The IDEA of tower windmills is an attractive one. IF they
only cost 1/10 of what they actually cost to build, and IF they ACTUALLY
supplied more than 1/5 of the electricity they are promoted to allegedly produce,
and if they weren't so complex that they constantly broke down, they
could be great! They might then even be PRACTICAL regarding supplying
electricity! But that REALITY is not likely regarding tower windmills,
providing future electricity. Maybe some day, but no time soon.|
By the way, people get all excited about solar electric panels, but that involves massive optimism! A Network News story recently said that in order to produce as much electricity as a SINGLE nuclear power plant, you would need 50,000 square miles of solar panels! That would be about 33,000,000 acres of solar panels, plus all the area around it to walk on! For comparison, that is TEN TIMES THE TOTAL AREA of the State of Connecticut! And that would only be to replace ONE nuclear power plant, and we currently operate 102 of them! That is about the entire State of Alabama or Illinois, some pretty large States! You might calm down about thinking that the U.S. has any realistic chance of getting substantial amounts of its electricity from solar panels. Part of that is because the inexpensive Gallium Sulfide solar panels are only about 7% efficient.
The very different CW (Community Wind) design described here only costs around 1/8 of what a modern giant tower windmill costs. It even works on a somewhat different process, being more of a Pressure device rather than a Momentum device. Its $1.8 million (US) cost is essentially a combination of about a million dollars of wages for one hundred LOCAL workers and around $800 thousand for needed LOCAL materials, mostly sand and aggregate for the enormous amounts of concrete involved, so essentially the ENTIRE COST REMAINS IN THE LOCAL COMMUNITY. This CW system also intercepts around six times as much wind and wind power as a modern giant tower windmill does; it is also more efficient than even modern high-tech tower windmills are at capturing that power in the wind; and it won't break down the way tower windmills are now regularly demonstrating, as it can be built with only ONE moving part instead of 800!
Re-phrasing this, Choice 1 is to spend $15 million to buy a 200-foot-diameter windmill on a 300-foot-tall tower that can collect wind energy from about 31,000 square feet (3,000 m2) of oncoming wind, but only when the winds happen to have certain speeds. Choice 2 is to spend 1/8 as much, about $1.8 million dollars to LOCALLY BUILD a CW system which can collect wind energy from about 200,000 square feet (18,000 m2) of oncoming wind, more than six times as great an area, and essentially at any and all windspeeds. CW is built by LOCAL workers, meaning jobs, and it is durable in the extreme. CW works fine in any windspeed, where tower windmills do not, and so the CW's overall performance in creating electricity is far greater than tower windmills have. Even the basic operation is quite different, where tower windmills allow a lot of wind to go BETWEEN the rotating blades, while the CW system requires (nearly) all wind energy to be subject to being captured.
The CW system is nearly silent, as compared to the throbbing sounds of tower windmill spinning blades which many people find to be offensive.
The CW system is designed to be LOCAL. No giant corporation would operate a complex wind farm hundreds of miles away from you, where you would have to pay such giant corporations for electricity forever (as you do today!) Instead, the CW system is built within a few miles of YOUR town, it is BUILT BY LOCAL WORKERS and it is OWNED BY YOUR TOWN or SMALL BUSINESSES IN YOUR COMMUNITY. These two approaches at getting electricity from the power in the wind could not be much more different, as the windfarms keep those corporations in control of important aspects of your life, while the CW system gives you enormous new LOCAL independence!
The CW system can realistically COMPLETELY PAY FOR ITS OWN CONSTRUCTION IN AROUND TWO YEARS of supplying electricity to a local community! After that first two years, it is all gravy, essentially free electricity forever!
Nearly any rural town or community can hire around one hundred of its own residents as construction workers to build some structures (primarily fairly simple but very large reinforced concrete walls), which can then provide at least 1.2 megaWatts of electricity locally from wind power (sufficient for about a thousand local houses or other buildings); the total cost involved is low, only around $1.8 million (US) (preferably provided by local businesses or banks), nearly ALL of which then stays in the local community! We happen to be VERY conservative people and we easily could be telling you about the 3 megaWatts of electricity which you might commonly be receiving, or even the 5 megaWatts or even 10 megaWatts which the system COULD produce (during stormy winds). But we prefer to stay with the 1.2 megaWatt amount of electricity that about a thousand American homes generally use in modern life. If and when you receive MORE electricity, we trust that you will not complain!
