglass is appalling, since there is no way to salvage the fibers from the adhesive binder, fiber-glass blades are landfilled when their short useful life is reached. Steel can be indefinitely recycled allowing the turbine owner to recuperate most of the steel’s value, since the cost of alloy steel is principally the high value of the molybdenum and chromium, not the iron itself, which is effectively free. Fiberglass, which derives its rigidity entirely from the epoxy resin, degrades due to moisture, abrasion, and UV which limits the useful life of the blades to at best 20 years. Using steel, the useful life of the blades can be extended to at least 30 years, lowering the LCOE even further. Fatigue stresses are often cited as a reason to choose fiber-glass, but upon further examination, this is not a valid rationalization. The maximum stress that will occur on the blade is not from the force of the lift causing it to rotate, this force is marginal, only around 4-5000 N would be experienced by a single 750 kW turbine spinning at 30 r/min with a blade diameter of 44 meters. This force is insufficient to cause but a tiny bending moment in the spinning blade. Centrifugal forces do not operate in the reference frame, so the only major loads on the blades are from major gusts which can suddenly hit the unfurled blade at a high angle of attack from the from. For a maximum wind rating of 67 m/s, a maximum force of 125,000 N is placed on the unfurled blade for our design criteria, this causes a stress of 450-500 MPa and a midpoint displacement of 250 mm for our guyed design. The blade’s surface area is around 6 square meters producing a life force of around 7500-8000 N. This level of stress is still half the yield strength meaning that the blade will not come close to failing even during a severe storm, while fiberglass blades will be torn off within seconds at such forces. In contrast, without or blade restraint cable, the total displacement of the blade is five meters! and the yield stress 2000 MPa, more than twice the tensile strength of the material, since a steel blade cannot handle such a loading regime, no fiberglass blade in existence could withstand a full wind load on its surface unless it were as thick as concrete bridge beam. With the braced design, the stress amplitude is still below the 180-200 MPa fatigue amplitude for failure to occur at 10^9 (1 billion) cycles for vacuum melted aluminum 7068 (AlZn7.5Mg2.5Cu2), and therefore the blade could theoretically be operated for 58 years before failing.
An S/N curve for 7075 aluminum showing a fatigue strength of 200 MPa over 1 billion cycles. From: Gigacycle Fatigue Behavior of High Strength Aluminum Alloys, QY Wang.
Of course, the actual fatigue strength will always be somewhat larger, since the specimen size is larger and the bolted connections created stress concentrations. Since the turbine blade spins at 30-32 r/min at full speed, it will incur 430 million fatigue cycles over a 25-year lifespan, wind loads are relatively constant and add little to the fatigue load, the bulk of the load is from the constant bending of the blade as they spin around the hub creating root stress. Of course, since fatigue failure is primarily caused by inclusions, a larger member will by definition have a larger volume of inclusions, while vacuum melting can reduce this dramatically, about 150 MPa greater stress amplitudes required to cause failure than air-melted steel, it is unlikely the components at a global level can parallel the fatigue strength of small test specimens, although it can be close. The effect of size on fatigue strength is called the “size effect” and seems to show a diminishing effect as size increases above 250mm indicating some form of “saturation effect”. Shigley and Mitchell proposed a reduction factor for size using an empirically derived constant of 1.189 times diameter to the negative 0.097 power. For a 250mm member, the fatigue reduction is 0.6959 compared to 1.017 for a 5-millimeter diameter member, or a 30% loss of strength from the type specimens to a full-scale member. For a 500mm member, the reduction grows to only 35% or 0.65. The relationship between fatigue strength and specimen size is logarithmic, so a large increase in the size of the member brings a much smaller reduction in fatigue strength.
Fatigue stress has been cited as a reason to choose fibrous polymer composites over classic metallic materials, but upon closer examination, there seems to be little data to substantiate this assertion. Throughout virtually any industry, schools of thought or “dogmas” evolve through a combination of experience and spontaneous circumstances, but often, flawed assumptions take hold and perniciously cement themselves and create entire generations of designers that religiously adhere to the dogma. This serves to dissuade any deviation from the canonical approach since other designers dare not deviate from the “tried and true” method. If we examine the “fatigue argument” against metal blades, we can obviously scoff at this claim by simply citing the fact that aircraft wings, which are subject to constant flapping, bending, and twisting, last over 160,000 hours before retirement is needed, and aircraft travel at hundreds of kilometers per hour and have wing loadings of up to 50x higher than wind turbine blades, hence will generate immensely more stress in their wings than a wind turbine blade experiences. An aircraft wing, while not rotating, is subject to a very similar loading regime. One has to remember that while a wind turbine blade does experience inertial stress from the rotating mass, this stress amplitude is very minute. The bulk of the stress is from the stat is lift pressure bending the blade since there is torque on the shaft, that is the resistance on the shaft prevents the blade from spinning freely and hence generates a vending moment at the root, there is very little stress at the midpoint or the tip of the blade. But this is obviously not a cyclical load, since the lift force is constant as long as the wind is blowing at 12 m/s. If the stress amplitude of the lift force is around 45 MPa as mentioned previously, if the wind speed drops every to 6 meters per second every second, then that would produce a force difference of around 5000 N, since lift is a square of the velocity, the net stress difference would only be a <25 MPa. Of course, in reality, the wind speed does not change every second, but even if it did, it would still only produce a stress amplitude of around 33 MPa, still far below the amplitude needed for failure to occur at 10^9 cycles. If the wind produces a cyclical load of 1 Hz, then over the 30-year lifespan, it will have incurred 8760 x 3600 = 9.5 × 10^8, or just under 10^9 cycles. But this is a highly conservative estimate because wind loads do not halve every second, which would mean the power produced would be only half the actual power that is produced in the field, which is obviously not the case. Thus, while wind loads are nonetheless a variable load, on a per-second basis they cannot generate anywhere close to a stress amplitude of 18-200 MPa required to reach the alloy’s fatigue life.
It should be mentioned that carbon fiber aerostructures are ultimately fatigue “bottlenecked” by the resin, and the shear strength of the resin is no greater than the shear strength of a sheet-metal lap joint. The carbon fibers themselves possess no stiffness, they are only rigid because they cannot longitudinally slide with respect to each other because of the adhesion to the epoxy resin. To estimate the fatigue life of the adhesively bonded metal blade, we must look at the experience the aerospace industry has had with composite structures. Recall that conventional aluminum aero-structures can endure up to 165,000 hours before fatigue sets in, and the limit is not the wing, but rather the fuselage from depressurization and pressurization occurring during each flight. Little data exists for wings, but observation suggests the wings outlast the fuselage. Evidence from aircraft operators suggest that microcracks develop around rivets and window openings in the stressed-skin fuselage.
Why is aircraft data more useful than the existing wind turbine operating experience? One of the reasons is that aircraft experience much higher loadings than wind turbine blades for obvious reasons, their static pressure and hence bending moment are a tiny fraction of commercial aircraft, therefore, aircraft data may prove to be a very conservative benchmark. Secondly, it may not always be useful to use data from fiberglass blades and extrapolate it onto our metallic design, since most large aircraft built before the 2000s use aluminum, there is immense fatigue data that can be used and extrapolated to estimate the fatigue life of a steel bonded structures by simply adjusting for the fatigue life difference of aluminum. Thus, if we can safely assume that it is not the fiberglass yarn itself that fails, but rather the bonding resin, then existing non-metallic wind turbine blades can be assumed to be subject to the exact same adhesive stressing regimes as our adhesively bonded metal blade. The adhesive strength is not the limiting factor, but rather the shearing of the adhesive itself across the center, since the surface energy of steel is very high. Conventional fiberglass blades are constructed in two separate pieces constructed in their respective molds and then sandwiched together forming the blade unit, of which an adhesive joint ultimately keeps the blades fastened together, much like our metallic blade relies on the adhesive to keep the spar fastened to the skin and to bond the spar to the ribs and the ribs to the skin, etc. It can thus be assumed that a metallically bonded blade will experience nearly identical fatigue regimes in its adhesively bonded parts to a fiber-glass blade.
Returning to comparing the loading regimes of aircraft wings and wind turbine wings. It’s worth mentioning that a wind turbine “blade” is not really a blade at all but rather a rotating wing, a blade is more redolent of something that generates thrust by moving air, a wind turbine blade much like a helicopter generates a tiny pressure difference producing lift, it generates a rather minimal thrust, only about 21,000 N at the midpoint of 44-meter 750 kW turbine blade. An Airbus A380 has a wing loading of 680 kg/m2, while a wind turbine blade with a free stream velocity of 12 m/s at a 1.6 lift coefficient generates a lift pressure of only 14.7 kg/m2, or just 2% of the aircraft. Aircraft wings must also be designed to endure the occasional freak horizontal or vertical gusts that can generate loads that greatly exceed the normative loads it experiences during flight. In fact, the 1.5 factor of safety has established itself as the universal number in aerospace engineering but is likely unable to possess nearly enough reserve load for freak winds. Thankfully, they rarely occur and have proven a minimal risk to aircraft, likely because they almost always blow either towards or behind the aircraft, which is a highly streamlined body, if winds were suddenly to flow up beneath the aircraft, in-flight disintegration would be inevitable. The same can be said about our stayed blade design, if the direction of the wind suddenly changed and a 67 m/s gust below from behind, the blades would snap instantly, so it is critical for the turbine to quickly yaw into the wind since it can safely endure a full frontal load. If the yaw motor fails and the turbine cannot rotate into the wind, the blades must be immediately furled into a 90-degree position as to make their bodies streamlined, reducing their drag coefficient from 1 ( flat plate where the entirety of the static pressure of the wing bears) to an aerodynamic body that has a drag coefficient of at best 0.05. Catastrophic blade failure can thus only occur if a double failure occurs, namely that of the yaw motor and the blade pitching motor, which are both low torque high-speed electric motors (<1 kW) that feed into a reduction gearbox to increase their torque. The motors since they are inexpensive, only a few hundred dollars each, can be doubled up for redundancy.
Considering that aircraft wings are also designed with a factor of safety of only 1.5, which is the most aviation can tolerate due to the mass penalty that any higher safety factor would entail, the performance and reliability of aluminum aero-structures is simply breathtaking and should serve as an inspiration for structural designers in disparate industries.
Aside from the clear superiority held by ferrous alloys, we can turn to another conspicuous advantage that metallic construction boasts: built-up modular construction. Fiberglass is after all a fibrous material, long sheets of woven cloth are laid down on a mold the size of the entire blade since fiberglass is too brittle to perform intermediate fastening of the blade. The sheets are then cut to fit and overlapped and resin is plastered on by hand and then vacuum bagged for curing.
Mechanical fasteners are useless in fiberglass construction since concentrate loads in the direction in which the material is weakest: perpendicular to the fiber’s longitudinal orientation. It should be remembered that fiber-glass or any fiber-reinforced polymer is anisotropic, that is its strength, but especially stiffness, depends to a large extent on the orientation of the fibers, which is why classic finite element method programs cannot simulate these types of materials. This makes it especially tricky to design and results in overbuilt structures, since high fidelity stimulation cannot be relied upon. In the case of metals, their strength is uniform in compression, traction, and torsion, but their fatigue strength in torsion is usually only 0.8 that in traction or compression. Metals are very easily simulated in ubiquitous finite element programs allowing virtually anyone to design a metallic structure to the desired factor of safety.
In light of these handicapping properties possessed by fibers, the blade must be constructed in unison as a singular member, requiring massive molds which are costly to construct. Since segmenting the fiberglass blade greatly weakens them, they cannot be transported in a standard U.S 53-foot trailer or shipping container, massively raising transportation costs. Christophe Pochari Energietechnik has designed its 44-meter blades to be dissembled into easily handled 10 meter sections to fit on a standard flatbed or equipment trailer. From a fabrication and manufacturability standpoint, which ultimately determines the price of the technology, aluminum machined metal blading is inordinately simpler to fabricate and assemble. The solid machined spar is then fitted with the skin material, stamped aluminum panels that up make up the shape of the airfoil. Since the skin thickness of the blade skin is so small (<3-8 mm), the individual sheets can be easily formed using standard automotive panel stamping technology. The size of an individual skin panel is little more than 1.2 meters squared, and can be easily manipulated using standard metal fabrication equipment. Since the skin only contributes to the lateral stiffness, not the bending stiffness, only the spar needs to span the entire section for optimal stiffness. When it comes to fabricating the spars and ribs and cutting the skin to size, low-cost laser cutting equipment can be used. Another crucial advantage offered by metal is the ability to perform local repairs. For example, imagine a drone strikes a fiber-glass blade, since fiber-glass cannot simply be cut and fastened back in place since the overall structure would be gravely weakened, the entire blade has to be scrapped, wasting resources and manpower to construct an entirely new blade. Since we have not mentioned fracture resistance, fiber-glass is far poorer than steel which means that our metallic blade will be much less prone to bird strikes, pitting, and the infinitesimally small chance of a drone strike. A sheet metal blade will crumple, much like the images of bird-struck aircraft where the nose is severely dented, but it would not fracture.
Returning to the core technology in question, the basic rationalization or “raison d’etre” of the invention, is that since wind speed decays rapidly towards the ground due to surface roughness, there is a strong incentive to design a new generation of high-altitude wind turbines. The impetus of the invention is the inability of classic tower technology to facilitate such heights feasibly and cost-effectively. Conventional steel wind turbine towers rarely exceed 100 meters onshore, squandering the vast potential of higher speed above. There exists an almost unlimited potential to tap into this vast reservoir of relatively dense and free energy, but man presently lacks the capacity to due do, as always because of a lack of technology. The principal limitation preventing designers from reaching these higher speed winds at 300 meters or more is the weight and concomitant cost of the conventional steel tower begins to escalate dramatically since the diameter has to be held constant for transportation reasons. This means the thickness of the tube increases exponentially with its height to maintain the same degree of rigidity as could be achieved if the thickness remained constant and the width merely increased. But if the thickness is held constant but the diameter is allowed to increased, the failure mode is now turned to flexural buckling, so there is no other option but to throw more material and cost at the problem. Conventional wind turbine towers would be as if a Neanderthal was tasked with its design, he just piles on more and more material until it is strong enough, never considering a more complicated and ingenious method to obviate the classic failure modes. Conventional wind turbine towers are constructed from colled-rolled steel drums, and as the thickness of the plates grows, the cost of the slip roller escalates dramatically. This cylindrical column is subject to both compressive loads from the weight of the nacelle as well as tensile and compressive loads from the mast bending moment due to static wind loads. In order to achieve a minimum degree of rigidity, for a 750 kW wind turbine, a 350-meter conventional steel tower would weigh over 1000 tons. The cost of fabricating and erecting such a heavy tower is prohibitive, hence the current practice of remaining at around 100 meters or less of hub height for onshore turbines. In light of these limitations, a better solution is called for, the aim of this invention is to facilitate the design of high-altitude wind turbines using a lightweight low-cost structure employing above mentioned principle of hydrostatic force. Assuredly, by using this elegant structure, the material reduction and subsequent power density of wind energy are improved dramatically. The benchmark for energy density and EROI (which are closely related) has always been nuclear fission, with deuterium-tritium fusion the only conceivable energy technology that surpasses it. But in practice, a fission reactor in a pressurized water configuration actually has a lower power density than diesel or gas turbine powerplants. This is evidenced by the fact that the average pressurized light water reactor constructed in the U.S during the 1970s used approximately 45 tons of steel and 120 tons of concrete per megawatt of electrical capacity.
The average coal Rankine powerplant uses 98 tons of steel and 160 tons of concrete per megawatt. The “Dongturbo model N1.5-2.35” 1.5 MW condensing impulse steam turbine weighs 18 tons, such a turbine uses 10 tons of steam per hour, a typical 10 ton grate boiler weighs 58 tons, such as the DZL10-1.6 by Henan Taiguo Boiler Products Co., Ltd. But the boiler below is likely an underestimate because the temperatures and pressures do not corrospond to the steam turbine’s specifications. But for the sake of simplicity, we will take this as the achievable power density of a corresponding size Rankine therma, powerplant, to see whether it is true that wind has low power density. The total mass excluding the generator is thus 76 tons per/1.5 MW, or 50 kg/kW. The alloy composition in the steam turbine and boiler are very similar to the wind turbine, since they must widnstand high temperature and be creep resistanct, a high use of nickel and chromium is common.
A typical impulse condensing turbine in the 1 MW class
While the power density of a steam turbine higher than a high-altitude wind generator, a steam turbine is not a standalone unit, it must be paired up with a boiler. Boilers are very heavy since heat transfer kinetics are sluggish and coal burns poorly. The turbine uses 6.5 kg of steam per kW, and the specific enthalpy is 3131.19 kJ/kg (0.869 kWh) at 1.27 MPa and 340°C, the gross heat input is 8700 kWh and the net electrical power is 1500 MW, yielding a brake thermal efficiency of only 17.2%. Since coal costs €150/ton and contains about 7000 kWh/ton, we generate only 1191 kWh from a ton of coal, resulting in an LCOE of 12.59¢/kWh, or 151.7 times more expensive than a high-altitude wind generator. This makes perfect sense, since the manufacturing cost of the steam turbine and wind turbine are very close, but the steam turbine consumes 10,075 tons of coal per year worth $718,000 million, in a single month we have practically paid for the cost of the high-altitude wind generator, and over a period of a single year, we have paid for 7x 750 kW high altitude generators.
In our analysis, we conclude that a 1 MW+ steam turbine plus boiler setup weighs about 80 tons, while a high-altitude wind generator weighs a total of around 35 tons and generates 750 kW. While a typical conventional wind turbines use far more than this, it cannot be compared to the high-altitude wind generator since a large preponderance of this weight is concentrated in the tower structure and since the rated output is limited to the slower winds found at lower altitudes, when the load-bearing tower structure is eliminated and the higher wind speeds are factored in, the material required is reduced markedly since the power density rises sharply. Since the total weight of a 750 kW high-altitude wind generator is 35000-40,000 kg, translating to a power density of 52.85 kg/kW, or barely above that of a nuclear reactor. This means high altitude horizontal axis wind power has a superior power density than solid hydrocarbon (coal) combustion in a steam Rankine cycle! That is an impressive and unparalleled feat of engineering. The ability of a wind energy system, harvesting free terrestrial energy, to achieve a gravimetric power density almost as high or equal to state-of-the-art nuclear and coal power plants is nothing short of astonishing and achievable only with Christophe Pochari Energietechnik‘s high pressurized tower technology. It should be stressed that we are only referring to a strictly gravimetric or material power density, expressed in terms of kilos per kilowatt, not an area power density, expressed as kilowatts per hectare of square meter. Wind energy trades area power density for low cost, one cannot have it all.
The notion that nuclear energy has superlative power density is only correct insofar as the heat release per gram of uranium is immense, but the requirement for containment structures to fulfill conservative regulations translates into a need for a high factor of safety, which leads to substantial material requirements. If one examines a picture of a nuclear reactor cutaway diagram, one will notice the actual reactor core is a tiny little thing in comparison to the total ancillary and containment systems. Notice that many of the “new generation” reactors use just as much steel per megawatt as the old boiling and pressurized water architectures. The Russian “Gas Turbine Modular Helium Reactor” requires just as much steel as a 1970s PWR. If such a complicated and advanced technology, advanced to the point of being undeniably impressive and elegant, far more so than a coal-burning machine let alone a windmill, ends up using just as much material as a lowly windmill to generate a kilowatt of power, one has to ask whether it is worth the price of assuming the complexity factor that comes with the more advanced technology. But one also has to remember that nuclear reactors do not only use steel, they require beryllium for neutron reflection to protect workers, hafnium for neutron absorption, niobium for alloying the reactor core components to prevent neutron embrittlement, and zirconium for cladding. Neutron embrittlement is the Achilles heel of fission power, the current Électricité de France S.A. (EDF) Framatome PWR fleet, viewed as the poster-child of successful PWR technology deployement, is currently experiencing corrosion in its piping systems which has resulted in a total of 12 of the 56 in the fleet being forced offline. Although the official report states “stress-corrosion” detected with ultrasonic analysis, which is not inherently caused by neutron embrittlement, it’s likely the etiology can be traced to some form of grain structure weakening from neutron bombardment, since distilled water alone is not very corrosive to the high nickel alloys used in the reactor. Neutron bombardment of metal does not only cause embrittlement, it also induces elemental movement and segregation and migration within the alloy as well as negative evolution of the grain structure towards a more brittle and crack-prone state. Breeder reactors, due to their much higher neutron flux, would experience even more rapid metal degeneration from embrittlement since embrittlement is a direct function of the total neutron flux. In terms of scalability, arguably the most salient criteria for choosing an energy technology, is far from rosy. The global reserves of these respective elements, unlike neodymium, places a clear cap on fission scalability, and even if the unlikely event of commercialization of confined fusion happens, there will not be the capacity to produce the lithium-6 needed, so it evidently looks as if lowly windmills will play a pivotal role in hydrocarbon-free energy for the foreseeable future assuming no groundbreaking inventions occur this century, which judging from the past 50 years, seems highly unlikely. Inventions, of which most occurred in Europe and later America from 1700 to 1950, were clustered in a rather narrow period, and most of the most important technological discoveries occurred during the 19th century, the most consequential century in all of human history by far.
In addition to the promising application for wind technology, the communication tower market is a prime first application for pressurized media technology. Present guyed mast systems have abysmal payload capacities, are prone to wind-induced swaying and fatigue failure, and are cumbersome to erect. Most guyed masts in the 100-meet range are able to bear only 45 kg of antenna weight excluding the weight of a maintenance worker. With Christophe Pochari Energietechnik‘s self-tensioning tower technology, the same diameter and weight tower can carry tens of tons, many orders of magnitude more than a steel lattice structure. This has the potential to utterly transform the communication tower industry, allowing designers to place much heavier higher capacity antennas or place heavy long-term batteries to eliminate the need for backup generators or any power supply for that matter. The technology also eliminates the need for costly and dangerous rotorcraft erection.