In the US today, there are people who talk about Infrastructure as the way to create new jobs but they never seem to actually do anything that helps. If ten thousand rural US towns or communities each build this CW system, NOW, that WILL provide excellent employment and wages for a million construction workers and collectively create at least 12,000 megaWatts or 12 gigaWatts of electricity, without most of the large losses of the electric Power Grid. Depending on legal stuff regarding the land ownership and Zoning and some Engineering choices, construction could begin within WEEKS, meaning A LOT OF GREAT JOBS NOW! This total amount of National electricity production is comparable to the entire output of a dozen Nuclear Power Plants, or around 3% of all the electricity produced and used in the United States, a significant amount. Even greater amounts of electricity are easily accomplished if that is desired, by just building duplicate installations.
NO government money would be required to do this, or even desired, and local businesses and banks could greatly benefit from these many PROFITABLE LOCAL construction projects and the future profits from selling electricity.
This system captures wind energy in a unique and extremely efficient way, to therefore produce absolutely GREEN electricity. Actually, the CW system is somewhat of a brute-force approach to capturing wind power! We BLOCK nearly half a mile wide of oncoming wind, for 100 vertical feet! INSIDE EACH of the ten pairs of curved concrete walls, which act as air funnels, there is always around 375,000 pounds of air, representing what is called Momentum, moving at substantial speed toward the giant revolving-door-like rotor we put at the rear end of each air funnel, which blocks that air! That total mass of about 3,750,000 pounds of air, all moving forward at more than 40 mph (when oncoming winds are at the AVERAGE 10 mph speed, the faster speed being due to our tapering air-path shapes) leaves no alternative but for all that momentum to cause the rotor fins to be pushed out of the way, that is, rotated, which we then capture to produce electricity. There is actually rather little 'technology' here but a lot of 'brute force' due to the very large size of the concrete structures. We only add Technology to REFINE everything to ensure maximum possible performance! The fact that AVERAGE wind of about 10 mph can be collected in such enormous quantities as nearly 2,000 tons of air moving at 40 mph, indicates the reasoning of why CW works as impressively as it does.
Each such town can therefore become more independent in providing most of its own electricity in great abundance, along with employing many of its own residents to build it and using local materials and products to construct it. AND TO OWN IT!
By the way, nearly all modern product-related concepts seem to always be presented as either advertising or promotion, where everything is described under absolutely perfect conditions, to try to seem most impressive for anyone who might have money to put up! In the case of tower windmills, that means avoiding referring to windspeeds, or usually AVOIDING ever mentioning ANY details of how their products might someday operate! So it rarely occurs that ANY actual information is ever presented which might some day show them to have been misleading or deceptive! And so the promotions always describe glorious amounts of production, such as electricity generation, but which is realistically only likely to occur during one or two percent of the time!
The deception seems to be everywhere! ONLY the OPTIMISTIC HOPES seem to ever get expressed by anyone! Look in Wikipedia or anywhere else. The Wikipedia presentation on this shows an enormous failure of Wikipedia. They do NOT allow a reader to know WHO WROTE any article, or WHO LATER EDITED IT. In this case, it is very clear that extremely biased employees of the American companies involved in tower windmills wrote the text in Wikipedia. There are NO reference at all to the fact that China has built and is manufacturing far more tower windmills than the US has and is making. The text also is essentially a COMMERCIAL for tower windmills, as there are NO REFERENCE WHATEVER to any negative aspects, ever! The fact that US governments have spent around $150 billion so that Texas could build about 10,000 tower windmills is never mentioned. Private businesses are too smart to invest such enormous amounts of money when the chance of ever paying it back or making a profit is very slim! The text is always very distorted to suggest magical abilities of tower windmills. Whenever any numbers are ever cited, BY ANYONE, they are (very optimistic!) capacity or potential figures, which can never even be supplied or confirmed by anyone other than BY the equipment manufacturers! Virtually NO data is ever cited regarding ACTUAL DELIVERED ELECTRICITY! An interesting example was in Texas in the summer of 2010. Texas brags about having built around 10,000 tower wind turbines, with a "total installed wind energy capacity" of 10,085 megaWatts (as of 12/31/2010). An attractive number, even though it required roughly $150 billion of Federal (taxpayer) money to build them. What is not stated is that during the hot days of late summer 2010, when millions of people in Texas turned on their air conditioners, the ACTUAL SUPPLIED ELECTRICITY was only 570 megaWatts! NOT the advertised 10,085 megaWatts, but just ONE-TWENTIETH OF THAT, at 570 ACTUAL megaWatts. Only FIVE PER CENT of what the total PEAK RATINGS indicate! (TRY to find that data anywhere where the public could see it!)