A stress-optimization-centric design
The weight of the system is a function of the loading regime, the intensity of the loading, and the tensile strength and density of the alloy used. The mass of material can carry more or less force depending on the optimal distribution of stress, which is a function of the part’s geometry and shape. The structure, like most structures, is not designed for the average ordinary load, but freak loads that will occur perhaps once or twice across the lifespan of the structure. The aircraft aero-structure is designed for a so-called “factor of safety” of only 1.5, because gravity forbids any greater structural reserve. The reason aircraft can get away with such skimpy structural reserves is due to the predictable nature of their encountered loads. The forces of drag, landing, takeoff, and the occasional gust are relatively consistent across the aircraft’s operating window. But on the other hand, terrestrial structures face a challenge that is in a way far worse than for the airplane. An airplane is cruising parallel to the wind’s gusts, the winds pass over the aircraft generating minimal force. Gusts do not blow below the aircraft from atop. In comparison, a skyscraper, wind turbine tower, or offshore oil rig is placed directly orthogonal to the wind’s maximum velocity, a large flat surface area absorbs the entirety of the static pressure of the wind, placing immense bending and shear loads on the structure. In spite of this, there is actually no documented case of a high-rise building failing due to freak winds, simply because of the fact that the mass of steel is so great as to require a bending moment for the metal to yield that would be so immense as to dwarf any wind gust. There is a 300-meter guyed tower in Scotland called the “Black Hill transmitting station” that has stood firm since 1961. The site is located at 55.861944°N 3.8725°W, the mean wind speed at the site is 11.5 meters per second and the 99.7th percentile gusts would be 35 meters per second. It is interesting to note that the tower survived the extratropical cyclone of 1987 which produced peak gusts of 61 m/s.
While wind would seem like something that can easily be estimated, in reality, is quite difficult to calculate the exact probability of a freak storm. Even nuclear power plants have to be designed with freak hurricane wind gusts, in this case, the powerplant designer is concerned with what’s called “tornado-generated missiles” which consist of very high-velocity projectiles carried by the winds which can smash into the reactor and potentially cause a meltdown if it destroyed the cooling system.
In a paper titled “Application of spatial visualization for probabilistic hurricanes risk assessment to build environment”, the authors assign the 150 MPH hurricane winds as a once-in-a-thousand-year event and 130 MPH as a once-in-a-100-year event. for South Florida. Of course, where the turbine is installed is not in the tropical climate where cyclones occur, since the regions in which turbines are installed are usually cold and low pressure. Anti-cyclones are much rarer. In Iceland where the E-44 data was collected, the standard deviation was found to be 62.8% of the median and 59% of the mean. If we calculate Q (probability) from Z we find that the probability of a 67 m/s second gust is infinity, a 50-meter gust is also as infinity, and a 30 m/s gust is one in 3486914. Of course, reality has a way of being very different than what mathematics and theory suggest, but while the real world odds may be somewhat higher, they are still very low, and hence our design for a maximum wind load of nearly 70 meters per second is extremely conservative.
Most fixed terrestrial structures, that is buildings, are massively overbuilt because the quality of the steel they use is quite poor. Moreover, the fatigue life of welds is a small fraction of that of base material, so the structure’s factor of safety is not merely based on yield, but also based on assumed fatigue cycles over its lifetime, which for a high-rise may be significant in a windy area since vortex shedding causing an oscillatory loading regime. For our structure, the factor of safety chosen depends on the nature of the component. For example, in the case of the heart of the system: the main pressure bearing tube, designed with a steady-state hoop stress of only 130 MPa, the factor of safety is 5.23x. The burst pressure will will never be reached since a relief valve can be installed. In other words, because we know the maximum force that the structure will encounter, we can safely assign a relatively moderate FOS. On the other hand, for structures whose loads are unknown and cannot be confidently predicted, assigning an FOS is a much more tricky matter. For example, if we are designing a ship, we could be very aggressive and merely design it to withstand the 98% percentile wave size, which for a normal distribution where the mean significant wave height is say 5 meters and the SD is 0.6 meters, a wave height of 8 meters is in the 99.9999 percentile. A wave size of 20-meter wave which could exceed ree hull’s breaking strength, will occur at a frequency of basically zero, or a Z score of 36 which is so many zeroes after 99.99 that it can’t even be calculated on a pocket calculator! A Z score is merely the raw number minus the mean divided by the standard deviation. A Z score of 5 is 99.9999, so 36 would be simply statistically impossible or towards infinity. Of course, wave height is unlikely to be normally distributed, it could have a negative kurtosis or a positive kurtosis, a normal distribution is a so-called “mesokurtosis”. It could also be a skewed distribution, either negatively or positively, where the probability distribution is fatter or narrow on one side of the mean. Either way, we can now clearly understand why so many oceanographers were skeptical of sailors’ tails of rogue waves because the so-called “linear model”, basically what we did using a Weibull or some modified Gaussian probability distribution for wind, predicted that waves of such size would occur only in a few million years. For a long time, vessels went missing with no good theory as to why. Prior to the measuring of a rogue wave on the Draupner Platform in 1995, rogue waves were considered a “myth” as they were never actually recorded even though they were first proposed in the 1960s by Laurence Draper. Most modern vessels, bulk carriers, oil tankers, LNG carriers, container ships, etc are designed for a static loading of 15,000 kg/m2, a rogue wave can generate 100,000 kg/m2 of force, far in excess of what would be possible to design. Rogue waves have been implicated in the sinking of a large number of vessels in Cape Horn, where the Agulhas Current flows directly into the opposing Westerlies current which induces so-called “shoaling”, which is when the wavelength is compacted and hence the same mass of water is then much shorter but much taller. In reality the mechanisms behind the occurrence of rogue waves is far more complex and not yet fully understood. 30 larger ships were severely damaged or sunk by rogue waves along the South African east coast between 1981 and 1991. Today an estimated 50 vessels disappear and sink a year without sending a signal. Their sinking is likely so fast from an immense rogue wave that shatters the hall that the captain and crew do not have time to send a signal. The point of this short inquiry into ship design, is that like a tall structure, it’s ultimately limited by the occurrence of freak events, which may not even be possible to withstand with the heaviest structure the designer could throw at it. Rogue waves illustrate the difficulty that the structural engineer faces when confronted with loading conditions that he cannot even calculate, and worst yet, he does not know when and if such a condition will even occur. It’s very easy for a high-rise engineer to hire a SODAR operator and find out the wind speed at the tower’s height, he calculates the vortex shedding frequency and determines whether he needs a damper or not, such engineering is very easy. But the ship designer, judging from the shear force of a rogue wave, would need a hull so thick to withstand the load that no hull in existence could withstand, no matter how overbuilt it is. while it would be theoretically possible to design the ship to be very short and robust minimizing bending, such a vessel is uneconomical to operate since hull speed is the function of the hull length.
Design variables of a pressurized media tower
A number of interesting geometric and mathematical phenomena impose design constraints on the technology. Surface-to-volume ratios and surface-to-length ratios play a major role in determining the design criteria that must be adhered to. From a material usage perspective, it is obvious that wind turbines desire to be as small as possible to achieve the highest power density. This is evident as the power output is directly proportional to the area, which is squared as a function of scale, while the material mass of the blades, nacelle, and tower are cubed. This means as the turbine grows in size, its mass relative to power increases exponentially. If the mass of a 44-meter diameter 750 kW turbine is say 15,000 kg, if the diameter of the swept area is doubled, the mass of the major components, whose size is a function of their loading (which scales linearly), increases 8 fold to 120,000 kg, but the power only grows to 2990 kW, or four times. So this would seem to suggest we should design very small turbines as to limit their mass and hence material cost, which is by far the single biggest contributor to the cost of building the unit, since labor intensity is relatively low thanks to automated machine tools. But there is a practical limit to how small a unit we want. Firstly, since each turbine has to be serviced and installed using heavy equipment to dig foundations and connect electrical cables, a massive number of tiny turbines would be impractical since site preparation would offset the lower cost of the lighter turbine. So there is a clear floor on how small it makes sense to design each turbine. With the pressurized media tower, there is a very convenient factor that helps us size the turbine. Since we want to minimize the number of mooring sites for the cables, we can simply find the distance between two towers holding the cable angle constant, in our case, the ideal cable for maximum stability is 55 to 60°C, with an ideal spacing of 8 times diameter translates into an optimal size of 55 meters of rotor diameter for a 350-meter tall unit. We can then connect the guy cables for a separate turbine to the mooring site for the first turbine, allowing two turbines to make use of a single mooring anchor.
With respect to maintenance and repairability, some may be skeptical about how such a tall tower could possibly allow a person to visit the nacelle to perform servicing. Current wind turbine towers have a ladder and a series of platforms effectively serving as floors spanning the inside of the tower allowing the worker to climb inside the tower and reach the nacelle. Christophe Pochari Energietechnik, in rethinking the entire technology from the ground up, has dispensed with this option altogether. To reach the turbine platform, a hoist is used rather than a ladder, which is far safer and faster. A hoist, much like on a rescue helicopter, is kept mounted to the turbine platform at all times. A heavy sandbag (to prevent fluttering during winds) is suspended from the hoist allowing it to be remotely descended to ground level where the technician can fasten the load hook to his harness and lift himself up alongside the side of the tower. This technology is widely used in search and rescue rotorcraft and has proven very safe. In fact, when the worker climbs the nacelle, he is temporarily trapped inside, were anything to go wrong, we would not have the time to bail out so speak, such as in the case of a fire. In the case of the guyed tower, the worker has the option of rapidly descending to the maximum descent rate to escape to safety in the event of a fire since he remains out in the open during the climbing and descending phase. Nothing about this technology compared to conventional turbines compromises safety.
Since there is no seal, as the hydrostatic medium is contained within a hermetic system, failure can only occur if the guy wires are cut or terrorists fire at the column with large-caliber ammunition. The same vulnerability exists with conventional turbines since sabotage is readily performed by cutting power cables or firing at the nacelle which could cause a generator fire. Another immensely powerful advantage afforded by pressurized media tower technology is the ability to perform rapid tower descent, the entire turbine can be brought down to the ground level for inspection, maintenance, and overhaul without the use of a single crane. In fact, the turbine itself need not be disassembled, it can merely be lowered to ground level and remain fully operational. This is somewhat unprecedented, since in the case of a conventional wind turbine, once is installed, it is considered a peremant fixture of the landscape. Workers operate from the safety of a concrete and steel silo when removing the tube sections consecutively until the entire unit has been lifted down to ground level and the guy wires retracted into their underground winches. In the case of the pressurized media tower, there is another factor related to the tube diameter that plays an important role in its design. While the wind load of the tube can easily be born by the hydrostatic force on the piston, this is only the case as long as the length/diameter ratio is sufficiently low. If the length to diameter ratio is allowed to grow above a certain threshold, the wind force on the hydrostatic tube will exceed the upward force on the piston even at very high pressures. Since the ratio of tube wetted area to piston surface area is directly proportional to the diameter since the length is held constant, as the tube diameter is increased, its piston area to wetted area increases dramatically, allowing the designer to carry more wind and dead loads. At a pressure of 3.39 MPa, a diameter of 750 mm is ideal, giving a low drag coefficient of 0.3-0.35 at a high Reynolds number and allowing the design to place as much as 150 tons on the structure. Since the weight of the tower is approximately 18,600 kg and the nacelle and blades are 17,000 kg, the net force acting on the cables is reduced to 115,000 kg, providing plenty of “reserve” force needed for carrying severe wind gusts and the bending forces they generate.
if the turbine size decreases, the tube’s load-carrying efficiency falls to levels less than ideal. This leads us to settle on an optimal trade-off between turbine mass and tube load-carrying efficiency. Another factor mentioned in greater detail is the wind load on the guy cables. The smaller the turbine, the smaller the upward force required in the hydrostatic tube, this means very small cables can be used. But if cable size falls below 3 mm, their drag can exceed their rated load capacity, this effectively places a lower limit on the size of a hydrostatic guyed structure or any cabled structure for that matter.
Before we discuss aerodynamics and drag, it must be emphasized that the choice of fluid impacts the final performance of the tower considerably.
#1 Pressure gradient with altitude: If a high-density hydraulic fluid is used, a greater pressure gradient will occur due to gravitational acceleration. Fluid at the bottom of the tower will be compressed by the weight of the fluid above it. For gases compressed to moderate pressures, the pressure gradient for 49 kg/m3 nitrogen gas is 2.66 atmospheres for 350 meters, or 0.0076 bar/meter. The density of nitrogen at 4 MPa at an average site temperature of 7°C is 48.66 kg/m3. The mass of the total volume of gas is approximately 13,500 kg for nitrogen. Nitrogen has a cost equal to the power consumption and capital expenditure of the pressure swing absorption plant. The realistic cost of self-produced nitrogen is virtually nothing, less than 5¢/kilogram, or €700 per fill. Since the leakage rate is very very small, the gas once installed will last virtually a lifetime depending on the number of erection-retraction cycles, since leakage occurs during tube coupling.
#2 Center of gravity: Another design variable before we discuss drag is the design of the stabilizing or torsion platform. The stabilizing platform is the component that transfers the piston’s upward pressure to tension in the four lateral guy cables and the four vertical restraint cables. The further away the wind turbine’s bending moment is from the center of gravity, which by definition is directly above the piston, the wider the stabilizing bracket has to be to transfer the bending moment of the turbine to tension on the vertical cables and prevent the opposite cable from experiencing excessive slack as the platform pitches down slightly. There is also an option to place some form of base isolation mechanism to prevent excessive lateral movement from being transferred to the piston which places stress on its plastic seals. The stabilizing bracket is a critical component, but its mass is minimal due to its high structural efficiency. The stabilizing bracket consists of a laterally projecting pressurized column that exerts force perpendicularly to the tower, that is outward. This outward tension allows a series of cables to span at a 50-degree angle to the nacelle pivot structure. Any bending force from the nacelle is transferred into tension which is then transferred to compression at the laterally projecting columns, which then ultimately transfers itself to tension on the four vertical cables. Bending moment is all but prohibited from occurring since the four vertical cables are tensioned to 40% of their load capacity, generating an extremely stiff structure.
#3 Choice of hydrostatic media and optimal pressure: Hydraulic fluid is too heavy and costly to be used throughout the entire pressure column, leaving nitrogen as the only practical option. Hydraulic fluid is used only at the top and bottom of the tower just below the constant pressure sealing mechanism separated from the gas with a plastic or metal diaphragm partition. Lower pressure is ideal since the pressure column’s diameter can be increased with a thinner wall section providing greater lateral stability without the use of internal spars and allowing fewer guy cables to be used, simplifying assembly. The diameter for a 1400 kW turbine of between 750 and a 1000 mm is ideal, operating at a low pressure of 4-7 MPa. Lower pressure columns are heavier per unit of force generated, but require more frequent guy cable mounting points to maintain lateral stiffness during storms. As mentioned already, the larger the diameter of the cylinder, the more force we produce compared to the amount of drag that has to be withstood, since the ratio between the area of the cross-section of the tube increases relative to the length of the tower. Moreover, as the cylinder grows in diameter, the physical dimension increases (surface to volume ratio), increasing the Reynolds number and reducing the drag load. This would suggest the designer should lean towards lower pressure but somewhat larger tubing, but still narrow enough to be easily fabricated and handled in the telescoping silo. Wider tubing also enjoys the advantage of being literally more stable, requiring fewer stabilizing intermediate guy cables to prevent it from bending in the wind.
#4 Sealing options and leakage: It is critical to minimize the amount of friction occurring between the piston and cylinder walls to ensure only a small load can ever be transferred to the pipe before the piston reciprocates inside the cylinder. In act, this could be argued to be our sine qua non, in that if we cannot achieve this, the structure fails to live up to its promise.
The constant flow-hydraulic seal
Christophe Pochari Energietechnik has evaluated a number of different frictionless sealing options and settled with a closed cycle constant flow high viscosity oil seal. A closed cycle constant flow high viscosity seal uses high viscosity oil passing through a narrow gap between the cylinder and cylinder wall to induce pressure drop, keeping the flow to manageable levels. As the oil makes a complete passage from the bottom to the top of the piston, it has lost all its original pressure by using up its momentum to overcome viscous and internal drag and when it exits the cylinder gap it possesses a pressure barely above atmospheric and must be repressurized to be introduced back into the column. Using ultra-high viscosity gear oil designed for achieving large film thickness on gear surfaces, the pressure drop across a long piston with the average surface roughness of polished steel is sufficient to keep the passage of oil through the gap very small. A certain amount of fluid is allowed to pass through a 0.2-0.5mm gap between the piston sleeve and the cylinder wall, as the high viscosity fluid is pressurized to the pressure of the gas inside the column it passes through the high surface area gap, viscous friction causes the pressure to drop, maintaining a very low flow rate. The flow rate for high viscosity hydraulic fluid is only 12 liters per minute. A hydraulic pump mounted on the tower head repressurizes the fluid to the operating pressure of the gas column. Since the gas and fluid should not mix, a flexible partition liner is placed just beneath the piston, the oil is merely suspended beneath the piston a few centimeters, the rest of the column is filled with air which maintains the pressure of the fluid suspended above the partition diaphragm. The design has the added advantage of achieving absolutely zero friction, since there is no force pushing a piston ring against the wall. The fluid pressure is both acting outwardly on the piston and on the outer wall. The viscosity of Mobil SHC 6800 at 40 °C is 8200 centistokes, at 20 °C, it increases to 23,000 centistokes, and using the Andrade correlation, its predicted viscosity at 5 °C (the operating temperature of the tower head), would approach 56,000 centistokes (mm2/sec). The flow rate of the gear oil is 8 liters per minute at a viscosity of 56,000, corresponding to the average operating temperature at 350 meters, the power required to repressurize the fluid is only 600 watts.
Pressure drop calculation for the piston-cylinder gap. The pressure drop is simply calculated by calculating the cross-sectional area and increasing the length of the pipe until the surface area is equal to the area of the cylinder gap.
The surface area of the 0.45mm thick gap between the piston and cylinder is 3.8 million square mm, equal to a 37-millimeter pipe 32 meters long.
The above image illustrates the closed cycle oil seal. The piston slides inside a submissive oil bath, there is no mechanical contact between the piston wall and cylinder. The pumps on the side repressurized the oil which has lost all its pressure at the exit of the flow path to the inlet pressure. The flexible partition can be made of a number of plastic materials, alternately a thin wall metal liner can also be used. If the tower is to be installed in a hot climate, an oil cooler can be installed using ammonia refrigeration to keep the oil at no more than 5°C even if the outside temperature is 30°C or more. The power required to bring the temperature of the oil down by 25°C is only around 1 kilowatt since only 100 kilograms of oil is present.
#5 Thermal-density fluctuation. An obvious drawback of using gas is its change in density with temperature. The change in density affects the total hydrostatic force on the piston. For the tower at 350m, the temperature lapse will be 3 °C at the top. From minus 30 °C to 40 °C the density of argon decreases from 172 to 118 kg. Of course, the typical diurnal air temperature variation is rarely above 10 °C, so such a wide range is of little relevance. In the Midwest of the U.S, the maximum temperature variation is 11°C while the average surface temperature is 7 °C minus 3.5 °C adjusted for altitude. This means if the average temperature is 20 °C during the day, the temperature falls to 9 °C. At an 11-degree temperature change, 282 to 293 K, a trifling 5% change in density will occur in the argon, this would translate into a plus or minus 5% change in hydrostatic pressure, more than tolerable by the system. We can conclude safely that thermal fluctuations and their effect on density are negligible. Nitrogen, which has three times the heat capacity, will experience a much smaller change in density, this would suggest its use would be desirable in regions where thermal fluctuation is more severe.
#6 Power cable selection. At first glance, the transmission cable may seem like a trivial issue, but there is some nuance in conductor selection, including making a balance between voltage drop and cable size and cable size vs temperature.
Since our turbine is so much higher than most, we must carry considerably more conductors and will encounter greater voltage drop due to the greater resistance, 350 meters vs only <100 meters for most turbines. Moreover, a standard induction or synchronous motors operates at only 400 volts, which necessitates a heavy ampacity.
For a 750 kW 500v synchronous generator operating at 8600 r/min, the current is 1500 amps, which requires 3x 1000 MCM (27 mm dia) aluminum conductors. At 90°C, each conductor can handle 500 amps. The voltage drop is approximately 12.72% or 63 volts, and the hourly heat flux is 3.47 kWh per cable, or 10.4 kWh, or 1.38% of the developed power. The weight of the bare 1000 MCM cable is 0.45 kg/m, or a total of 405 kg. At an aluminum price of €2.5/kg, the cables add €1,012 to the turbine, which is a trivial addition.
In light of all these salient design exigencies, by far the most important design variable is withstanding the static wind loads that occur during a rare gust. The dead weight of the turbine module is relatively insignificant, the 750 kW 10.5 m/s turbine built entirely with aluminum 7068 (AlZn7.5Mg2.5Cu2) excluding the gears, weighs only 35,000 kg. The wind load on the blades during a maximum wind regime of 67 m/s is assumed to be static, which is equal to a flat plate when the blades are feathered at a zero angle of attack. During the maximum wind regime, the turbine module is pivoted to face the wind head-on. It is expected the majority of the total storm wind loads will be subjected to the tubular tower.
Drag is caused by a combination of viscous and internal forces, this is what the widely used Reynolds number attempts to quantify. At high Reynolds numbers, drag is preponderantly inertial, that is the kinetic energy of molecules impacting the body, while at low speeds it is primarily driven by the friction or viscous resistance of the fluid passing along the body. At very high speeds, above the speed of sound, air is compressible, this is referred to as pressure drag. For a high altitude structure with a tubular column and cables, on the column, drag force is primarily inertial and the flow is extremely turbulent, while on the cables, while the Reynolds number is much lower, the flow is still turbulent. For blunt bodies such as the nacelle, flat plate drag can be used or simply the static wind force, which is 278 kg/m2 at 67 m/s. The total wind loads on the nacelle and blades, that is the entire wind module, is around 25,000 kg, while for the tower it is around 35,000 kg.
A slender body is experiencing drag from the fluid passing over from friction, the fluid impacting it from inertia, as well as the de-pressurization at its back caused by an exhaustion of the fluid’s momentum, which causes the higher pressure in front to push the body into the low-pressure zone behind it. For a cylinder, the static pressure zone is only a small slice of the frontal area. When calculating drag coefficients, a common cause of confusion and miscalculation is the issue of a reference area. The reference area is either calculated as frontal area (planform area or projected area) or wetted area. The use of wetted area is usually used for highly slender bodies, such as a fuselage, while cylinders and blunt bodies are typically calculated using the projected area. This means taking its 2D cross-sectional area, which is slightly under a third of the wetted area.
After the wind loads have been calculated on the main structural components, we must calculate the drag on our guy cables. The drag coefficient of a 20mm smooth cable is around 1.1 at 30 m/s.
The lateral support cables are only 7 mm in diameter and hence only yield a Reynolds number of 7500. According to the data below, a 3/8 inch (9.5mm) cable experiences a drag coefficient of just around 1.146 at a Reynolds number of 5600.
The numbers below are from a report available at the Defense Technical Information Center (DTIC) website. The measurements were taken at varying Reynolds numbers and cable diameter as well as angles of attack. If the angle of attack is reduced to 45 degrees, the drag coefficient for a 3/8 inch hollow woven polyethylene cable drops to around 0.5 at a Reynolds number of 17,000. The drag coefficient drops as cable size increases, since the Reynolds number rises with a lower surface to volume ratio (characteristic length) so the main load retainment cables experience less drag than the small diameter pressure column stabilizing cables.
Each main piston restrain steel wire rope cable is 24mm in diameter, with a characteristic dimension of 0.006 meters at 67 m/s, and thus has a Reynolds number of 27896. The dynamic viscosity of air at a density of 1.26 kg/m3 is 0.0000181 kg-m/s. Since the cable is at a 90-degree angle of attack, the drag coefficient is around 1, while for the lateral restraint cables which span at a 55-degree angle of attack, the drag coefficient drops to 0.7. The drag force is thus 7,700 kg at the maximum encountered wind speed, or 11% percent of the total load capacity of 65,000 kg. The smaller the diameter of the cable, the greater the share of drag as a fraction of its rated load capacity as the surface to volume decreases. Drag is a linear function of wetted surface area, and drag coefficients increase with smaller diameters and with lower velocities. The drag load on the cables is ultimately transformed into tension which is born by the mooring anchors in the ground, as the wind passes over the cables and creations a suction force, the cables wants to elongate, placing a tensile load on the ground anchor. Since the wind load can only act in a single direction at a time, the cable that is receiving the wind load from its rear, that is the wind is acting in the direction of its forward tilt attitude, will act to pull on the cable from the ground, placing no load on the tower. The cable that is receiving a frontal wind load acting in the direction opposite to the tilt angle will act to pull on the cable from top-down, placing a load on the tower which is transferred to the pressure column which thus reduces the tension on the restrain cable. Therefore, in the design of the high-altitude guyed pure tension tower, cable wind load can be assumed to be a uniform load born by the ground structure. The designer must then design the tower to withstand the wind force on the main turbine assembly and pressure column.
Working principle of the self-erecting silo
Now we can turn to the final highlight and core competitive advantage of the pressurized media tower technology besides increased energy yield. This is the ability to perform what is called “self-erection”, whereby the gas tube can be slowly built into place from individual 15-meter sections with a novel underground silo that allows the hydrostatic media to be retained in the tube at any given time while allowing a new tube section to be threaded or locked into place. The core functionality of the self-erection systems derives from the ability of the fluid to generate upward force, thereby acting as a crane. The first tube section is inserted into the underground silo, the end of the tube is then allowed to pass through an opening in the ground module. The bottom of the tube is placed on a special moveable fitting that inserts compressed nitrogen inside the tube. The moveable fitting is raised with four cabled winches until it extends all the way to the maximum retraction point. When the tube reaches its maximum retraction, another one is inserted. To achieve this, the compressed nitrogen must be contained while also allowing the end of the tube to be accessed for connection. In order to facilitate this process, a series of pressure containment mechanisms are fitted on the outside of the tube. When the tube extends beyond the pressure containment module at the top of the underground facility, a pressure containment plate is placed underneath sealing the gas. The pressure containment mechanisms uses oil-lubricated rubber seals to minimize leakage. All the moveable mechanisms are hydraulically actuated and controlled electronically by a human operator. The main pressure containment module is then purged and opened, allowing another tube to be introduced inside. The module is then sealed around the parameter of the tube. The tube is then filled and sealed from the bottom. After it has been filled, the upper sealing plate is removed allowing the compressed gas inside the previous tube to merge with the gas from the freshly inserted one. On this pressure equilibrium is reached, the tubes can be threaded or locked together sealing off the internal gas. The gas inside the containment module is then purged again and the process repeats. To raise the tower, the piston is allowed to climb along with the tube, by pulling the tube along with the climbing piston, the tower can be raised in a single day, obviating the need for expensive cranes. Since the entire pressure column effectively “suspends” from the piston as cables attached to the piston but do not transfer downward force, if the pressure is increased and or cable tension decreased, the entire module climbs vertically. This is an important fact to highlight, since even if some force is applied to the pressure column from the piston at the top, say the seal failed and there was some friction, the piston could not be compressed or experience any load since it reciprocates at the same frictionless seal at the bottom. Of course, if both seals failed then the tube could experience compression. This article provides a brief overview of the technology, its design exigencies, and its applications, including not only wind power, but pile drivers, novel high elevation structures for human habitation, communication towers, cell, radio etc, and also potentially for stationary gantry cranes.
What this novel technology offers the rural energy user
“Renewable energy” has gotten a bad rap, primarily due to foolish political endeavors to “decarbonize” the electrical grid. Renewable energy technologies, mainly solar and wind, are useful and sometimes invaluable for users of energy who are not in close proximity to major industrial areas. But an additional factor is merely the levelized cost of the power they can offer, if situated in the most optimal locations. Hydrocarbons, by virtue of their energy density, mobility, and convenience, naturally hold a premium in the marketplace. Photovoltaic and wind energy, properly located in ideal geographies, often produced power that, while being virtually worthless for the mains grid, is nearly free with only the amortization of the initial purchase as the generation cost. The wholesale price of natural gas is only available to larger industrial buyers, for mid-size and small consumers, the “commercial” price is all that can be had. Industrial users can benefit from near wholesale or producer prices, around $5/MBTU, but smaller consumers such as farms, small factories, etc, will not be able to purchase large enough volumes to meet the requirements of the industrial price. This is the nature of oligopolistic or cartel-like entities, (most modern economies), so apart from drilling for your own gas, there is little that the small-scale user can do. Another factor endorsing the use of self-produced energy is the inherent resilience against future price instability and outright available risks. A small consumer does not possess much bargaining power and may be priced out of the hydrocarbon marketplace during periods of intense demand. Major producers and distributors of hydrocarbons will favor large cash-rich buyers over small users. The mean price of commercially sold gas in the U.S. since 2000 is $8.84/MBTU, with a standard deviation of $1.59. If we convert to the price per kWh thermal, the price is 3 cents, since the maximum practical efficiency of a thermal powerplant of the sub-megawatt scale is 40%, and generator losses are assumed to be 4%, the price per kW electrical is 7.81 cents. The 44-meter 300-meter high-altitude turbine generates, in a 10.5 m/s regime, will produce a steady state power output of 700 kW, or after gearbox and generator losses, 5,700,000 kWh in a year. If we had purchased natural gas equivalent to this energy output, the total cost would be $445,600. The direct-at-volume unit manufacturing cost of the aluminum turbine module is only $100,000. The low cost compared to current steel and fiberglass turbines are attributable to a number of factors. Since aluminum is so easy to machine, fabrication involves minimal labor as largely automated CNC machines churn out the major structural components at a high rate. Secondly, the elimination of steel parts eliminates the need for welding, a labor-intensive process. In addition, the absence of forging reduces machinery capital costs. The lifespan of the unit is 25 years, with a gearbox overhaul every 5 years at a cost of $3000. Over the lifespan of the turbine, if we include a 1.5% annual price escalation for natural gas, the high-altitude wind turbine will have saved the owner $11,150,000. This is a sum of money sufficient to buy 111 high-altitude wind turbines, which could in total, provided the land is available, generate 633 million kWh, equal to 49 million dollars worth of natural gas. Of course, these numbers assumed the turbine is installed in the U.S Midwest, where at altitudes of 300 meters, wind speeds of 10.5 meters per second prevail. It also assumes the method of manufacturing we proposed is employed, currently, laborious steel and concrete-intensive wind turbine manufacturing is highly inefficient and cost-intensive. The turbine module we have designed is a modular nacelle, concatenated from smaller individual iso-grid aluminum frames. The blades are machined from a single block of aluminum, with virtually no labor required. The aluminum that goes into the turbine is indigenously produced, reducing the cost to the bare minimum, electricity, carbon electrode regeneration, and reactor module degradation and overhaul.
Previously energetically prohibitive processes are now possible, such as electrochemical machining becoming cost-competitive with mechanical machining. A prime application this machine is targeting is small-scale mining (yes) of low grade ultramafic ores where high comminution energy is required.
Breakeven wind speed for photovoltaic parity in LCOE
Christophe Pochari Energietechnik designed the high-altitude self-erecting tower to provide a low-cost energy solution for small-scale users. We had essentially no intentions of “pitching” it as some panacea to the world’s putative energy problems as most “renewable energy” companies do. We designed it with almost exclusively small-scale users in mind, we designed it to be easily erected without specialized equipment and to be maintenance friendly and long-lasting. Natural energy harvesters are terribly inconvenient for use with massive national grids, they are a technology that should be used wisely, without emotions and fantasy guiding their use. Because a guyed turbine does not take up land in the strict sense of physically obstructing activity on the land as a solar farm does, it is ideal for operations where the land is being actively used as a revenue-generating process. It should be said that while a high-altitude tower does not directly occupy land, preventing it from being used, it does “take up” space insofar as a mooring anchor is needed, there is no perfect solution evidently. But a mooring anchor only obstructs a small footprint, tractors can easily drive right beneath them. They occupy the “air”, and are more of a nuisance for helicopters than humans. For small mining, ammonia production, manufacturing operations, or any other energy-consuming activity, we may need half a megawatt of continuous power. In a 7 m/s wind regime, the Global Wind Atlas cites a 0.75 hourly temporal variation, compared to photovoltaic which by definition has a variation of zero, since it goes from producing energy to none at all. A high-altitude wind generator confers to the operator a significant reduction in energy storage cost, since the user can still draw current from the wind turbine at night powering the activities in question. If the wind speed at 350 meters is 7.5 m/s, the turbine will generate 400 kW, so barely two are needed for a megawatt. The breakeven wind speed for the high-altitude turbine to reach parity with photovoltaic corresponds to much less than the average national wind speed at the operating altitude targeted. Our 350 meter 80-ton high altitude turbine, for it to break even with the lowest cost solar panels produced in China, the turbine need only to generate 90 kW! 90 kW would correspond to quite a slow wind speed of 5 m/s, available at 350 meters in virtually 100% of the U.S. Very few sites at 350 meters feature wind speeds much below 6 m/s except for tropical regions where little industry is based. The baseline for any energy technology is not natural gas combustion, but photovoltaic. We know that the direct cost of the panel modules is around $234/kW, (https://www.energytrend.com/solar-price.html, it was only $180 in 2021). Inverters (Switching power supplies, $30 for 1000W units), frames (steel), and mounting foundations (concrete pads), excluding installation labor or batteries, add another $100 or so per kW. Note that these prices seem “low” compared to the figures for gigantic “grid-hoop-up” solar farms, this is for obvious reasons. We are merely adding the cost of the wafers, glass, and aluminum (basically all a solar panel is), we are not including expensive grid hookup or utility work, nor are we including the cost of the site preparation either. Average solar irradiance in the continental U.S. is around 1600 kWh/kWp, or 1480 after 7% inverter losses. Over the system’s 22-year lifespan, the direct power cost is exactly 1.06 cents per kWh, which includes purely the amortization, in reality, there may be occasional inverter replacement, but this is negligible. This figure does not take into account yearly degradation due to oxidation of the silicon wafer (perhaps vacuum chambers could be used?). If we account for inverter repair at 10 years and degradation, the LCOE goes up 0.1 cents, The industry average module degradation is 82% at 25 years, or 0.48% percent annually. This means the average mid-life production is 5.28% less, raising the LCOE to 1.129 cents/kWh. Realistically, the panels will be badly weathered and need replacement at 22 years, which is why we chose that figure instead. In comparing the small-scale photovoltaic power plant to our high-altitude wind turbine, we have to arrive at a rough estimate of the mean wind speed at the site. If we take an average wind speed of 7 m/s, which is common in the Piedmont basin (where we want to mine ultramafic rock), at 200 meters, most of the eastern U.S that isn’t the central plain is 7 m/s at 200 meters, increasing according to the vertical shear profile of 1.075-1.09x to 7.5 m/s at 350 meters. So assuming the same blades are used as the E-44 (highest CP blades known), the turbine will generate 460 kW at 7.5 m/s. Since its direct mfg cost is only $175,000, the 22-year LCOE is 0.21 cents per kWh. So the breakeven wind speed to reach solar LCOE parity is considerably lower than 7 m/s and is around 5 m/s since wind turbine power declines exponentially. Since the unit price of the turbine is $175,000 and installation costs are very low due to the absence of cranes, the breakeven power generation is 543,000 kWh/yr, since the turbine is constructed from stainless steel, the lifespan is closer to 25-30 years, giving it more amortization time. 543,000 kWh/yr is 62 kW, corresponding to a wind speed of 4 m/s or less. At 4 m/s, at 350 meters, this is virtually the entire world except for the tropics. So in this respect, our turbine has the same “distributed” potential as any photovoltaic panel as long as there is a place to moor the anchors.
Pressurized Water Reactors: An Intrinsically Unscalable Technology
Unfortunately, the physics are rather grim. Global energy consumption is simply so immensely huge that no currently available energy technology can scale, regardless of how much time we give it. Natural energy harvesters, technologies not suitable for grid-scale steady state use, will clearly not suffice, not only due to their poor reliability, but low power density. The one and only solution to replacing hydrocarbons or fossil fuels is the breeding of natural uranium. While nuclear fission can in theory produce near-free power using advanced designs, the problem is that unlike a wind turbine or solar panel, nuclear technology is inaccessible, highly regulated, and is the subject of intense scrutiny over proliferation concerns. Only with central government support, subsidies, and the removal of the burdensome regulation, can any advanced nuclear reactor technology be deployed at-scale. So-called SMRs or “small modular reactors” will likely never see the light of day due to their obvious ability to be smuggled, exported, and used to produce plutonium if converted to run on heavy water or cooled by gas such as carbon dioxide which does not absorb neutrons. Any breeder reactor by definition is a plutonium 239 factory. Furthermore, even if the regulatory system approved their sale, they would be multi-hundred million dollar devices out of reach of small businessmen and producers in search of cheap power. As is rather self evident in the case of small modular reactors, all it would take, knowing human irrationality and our inability to gauge risk, is one accident that leaves twenty people crispy fried from gamma rays and it would be the end of that, the entire small modular reactor industry would cease to exist since no insurance company would be willing to offer coverage, making it impossible to finance using debt. Nuclear risk is much like murder, it’s extremely rare and much less likely to occur than a car accident or drowning, but we find it more frightening due to the intensity and horror of a silent, invisible poison that pollutes our air and water for decades. Unlike a steam turbine boiler that occasionally blows up killing a single worker, a nuclear meltdown has a number of unique attributes that potentiate its scare factor, one of them being the silent killer that is gamma rays and the ability for isotopes of strontium 90, cesium 137, polonium 210, etc to be blown by winds across long distances and settle in the soil. Strontium 90 is a so-called “bone seeker” that mimics calcium and hence accumulates in the bone of animals that eat grass exposed to the fallout. The worst that can happen with a wind turbine is it collapses and kills a cow or hurls a small piece of metal into a barn. Furthermore, even though the power density of a fission reactor is immensely high and the cast of the basic metal and raw materials to construct it forms a relatively small overall component, once the device has to be certified and approved by governments, it becomes a technology that is effectively a monopoly produced only by the manufacturer that has been given the stamp approval, much like overpriced aircraft parts. This means that even with further innovation, and small modular PWR will not offer a competitive LCOE, and if fission ends up being more expensive than photovoltaic, so why on earth would anyone bother with the complexity and tediousness of fuel disposal when they can go Alibaba and buy a solar panel let alone a high-altitude wind generator turbine?
Conventional light water reactors, scaled to satisfy the global energy budget, would consume entire economical uranium reserve in 3 and a half years
A number of IV-gen reactor advocates have claimed that a uranium reserve of tens of thousands of years exists, this is but a lie and assumes seawater extraction of uranium, a technical near-impossibility, provides the source of uranium. With conventional mining, virtually all of the world’s uranium would be burned in less than a century, providing an energy source about as “sustainable” as burning coal. The principle limitation of fission is the low utilization of uranium and its extreme scarcity in the crust. Total global energy consumption totaled 177 terawatt hours in 2022, 1.77 × 10^14 kWh. Existing reactors that use only 0.7% of the natural uranium would burn through the world’s entire economic supply within a few hundred days if scaled to global use, so existing nuclear technology is effectively useless. Breeding has proven technically difficult, but not insurmountable, with primarily sodium fires as the technical issue faced by designers and operators. High neutron fluxes and a positive void coefficient make breeders inherently meltdown prone, the need for sodium coolant imposes corrosive stresses and the risk of stress corrosion cracking, not to mention neutron embrittlement being amplified by the much higher neutron flux. The typical PWR produces 45,000 MWd/ton (megawatt thermal per day per ton of enriched U), or 1,080,000 MWh-thermal/ton-year of 3.5% U-235. A breeder, such as the French Phenix reactor, may have burnup as high as 150,000 MWd/ton, although 200,000 MWd/ton is possible, or 4,800,000 MWh-thermal/ton of natural uranium. The net electrical output per ton of enirhced uranium in the light water reactor is 1,000,000 MWh, or 378,000 MWhe. Since the net electrical power is around 35% of thermal since the best in class Brayton cycles rarely achieve more than 40%, and most Rankine cycles max out at 35%. Scaling to 177,000 TWh, 470,000 ton of 3.5% uranium would be burned, or 2,350,000 ton, 30% of the total economical reserves in a single year. Of course, theoretically, if all the uranium present in the upper crust, say the first 2 kilometers, were mined, it could last hundreds if not thousands of years, but such extensive mining is physically impossible since the concentration of uranium is so small. Uranium occurs at an average concentration of 2 mg/kg or 0.002 kg/ton of crustal rock, if the entire earth’s first kilometer were mined, the total surface of all land is 148 million square kilometers, since we would mine 1 kilometer deep, the volume would be exactly 148 million square kilometers or 1.48e+17 cubic meters = 7.696e+14 kg of uranium or 7.696 × 1011 tons, 769 billion. Of course this is ridiculous, but scientifically amusing. But even if the “accessible” 8 million tons were all mined at once, it would be technically impossible to mine so much uranium in such a short time, it takes years if not decades to bring a mine in operation, there would be simply insufficient time to provide the necessary uranium. The grades of ore are so low that gargantuan amounts of rock have to be hauled and processed, requiring huge facilities and consuming substantial energy in the process. In theory, with a helium Brayton cycle, it is possible to squeeze as much as 2,160,000 kWh-electrical per kg of natural uranium, or 2,160,000 MWh-electrical/ton. To power 100% of global primary energy consumption, 81,940 tons of uranium are needed. The depressing fact is that this means only 97.6 years of reserves exist. The breeder reactor “only” extends uranium reserves by 29 fold, which is a huge number, but still insufficient to render a scarce element like uranium sufficient richly yielding in energy to make it a long term solution. Total extractable uranium reserves are placed at 8 million tons, this sober picture highlights how desperately man is chained to hydrocarbons, we could see that even breeding is nowhere close to an inexhaustible source. Another fact to remember is that even though breeders can burn all the uranium, it still require the starting fuel source to be enriched to 20% U-235, requiring centrifuges or diffusion plants, or perhaps “Helikon” vortex separation enrichment used by the South African government. Coal is thought to have reserves of 250 years, and even though it is atrociously foul, it’s not terribly great news than such a wonderous technology like breeder reactors end up being just as depletable as coal, in fact even more so. Breeders can fission about 49% of the the atoms in U-235, about 70 times more than a PWR. In reality, a breeder, as evidenced by the operational experience of sodium cooled breeders, such a fleet of reactors would be far too failure prone for long term use. These numbers mean that the reserves of coal exceed that of fissionable uranium, quite counter-intuitive and definitely contrary to what you would hear from nuclear activists. Of course, such a comparison is not entirely fair, since we are placing an unrealistically high bar on the nuclear technology, requiring it to scale to 100% of global primary energy demand, whereas coal serves perhaps 40%. It should be emphasized this analysis is totally dispassionate, we ourselves would love for small reactors to be made commercially available, but we are not placing high hopes on the prospects! Seawater extraction would be nearly impossible because the concentration would begin to fall exponentially, rendering the process totally uneconomic within a few decades. The amount of water that would need to be processed is simply so huge, and with that the amount of brine that would need to be disposed of makes such a proposal a technological nonstarter. Molybdenum, boron, lithium and strontium are more far abundant than uranium in seawater and no proposals have been made to extract them despite their very high industrial value. In short, unless breeding technology can be made reliable, it is unlikely fission will be the panacea that proponents claim. This figure, the certain inability for breeder reactors to provide an “energy panacea”, is perhaps a true testament to the shear wonder of the hydrocarbon molecule, but also a testament to man’s dire dependence on her, with perhaps devastating long term consequences. The final takeaway is perhaps only philosophical, a humbling statement of man’s limitations, a rude awaking that man is not technically omnipotent, and quite the contrary, wholly incapable of severing from his bondage to the molecules beneath his feet. If hydrocarbons cannot continue to be produced at the scale and intensify than they currently are, much of the world’s less productive human societies would vanish. Once all the easily mined sources of coal are burned, Africa, India, and the Middle East, would likely disappear, leaving the hydropower rich Fjords of Norway, the Windy planes of the Midwest, and the Field of Northern Germany, all abound with natural energy, to survive. The tropical human settlements are impoverished of natural energy, while the temperate and northernly civilization are much better endowed. China would survive as its population would to a level that could be sustained with hydropower and wind.