If leaders were honest with the public about such things, fine, but that is not remotely the case. The fact that all those promoters only refer to installed wind energy capacity, which simply is the TOTAL of all the absolute maximum capacities that the 10,000 installed wind turbines COULD produce in absolute maximum wind without self-destructing! There is NO CONNECTION WITH REALITY! In fact, NO ONE even has any way to confirm the accuracy of such CAPACITY or RATING numbers, as they only ever are provided BY THE MANUFACTURERS of the products!
So watch carefully when you see any speaker or article about any of this! You WILL regularly see references to CAPACITY and POTENTIAL PERFORMANCE. You will find it darkly amusing that they NEVER refer to any ACTUAL PERFORMANCE!
I also seem to have a unique perspective that I insist on regarding any alternative energy devices for either me personally or for larger areas. I INSIST on knowing how long it would likely take to amortize the construction cost. That is, FOR THE PURCHASES TO PAY FOR THEMSELVES, such that actual savings might then be possible. For example, the Solar Power Tower that was built near Albuquerque, New Mexico in 1978, has not yet remotely paid for its construction as of 2012. There was enormous publicity about the Power Tower being THE solution for future electricity needs, but the repairs and maintenance costs of the Solar Power Tower eat up essentially all the income from selling electricity, so it is not even clear whether the Solar Power Tower has even BEGUN to start paying off its own construction costs. The data we have from Texas for 2009 provides us with a rough idea regarding this. You can do this same analysis regarding any alternative energy devices you buy for your own home, or that you see politicians spending your taxpayer money on! We need two numbers: (1) Total cost spent, which we will take as being $150 billion dollars for those 10,000 tower windmills now in Texas. (2) The amount of value of electricity that is provided. We will see below that published data for Texas in 2009 says that 19,351 GigaWatt-hours of electricity was provided by all of them during that entire year. In such large quantity, ten cents per kiloWatt-hour would be tough to get, but we will be generous here and use that number. That rate would mean that $1.935 billion worth of electricity would be created (per year). So if NO MAINTENANCE OR REPAIR would ever be required, then ($150 billion / 1.935 billion) about seventy five years of operation would be needed, before the basic costs of installation were ever paid for. When repairs and maintenance are included, this rises to at least 200 years before amortization.
That is not necessarily a horrible thing! IF the equipment can be made reliable enough where repairs and maintenance are moderate over many years, then this DOES have potential! But it means that investment NOW probably will not show real benefits regarding providing electricity for at least a couple decades, and may be centuries! The troubling part is that no one has ever done any long-term studies on how tower windmills do over several decades. So data regarding maintenance and repair is still rather speculative. (If they charge a lot more for the electricity made by tower windmills, which is quietly implied, then, yes, amortization can occur faster.)
In April 2012, the Japanese government told its people that the wholesale cost of electricity from windfarms will likely rise to around 28 cents per KiloWatt-hour, where it was currently around 5 cents per KiloWatt-hour. This seems to be the first actually honest admission regarding FAR higher electricity costs due to wind turbines. The public is allowed to think that wind being free would mean that wind-generated electricity would also be nearly free. I suspect that few in the public will be pleased to get electric bills which are six times more money than now, just because a windfarm produced it. We think rather differently than that! Since a local town or community would OWN the entire Community Wind system, and it is very efficient and rarely would need any repairs, we do NOT see any reason that electric bills should be any greater than they are today, and quite possibly would be less!
We can see another useful thing from the Texas published data discussed above. We see that 19,351 GigaWatt-hours of electricity was provided by all of the 10,000 tower windmills in Texas during the year 2009. Since a year contains 8766 hours, we can see that all those 10,000 tower windmills produced an average of 2.21 GigaWatts. Dividing by 10,000 we see that the average windmill in that group of 10,000 that is being bragged about only produced an average of 0.221 MegaWatts, not remotely the impressive electricity production that the public and the politicians were led to believe! We will see below that there is other solid evidence and calculations that the average electricity production of giant tower windmills is in that same range of about 250 KiloWatts. The promoters know that no investor or politician would provide funds for $15 million products with that minimal performance of about $12 of electricity per hour (average 250 kW electricity production times 5 cent value per kW). I realize that no one but me seems to care about amortization cost, but I feel it necessary to note it again here, that $12 per hour is about $100,000 of electricity produced over an 8766 hour year, where the $15 million tower windmills will take at least 150 years to even pay for their own construction costs. I only wonder how long it will be before leaders realize the silliness of this sort of approach. So no one ever mentions any actual numbers. Below, you will see WHY the average production of electricity is so poor, where the wind turbines are commonly described as being RATED at 1.8 MegaWatts or more. To me, that seems like outright deception.