Uranium has a market value of €110/kg, or €11,000 per ton. Uranium is found in the crust at a very low concentration of 1.8 ppm, rarer than caesium and beryllium and most of the so called “rare earths”, but more abundant than gold.
Since five tons of natural uranium are needed to produce a ton of 3.5% enriched uranium to produce a total of 378,000 MWh-electrical or 378 million kWh, the cost per kWh for the fuel excluding enrichment, transportation, and disposal is 0.23¢. If we assume spent fuel storage, transport, enrichment, and processing the uranium into uranium oxide which is then fabricated into zirconium clad billets adds 50% to the cost of the base metal, the total increases to 0.34¢, still more than the total levelized cost of the high altitude wind turbine. As for the CAPEX of the plant in the West, due to an inordinately complicated safety and regulatory environment, the construction cost is absurdly high, as high as €7000/kW. In China, the cost is more reasonable, at around €3000/kW. The PWR fleet in France, most of which were built during the 1980s, cost on average about €1500/kW to construct, while in the U.S before costs began to dramatically escalate due to regulatory changes after Three Mile Island, costs were below €3000/kW. Since the current costs of nearly $8000/kW do not reflect material and labor, we can use the estimate of the pre-Three Mile Island costs to more accurately reflect the real hard costs of actually building the reactor, not inflated regulatory and environmental fluff. Of course, the U.S Nuclear Regulatory Commission has good intensions, as do most government regulatory bodies, but they might actually be counterproductive, because more money could be allotted to better and more redundant designs, that is the money spent on compliance could instead be spent on more frequent replacement of critical parts. All the money spent and construction time lost complying with regulatory paperwork and sclerotic bureaucracy could be invested in actual physical systems, materials of better corrosion resistance, valves with better mean time before failure etc. Japanese reactors averaged €2250/kW or 300,000 yen across the 1970- 2000 timeframe. Assuming a reactor life of 50 years, which is limited by neutron embrittlement to around 60 years, a €2500/kW reactor has a levelized CAPEX amortization of 0.57¢/kWh. Of course there is also an annual maintenance bill, but this is hard to estimate since it varies substantially by reactor and location.
Construction CAPEX of the French reactor fleet.
Nuclear is a prime case study of a sharp divergence between hard costs and soft costs.
A 1975 U.S department of energy report found that it took on average between 5 and 6 manhours per kW to construct a pressurized water reactor plant in the 1960s, but by the 1970s, it had increased to 8 to 10 due to more complex designers. It would take around 1200 workers to build a 1000 MW plant in 5 to 7 years. Since most of the work is welding, assembly, pipefitting, fabrication, and installation, and not engineering, it’s moderately skilled, we can assign a wage of $30/hr. According to the BLS, the average wage for a pipefitter in the U.S is $28.79/hr. In France, the average wage for a pipefitter is around $15/hr, this difference is explained by the fact the French worker has more purchasing power due to free government services. This means the labor cost is only $300/kW, which sounds very reasonable. If we then assign a material processing cost of $10/kg, this represents another $400/kW. The total including soft costs such as permitting and engineering fees for the design adds another few hundred, taking the total to a $1000/kW, which would likely be the real price were it not for the regulatory and environmental factors.
The average material consumption varies widely, but the best estimate is about 40-50 tons of steel per MW and 300 tons of concrete. If modern plants cost as much as $7000/kW, around 6 six times more than the French reactors built in the 1970s, that means the per kg cost of fabrication and installing the metallic components only is $175/kg, which would be like building the nuclear reactor out of a material three times the cost of cobalt! In other words, we could build the plant cheaper if we used pure cobalt to construct the entire thing!
Labor costs add a nontrivial cost of production since nuclear reactors are extremely complex and require numerous human operators in the control room as well as to replace critical parts including sensors, valves, and emergency systems. The 2x 1500 MWe Civaux Nuclear Power Plant employs 1300 people, this is assumed to be relatively consistent accross PWR plants. Assuming a salary of $50,000 per anum which is typical for a moderately skilled worker in a high income country, the cost of the human labor alone is 0.248¢/kWh!
The 3120 MWe Chooz Nuclear Power Plant employs 1000 workers, the 1912 MWe Saint-Laurent Nuclear Power Plant employs 600 full time workers.
The now decommissioned 1840 MWe Fessenheim Nuclear Power Plant employed 900 workers.
The net levelized cost for PWR fission seems to converge at around 1.1-1.2¢/kWh based on our estimates, but the numbers are aggressive and probably underestimate maintenance and exclude decommissioning, which sometimes can cost as much as the construction of the plant itself. The estimates also excludes insurance, which is likely substantial since the cleanup costs in the event of a meltdown are simply incalculable. This stands in stark contrast to the high-altitude wind generator, which costs $150-200,000 to mass produce and €5000 to install yet still generates 10-12 million kWh annually for over 20 years, costing less than 0.08¢/kWh, or 14.55 times cheaper than current nuclear fission! Remember that the high-altitude wind generator turbine uses only 35 tons of aluminum which has a direct manufacturing cost of only €1500 per ton.
The “Thorium” fad
With regards to fusion, it is merely an amusing thing to watch, but its not worth discussing aside from amusement. The sun is 265 petapascals, the ITER reactor is 14 bar, quite a difference shall we say. To overcome the Coulomb barrier one needs immensely high pressure (not temperature) which ultimately comes from mass. The sun’s mass is so great due to its size naturally its gravitational field is much stronger, this allows immense pressure to accumulate in the core. Apparently, ITER people have either never considered this or they do not think it poses a problem. No confined magnetic fusion can occur with such low pressures on a relatively low mass planet like earth unless pressures approaching the cores of the smaller stars can be replicated in man-made devices, irrespective of the hundred million degree temperatures they achieve. Replicating the conditions of massive stellar nucleosynthesis bodies is doubtful since the thing would merely burst under pressure since the material could not handle both the temperature and pressure. Fusion is so patently a fraud that it questions the assumption of human ingenuity. Confined fusion has been done since the 1950s in its modern form using toroidal reactors heated with plasma. Magnetically confined fusion is attempting to use high temperatures instead of high pressures, it would be like synthesizing diamonds at atmospheric pressure. Diamonds can be synthesized in a very high vacuum, but never at ambient pressure. There is no evidence the Coulomb barrier can be overcome using a vacuum, all the evidence suggests immense pressures resulting from huge gravities are needed.
Energy is perhaps one of the few topics where everyone in the general public has an opinion. Climate change is another such topic, perhaps also nutrition and dietary science. These scientific subjects that are “popular” are usually field with egregious misconceptions and falsehoods. Since all of us pay an electricity bill once a month, most people feel somewhat qualified to “chime in”. There is nothing wrong with sampling public opinion, but the issue is that public opinion is often ripe with myths, falsehoods, ignorance, and sheer stupidity. It is not that we should be elitists, after all, elite is a purely arbitrary definition, what matters is whether a person has a decent grasp of the pertinent and salient facts, irrespective of their beliefs. Most of the public simply fails to grasp the realities of the difficulty of being reliable, cost-effective, and safe energy technologies.
Anyone who has spent any time on the internet has noticed a growing trend in recent years. The so-called “climate crisis’ has prompted a whole host of former environmentalists to become “pro-nuclear” and “embrace the atom”. Reddit is now full of “thorium evangelists” who repeat unsubstantiated claims made by Kirk Sorenson, who single-handedly revived the so-called molten salt reactor program investigated by the U.S Air Force for an atomic-powered bomber. It is now common parlance to repeat blindly “thorium is the answer” without knowing anything about thorium and how it can even be fissioned in a workable reactor. Thorium is firstly a “fertile” isotope that must absorb neutrons to transmute into uranium 233, this requires U-235, the starting “catalyst” if you will for any fission process.
Were it not for Gordon McDowell, a software engineer who started filming thorium conferences and interviewing Kirk Sorenson, the internet would not be full of “thorium bots”. McDowell has accumulated tens of millions of views and singlehandedly made thorium and or molten salt reactor architecture famous. His intentions like all of us are good, but they miss the point: we do not need to spin, market, or promote technologies that are inherently good. They will eventually be discovered, built, and tested and then people will desperately clamor to be the first ones to commercialize them, it will be a veritable arms race. In the modern tech landscape, this dynamic has been inverted, it’s an arms race of “pitchers” imploring investor attention.
Molten salt reactors as their name suggest employ a liquid salt as a working fluid to absorb heat from the reaction, carry the fissile fuel as a liquid mixture usually as uranium fluoride, and prevent the excessive absorption of neutrons if breeding is desired as to maintain a high neutron economy. Mixtures of lithium fluoride (LiF) and beryllium fluoride salts have been proposed. But these salts are not exactly benign compounds, they are highly antagonistic to most alloys used in reactor design. Not only are these elements hardly abundant, the entire reactor plumbing would need to be made of a high molybdenum and nickel alloy to withstand the fierce corrosion that would occur. Corrosion rates as high as 10 MPY (mills per year) are observed. This means hundreds of tons of molybdenum and nickel may be needed for each reactor. The Oak Ridge laboratory reactor used a salt mixture consisting of sodium, zirconium, fluorine, and uranium. A molten salt reactor can either be a moderated thermal neutron reactor used to fission U-235 or it can be a breeder used to transmute U-238 into P-239, or it can run on a thorium fuel cycle burning U-235 to generate excess neutrons to transmute Th-232 into U-233.
Very few people actually discuss these realities and to this date, no molten salt reactor has been built, not because of some problem with the physics, but because of the insanely strict regulatory environment that small companies simply cannot surmount. These “pro-nuclear” environmentalists are concerned about CO2 and climate change, but see themselves as too technologically savvy enough to accept lowly “solar and wind” who just can’t pass muster. It has become a badge of honor to be a thorium expert and denounce solar for being “low tech”. If one reads comments on an article criticizing molten salt, you will find countless comments that are quite emotionally invested in it, and any negative comment is downrated. The comment sections often become vitriolic, as with most places where human beings, especially men congregate. But the issue is not human emotions, but what the evidence, physics, metallurgy, and chemistry suggest. Technology does not care about our emotions, the truth is always just below the surface, if any of these alternative fission technologies, regardless of architecture, were an attractive option, at least one country would rapidly deploy it for national strength in this very competitive and energy scarce world. Note that we are not saying U-235 burned in boiling or pressurized water reactors is not an extremely capable technology, is is, very much so, but they are not more competitive than hydrocarbon combustion, a cardinal requirement that any energy technology must fulfill to succeed. Our world is still propelled by 85% hydrocarbon, and this number is not showing any sign of budging. There is this deep-seated belief that any technical problem can be solved by merely throwing money and brainpower at it, what we call “R&D”. But this is far from the truth and extremely naïve, since one cannot solve the problem of corrosion of a metal by salt with technology, either the chemical element can withstand the corrosion or not, nor can one stop the spread of radionuclides from spreading across to the nearby town. Clearly, there are a number of severe technological challenges that have handicapped molten salt reactors, regardless of whether they burn thorium or uranium. Pumping molten salt requires a very delicate and appropriately engineered pump, and the corrosion within the plumbing system is going to place a severe limitation on the lifespan of the reactor. Extremely high-temperature salts, not to mention the exotic beryllium and lithium fluoride salts are so incredibly corrosive that even the molybdenum titanium alloy proposed may not hold up when faced with neutron bombardment. It is interesting to note that the only molten salt reactor ever built failed after 5 days when a plumbing component cracked and released xenon gas.
It should be remembered that while molten salt reactors have not been built, liquid sodium breeders have been built and two currently operate, all in Russia, they are the BN-600, the BN-800 and the planned BN-1200. In Europe, the French Phénix and SuperPhénix were built and decommissioned, the German SNR-300, while in the U.S the EBR-1 and 2, Fermi-1 sodium fast reactors were constructed and studied, but never used to produce commercial power. Hot sodium shares many characteristics with liquid fluoride metallic salts, but is much less corrosive and more of a fire hazard. It is interesting to note that the BN-800 cost 2 billion dollars to build or 140 billion rubles, that’s a cost per kW of $2500. The BN-600, during the first 15 years of operation, experienced 12 incidents involving sodium/water interactions from tube breaks in the steam generators, a sodium release causing a fire from a leak in an auxiliary system, and a sodium fire from a leak in a secondary coolant loop when the reactor was shut down. A total of 27 sodium leaks occurred in the BN-600. The operating temperature of the liquid sodium is 550°C at the inlet and 370°C at the outlet. The flow rate is 25,000 tons per hour. The BN-600 has enjoyed a relatively low load factor, at only 74%, while most PWRs operate at over 90%. All we need to know about fission reactor architecture is that no Navy in the world would use a sodium reactor in a submarine, only distilled water with its low viscosity, low corrosivity, negative void coefficient, and extremely smooth and reliable operation can be considered safe for submarines.
M. V. Ramana describes the operating experience of the first molten salt reactor built at Oak Ridge:
“Operations were anything but smooth. At the most general level, the fact that the reactor operated for just 13,172 hours over those four years, or only around 40 percent of the time. In comparison, the average commercial nuclear power plant in the United States operates at upwards of 90 percent of the time. The longest periods of sustained high power operations in the Molten Salt Reactor Experiment were between February to May in 1967 and late January to May in 1969.
During its operational lifetime, the Molten Salt Reactor Experiment was shut down 225 times. Of these 225 interruptions, only 58 were planned. The remaining interruptions were due to various technical problems, including: “chronic plugging” of the pipes that led into charcoal beds intended to capture and remove radioactive materials so the reactor could operate; failures of the blowers that removed the heat produced in the reactor; and fuel draining through the so-called freeze valve safety system intended to prevent an accident”.
Christophe Pochari Energietechnik is completely impartial in its analysis, if we had the capability and were it not for the law, we would be taking the risk and experimenting with building miniature fission reactors (limited by the critical mass of U-235) of various types, but the reality is the world does not work this way. If we lived in an anarcho-capitalist world, which the author supports in theory, we would take out a private insurance plan to protect our neighbors from fallout and accept the risk of early thyroid cancer. But in the real world we have massive states which have a monopoly on violence, and only they can approve what gets done from something as potentially dangerous as a fission reactor, so no “entrepreneur” in the world no matter how smart is ever going to build a private nuclear reactor, it simply isn’t going to happen. Pressurized water reactors are useless for producing plutonium, most of the fission products are useless actinides. One needs a heavy water reactor and or breeder to produce the valuable PU-239 that is needed for an MIRV that every serious country yearns for. We will never see lots of fission reactors that use alternative architecture for this reason. Moreover, if one wants a standard PWR, they still need centrifuges to bump up the U-235 content to 3.5%, these centrifuges can be dismantled, exported, and reassembled to produce 90% U-235 which is perfectly satisfactory for a small kiloton range device. This is presently Iran’s strategy, just like Pakistan which at first tried getting a heavy water reactor to produce plutonium, took the easier route which was procuring centrifuge equipment from Europe while the CIA was busy fighting the Soviets in Afghanistan.
There is evidence of so-called “radiation hormesis” where relatively small doses, millisieverts, can be salutary, but any accident is sure to expose the operator to fully sievert does, which are deadly and or sure to eventually give you cancer.
Fission produces two main forms of radioactive product, photonic and atomic and or electronic. The atomic and electronic are alpha particles (helium nuclei) along with neutrons and beta particles (electrons), but these do not form the principle radiation risk, rather it is the photonic radiation which are gamma rays, ultra high-frequency ionizing radiation, that is potentially one of the most dangerous technologies known toman with respect to its ability to inflict harm upon biological tissue. Gamma ray is perhaps the most dangerous thing known to man surpassed perhaps only by the organophosphorus compounds which block the acetylcholinesterase enzyme from hydrolyzing acetylcholine into acetic acid and choline, blocking nerve conduction and causing rapid asphyxiation. These compounds are used as fertilizers and form the basis of the Sarin, Soman, and Tabun nerve agents. Gamma rays possess the energy of millions of electron volts, enough to strip any electron and form a radical (ion), which explains their carcinogenicity. Gamma rays have such high frequency they are measured in exahertz, a thousand petahertz, which is a thousand terahertz. Such a frequency is difficult to even comprehend. Because gamma rays are such high-frequency waves, they can be stopped by air or shielding (usually beryllium), but in the event of a meltdown, while the air molecules ionize and rapidly attenuate the gamma rays from propagating, they can still inflict immense harm upon nearby personnel. But the concern is not merely that the gamma rays may propagate from the center of the reactor in the event of a meltdown, actually, the main risk are flying radionuclides carried by the wind, particles of strontium 90 and cesium 137 which have very long half lives. These particles will continue to emit gamma rays for decades, and unlike beta or alpha particles, can penetrate deep into biological tissue including bone marrow. After a thousand meters, more than 99% of the 1 million electron-volt gamma rays have been absorbed by the air, so it is not a matter of the meltdown beaming radiation at people nearby, but where and how far wind can carry radionuclides of plutonium 241, strontium 90, and cesium 137. Most other radionuclides decay into benign isotopes within days or hours.
Geothermal: Fusion’s little sister
The low thermal conductivity and porosity of the crust, the technical difficulty of lowering drilling costs, and induced seismicity, bode poorly for geothermal and risk rendering it only a marginal player in the future energy mix
A relevant discussion of all the competing energy systems is required in order to evaluate the relative strength and standing of the high altitude wind generator. In doing so, we have reviewed nuclear (both uranium and thorium), existing hydrocarbon systems, and even geothermal.
For those that are interesting in developing advanced deep drilling technology for applications other than oil and gas, “heat mining” is the prime candidate. For those unsatisfied by terrestrial energy harvesting schemes, be they solar or wind, it seems only obvious to the astute energy engineer to look down upon the crust for heat. The mantle is a block of molten iron and nickel whose heat emanates from the radioactive decay of thorium, uranium, and other trace isotopes. But heat does not only emanate from these decaying isotopes as they form lighter elements with a mass deficit, yielding energy, it also emanates from the slow cooling of the mantle’s initial formation temperature. This residual source of heat is more than mankind could possibly consume, but most of it is inaccessible for reasons of distance and geology. But this source of heat should not be confused with renewable forms of heat such as the sun or its downstream cousin: the wind. In strictly scientific terms, this mantle residual heat is not by any means a renewable source, since it will gradually decay until it cools down completely. But within anthropogenic terms, this heat budget might as well be treated infinite. For all practical intents, man is limited to drilling about 12 or about 50,000 feet with present surface driven rotary bits. Such a depth is difficult to visualize on paper, one way to visualize what such a depth represents is to look out the window of an airliner at cruising altitude when cloud cover is sparse. The typical cruising altitude of a wide-body airliner is 12 kilometers, one has to imagine a contiguous tube stretching out this entire distance! Due to differences in thermal conductivity, elevation, and tectonic activity (magma intrusion, presence of aquifers that transfer heat through advection), certain localities have more heat available at shallower depths. If there is such a thing as a geothermal industry, it practically exists solely in Iceland where magma intrusion and highly active aquifers transport enough heat to where it is nearly 200°C as a mere 1.5-2 kilometers in the “Hengill” site. In a strictly thermodynamic sense, there are two forms of geothermal well, one being a convective system, which is highly effective and currently exploited, and the other being a conductive system which is presently unexploited. A number of sites possess thermal gradients in excess of 35°C/km, these locations are found in Iceland, Western Italy, the Anatolian Peninsula, many parts of Australia, and the Pannonian basin in Hungary and much of Japan, although a lack of accurate data exists for much of the earth. A geothermal gradient of 35°C/km can be found in about 2.8% of the U.S landmass, principally in the Great Basin, Mojave, Sonoran, and Chihuahuan deserts. These sites may be highly attractive to prospective drillers due to low land costs and a propitious regulatory environment due to a lack of population density. Drilling technology, while no doubt subject to a number of exogenous physical limitations, is still nonetheless a primarily technical problem, in which fewer restrictive natural barriers are present, one that can be designed to perform at levels significantly than its baseline performance through the augmentation of an array of ancillary components. Geothermal, or crustal heat extraction, is primarily a non-technological and physics problem, one in which natural and restrictive variables such as thermal conductivity, porosity, geology, rock density, and thermal diffusivity limit performance. This dichotomy is critical to understand and should not be overlooked. Engineered techniques cannot fundamentally alter these natural variables and parameters that affect them or significantly change thee degree to which these natural parameters permit or forbid further exploitation. In fact, one can argue that the lack of geothermal energy deployment is not due to the popularly adduced problem. In fact, before we continue, it is important to highlight the inherent problematic nature of the word “challenge” which following the word technical or technological. The fact that rock has low thermal conductivity is not a “challenge”, it is an attribute indifferent to our pessimistic categorization, this mutable connotation should be dispensed with entirely. This peculiar phenomenon is the result of the immense success of communication and computational technology that paints the false picture of technical omnipotence and the infinite mutability of everything around us. Perhaps the best example of this elusive “infinite mutability” is the subject of man-made fusion. The belief that simply using a high enough temperature and a tight enough magnetic confinement one can replicate the multi-hundred billion bar core pressures found in even small stellar bodies like brown dwarfs, which are only 0.075 times the mass of the sun and not even high enough to sustain fusion, speaks for the lack of scientific consistency and unfounded technological optimism. Stellar bodies such as the sun have core pressures of 265 billion bar, and Brown Dwarfs boast core pressures of 100 billion bar but do not achieve any nuclear reactions and merely produce intense glowing red thermal radiation. The highest pressure achieved by a man-made Tokamak is 3-10 bar! But according to modern physics, “theory” backed up with much constructed mathematical dogma insists that if temperature is raised high enough, then somehow high pressure is not needed! But this defies all understanding of ionized gases, or ordinary gases for that matter. The higher the temperature of a gas body, the further apart gas molecules collect, making it ever more difficult to overcome the ever elusive Coulomb barrier. While this brief inquiry into the impossibility of man-made fusion is not relevant to drilling technology or geothermal energy, it is relevant to our perspective that one must strictly partition technique, which represents at best a crude art and often haphazard endeavor, from naturally defined attributes that obey strict scientific laws and physical constants. The conclusion of this statement is that any geothermal endeavor will be rigidly constrained by these physical attributes which characterize the upper crust, and will not be nearly as receptive to man’s contrivances and techniques than commonly assumed.
In our criticism of geothermal, Christophe Pochari Energietechnik could be argued to have a conflict of interest since we are promoting a form of wind energy technology and therefore could be viewed as feeling threatened by the geothermal industry’s potential future success. The reality is quite the opposite, we have developed an advanced electro-drill using a highly novel strategy of cooling the down-hole motor which has to remain undisclosed due to a pending patent. But what can be said is that the technology is conceptually proven and is merely a synthesis of existing technology into a novel package. It represents the only technically viable method for drilling deep wells to access very hot dry rock reservoirs. If anything, we would stand to gain tremendously in the event of a successful geothermal development scenario since the drilling technology in question is really only useful for geothermal, since natural gas and oil rarely occur below the shallow sedimentary deposit. But due to the extreme caution we take before proposing any new idea, to avoid misleading the public, investors, and for the sake of scientific integrity itself, we cannot help but to remain extremely conservative, even if that means being “pessimistic”, when discussing geothermal energy. To cut to the chase, the primary reason we are pessimistic is the fundamental physics of the crust. We can develop the best drill in the world and even if the drill can be operated cheaply, the elephant in the room is how on earth these deep holes will actually yield enough heat to justify the massive investment needed. The issue is therefore fundamentally a physics problem, and not one that is receptive to technical solutions. The two issues are the low porosity of the crust and the low thermal diffusivity of the crust. These two attributes of the silicate molecules that make up the crust make it extremely difficult to extract meaningful quantities of thermal energy from a given mass of rock over an extended period of time. The first issue relates to the low porosity and high degree of compression of the deep crust. By deep, we mean anything over 7 km. Geothermal advocates claim that all we have to do is drill enough “injection wells” and pump water at higher pressure and tens of megawatts of thermal energy will suddenly come rushing out like a geyser. But real-world experience with hydrocracking geothermal wells, what the industry calls “EGS” or enhanced geothermal systems, suggests otherwise. Dozens of attempts have been made all over the world to drill 3-5 km wells in bedrock and use water pressure to induce fracturing and none have yielded more than a meager few megawatts. The current and only viable method to extract heat from low-porosity rock bodies is to somehow hope that if enough water is pumped into the well for long enough, existing fissures will open, the rock will form millions of tiny cracks, what they now realize are “wing” cracks which form when cracks from on slip plane of an angle primary crack. Water will then percolate by forming a massive heat exchanger with many square kilometers of surface. The puzzling question is that if hydrofracturing technology is as mature and developed as geothermal proponents make it out to be, why is existing drilling technology not used to dot the landscape with 3-4 km wells in impervious crystalline rock?
The reason to be suspicious is that existing drilling technologies can more than easily reach temperatures of under 350°C, which is the point where PDC bits begin degrading rapidly. 320°C is the typical exit temperature of a pressurized when fission reactor, it is hot enough to generate electricity at up to 35% efficiency. Many geologies around the world have gradients as sharp as 40°C/km where a depth of only 5 km will produce heat of 200°C, being not much colder than a small steam turbine boiler which has efficiencies of 20%, this is enough to extract a sizeable amount of power. But virtually no widespread deployment of something as trivial as drilling two holes, pumping water in it, and driving turbines, is happening. Instead, the “industry”, if one can call it that, insists that the abject failure of so-called EGS is a rather a “drilling problem”, pointing the blame not at themselves for failing to extract enough energy from the dozens of attempts, but at the drilling industry for not having the “right” high-temperature drill bits! This seems like a glaring admission of guilt. They continue to gripe about how drilling costs are “exponential” with depth, which is not even technically accurate, and even if it is, there are more than enough places on earth where depths of only 5 km are sufficiently hot to justify the investment, and 5 km is not even considered deep with current drilling technology. The hard truth is that this purported energy panacea is not happening because each time drillers spend millions on boring a hole into the rock, and millions more are spent casing, grouting, installing blowout preventers, and pumping water, they are met with miserable energy output and rapidly declining output due to thermal drawdown. Another red flag is the lack of scrutiny and criticism the industry receives. Geothermal, while not receiving the attention that solar and wind does, does not seem to incur much criticism, especially from a technical angle. News articles abound on gripe about the issues of solar, wind, or another so-called renewable, but there is little to no serious discussion on how viable these hydrofracking schemes really are. There is immense criticism of nuclear, and even quite a bit of criticism of electric vehicle batteries, both far from perfect technologies, but we have yet to see anyone adduce serious criticism on how geothermally is plagued by two physics issues: the fact that rock is an insulator and not a conductor! and the fact that fracturing deep strong granitic rock seems inherently difficult and even perhaps impossible compared to soft shallow sedimentary rocks like shale.
Our personal opinion is that the geothermal “industry” really does not exist as a standalone entity made of well-meaning individuals trying to promote an idea they believe in. Of course, the individuals staffing these various startups that dot the geothermal landscape probably do fit that bill, but the driving force and financial backers are but cynical opportunists. There is a widespread and truly baffling consensus among experts that modern industrial civilization, namely in the West, will magically “pivot” away from fossil fuels and become an entirely carbon-free society. It is thus highly probable that most of the interest in geothermal is simply a clever business decision on behalf of the oil and gas industry to label itself as “dual-use” (not plutonium!), and even as a defense measure against the unwarranted persecution it receives from environmentalists. Geothermal stands as the only energy technology that could possibly provide even just a tiny fraction of the present demand for drilling systems, including rigs, bits, and the entire oil and gas paraphernalia they currently boast. If decarbonization does truly occur, their investors, board members, advisors/consultants are whispering in their ears telling them to find ways to “deploy” their assets in some green endeavor, however technically unproven, to avoid a situation where they are left with trillions in “stranded assets”.
It’s actually possible to go over most of the salient details on the problems with geothermal and why it will likely never be a large contributor in a relatively short text.
Hardly anyone can argue geothermal is a “convenient” source of primary energy. Deep holes must be drilled in the hard rocky crust at great depths which comes at an immense materiel and manpower cost. Wages for rig operators are high due to the inherent danger of the work and rapid wear and breakdown of equipment is commonplace. Gigantic 30-meter tall rigs must be erected and multi-hundred-ton drill bits suspending kilometers in the earth. Steel casing must then be inserted and sealed and cemented place with concrete or grout, otherwise, the high-pressure injection water will just seep up the gap between the rock and the metal casing rather than cracking the dense compact rock below. Water will take the path of least resistance if there is not a very effective seal somehow along the bore, much of the energy of the fracturing water will be squandered since it will travel into the soft sedimentary layer above. The metal casing also corrodies due to the presence of chlorides and sulfides so its lifespan is unlikely to exceed a few decades. But unlike an oil and gas well where energy just sprays out in your face, for a well to produce thermal energy, a massive volume of fractured rock has to be generated in order for the water to pick up heat from the rock. If this cannot be achieved, the well will simply be capped and abandoned and the investment will have been in vain. Unlike a solar or wind farm where there is something left physically present that can be recovered for scrap value or rebuilt, the cost of a well is primarily directed towards the earth and placing long steel pipes into these holes, there is nothing recoverable, once the money is spent, its a sunk cost. Lastly, when this water injection takes place, it naturally displaces volume in the rock body, this creation of additional volumes disturbs the crust and causes vibration, since energy is always conserved, this hydraulic displacement energy is rapidly released in the form of pulses, which invariably results in mild to even moderate seismic activity. This is not an issue in unpopulated regions, but since the entire raison d’etre of geothermal is to be the so-called “baseload”, accordingly, many proponents advocate building plants outside of major consumption centers. Even if these earthquakes are relatively mild, usually below a Richter scale of 5, and even if the region is outside of major plate boundaries, tremors will irritate the local population and potentially result in a campaign to stop the program altogether. Two microquakes were already experienced during good stimulation in Switzerland and South Korea and both projects were swiftly canceled. All it will take is one bad earthquake causes cinderblocks to crush a few elderly women and geothermal with hydrocracking is done for good just like with nuclear. The worst that can happen is a wind turbine kills a cow by falling over in a storm. Until hydrocarbons become so scarce that people become extremely desperate and accept even the worse solutions, it’s very unlikely this extremely difficult technology will be widely deployed, especially when photovoltaic becomes cheaper and there is immense room for improving existing wind turbines, both in the tower and drivetrain technology. There is also a very serious risk that advances in thermal or ammonia energy storage make much of geothermal’s purported advantages obsolete. In the event of truly extreme desperation and the energy predicament becoming truly grave, which it is currently not except for certain parts of Europe, environmental regulations to be eventually relaxed, and investors will favor more dams and expensive pressurized water reactors to provide far more rapidly deployable energy than the entirely unproven scheme of deep hydrofracking. Climate change fears alone are not sufficient to provide the impetus to develop inconvenient, expensive, and potentially socially disruptive forms of energy.
And this forces us to bring up the elephant in the room again, and that is the fundamental motivation behind the development of these technologies in the first place. Few any longer advocate for alternative energy as a way to mitigate depleting oil and gas reserves. “Shale” and “Tight oil” has shut the mouths of peak oil doomers and Malthusians alike. This view, a resource depletion perspective, is now considered anachronistic and is met with ridicule. Perhaps the last to hold this “outdated” view is the late Texas oil “baron” T Boone Pickens, who, fearing imminent depletion of precious hydrocarbon resources, rushed to build as many wind turbines as humanly possible under what has been dubbed the “Pickens plan”.
Returning to the inevitable nightmare that geothermal will face.
We should first state that the geothermal industry is at best worth a few hundred million annually, while wind a solar combined are 100 billion-plus dollar enterprises with 50-year track records of operational success. Wind turbines and solar panels might not be nuclear reactor-level power density, but they perform as expected for two decades and generate very low direct LCOE if one excludes grid hookup and storage costs. The paradox of increasing residential electricity prices in all the countries that have installed photovoltaic and wind despite these two technologies declining in price is entirely due to the unrealistic expectation that they are integrated into power grids directly.
Geothermal has a serious risk of repeating the failed hype cycle of nuclear, with early proponents claiming uranium PWRs would produce power “too cheap to meter”. A half-century later, the nuclear industry is a gigantic waste heap of bureaucracy, delayed projects, and massive cost overruns. Fast forward to the 21st century and the trusty methane molecule has proven the resource the last resource for European consumers. Were it not for liquified natural gas, most of European industry would have to close down unless a massive effort to mine domestic sources of coal was initiated. Offshore wind is finding itself short of shallow maritime real estate, and photovoltaic does not warrant installation in regions with an irradiance less than 1700 kWh/kWp nor is there enough land to install these mega-farms, so there is no choice but to rely on a technology centuries old, burning a hydrocarbon to produce heat and to convert this heat to mechanical power. George Westinghouse would not be taken aback by our energy landscape, he might even be surprised to learn how little it has advanced. This is no less than a serious indictment to the grifters who hype breakthrough energy technologies or even proponents of advanced reactor designs. The reality is even if modern man can etch a transistor 4 nanometers in diameter in a silicon wafer using ultraviolet light, he cannot overturn the laws of thermodynamics or the elemental composition of the earth and still has to resort to “primitive” technology of burning what is most probably decomposed keratin.
Since geothermal wells need to be approved, permitted, and seismic reports have to take place, they can take a years if not decades to come online. While this may also be the case with a wind or solar farm, it only applies to urban areas. But since wind and solar do not generate baseload power, there is no real incentive to place them on the grid anyway, a much better strategy would simply be to pack the best windiest and sunniest sites with these inherently mobile powerplants, and either use the energy to produce storable fuels (ammonia) or use to heat molten salt to delivery to consumers directly by converting the molten sodium to electricity at the powerplant and putting it on high voltage lines, or alternatively, simply transporting the molten salt containers directly to consumption centers.
Speaking of geographic mobility, while many may view a wind turbine or solar farm as an inherently stationary asset, it is really quite mobile in fact. A wind turbine, especially a self-tensioning high-altitude machine, can be disassembled in mere days and transported anywhere in the world, massively increasing its value. Everyone believes their chosen method is superior, this is a natural psychological bias that tends to distort our perception. An impartial analysis is critical to avoid confusion and to reduce the risk of misallocation of capital. Proponents of geothermal argue the resource is potentially far more scalable than photovoltaic or wind. In comparison to conventional wind, (note we should avoid comparing existing wind turbines and compare them only to high-altitude turbines), geothermal does not appear to possess any intrinsic cost or power density advantage. For example, if we add up the amount of steel needed to case the wells this alone may very well result in an equivalent material consumption per kW compared to improved wind turbines. A high-altitude wind 800 kW wind turbine can be constructed in a factory at high output for around twice the cost of the raw materials, principally alloys of steel, for around $250,000 with more efficient manufacturing processes, (not that this number seems contradictory to current industry figure, but that’s the whole part of this article!). In contrast, the minimum drilling cost per 5 km well is at least ten million, even if drilling costs are brought down to a minimum, both direct consumables and capital expenditure from equipment wear down and usage is at least 2.5 million, since the number of wells per plant is at least two, an equivalent 800 kW geothermal plant will cost at least ten times more than the wind turbine, but it will not last any longer since one the fracture zone is depleted, the energy output falls drastically. To produce a multi-megawatt geothermal plant, dozens of wells must be drilled, both injection wells and extraction wells. The power output per well may only be a few hundred kW, resulting in a cost per kW in excess of a pressurized water reactor, or at least $3000/kW. Moreover, the cost of a geothermal well is not subject to improvements in manufacturing efficiency and technical innovation, most of the cost is the usage and wear down of expensive mechanical equipment, manpower, site infrastructure, trucking, permitting, and legions of environmental reports, prospecting, etc. If we examine the surface area power density over the life of the plant, unless a very deep fracture zone can be created, the power density is unlikely to surpass photovoltaic and it will very unlikely surpass high-altitude wind, especially in the best sites such as the U.S Midwest, Southern Argentina, and North Africa.
The usual answer from the geothermal crowd is that photovoltaic and wind are not “baseload”, which is a fancy word for the power output being either constant or modulable. Grids require a constant frequency and more importantly, the ability to actively fine-tune the delivery of current to customers to avoid having to load shed. In any electrical system, no more current can be drawn than can be produced, there is a misconception that somehow too much power can be “drained” from the grid damaging it. This is true to some extent since a sudden load will cause the current to spike potentially damaging circuit breakers or overheating transformers. But the amount of current available is directly related to the output of the dynamos themselves, any user of a Generac knows this, you cannot damage a generator by connecting to a large current sink, the number of electrons produced by the dynamo is strictly finite and cannot be exceeded.
But a grid still requires the ability to suddenly produce a burst of current when everyone turns the lights on and turns on the stove, if one cannot “dump” this power onto the mains within a few minutes, load shedding is required. The same can be said when demand falls sharply during night-time or when people are at work during the day, if the generator for whatever reason cannot be slowed down, curtailed, or “shunted” of current into some conductive body is required.
Grids get around this issue by having a fixed quantity of power plants to meet the minimum average hourly usage and accounting for the difference by selectively adding or removing additional capacity with rapidly initiated power plants, namely gas turbines. Of course, before gas turbines became widespread in the latter half of the 20th century, steam turbines would have their flow rates reduced or increase or large reciprocating gas engines would be used. Modern power grids are kept to within 200 millihertz of the standard 50 or 60 Hz frequency. When the current drawn exceeds generation, the frequency falls slightly and vice versa.
Returning to the claims of geothermal’s advantage of being “base-load”, even this claim is doubtful because it assumes no progress can occur in non-battery energy storage, which is wrong. In the conventional dogma, batteries and pure hydrogen (not ammonia!) are the only energy storage solutions, with molten metals receiving little attention due to their flammability and a general consensus that salt molecules are the best option.
Demystifying drilling technology and geothermal energy
Rock is not an “infinite source” of energy. Aside from drilling, which is likely somewhat improvable with better technology, the critical limitation is not technological ,but rather a purely physical limitation arising from the sluggish thermal diffusivity of crustal rock, of which the most common is plagioclase feldspar. Besides the slow rate of thermal transport in the crust, the difficulty of creating effective heat transfer volume through hydro-fracking makes geothermal energy itself far more uncertain and challenging than the drilling technology itself. The upper crust is assumed to have a thermal conductivity of 2.1 W/m-K, with a relatively high heat capacity of 790-1100 J/kg-K. With a moderately high density of around 2650 kg/m3, these numbers translate into a very sluggish thermal diffusivity, the most crucial variable in determining how fast we can “draw” heat from a given rock mass. Many people mistakenly assume thermal conductivity is the only metric that matters, this is incorrect. Thermal diffusivity is the crucial variable because it is a direct measurement of the propagation rate or speed at which thermal energy (heat) travels across a surface of a material measured in square meters or millimeters per second. Thermal conductivity measures the total flux of energy across an arbitrary body with a given temperature difference, but it does not measure the distance this thermal energy travels. Thermal diffusivity is arrived at by dividing the thermal conductivity by the heat capacity multiplying by the density. Thermal diffusivity, unlike thermal conductivity, takes into account the material’s ability to absorb heat as it conducts. When heat flows through a body which has a temperature gradient (which is a tautology since no heat can move without a gradient) some of the heat is reabsorbed by the material’s depleted thermal energy, thermal diffusivity adjusts for density and conductivity, and heat capacity to estimate how fast thermal energy can move in a solid material, gas or liquid after subtracting the energy used up re-heating the cooled or warmed body. A material with a low density, high conductivity, and low heat capacity, will have a very high thermal diffusivity since there is little mass and heat capacity to absorb the energy that is propagating across the material. Conversely, if the material has low conductivity, high density, and high heat capacity (exactly what rock is!), the thermal diffusivity will be sluggish since the bulk of the energy traveling is reabsorbed by the dense high heat capacity material. It might seem as if we want a high heat capacity in our rock, after all, if we reduce the temperature of a given rock mass by x amount, the power available is directly a function of the heat capacity. But unfortunately, the situation is not so simple, because if we draw down an arbitrary section of rock around or geothermal well flow area, we have temporarily “stolen” the heat of that rock and transferred it into our flowing water which is then pumped to the surface. This energy has now been permanently removed from the rock and the rock body is now infinitesimally colder. If we then continue to draw heat down from this rock mass since our water is still flowing, we will now be pulling heat from an arbitrary rock section gradually further away from the well water flow area, so heat must now spend more time to flow across the just-depleted rock. But since we are constantly sucking this heat out, this energy that is now flowing due to the temperature difference will not go to replenishing the rock since we are constantly depleting it, the difference between the depletion rate and the supply rate is proportional to the mean distance between the “draw-down” distance. As this process repeats, the radius of “thermally drawn” rock will grow as the inverse square of time around the water flow area infinitely. Since heat flow is a function of temperature difference, the more we cool the rock the more energy actually flows, so in this respect, this is exactly what we want. But since this heat flow is immediately captured, the rate at which this heat flow travels from the outer radius of the flow area to the center determines the amount of energy we can extract per hour. The mathematics now becomes interesting, because the equation for thermal penetration length or thermal penetration rate is the square root of 2 times the thermal diffusivity coefficient and the time, thermal penetration is thus directly proportional to the square root of time. Therefore, the speed at which heat propagates is very fast at the center but slows down logarithmically towards the outer radius. If we double the elapsed time from which heat can travel, the distance reached grows by only 1.4142 times. This inverse logarithmic relationship causes well bore output to sharply fall in the first few hundred hours of operation and then level off only very gradually declining. 1.4142 is an irrational number and happens to be the square root of 2. The equation is written as √2αt, where α is the diffusivity coefficient and t is time. The diffusivity coefficient is also sometimes denoted as d or k. A substantial portion of the earth’s heat core and mantle heat budget is residual heat from its formation, the balance is isotopic decay. Anyone who claims geothermal is renewable is ignorant of thermodynamics, of which many people unfortunately are. Photovoltaic in comparison is not a finite source because one is tapping into a constant stream of photons, and it would be, by definition, physically impossible to capture more of them than are arriving because it would require an invisible solar panel to allow them to be stacked in front of other! Since a solar panel can only capture 18% of the prevailing ultraviolet and visible flux, one cannot drain down this source, only tap it to its maximum, but never deplete it. Wind is like solar, you cannot pack more wind turbines in a square kilometer than the minimum wake losses permit, so once you max out the area, the energy source is tapped out, but it does not decline since only a tiny fraction of the wind’s kinetic energy is captured by the turbines and in theory, keeps going on forever as the wind blows. In contrast, geothermal is no different than petroleum or oil, only in relative scale, it is still a finite source. This slow thermal diffusivity limits the amount of power extractable to between 9.5 and 19 watts per kg of rock over its lifetime depending on the geothermal gradient and the minimum temperature required by the steam turbine.