You will see below the math which shows that the MOST ACTUAL DELIVERED ELECTRICITY from tower windmills is generally only around 1/10 of the actual energy IN THE WIND or around 1/5 of what those RATED CAPACITY numbers suggest. Isn't that total deception? Shouldn't SOMEONE admit to the ACTUAL performance of such devices? Wouldn't that be HONESTY to the public?
First Presented in June 2007
Yes, wind power CAN provide some electricity for our societies.
But does it have to be promoted in such extremely deceptive ways?
These graphics show the rotor exposed so it is visible, which is not true in actual operation, because it is entirely enclosed. There are some details which are not included here either, such as the curved air guides around the spinning rotor, or the drive system and alternators. The fact that the rotors are entirely surrounded is both for the safety of anyone nearby and also for extreme quietness of operation. These graphics are intended to show the general concept of the system. The size of this system is significant, as can be realized by the three specks near the incoming air arrow in the upper graphic which represent adult humans! Remember that this is only one of the ten identical, adjacent assemblies of the full system discussed here, which also clarifies how more than four million watts of wind power can be gathered from such a large area of wind! You can see how the large amount of air collected from the right is all funneled into causing at least one fin on the rotor to receive torque to then rotate the rotor and an alternator. The second graphic shows an approximate speed of the spinning of the rotor in normal use.
The drive system for the alternator has great flexibility, since we designed the system where each rotor only generates around a constant 190 horsepower of mechanical energy (in average winds), such that a wide range of gear drives, chain drives, or even automotive transmission drives could be used to transfer the power to the alternator. Coils of wire could even be mounted around the perimeter of the rotor base, for an entirely electromagnetic system with only a single moving part, the rotor itself.
It is useful to point out that tower windmills virtually always cite PEAK POWER when they describe their performance, the greatest their system could ever produce, where we feel it far more realistic to cite AVERAGE POWER, what can be expected in normal wind conditions. We will see below that these two are generally quite different!
Self-Sufficiency - Many Suggestions|
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Our Exponential Horn air funnel causes a SLIGHT increase in air pressure, which is actually not even noticeable! Our design choice causes an increase of around 1/1400th in that air pressure, which increases the natural 10,000,000 pounds acting on the front of the fin up to around 10,007,000 pounds instead. This results in an IMBALANCE in the forces on the front and back of that fin, and there is a CONSTANT NET force on the fin of around 7,000 pounds, which is the whole point. The increase in natural air pressure of 1/1400 on the front of the fin simply means that a weather barometer near the rear of the Exponential Horn would show a NATURAL air pressure there which is 1/1400 higher. Instead of a common barometric pressure of 30.00", it might read 30.02". No one would even notice the difference! The windspeed inside the rear of the Exponential Horn is somewhat higher than normal, due to the funneling action of the Exponential Horn shape.
Continuing, we now have a net force of around 7,000 pounds acting on the face of the fin, which acts to rotate the rotor axle shaft, due to a TORQUE which is created. That torque is the 7,000 pounds acting at an "average" distance from the axle, which is around 33 feet. This results in a torque of (7000 * 33) around 230,000 foot-pounds, a tremendous amount, which EASILY starts and rotates the huge rotor and produces all of our electricity!
Below, we will see that Rankine's actual formulas for this stuff give a value of around 11,500 pounds where we are describing 7,000 pounds here. Similarly, this number is calculated a different way. If the rotor was braked to not permit any motion, then the pressure that exists is called the Stagnation Pressure or Dynamic Pressure. This is easily calculated as being the mass-flow of air times its initial velocity. For wind that begins at 10 mph (15 f/s), this is (1/415 slug/ft3 * 15 ft/sec * 1 ft2 area) * 15 ft/sec which is 0.542 lb/ft2 of area. Since one assembly has a frontal area of 20,000 ft2, this multiples to 10,840 pounds of maximum Stagnation force. So if the rotor is NOT turning, and the natural average wind is at 10 mph, there would be roughly 11,000 pounds force acting on the fin to rotate the rotor. As the rotor starts to spin, the calculations get much more complicated, and in ACTUAL PRODUCTION OF the designed amount of electricity, this force drops to around 7,000 pounds. The measured force actually depends on how much load is applied to the rotor to make electricity. If NO load exists, due to no desire for electricity, the rotor can spin much faster. In fact, the rotor will spin at a speed where the only remaining force against the fin is that needed to overcome the friction of the bearings, which is minimal with our design.