The available power from a well is very easy to calculate. Simply find out how long the “thermal drawdown” period is in seconds (this is the desired well life and an entirely arbitrary number), multiply that by the thermal diffusivity coefficient, multiply it by two and then arrive at its square root. This will give the distance of thermal penetration across the elapsed timeframe. Then take this distance that heat travels in fifty years and add up the volume of rock that represents and find the energy that a given temperature drop represents. Since the velocity of thermal inertia is the inverse square of the distance, if distance increases by two times, the time taken grows by four times. As the thermal drawdown region grows in radius around the pumped liquid flow path, the power output of the unit declines logarithmically until it is close to zero. It makes no difference whether you extract heat from the sides of the well, a fissure at the bottom, or from horizontally drilled holes such as the “EavorLoop”. The geometry, surface area, orientation, or number of flow paths, have no bearing on the thermal budget of the region that surrounds these flow paths unless of course new flow areas are generated to keep up with this drawdown. For fixed flow geometries, the thermal diffusivity number alone determines the thermal budget available and the lifespan of a given flow area. In fact, many people assume going deeper results in more energy, but as most things are counterintuitive, the reality is a bit more complex. While the total heat flux is always greater at high temperatures because the potential temperature difference can be raised, the rate at which heat is replenished actually drops somewhat compared to lower temperatures. This is because the thermal diffusivity is thermally dependent, hotter atoms are vibrating more intensely and repel each other and inhibit heat transfer. For rock, thermal conductivity decreases with temperature and heat capacity increases. Since we have mentioned many times before that thermal diffusivity is the sine qua none, drawing the bulk of the heat from greater depths actually slows down thermal penetration. This means that the thermal drawdown regions grow slower (the distance between the hot rock and the flow area enlarges) and hence the mean power density falls. Thermal diffusivity drops for all rock types as temperature increases.
Thermal diffusivity does increase with pressure since the atoms of the rock are packed more tightly together, but the increase is very gradual and thus the hydrostatic gradient does not compensate the loss from temperature. A further drop in the rock temperature will increase the heat flux and power output, but it cannot alter the thermal diffusivity, which is a temperature invariant constant, so the well will simply produce a larger amount of power over a shorter time, but its mean power output per unit of time is constant. A faster thermal drawdown means a large radius of rock’s energy absorbed, therefore distance for heat to travel, and hence a small energy value. If a longer life of the well is desired, more land is simply used, and the net number is the same as a shorter well life that produces more power. Cooling a material faster does not yield more energy, it yields more energy in a shorter window. The law of proportionality and the conservation of energy dictate this. Technology, no matter how advanced, cannot alter this basic physical law, and no geothermal well will be able to produce a continuous sum of energy over its life.
The realities of “hot dry geothermal”
The only modern textbook on the subject is “Mining the Earth’s Heat: Hot Dry Rock Geothermal Energy” which provides a glimpse into the rock mechanics and explains the strategy without corporate spin. The idea of pumping water into a rock body to induce fissuring is not new, it was developed by multiple individuals independently in the 1970s motivated by the energy crisis. The U.S. government commissioned numerous reports on the prospects of this scheme and abundant literature is available publicly on Google Books or OSTI. Bob Potter working at Atomic Energy Agency issued the first patent in 1972 on the principle of fracturing rocks using water pressure, US3786858A “Method of extracting heat from dry geothermal reservoirs”. Potter was envisioning wells not much deeper than 5 km in his patent. The underlying physics and fluid mechanics undoubtedly bode well for the concept. Since any material contracts when it cools, as thermal energy is drawn down, the rate of fracturing is expected to increase along with the flow of water since the viscosity of water is significantly lower at high temperatures. The combination of these two beneficial phenomena may serve to partially arrest the natural thermal drawdown of a given rock fissure volume. The idea is extremely simple, use a slight excess of pressure above the formation pressure to slowly enlarge existing micro-fissures. Most rocks have extremely low tensile and shear strength, so intuitively if any stress is applied to a rock that is not entirely isostatic it will fracture. Since rocks are highly anisotropic materials, a uniform pressure distribution will not result in uniform stress in the rock, but rather concentrating stress in the weakest direction. The crust is thought to be rich in tiny fissures or fault lines that exist perpendicular to the hydrostatic gradient. Since the force of gravity manifests in the vertical plane, displacing the rock tangent to the surface plane is much easier. While the permeability of the crust is estimated to be in the nano-darcy range, existing micro cracks are liable to be expanded slowly over time with enough pressure, although there is considerable variability in the presence of pre-existing micro cracks. Many hot dry geothermal projects were attempted in the 1970s and 1980s, but few produced more than a few MW, and to this day, there is not a single (>8 km) hot dry “hydrofracked” well in the world. Perhaps the best case study is the Fenton hill well in New Mexico. The Fenton hill hot dry well barely managed to produce 4-5 MWe after years of stimulation. While there were several successful runs where fissures were formed after substantial pumping effort, many wells refuse to “open” and power output remained low. An article by science writer Richard A Kerr in Science Magazine entitled “Hot Dry Rock: Problems, Promise” chronicles some interesting findings without placing a positive spin on it. Kerr is quoted as saying: “After a decade of hard lessons and limited success, tapping the enormous heat reserves in rock too dry to yield steam or hot water on its own faces more challenges”. He goes on to say: “No one has figured out why some fractures open and others do not”. “Hot dry rock has proved to be a recalcitrant, even devious foe, demanding greater respect and subtlety of design than pioneers in the field imagined”. Kerr describes how some of the wells drilled and hydraulically stimulated that performed well were because of natural openings and not due to the hydraulic fracturing itself, leading to false positives. A major scientific error made by geothermal proponents is comparing existing hydraulic fracturing strategies used in highly brittle, soft sedimentary shale rock to that of dense, strong, hard igneous, and metamorphic rocks. Not only do these rocks possess vastly different shear and tensile strengths, they have greatly differing levels of porosity. If there is little to no porosity, establishing sufficient volume for water flow can be difficult. Logically, it must follow that it is considerably harder to induce fracturing in highly compressed crystalline rock over a soft shallow shale formation barely a few kilometers deep. Crust porosity decreases sharply below 4 km, at 5 km the pore space is about 11-12%, but at 10 km it drops to less than 3%. At 4 km, the depth of the Fenton Hill project, the crust still contains at least 20% sedimentary rock, but at 10 km the sedimentary share is close to 0%. Moreover, quartz becomes quite ductile above 350°C and would be much more liable to elastically deforming as opposed to shearing at depths below 10 km. One thing can be said, regardless of how successful the efforts at developing new drilling technologies are, the entire effort is ultimately determined by how much and if we can fissure deep rock strata. If it should prove too difficult to reliably induce fissuring to achieve the necessary surface area and flow path, geothermal energy will remain in obscurity regardless of the efficacy of improved drilling. This will mean any alternative drilling technology will need to be seen as an asset to aid in deep gas exploration in hard rock strata and not merely a geothermal technology or else the development risk is too high since there is a lack of established market demand. Natural gas will remain the energetic backbone of modern civilization for decades to come, and therefore any technology that drill deep into the earth to tap into hydrocarbons that were pulled down due to subduction. The Z-44 Chayvo Well, which as part of the Sakhalin-I drilling project, reached a depth of 12.36 km and continues to extract natural gas. Considering the only successful and proven site was Fenton Hill which was only 3 km, where hydrostatic pressure is much less than at 12 km, one cannot extrapolate these results to ultra-deep 10+ km wells. Another suspicious fact to highlight is why we don’t see mature medium depth rotary drilling technology being used to say 7 km depths to reach temperatures of 245°C? These depths are well within the reach of current cobalt-bonded poly-crystalline diamond bits. This suggests that our thesis is correct, that is a lack of certitude regarding rock fracturing mechanics, which ultimately determines power yield, dissuades investment in geothermal. Lastly, even if effective deep hydro-fracturing can be developed successfully, induced seismicitiy remains a non-technical impediment to widespread geothermal adoption and may force it in a select few unpopulated geographies with low active seismic risk potential. Drilling a 10 km deep well in the Hayward Fault Zone may not be a very bright idea. It should be also be emphasized that crack growth in the hydrofracturing zone cannot be directly observed with any down-bore instrumentation, it is physically impossible to know what kind and how much growth has occurred. The only real way to know how much rock has been fractured is by using the heat output of the well as a proxy, but even this is quite crude.
Another major limitation of “EGS” is the issue of thermal drawdown. A phenomenon called “flow channeling” typically occurs due to the preferential flow of water towards larger aperture fracture zones, this causes more heat to be pulled from this fracture zones and induces thermal induced fracture which further enlarges these zones, causing even more water to flow. This disproportionate flow in a small portion of the total fracture area tends to concentrate the heat extraction area to a small volume of rock and causes rapid thermal drawdown leading to declining power output. This issue, along with the low permeability (caused by low porosity), slow thermal diffusion, and inextricably high drilling cost will plague geothermal for centuries to come, no matter how many attempts are made.
In short, there are simply too many fundamental physics problems and uncertainties that don’t show signs of being amenable to technical solutions that will forbid geothermal from plying a major role in the energy future. One thing can be said, a $300,000 high altitude wind turbine spinning away in the Nebraska Sandhills will always outperform a multi-million dollar “hydrofracked” plant by a long shot.
It is interesting that the most energy dense technology we know of is unable to scale, whereas very low energy density technologies like photovoltaic and even hydropower, can in theory scale to worldwide primary energy needs without using up all the available input materials. Realistically, none of these technologies will likely ever be scaled to anywhere close to these theoretical scales needed to replace hydrocarbons, neither the high-altitude wind generator nor existing photovoltaic arrays. Christophe Pochari Energietechnik strongly shares to a philosophy of technological and scientific conservatism, progress in technology has been slower and less dramatic than made out to be popular media, and most if not all technologies suffer major limitations to their proliferation. But regardless, it is amazing to realize and even humbling that the mighty hydrocarbon molecule burned in our three century old engines can produce more energy than the most powerful nuclear fission reactors known to man. For photovoltaic to scale, unlike the high-altitude wind generator, a large area has to be cleared and leveled in order for the panel mounting frames to be installed securely. Since deserts feature highly abrasive wind storms, especially durable protective coverings must be installed on the panels. Photovoltaic has a gross power density of just over 108 MW/km2, since the average “capacity” factor is 1900 kWh/kWp after DC losses, the net power density is somewhere over 22.58 MW/km2. Since global energy demand is 14,000,000 MW, around 622,000 km2 would be needed, or approximately 35% the size of Libya. Such a farm could in theory be constructed, but it would be highly pregnable to terrorism and would require an armed force presence around its perimeter at all time to prevent sabotage. One of the central disadvantages of photovoltaic is manufacturing complexity and the relative infrastructure intensity of the silica reduction reactors, trichlorosilane reactors, Czochralski crystal growing furnaces, phosphorous and boron doping machines, and wire cutting for wafer fabrication. Compared to a high-altitude wind generator which is machined and fabricated using cold rolled steel, the manufacturing complexity of a photovoltaic panel is many times greater. The current photovoltaic module manufacturing capacity is 170,000 MW, of which 87.1% is in China, Vietnam, South Korea, and Malaysia. China alone produced 70% of the world polycrystalline and monocrystalline modules. Assuming the world-grid farm would be built in a 20 year period, a total of 3.93 times current production would be needed, assuming all other consumption would be diverted. Such a number is by no means unrealistic, the skilled workforce of East Asia is plenty large enough to ramp up production by such a margin, especially considering the labor inputs are relatively minimal. Of course this is impossible since the free market will merely sell to the highest bidder, for such a project to succeed, a special relationship has to be establishment between the major Chinese photovoltaic manufacturers and the “global grid commission”. Of course, since the panel modules cannot be expected to last more than 20 years, this number has to be doubled since for every panel installed, another must be replaced in 20 years, so an additional module needs to be produced as a “reserve”. The farm would then feed into large high frequency AC conductors (to minimize transformer cost and size by using nanocrystalline cores) to feed Europe’s baseload mains, whatever is not drawn by the grid is siphoned off into the modularized ammonia synthesizers and sent by vessel to consumption centers across the world where the ammonia is reformed into hydrogen and burned in high efficiency closed cycle oxy-hydrogen argon powerplants (see https://hydrostatussystems.com/2019/03/01/closed-cycle-hydrogen-internal-combustion-engine-technology/#:~:text=A%20conventional%20two%20or%20four,monatomic%20inert%20gas%20(argon)) at 60% efficiency. Of course, irrespective of how good the technology is, there would still be a need for a global commission, tasked by a major government, willing to use military force to secure the project. Many of the North African governments in question might demand excessive royalties for the use of their land, there may be a need for military intervention to topple and put into place more supportive governments. This seems beyond the capabilities of the presently languishing West, if any such “megaproject” occurs, evidence points to China.
Our vision with the high-altitude wind generator is not necessarily scalability, we do not believe the world will ever free itself entirely from its dependence on hydrocarbons, coal and natural gas (methane) will continue to power the world likely for centuries irrespective of political babble. The world will undoubtedly have a larger penetration of photovoltaic, high-altitude wind generators, hydropower, and perhaps some fission here and there, but the preponderance of our BTUs will still emanate from the combustion of carbon hydrides. As opposed to scaling the technology to meet world energy demand, which we believe is going to be challenging, but perhaps not only from a purely technical perspective, but from a sociological and geopolitical perspective, we propose to facilitate the formation of a number of “zones” of ultra low cost electricity, much like Norway’s near free hydropower allowed for heavy water production via electrolysis or nitric acid synthesis from Birkeland-Eyde. We foresee the construction of vast electricity-intensive industries in the U.S Midwest and Southern Argentina, along with Western Sahara and Mauritania. These facilities will not come anywhere close to “powering the world” but they will produce a large fraction of these energy-intensive commodities. For example, modularized containerized ammonia production is something Christophe Pochari Energietechnik has extensively investigated. Let us assume we wanted to produce 100% of global ammonia, which totals 200,000,000 tons. Each ton requires 8.5 MW of electricity to produce, primarily for the electrolysis of the hydrogen. If we had a site in Southern Argentina or Nebraska at 12 m/s, we would need only 6,200 square kilometers, or barely 3% of Nebraska’s land, and a similar number for Southern Argentina. Such a number is manageable, if we add aluminum to the list, we might increase this a few percentage points, but it still remains manageable, whereas powering 100% of global primary energy is practically impossible from an infrastructure perspective, even though it’s theoretically possible.
Aside from enabling previously economically impossible technologies (electrochemical machining), a number of industrial processes can be linked directly to the high-altitude wind generator site in high wind speed geographies and draw the variable but near free power from the high altitude turbine. Since we want to construct these harvesting machines in regions with high-velocity winds, we must be able to transport cost-effectively the produced energetically embodied substance. If we locate the turbine in Santa Cruz Province of Argentina, we can cheaply transport the product a short distance by truck to a small port to load an ocean-going vessel to transport the valuable product to centers of consumption. No power grid in the world can connect the vast wind potential of Southern Argentina to consumption centers other than ammonia, aluminum, silicon, or synthetic hydrocarbons. But rather than building expensive centralized ammonia plants, modularized plants mass-produced in factories and stacked to form a large unit can be installed for a tiny fraction of the cost of present-day systems. A number of industrial processes can be modularized and integrated with high-altitude wind generator’s allowing for very cheap silicon reduction, magnesium from seawater, the comminution of very low-grade ore, aluminum electrolysis, salt electrolysis (Chlor-alkali, allowing for cheap hydrazine), and very inexpensive hydrogen that can be used for ammonia production, as fuel directly, or for CO2 free iron oxide reduction. The levelized cost of energy (LCOE) from a pure tension tower-mounted high-efficiency wind turbine would be approximately 0.075¢/kWh over a thirty-year life for direct system amortization. Including 5-year gearbox replacement, an additional 0.0059¢ are added, increasing the LCOE to 0.08¢. We can also add the cost of replacing the gear oil, which is performed twice a year for satisfactory performance and longevity. Gear oil is typically around €1.5-2/liter, for our gearbox, we have a total of 200 liters of oil, an oil change will therefor cost €200. Since it takes two hours of labor to replace the gear oil, we can add another $70 assuming a wage of $35/hr. The cost of the gear oil replacement is not significant enough to be considered for an LCOE analysis. The blades constructed from high-strength steel can easily outlast the fiberglass benchmark of 20 years since their stress amplitudes are far below the stresses needed to cause early fatigue failure, usually multiple hundreds of megapascals. The gearbox is the only component that has to be replaced frequently. The manufacturing cost of the turbine is low due to our use of much less steel per kW than corresponding systems and our use of concatenated manufacturing, with a heavy use of CNC machining, which is cheap, and no use of forging, a far more expensive manufacturing process due to low volume. The total labor to construct the 800 kW machine is 4900 hours. The major costs of the machine are self-evident, the materials, labor for assembly, and the amortization of the tools and equipment needed for their fabrication.
Direct “hard” manufacturing cost
Price is an entirely relative and a highly liable concept, while cost is technological, a reflection of how efficiently a given thing is being made. All manufactured goods are comprised of hard material, unless we’re making a hot air balloon that is mostly just that: air. Our product is made out of something valuable, mostly metal or plastic. Metal is not free, it has to be dug up, processed, and melted into a useful starting material. Metals also vary exceedingly in scarcity, if your component is made up primarily of scarce elements, no degree of technology or ingenuity will lower its price. On the other hand, if something is made out of polyethylene or steel and it remains expensive, something is wrong with the manufacturing process or the way the product is designed. In other words, systems made of low cost abundant materials should converge to their material + labor costs or there is an inefficient process that is bottlenecking the manufacturing.
The degree of precision and or tolerances required by a product can heavily affect the cost. A truck axle is a relatively low precision item, while an ICBM stage decoupling mechanism is a high precious item, even if they are made out of the same material their costs might differ by 100-fold.
If something is machined, the hardness of the alloy has a very significant impact on its cost. If the metal that is to be cut on a lathe is milled before it is quenched or hardened, the wear rate on the tool piece is greatly reduced. But imagine a scenario where the metal component had to be machined after it was hardened, in that case, a diamond or cubic boron nitride insert would be required, which cost far more than tungsten carbide, around €500/kg vs €45/kg. Worst yet, some alloys cannot ever be machined due to their tendency to “work harden” and can only be machined using electrochemical machining. Electrochemical machining is so energy intensive that any country that has electricity over 5¢/kWh cannot produce a cost-effective part using ECM. This is why one cannot use “rules of thumb” when trying to estimate cost, it is an impossibility, because cost is a highly complicated application and case-specific phenomenon, that relies more on physical, metallurgical, geological, chemical, thermodynamic, friction, kinetic, abrasive, and mechanical factors than economics.
Another critical factor is assembly and the labor intensity of such. A battleship is expensive to build because of the need for nearly 800 man hours per gross ton of ship, while a container ship only requires 60 hours per ton. The large number of weapons, sensors, machines, and components that have to be installed on the battleship all have to be bolted down, wired, and inspected, which cannot be automated and hence relies on dexterous manual labor. In contrast, the container ship merely needs to be welded together and have its single engine installed before it is ready for use. Many electronic components have to be manually soldered, wires snipped and routed through labyrinthine patterns and inspected, this requires human labor, whereas a semiconductor is 1000x more complex, but is produced entirely with machines, and hence despite its inordinately high complexity, may be cheaper to manufacture than a crude circuit board. Semiconductors are perhaps the best case study of highly complicated and difficult components that have been successfully made cheap, whereas furniture upholstery, despite being centuries old and rather simple, remains expensive due to the low productivity of manual upholstery. Garment and textiles remain an industry with very low automation penetration, since large pools of mostly female labor in Bangladesh can be readily utilized. If this labor pool were to dry up for whatever reason, no robotic system in existence can replace the reliable human worker, so clothing would dramatically escalate in price and Western consumers would simply buy far fewer clothes since it would be economically prohibitive to pay a Norwegian person 200 kroner an hour to sit on a sewing machine all day long. High-cost Western labor is only globally competitive if used for high-value-added manufacturing, for example, a tunnel boring machine or high-end laser-guided weapon systems, whose value is high enough to justify the expensive labor. The cost of the Western worker exceeds the marginal value of the textile he has produced, making it an economic impossibility to “re-shore” textiles. In fact, most of the debate around “reshoring” and its antonym “offshoring” fails to comprehend the concept of marginal value and labor intensity.
The most vivid example of this inherent variability in cost is best exemplified by the dramatically different levels of purchasing power and living costs across different countries. A house in Poland might cost €50,000, but one in California costs €700,000, but the home requires the same amount of labor and material to construct, yet the “market” perceives a difference sufficient enough to warrant a order of magnitude difference in its “price”. A solar panel kit bought from “Solar City” might cost €10,000, but one from a Chinese supplier bought directly, only €2000. If you buy a ground-beef patty from Safeway, it might be 10x higher than if bought in bulk from Cargill. Different levels of per-capita wealth lead to different “prices” for the same items, despite being made of the same material and requiring the same amount of labor to produce. The average Russian has an income of 55,000 rubles a month, about €900, but such an income is considered “poverty” in America or England. But this €900 can go very far in Russia, affording the person food, housing, and enough discretionary spending to buy an electronic item on Aliexpress once a year. The average Russian is not starving on his lower income, and can eat just as many calories, drive as many miles, or live in as many meters of floorspace as his European counterpart on a tenth of the income. In fact, since the cost of energy is so much lower in Russia, he might actually enjoy a more luxurious lifestyle than his Italian or German counterpart, despite earning a fraction of the salary. The Russian can keep his heat on all day long while his counterpart in Europe has to put on a jacket. The average cell phone connection cost in China is 30 RMB a month, around €5, while in the U.S the price is over €50, ten times more. Yet the cell towers are the exact same, American cell towers are not made of gold or something! the technology is identical, but it is “priced” far more than its baseline technology cost because Western consumers are wealthier and hence corporations can charge them more to make more profit. Therefore, the concept of price, which is entirely economic and financial, must be detached from the concept of cost, which is entirely technological. Cost is a function of the complexity, time, and resource intensity of a particular product. In other words, cost is what is takes to do something at the minimum, but it does not include markup or obscene price inflation caused by market distortions, monopolies, or government subsidies, let alone taxation. Price is a function of market conditions, financial and governmental policies, speculation, psychology, local conditions, profit, competitive dynamics, taxes, intellectual property, and business practices. The aforementioned list is highly variable, they are by no means fixed, whereas cost is, since cost is always and everywhere technological. Swiss watches are expensive precisely because they are not mass-produced but instead handcrafted by highly paid workers. The same watch can be produced in a Chinese factory for the price of the stainless steel and assembly labor, which might total less than 10 dollars per unit, whereas the Swiss watch, which weighs the same, might be priced at over €10,000. The Chinese watch might be less reliable or durable, but for it to equal the price of the Swiss watch, it would need to fail 1000 times more often, which is highly unlikely. Of course, as we mentioned, there is a tremendous difference between cost and price, cost is often mistaken for price and vice versa. The Swiss watch probably doesn’t cost directly €10,000 to produce in the factory, even with handcrafted labor, much of the price is pure markup, profit, which can be justified because of the prestige of the brand and consumer psychology. In the industrial realm, it is more difficult to command such a high markup, but markup nonetheless exists due to proprietary knowledge and competitive advantages which lead to a market with only a small number of big players. Patents and “intellectual property” (which is an oxymoron) can serve to inflate the price of technologies above production costs since only one firm can build the product. Thankfully, most technologies around us are ubiquitous and produced by a number of firms, but there are cases especially in the early phase of development where prices can greatly exceeds costs due to price gauging which is ultimately facilitated by the monopoly that a patent offers. It is not only a patent that protects an invention or technology competition, but rather the skill and intelligence of the designer and inventor that allows him to dominate the market through more shrewd engineering. The inventor is the one with the vision and ability to design and market is product. Who better than the inventor to design and commercialize the product? A shortsighted and covetous businessperson will lack the technological knowhow to succeed, he is best left for activities like retail where he makes money by marking up stuff other people produced. Existing firms are too conservative and myopic to embark on anything excessively novel. When hydraulic excavators began replacing cable-pulley shovels in the 1960s, the major manufactures of cable shovels failed to adapt and disappeared, leaving only the new entrants who had pioneered the hydraulic design. The same will happen with wind turbine platforms, the existing industry will never adapt and change its ways, it will continue building bulky and heavy cold rolled steel towers until it cannot survive in the Darwinian business landscape.
Perhaps the best example of the mismatch between cost and price is oil produced in the Middle East. Because Saudi Arabia is a sovereign nation, it possesses complete ownership of all its petroleum resources, but since oil is a global market, there is no reason for the price to be geographically dependent since tankers can transport it anywhere. This means that even though Saudi Arabian oil might only cost €15 per barrel to produce, it will still sell for the international price, whatever that might be. This is also the case for most mining operations, which generate huge profits since virtually no one can realistically compete with an open pit nickel or copper mine. The owner of the mine can jack up his prices say 50% above production cost to generate a healthy return without fearing new entrants, but if he tries going above 50%, he may incentivize new entrants, so there is always an upper limit on “price gauging”, but the limit can be quite high, especially in high barrier to entry sectors. In short, anyone who is in a position where it is very difficult to directly compete will sell its product at a price that is usually much greater than the direct “cost”.
Overhead, real estate costs, amortization of equipment not related to the production of the product, low volumes for niche items, passing on costs from unprofitable activities, markup accumulation, interest payments for high-interest loans, idle labor, excessive overhead, and a profligate management, can contribute to excessive costs compared to baseline production requirements in material and labor. The reason it almost always costs far more to buy a manufactured good, especially niche ones at the retail level than to make it oneself with the tools and labor directly is because of the phenomenon of supplier “markup accumulation”. By the time the raw billet has arrived at the factory subcontractors pile on their margins and overhead each time the unit is traded up the production cycle. By the time the raw piece of steel ends up as a finished product, twenty different supplies have all extracted their share of the value add, leaving the consumer with a ridiculously overpriced piece of metal. If one buys a bearing from SKF or a machining tool-piece from Sandvik Coromat, they might pay 100x times the cost of the steel that went into making the bearing even including the cost of machining, forging, and heat treating the bearing. This is why government-procured items cost so much more than in the private sector, the defense industry is an egregious practitioner of this scheme of supplier profit pileup, since it is taxpayer money, there is no incentive to conserve it and defense contractors will charge obscene markup precisely because they can. The reason Russian military equipment is so much cheaper is not that they possess some secret recipe to manufacture things far more efficiently, it is that the companies are state-owned, so it would be like the government ripping itself off! While the local wages do make some difference, it is not enough to account for the vast difference between U.S and Russian equipment. The average U.S manufacturing wage is $21/hr while the average Russian wage is $5.4/hr. Besides mere markup and price gouging, another factor is superfluity, U.S weapon systems are inordinately complex while Russian systems are designed to be simple, reliable, repairable, and manufacturable, even if performance might be slightly lower. U.S weapon systems make excessive use of high tech electronics, sensors, and exotic materials, while Russian systems are designed for massive production volume and low unit cost.
Of course, such an example does not apply for components whose cost is primarily the function of expensive raw material, for example, synthetic diamonds cannot be made “cheaply” since the pressures required are so immense it places extremely severe requirements on the anvils and production machinery, not to mention the fact the diamond crystallizes very slowly, so a given diamond anvil produces very little diamond per hour. Nor can catalytic converters ever be made less expensive than they currently are, since they use grams of palladium and platinum which is worth €50,000/kg. This is why historically conglomeration was always advantageous as it offered control over costs and eliminated supplier markup and overhead. “In-sourcing” is where the manufacturer performs most of the input process except for perhaps mining of the metal internally to reduce costs dramatically, not through efficiency or technological improvement, but simply by eliminating overhead and markup from the production cycle. Each manufacturing steps represent an addition of value where a less refined piece of material is turned into a more refined product, of which the producer demands a price that the market is forced to command, if this is done oneself, all that value is yours and looks as if the cost is lower, but the cost is the same, the same amount of labor and material went it, it’s just that all the profits, overhead and markup went to you instead. “In-sourcing” makes the most sense for things like machining, casting, or most metal fabrication. If the production is outsourced unless the contract is for a very huge volume, the markup will be very high. Another factor is simply resourcefulness, ingenuity, and creativity. Many companies are sclerotic institutions staffed by management types who have no real grasp of technology or manufacturing and are merely tasked with making shareholder returns. It is always possible to make tiny innovations in the process, there is almost unlimited potential for tiny improvements here and there. If the manufacturing is done yourself, there is always the opportunity to make improvements, while if you outsource, your are dependent on the company’s engineering sagacity, which may be far from stellar.
Now that we have explained why one cannot simply look at the “price” of something and assume that’s what it costs to produce it, we can go over the primary determinant of price and that is materials.
Another example of supplier markup is the case of tungsten carbide insert manufacturing. For example, a commonly used face milling insert for CNC machines is the APMT1135PDER, this insert has a volume of 0.144 cm3, since the density of tungsten carbide/cobalt binder is 14.5 grams/cm3, it contains 0.0020 kg of cemented tungsten carbide. The price of this insert is typically $1/pc, translating into a cost per kg of $500, even though tungsten carbide is worth only $45/kg.
One may be surprised to hear that for machining hard steels, the number one cost is not the machine or the labor of the operator, it is rather the cost of replacing the carbide inserts as frequently as every hour required during machining high hardness steels, in the HRC >28+ range. A paper titled “Wear Mechanisms of Milling Inserts: Dry and Wet Cutting,” Wear Processes In Manufacturing by Jie Gu Simon C. Tung found that C5 carbide inserts can last up to 3 hours at a machining speed of 307 m/min with a feed per tooth of 0.27 mm using coolant.
Data from the excellent Youtube channel CncFrezar from Slovakia found a life in excess of 3 hours for cutting pre-hardened injection mold steel 1.2343 X37CrMoV5-1 using a 52 mm cutter at a feed rate of 4000 mm/min at a spindle speed of 990 r/min, which mathematically translates to a feed per tooth of 0.8mm. The depth of cut was 0.7mm. At a tempering temperature of 700°C the steel has a hardness of 30 HRC. The owner of the channel confirmed he could get 3.5 hours out of the typical carbide insert machining the same steel. The durability of the carbide insert is primarily a function of the binder concentration, a lower concentration produces a part with less hardness but that is much tougher.
Note that all these above-quoted figures are adjusted for the hardness difference between steel and aluminum-zinc alloys, yielding a non-linear increase in MRR. No data exists for carbide insert life for aluminum machining, so we have used data for steel machining and extrapolated based on Archard’s law of wear.
“When roughing with spindle speeds of 30,000 rpm at 60 KW power in reliable production conditions, an MRR of 4,000 cc/min aluminum is achieved, similarly an MMR of 5,000 cc/min is achieved with 80 KW of power. Machines featuring an updated reinforced spindle with 120 KW are able to remove 8,000 cc/min aluminum”.
A single face-mill insert usually costs upwards of €1, a single face mill may have up to 12 inserts for maximum productivity, costing €12/hr just for the inserts. This means the cost of the inserts exceeds the cost of the labor needed to run the plant for many countries where manufacturing labor costs are below €8/hr. In consequence of this fact, it makes tremendous sense for the factory owner to incorporate a small insert production facility in-house so that he can continuously recycle the inserts and recover the cost of the tungsten carbide, rather than throw it away and recuperate a tiny fraction from the recycle value. The value of the used insert is practically zero, making recyclability a critical strategy in cost reduction. Cemented tungsten carbide by mass is 88-90% tungsten carbide and 9.5-10.5% cobalt, with a small amount of vanadium and chromium. The spot price for cobalt is about €50/kg, while the spot price for tungsten is only ¥115,000/ton, or €17,200/ton, far cheaper than cobalt. Tungsten reserves are estimated to be 3.2 million tons, with China holding over half at 1.8 million tons. Since tungsten carbide is by mass 93% tungsten, the price per kg for cobalt cemented tungsten carbide is €5/kg for the cobalt and €14.39/kg for the tungsten carbide, carbon adds negligible cost. Before tungsten carbide can be used as a machining insert, it must be mixed into the binder, this is done by turning the metallic tungsten into a powder, the same is done for the cobalt. Since the melting point of tungsten is so high, a gas atomizer cannot be used. A chemical oxide reduction process is chosen instead, but this need not be a concern for a small factory, since the owner would be wise to buy scrap tungsten carbide on the market which retails in bulk for less than €5000/ton. If virgin tungsten is to be used, the tungsten is reacted with iron forming an iron-tungsten compound which is then reacted with sodium chloride and hydrogen chloride to eventually form ammonium paratungstate which is then reduced to tungsten oxide and finally from tungsten oxide to metallic tungsten in small 10 micron granules. The reaction is complex and slow, which makes recycling existing carbide scraps a far more attractive option, since the cobalt binder is already present. The basic process for producing the inserts is the formation of the powder, the pressing of the powder, and the sintering of the powder, and then the grinding and coating of the inserts. The inserts are then milled for optimal surface sharpness and coated, milling of carbide inserts is called “peripheral grinding”. A tiny amount of carbide, usually only a few tens of cubic millimeters at best, is removed from the insert forming an extremely sharp edge. The grinding wheel is made of cubic boron nitride and poly-crystalline diamond since to grind tungsten carbide a harder material is needed. The wear rate for the grinding wheel is around 70 microns of face wear per 4000 mm3 per mm of face area removed according to data published by Sumitomo. Material removal rates for grinding wheels are abbreviated differently than for CNC machining. For grinding, a “specific Metal Removal Rate”, or SMRR, is used to represent the rate of material removal per unit of wheel contact width. Contact width refers to the area touching the specimen to be ground down. Since at best 10 cubic millimeters are removed for each insert, and and material removal rates exceed 5 cubic millimeters per second, the time to grind each insert is only 1.99 seconds. Realistically we can assign one minute of grinding for each insert for conservatism, in that case, a total of 0.24 cubic millimeters of boron nitride/polycrystalline diamond grinding wheel surface is expended per cubic millimeter of tungsten carbide removed. Since the cost of cubic boron nitride is around €650/kg and polycrystalline diamond around €0.06/carat (1 kg equals 5000 carats), the cost per kg is €300. Since the density of the two compounds is around 3 grams/cm3, we will expend 0.0072 grams of material per insert, or 0.42¢. It should be mentioned that the diamond wheel by volume consists not 100% of diamond or boron nitride, but it also includes a resin binder which occupies a significant portion of the volume, so our estimates are therefore very conservative. Phenol resin and polyimide resin are common binding resins for diamond powder grinding wheels.
Therefore, we can conclude the cost of grinding is minimal. It would be possible to recycle the precious boron nitride/polycrystalline diamond compound, but since it will be mixed with a larger concentration of tungsten carbide, appropriate separation schemes would be needed. So out of intellectual caution, we should add the cost of replacing the diamond wheel itself and not include the value of the potentially recyclable compound.
A critically important number for the techno-economics of insert production. The wear rate is only 75 microns for a total material removal of 4000 mm3/mm for grinding tungsten carbide. Note that this means that each 1 millimeter of face area will wear 70-80 microns per 4000 mm3/mm, not the entire face of the grinding wheel which may be as large as the total insert width.
Now we can add the cost of the grinding wheel turning machine. Taizhou Liyou Precision Machinery Co makes a peripheral insert grinding machine for $80,000, if one insert is machined per minute, the cost per insert is $0.16 for the 1st year, since the machine is expected to last for at least 10 years, the amortized cost per insert is only $0.016.
By far the most capital extensive portion of insert manufacturing is the sintering furnace, which retail from $300,000-600,000 for 1000-1500 kg-batch capacity units.
A 1500 kg batch capacity vacuum furnace capable of operating at 1550°C can be purchased for $600,000 on Alibaba.com from Zigong Cemented Carbide Corp Ltd. Since the sintering time is usually around 10 hours, the furnace cost per kg/yr is $0.46 for the 1st year, and barely 2¢/kg over the realistic lifespan of the unit. Since a vacuum furnace has no moving parts, it is expected its life will be in excess of 15 years. A large vacuum sintering furnace on Ebay from 2006 sells for a high price, suggesting it has plenty of useful life left. A vacuum furnace consists of a diffusion pump for creating the vacuum, a vacuum chamber made of steel and insulated with refractory insulation, and induction coils for heating the specimens inside. The power consumption of the furnace is 820 KVA, at a power factor of 0.8, the furnace uses 6560 kWh per 1500 kg batch of tungsten carbide. At a power cost of $0.05/kWh, the electricity cost is $0.21/kg. Now we must press the powder into the shape of the insert, this is done by machining a hard steel female mold and placing the male mold on the press. A standard powder press can be bought for between $20-100,000 depending on tonnage, size, and brand and country of origin.
A 400 ton powder press costs $40,000 on Alibaba by Shandong Jianha Baofa Heavy Industry, the press would be reconfigured to accommodate a die shaped to the tool-piece geometry desired. Coating and milling adds negligible cost, but an additional hundred thousand can be added to be conservative, the net cost per kg of carbide pressed is still below $1.
Since it is preferable to use scrap carbide and since the CNC factory must continuously recycle its used inserts, a viable method to effectively recover the powder and re-press and sinter it is crucial. To recover the recycled carbide, the tool-pieces are poured in molten zinc, the molten zinc dissolves the cobalt binder from the carbide, the zinc is then evaporated leaving the brittle carbide cobalt mixture ready to be crushed. Upon reacting with zinc, the carbide tungsten composite swells forming a brittle and porous “cake”. The zinc is then condensed and remelted for the process to repeat. The process is extremely effective and low cost since the zinc is continuously recycled.
Since effectively no raw material is wasted except for a the small abrasion indent in the insert, 90%+ of the original insert is still available for material recovery, reducing the carbide consumption to effectively zero and rendering only the operational cost of the plant as a consideration. The total processing cost is realistically around $1-1.5/kg of sintered carbide, yielding a cost per insert of $0.10 per unit including grinding and coating. A very conservative cost of $0.2 per insert can be used, which is perfectly in accordance with their retail price of around $0.80-1/unit. Since our turbine requires around 10 cubic materials of material removal for CNC machining, a 150mm 24 insert mill with a feed per tooth of 0.27mm, a cutting depth of 1 mm, and a cutting speed of 250 m/min can remove 512 cubic centimeters per minute, so our total machining time is 300 hours. Since the inserts cost 20¢/pc, the total insert replacement cost is $1,440. Even if we bought the inserts on the market for between $0.8-1/pc, the cost would still only be $5,760 per turbine.
Labor and assembly
If the labor-intensive manufacturing is done in a Western country (Germany, Spain, Italy, France) where worker wages for assembly workers and CNC operators are around $15-20/hour excluding benefits, the total direct labor cost would be be only $45,000/unit. In the U.S where wages are slightly higher, around $22-25 before benefits, the cost is more in the order of $60,000 per unit. If the manufacturing is done in a lower-cost country such as India, the cost would be only $7,300 since the average wage for a CNC operator in India is ₹13,000/month. The manufacturing is not done in a low-wage country due to quality concerns, since the use of ultra-high productivity machining affords low labor intensity, a higher quality well-paid labor supply can be utilized. The cost of the manufacturing aluminum 7068 (AlZn7.5Mg2.5Cu2) with non-baseload electricity and zinc at a market price of $2,900 is $1.5/kg, the direct material cost is thus around $52,500 since the weight of the unit is 35,000 kg. Since the unit is destined to be exported to North America, there is no VAT tax paid in the country of manufacturing. The U.S had no import duties on wind turbines.
Now we must add up the cost of the major capital equipment needed to manufacture the components, namely the CNC mill, lathe, and cold rolling and vacuum melting equipment. The total for this equipment is around $500,000 for a 24-unit-per-year plant, the lifespan of the CNC and lathe is 20,000 hours, and the lifespan for the vacuum melting and cold rolling plant is 100,000 hours. The total for the equipment translates to $12.5/hour, if each turbine takes 365 hours to manufacture, the cost of the capital equipment amortization per unit is $4562.
Icing is a concern for wind turbines that operate in very frigid climates. Christophe Pochari Energietechnik plans on leasing land from sheep farmers in Argentina to install its wind turbine and use them to export ammonia to Europe by medium-sized low-speed hydrogen turbine propelled vessels. Rio Gallegos and most of the arid plains of Southern Argentina in the Santa Cruz province and Magellan territory are very dry, with only 250 mm of annual precipitation. The average temperature in Rio Gallegos is 8°C, and since our turbine is 200 meters taller than normal turbines, we can subtract 1.2°C for the average lapse rate of 6°C/1000m, the air around our turbine is 1.2°C cooler than a standard 100-meter turbine. Most of the coastal portion of the Santa Cruz province is classified as a class 1 ice zone, which means the power loss to icing-induced aerodynamic drag is 0 to 0.5% of gross power output. The IEA divides up the different icing conditions into five zones from increasing to decreasing icing concentration in air, most of Nebraska is located in the class 2 zone, which estimates a power loss of 2.5%. In colder regions, class 3 imposes a loss of up to 7.5% of annual power, blade heating can be employed. If the frontal surface of the blade is heated using resistive heating (running high amp DC through the steel surface), the convective heat transfer from the cold air blowing at 12 or more meters per second is around 731 watts per square meter if the surface is held to 10°C and the air is minus fifteen. Conventional fiberglass blades are incapable of using resistive heating due to fiberglass’s low thermal conductivity, another major advantage of high-strength vacuum melted steel blades.
The above estimate is for a rather aggressive heating regime of maintaining the frontal area of the blade at 15°C while the surrounding air is -26°C, or roughly the mean temperature of the Yamalo-Nenets Autonomous Okrug in Siberia where very high mean wind speeds of 10.8+ m/s are available at 200 meters. Such a heat regime consumes 1590 watts per square meter, of which the frontal area of the blade critical to lift generation is around 40 square meters, the entire blade is 108 square meters. 56 kW’s of heat is available from the ammonia plant, so if we were to install the turbine in a class III area, we would need to expend 136 kW of power, or roughly 10%. In most installation sites, it will be an IEA class I or II, but in Newfoundland, Labrador, much of Norway and Sweden, Iceland, and Siberia, a class III is present. While it may be obvious to some, one cannot compare aircraft electrical de-icing power requirements with that of wind turbines, since the air velocity and hence convective losses are orders of magnitude higher since the number of molecular collisions is a function of the speed. Below is an estimate from the book Wind Energy Systems: Optimising Design and Construction for Safe and Reliable Operation by John Dalsgaard Sørensen and Jens Nørkær Sørensen.
Note that there estimate is considerably smaller than ours since they have a smaller T2 (temperature difference). The heat capacity of the blade is not the issue, it takes very little energy to warm a small sheet of steel, and since the leading edge sheet can be insulated to prevent heat transfer to the rest of the blade that is not desired to be heated, the bulk of the heat losses are convective.
Using the Boltzmann constant, we can estimate the radiative heat flux, which for a ten-degree body, is equal to 365 watts per square meter, placing our total heat flux to the surrounding air is 1100 watts at a surface temperature of 10°C, 10°C above freezing. Conductive heat transfer would be negligible, since air is an insulator. Since our high-altitude wind generator produces electrical energy to drive a modularized ammonia plant, an excess heat of nearly 350 kWh from the formation of the NH3 product combined with the excess heat of compressing hydrogen gas to 300 bar generates a total of 450-500 kWh of 300-degree heat that can be pumped into the blades in very frigid climates to minimize power losses, allowing 22 square meters of blade area to be heated, roughly enough to cover most of the leading edge plus a small area behind the leading edge. This would allow the turbine to operate in cold climates without excessive energetic penalties.
IEA ice class map, note that the regions in which we propose installing the high-altitude wind generator fall in classes 1 to 2, which less than 2.5% annual losses to icing.
Enercon’s pumped hot gas blade de-icing is perfect for the NH3 synthesizer turbine, which produces far more waste heat than needed to keep ice particles from forming on the active surface area of the wind.
Manufacturability and cost reduction through high-speed aluminum machining
Christophe Pochari Energietechnik does not rely on unproven future technologies to lower the manufacturing cost of the turbine. Instead, a number of simple, proven, and rational strategies are employed.
The first strategy is to use a material that is much softer and easier to machine than steel, yet just as strong on a density-adjusted basis. This lowers the direct cost of fabrication by at least 4-fold. By using virtually no hard alloy steels, cutting insert life is dramatically extended. On top of this, the lower hardness places less force on the CNC machine, allowing for the use of lighter and cheaper components. Another factor in the low cost is the use of an open-gantry custom-designed machining device. The machining device consists only of the overhead rail and servos, without the major enclosure which adds weight and cost to the machine. Excluding materials and labor, the primary cost of manufacturing a largely metallic component is machining, turning, forging, casting, and welding. If most if not all these processes are eliminated in favor of only one manufacturing method: high-speed machining: then the cost of fabrication can be brought down to represent only a very small fraction of the total cost. Instead of laborious sheet metal construction, the principal method used to construct airplanes, a solid-machined assembly method is employed. The iso-grid is perhaps one of the most rigid and structurally efficient ways of allocating material. Iso-grids are widely used in spacecraft and other aerospace vehicles where structural efficiency is paramount. It should be noted that the degrees of tolerance required for aerospace components do not transfer over to a wind turbine structure, so the CNC gantry does not need to be as “tight” in its construction as for an aerospace part. Slight mass imbalances in the blades can be corrected by adding or removing small steel or lead weights at the tip, similar to helicopter rotors. It’s important to stress that a fiberglass blade is intrinsically more mass heterogeneous than an even rough machined aluminum iso-grid, due to uneven application of resin and overlapping canvas.
The second strategy is to minimize the size of the major components. By designing each component to reach a manageable size and concatenating these components to form the super-structure using low-fatigue bolted connections, a reduction in rolling cost is achieved alongside a reduction in transportation cost. The single longest component in the 44-meter 750 kW turbine is 10.5 meters, enough to fit on a standard semi-trailer.
The third strategy is to eliminate altogether the use of labor-intensive welding and manual assembly. Unless the manufacturing is performed in a low-wage country where quality is often sacrificed, welding remains difficult to automate and stubbornly resistant to quality control, the result is that weld-intensive components will tend to be expensive. It may come as a surprise that machining a component is cheaper than welding, but this is obvious, since a machining center is a largely autonomous device, with a single operating having the ability to command multiple machines simultaneously.
The fourth strategy is to produce the material indigenously allowing overhead, profit, and indirect operational costs to be removed from the raw material supply. By producing high-purity aluminum in modular Hall-Heroult plants and purchasing the zinc and copper alloying elements on the wholesale market, the cost can be brought down to the direct cost of extracting, refining, electrolyzing, melting, and rolling the metal. By avoiding purchasing the specialized alloy from niche suppliers, who mainly supply the strictly regulated aerospace market, a drastic reduction in cost can be obtained.
The fifth and final strategy is the elimination of cranes during assembly. This is directly netted by the unique self-erection feature of the pneumatic tower and is not a manufacturing-based cost-reduction effect.
The direct machining cost of the module can be estimated by adding up the total time spent in performing what is called “roughing”, where the cutting piece removes the bulk of the material leaving an unpolished surface. The total mass of aluminum used in constructing the primary structural components, excluding the main tubular tower section, experiences an average of 85% material removal. This means if 15,000 kg of aluminum is used in constructing the turbine module, the total mass is 100,000 kg, representing 30 cubic meters of material removed. Since the average speed of machining is up to 4000 cubic centimeters per minute (0.24 cubic meters), the total machining time is 125 hours. A downtime factor of 25% can be included, which incorporates tool piece replacement, machine maintenance, workpiece insertion and removal, clamping, tool piece failures, etc. The total time increases to 160 hours for roughing machines, with an additional 50-60 hours for finishing passes, summing to a total of 215 hours. Since the cost of machining is highly influenced by the carbide insert life and operator labor, the insert life is conservatively assigned an increase to 5 hours, from a baseline of 3 hours achievable with hard steels. If the tool piece uses a total of 8 inserts, the cost per insert is $0.50/pc, the spindle uses 120 kW of power (at 3 cents/kWh), the operator wage is $20/hr, the machine CAPEX is $10/hr ($100,000/unit at 10,000 hr service life before major component overhaul), then the total hourly cost is $38. This places the total machining cost at only $8170. This extremely low number is not because of some magical cost reduction technique, the number is very conservative, it uses prevailing wages for CNC operators in Western countries, market prices for inserts, and a very conservative machine life of only 10,000 hours, when a more realistic number is more like 20-25,000 hours. The power cost for the spindle is highly variable in some countries electricity prices may approach 40 cents/kWh, making the spindle cost alone $48/hr! 3 cents per kWh is roughly the price of a photovoltaic module levelized over half its lifetime. But even with these highly conservative estimates, the direct machining cost is still under $10,000, giving the designer the flexibility to slow down machining speed. This low cost is almost solely attributable to the ultra-high-speed machining strategy using the high-power spindle, afforded only by aluminum’s high softness. Had we used steel, such a high material removal would have been entirely economically prohibitive and outright impossible.
The main iso-grid truss-shaped structural member which cantilevers the turbine hub from the center mounting point on the pneumatic tower. This structure member is machined from a single piece of rolled billet to maximum structural integrity. The image above is a FEA simulation of the structural member subject to a steady-state gravitational load of 2.7 tons per member.
The turbine is not inordinately bulky and large and hence difficult to manufacture, in fact, the nature of the design is highly conducive to machining, where mass-produced and relatively small components make up the bulk of the superstructure. Using a first-principles method, the major components are designed from a manufacturability perspective and then analyzed to see if the performance is comparable to comparable non-manufacturability-centric design philosophy. If the component has similar performance, but is even slighter inferior in longevity, but is much cheaper to produce, it is a superior option. For example, since forging equipment occupies a large footprint, there is an additional cost for real estate. Even in countries with very low wages, such as India, industrial real estate is very expensive, the ability to manufacture a relatively large system using a small amount of space is highly advantageous. Additionally, forging requires multiple workers to manipulate the forging specimen simultaneously. Conventional wind turbine hubs are forged in high-wage countries like Spain or Germany, which accounts for their high cost. A far superior method is to break the hub down into two sections and machine each section with a ubiquitous four-axis CNC machine, where one worker can supervise ten machines at a time. With forging, a worker must manipulate the specimen, and under the forging hammer, usually an electric screw forging press, automation is not possible. The cost of the forging press is very high compared to a CNC mill due to its large weight and mechanical wear attributable to the high cyclic frequency of impact.
A 50% aluminum main-rotor hub assessable with a 4-axis spindle. Each hub is machined from a billet block. The total material removed is 0.45 cubic meters per section, requiring only 5 hours to machine with a material removal rate of 3000 cubic centimeters per minute.
With concatenated built-up component manufacturing, complex parts can be constructed with a moderately sized gantry CNC. With this method, the cost is dramatically reduced since the labor hours are minimized due to the high automation potential of machining, even though the strength may not be as high as a forged specimen, it is more than satisfactory, especially considering the average load on the hub is only a few megapascals but the aluminum has a yield strength of 650 megapascal. The hub is made up of six machined sections only 130 centimeters long, which can be easily machined with a large 2.3-meter x 5 meters sized gantry CNC which cost <$200,000, compared to millions for corresponding forging presses.
The individual hub components are mechanically fastened together to form a single component. If high hardness parts a needing, such as bearings, quenching is performed after machining. A CNC machine is much cheaper, easier to maintain, and footprint friendly than a forging apparatus, not to mention the nearly entirely labor-free nature of the process except for swapping out the specimen and changing the inserts every hour. Forging is relatively rapid as far as material penetration and shaping, but it’s a very rough process and cannot produce a usable final product. Thus, even if forging is used, machining must be performed after. Since machining is less labor intensive, and machining is almost as fast, the cost can often fall under that of forging, especially for very large components where costs escalate beyond a linear relationship with volume. The only labor required is for tool piece replacement, specimen position, and securement, which can be performed on each machine during each startup shutdown interval allowing each worker to handle multiple machines. Forging is not amenable to automation, whereas machining is very much so.
Firstly, the bulky large diameter cold rolled tubular towers are dispensed with, saving a large alone. Secondly, high payload cranes are no longer needed. While cranes themselves are relatively cheap, the need to transport them to rural sites where wind turbines often find themselves is not, moreover, cranes have very slow turnaround times due to the need to assemble them into place since they are too large to transport by truck. Thirdly, for the height we are trying to achieve, notable 350 meters, no crane in commercial existence can work at such heights, only a helicopter can be used, which is too costly.
Thirdly, the use of solid-machined monolith spar aluminum blades saves cost by dramatically reducing the labor intensity of blade manufacturing from fiberglass. The fatigue strength of high-strength non-ferrous alloys such as aluminum 7068 is far superior to the best resin in a fiberglass blade. People often mistakenly assume fiberglass and other resin-reinforced fibers possess infinite or near infinite fatigue life. While the classic concept o the fatigue limit or “endurance” has been shown not to be valid by the late Claude Bathias, steel still nonetheless possesses extraordinary fatigue properties, making things such as railway axles that last for decades possible yet incur 10^9 cycles during their life. While the strict “fatigue limit” itself has been disproven, high-strength aluminum alloys, albeit small specimens tested under piezoelectric high-frequency fatigue testing machines, have been shown to survive to over 10^9 and 10^10 at stress amplitudes of up to 200 MPa. It is interesting to note that while low cycle fatigue is usually manifested by surface cracks, high cycle or ‘gigacycle” fatigue is primarily an internal cracking phenomenon caused by imperfections and foreign contaminants dubbed “inclusions”. Vacuum melting can increase the fatigue strength by up to 200 MPa in steel, while a similar ratio is expected in aluminum zinc alloys. In comparison to a fatigue life of up to 10^9 cycles for stress amplitudes as high 200 MPa, the best resins cannot take much more than a million cycles before delaminating and shearing.
A wind turbine will experience a rotational inertial stress amplitude as the blades rotate from horizontal to vertical planes corresponding exactly to the prevailing frequency of rotation which depends on wind speed, blade diameter and the tip speed ratio. One must remember there is no “centrifugal force” pulling the blade out from the hub, there is only inertia tangential force to the angle of rotation. Centrifugal force generates much confusion, since centrifugal force is put to work in washing machines, ore separation, isotope separation etc, one would assume that an actual stretching force is produced. The reality is while heavier particles will move out of a spinning assembly due to their greater mass, they do not produce any tugging force from the center of rotation, otherwise high speed turbines would fkly apart within seconds of their reaching operating speeds. As the blade spins, it possesses a certain amount of kinetic energy, and this energy wants to push the blade clockwise in the plane of rotation, causing a bending moment at the midpoint, not at the root. This rotational inertial stress amplitude is only 12 MPa for 25 rotations per minute, the stress amplitude is a function of speed, the fast the speed, the higher the inertia on the blade. The second stress amplitude emanates from cyclical wind loads, but this is a very low-frequency phenomenon, since wind speeds vary only across relatively extended time frames, not anywhere close to hertz levels. The third loading regime is the lift-induced torque and subsequent blade root bending. A wind turbine blade for a 44-meter turbine generating 750+ kW will naturally generate 10,000 N of bending force across the entire blade. Note the relative velocity, the speed at which the blades spin through the air medium is much greater than the incoming air velocity, but the direction of this speed would not be in the lift line of the airfoil, otherwise, a wind turbine would be like a helicopter rotor, with the plane of rotation in the same axis as the wind direction. This lift force bends the blade in the direction of the low pressure above the airfoil and generates stress on the root, but this load is not a cyclical load but a largely high amplitude low-frequency load, since the lift is constant as the blade rotates around its axis. The force of the wind produces a low-pressure zone and hence a force is constant with rotation, while it may decrease or increase depending on the temporal distribution of wind speed, it is not a high-frequency phenomenon. When the turbine accelerates and decelerates due to changes in wind velocity, there is stress amplitude generated. For example, if the turbine is spinning at 10 r/min during a slow wind regime, but a sudden gust doubles the wind speed to accelerate it to 25 r/min in only 5 seconds (this would be unprecedented acceleration for a wind turbine since the torque of the motors slows it down), a stress amplitude of 56 MPa is generated at the midsection of the wing spar. The total number of loading cycles for a 30-year blade would be 400 million, far below the fatigue failure of high-strength aluminum-zinc alloys. The greatest stress on wind turbine blades is not found when the turbine is operating routinely, but rather from rare gusts that catch the blades when they are facing the wind at a 90-degree angle from the lift plane, that is flat plate in front of the wind. When the blades are facing the wind, their drag coefficient is very low generating a small bending force. This loading regime, unlike the normative ones, can generate hundreds of MPa of stress, while the ordinary loads can only generate a few tens of MPa, thankfully, their occurrence is remote. Of course, the fatigue numbers derived from gigacycle regime testing of small specimens cannot be extrapolated confidently to large heterogeneous members like a wing spar, since by definition fatigue cracks, both internal or external, are caused by defects in the grain structure, either inclusions of non-metallic components or pores, these defects occur at a specific frequency as a function of volume, hence larger parts will fail earlier.
High altitude ultra-low-cost wind opens up the opportunity to make electrochemical machining a cost-competitive option for very hard metals. Electrochemical machining at 12 volts uses around 7.2 kW per cm3/min. Since a conventional carbide face mill can remove 500 cm3 per minute, the equivalent high volume electrochemical mill would draw 3600 kWh, at a cost of 1 cent from hydropower, the power costs are only 36 per hour, comparable to a CNC machine running in a first world country with an operator being made $20/hr. The downside of electrochemical milling is the large pumping and filtration system required to remove the metal particles and recycle the electrolyte, usually salt or sodium nitrate. The second major disadvantage is the high amperage, since the voltage is below 15 volts but the power requirements are so, one can imagine the need for a massive DC power supply. The cost of a full bridge rectifier power supply is usually around $20-30/kW, for a 3500 kW device at 150 amps/cm2, $105,000 worth of 80 amp 12-volt power supplies are needed, far more than the equivalent cost of a spindle, linear ball actuator, and gantry frame, which amount to little more than $20-50,000 for a 1000x1000mm CNC machine. The principle advantage of electrochemical machining is the machining rate is hardness invariant and there is no issue with work hardening for alloys such as manganese steels. In spite of this advantage, the technology remains uncompetitive with state-of-the-art carbide cutting technologies.
What is the “lifespan” of the high-altitude wind generator?
People often mistakenly assume the lifespan of a wind turbine is fixed at some designated number like 20 years. This is incorrect, one can browse marketplaces such as https://en.wind-turbine.com/ and find models from the early 1990s for sale in operational conditions. Many well maintained wind turbines are pushing 28 years of operation and continue to perform well. A structure does not have an exact lifespan, environmental factors can have a major influence, corrosive environmental dramatically compromise the lifespan of rotating steel components. Offshore wind turbines, which we have stated before are a terrible idea, will not last nearly as long as a wind turbine installed in the dry prairie grass of Kansas. In fact, the very sites which are the windiest are often quite dry, such as the U.S Midwest, a turbine installed in this region can easily last 30 years. If corrosion is inhibited with strong paints or coatings and their frequent replacement is performed, a metal structure, even in a highly corrosive environment can last close to a century. The Golden Gate bridge is still standing perfectly fine as we speak since it is continuously repainted, despite the fact that the iron itself would barely last a decade if left to oxidize in the salty and windy Pacific weather. New York is right on the ocean and yet the Empire State Building is still standing strong since the granite and glass seal the steel frame from the elements.
Wind turbines have limited lifespans, not due to corrosion or environmental degradation, these phenomena can be easily attenuated with technology, but due to the wear of moving parts. A number of man-made metallic structures can last upwards of half a century, including many offshore oil platforms, which despite the extremely antagonistic conditions they find themselves in, can last as long as 40 years. Many of the Gulf of Mexico oil rigs built in the 1970s and 1980s are still operating today. While many of the fasteners used on offshore oil platforms use so-called “duplex” stainless steel, austenitic stainless steel with higher chromium content, lower nickel content, but with higher molybdenum content, most of the structures is mild steel. These “duplex” alloys are only used as fasteners for flanges and bolted components due to their high cost. The bulk of the structure is painted and cathodically protected low alloy steel.
The limiting factor in their lifespan is not environmental corrosion, clearly, the offshore oil and gas industry has shown how to build structures that last a long time in a very corrosive environment. Since most of these turbines will be installed in dry onshore sites, it will be dynamic component wear that limits the life of the system. The dynamic components are subject to wear, no different than bearings in gas turbines, steam turbines, centrifugal compressors, or any other rotating component. In fact, wind turbine bearings, while subject to substantial axial and radial loads, are spinning at relatively slow speeds, so abrasion and friction is actually less than on a steam turbine which might spin at 3600 r/min. The main bearings, gearboxes, and rotor pitch bearings are the primary life-limited components. But just like an old DC-3 airplane that is overhauled and used in the 21st century, the basic frame can last upwards of 50 years if not more, it’s the moving parts that need replacement. Christophe Pochari Energietechnik has designed its gearboxes to be sealed with an argon atmosphere, minimizing oxidization and fire risks. The main dynamic components, the main bearing, gears, gear bearings, pitch bearings, swivel mechanism, electric actuators, yaw sensors, rotor speed sensors, rotor brakes, and dynamo are all life-limited components, but surprisingly, their cost does not represent anywhere close the entirety of the device. The gearbox is designed to be replaced every 5 years, the bearings since they are ceramic, every 15-20 years, and the swivel mechanism actuators and yaw sensors every 15 years. In fact, the sum of the total overhaul cost for the life-limited component represents only 25% of the total system cost, since overhaul means the components are remanufactured, and the material, which comprises over half the cost, is reused. The Pure Tension Tower (PTT) provides it is not corroded, can last half a century, since we know that guy towers have been successfully used for over 50 years.
Therefore, our estimate of the LCOE of the unit is actually quite conservative, because we take the entire capital investment and divide it by 20 years. Since overhaul represents 25% of the upfront cost, we can refurbish the 20-year-old machine to last yet another 20 years. Our LCOE then drops to only 0.042¢/kWh.
The high altitude tower turbine’s position in the broader wind industry
The wind turbine industry is one of the largest single power generation sectors, exceeding the size of the individual thermal generation sectors including Brayton and Rankine. The global wind turbine market was valued at 55 billion as of 2020, as big as the photovoltaic and even bigger than the global gas turbine market, which was valued at 22 billion, steam turbines at 16 billion, diesel generators at 20 billion, and nuclear fission at 38 billion. This is an impressive feat for a sector that did not even exist on the radar as early as the 1990s. By 2030, the wind sector is projected to grow to over 100 billion.
With a new radically improved tower technology, that increases the annual yield for a single turbine by a factor of 3, the industry will grow to new heights. It is not unreasonable to expect a majority of turbines to use the technology where suitable. There may be certain areas where the presence of guy cables is absolutely unacceptable, say next to an air force base where military jets frequently train. It should be noted that just like on communication towers, the cables can be fitted with high visibility lights to minimize the risk of collision. It would also be advisable for large wind farms equipped with these turbines to be marked on the airspace. For the majority of cases, the presence of guy cables or lack thereof, makes little difference, since the wind turbine blades already occupy the airspace to begin with, and collisions can happen with blades and towers, since the guy cables are equally visible thanks to the use of bright LED lights. As wind turbines are noisy and often perceived as an aesthetic nuisance, they are rarely approved in suburban or urban sites, so it makes no difference either way since we will not be building these systems in populated areas. Barely 2% of all U.S land is occupied by human beings in what is defined as “urban”, leaving the rest as pasture, natural parks, government land, forest, and of course agriculture. In Europe, wind energy is often more evocative of the ocean, but even in Europe, the majority of turbines are still installed in rural pastures, where the only living creatures to bother are bovines.
Of course, in the “real world”, not everything looks as good as on paper or on the simulation program, but with man’s present knowledge of materials, friction, aerodynamics, corrosion, and pressure, it’s quite possible to arrive at a high fidelity estimate of real-world performance entirely on paper. There is a common but flawed notion that one has to “build a prototype” before making any claims, and that it “looks good on paper but we don’t know until it’s tested”. There is a fundamental flaw with this stance. Firstly, it presupposes an inability to analyze at a purely analytical stage whether the working principle or enabling concept is able to function as intended based on the design assumption. This would entail as a precondition a lack of conceptual understanding, but we do not find ourselves limited by this problem. To require testing or prototyping is only necessary when the process of anticipatory analysis simply cannot be certain to parallel in the real world, this would only be the case if materials were used whose properties were not yet fully understood, or mechanisms employed whose dynamical operation are far from certain. There are many cases in engineering, such as dam construction where calculations have to be relied upon and material behavior must conform to expectations, because a dam cannot by definition be “tested” or “prototyped” in its full scale and scope prior to its installation. Since each installation is unique due to local geological conditions, it would be impossible to build an accurate prototype of a dam to strictly conform to the end-use conditions. Once installed, testing is useless since by definition since the system will perform the way it will perform irrespective of testing! Rocket launches are a similar case study, since these are instances where testing to see how the system behaviors in its entirety are not possible without putting the system into actual use. One can test the rock motors, turbopumps, or stage coupling systems disparately, but never in unison. A rocket launch could not possibly be “simulated” with 100% accuracy before it was tested in real life, and this testing meant assuming either success of catastrophic failure often with a human toll, meaning all the estimates made by its designers had to be correct. The calculations made in this technology proposal are to the highest fidelity achievable using the knowledge of contemporary literature, there will always be things learned in the field that separate prediction from reality, but these differences will not exceed an acceptable margin. There are many technologies where confident prediction is close to impossible, such as chemistry or metallurgy, it would be arrogant for a drug developer to predict with any high degree of accuracy how a drug will perform until it is tested first in animals and then in humans. In the case of metallurgy, it would not be advisable to make business decisions on a purely theoretical alloy until it has been tested in the real world. But this is neither a drug nor an alloy, this is a working principle, just like any simple mechanism and array of technological methods in practice, it functions at a theoretical level in the same manner it functions in physical actuality. The technology does not make use of exotic materials, mechanisms, or electronics, it is made of earth-abundant materials fabricated with century-old methods. It makes use of principles (pressure) understood by man since the days of Archimedes and Vitruvius, over two thousand years ago. It makes use of materials whose properties can be easily estimated from accumulated experience, the behavior of steel under pressure is easily simulated, or the elastic elongation of a wire rope under tension, something well understood by Victorian science. In summary, there is nothing preventing its deployment but a lack of vision, imagination, and intelligence, there is only the age-old incorrigible human stubbornness, aversion to change, our religious nature, and fear of novelty that stands in the way of this technology or any other truly novel invention. There exists another pernicious factor, vested interests, and arrogant industry executives that feel jealous that the real and useful innovations did not come from them or their coterie.