I realize that this is far more technical than most people want to have to look at, but we want to try to show WHY our approach works so amazingly well! Prepare yourself, as there is more math ahead!
You hopefully realize that this Community Wind system has fully and rigorously been studied in Engineering terms. In Engineering, there are nine different types of Analyses which can be done regarding performance. A couple of those methods do not apply to the CW system, but we did comprehensive analysis regarding Froude number considerations (regarding wind-wave action); regarding Weber-number considerations (regarding surface-tension action); regarding Reynolds-number considerations (regarding fluid-viscosity action); regarding Strouhal-number considerations (regarding vibration friction action); regarding Euler-number considerations (regarding various pressure actions). Air velocities are always low so Mach-number analysis is not necessary. We felt that there was not significant elastic activity so Cauchy-number analysis was not necessary, and centrifugal motion in the air only occurs in the rotor section, so that analysis was only done for that section.
Again, this is just our very conservative approach. This factor alone suggests that many towns could easily receive around one and a half times as much electricity as we are describing! We assume that no one will complain when they get MORE than they had expected to get!
If the rotor turns at around 10 rpm, (during actual full production of maximum electricity) or around 1 radian per second, then the torque times the angular speed is (230,000 * 1) or 230,000 ft-lb/sec. This is the same as around 420 horsepower! Due to assorted losses, we conservatively expect to only capture around 190 horsepower out of this system, which is around 140 kW of mechanical power. Since we have ten of these assemblies, we easily get 1.2 MW of reliable output electric power.
Even if inside the Exponential Horn, no birds or animals or people would have their eardrums blow out or likely be blown over! In fact, birds could safely fly THROUGH the entire system while it was operating! It might become a wonderful City Park area, especially the (ten) almost-acre outer sections! It might turn out to be a GREAT place to fly kites! This system is simply using the tremendous forces that exist due to natural, normal air pressure, by SLIGHTLY altering it and then benefiting from the result. In a rather different way, airplanes alter (decrease) the natural air pressure by around 1/200th to create "lift" due to the airfoil shape of wings and the Bernoulli Effect. In both cases, what first appears to be a very small effect can be made into great benefits.
You might note that since the air INSIDE the Exponential Horn is only such a tiny amount of pressure higher than outside (above) it (around 0.01 PSI), we see extremely little value in building a ROOF over the top of the Exponential Horn, although towns are free to build roofs if they wish! In my opinion, the amount of air lost upward is insignificant.
Engineers can read this and realize that many DIFFERENT design parameters could be chosen, such as a far narrower rear end to the Exponential Horn. Yes, that would reduce the size and expense of building the rotor, and make it spin faster, but that WOULD reduce the overall efficiency of the system and likely also then require a roof over the Exponential Horn, as well as making the interior of the Horn potentially dangerous for birds, animals and people. I prefer THIS design, which is extremely safe, and which has a rotor which spins slow enough to probably operate for at least 40 years before anything more than minimal maintenance should ever be needed.
Some people seem to think this next thought is somewhat flaky, but I really like the idea of asking local Schools to consider having students do artwork on the bottom few feet of the concrete walls! There is at least 96,000 square feet of area that is easily reachable by artistic children! And the point would be to PERSONALIZE the system to the community! Every kid in the community could have a square-foot-area assigned, for the next hundred years! Individuals and families would be proud to picnic near artwork done by family members, and it could add a Fine Arts aspect to Community life!
The local cost of the sand, aggregate and Portland Cement can be different from these numbers, as there are immense ranges of prices which exist, primarily because of the freight expenses of hauling those materials from source locations to the project. If local sources exist, the prices can be much lower than indicated here, while if the materials have to be hauled long distances, they can be higher.
It might be noted that the "million jobs" would NOT require re-location to some distant giant factory, but would instead permit staying in the home community, and also BENEFITTING that community in the process!
An improved method of building the reinforced concrete walls has been designed. Imagine a 15-foot-long slabs of 3/8" plate steel, each with a slight curvature, and maybe 6-feet tall, both controlled by hydraulic cylinders against a horseshoe-shaped sturdy frame. These Forms would establish the space for concrete to be poured. Once the concrete had set sufficiently, the Forms assembly could have the hydraulic cylinders back the Forms away from the existing wall(s). The Form assembly can then be moved 14 feet along the wall to then be able to pour the next portion of the wall, continuing until the entire 400 foot length of the wall is poured. That Forms assembly could be moved around to allow pouring all twenty walls of the ten exponential horn funnels. The design of the Forms assembly also permits hydraulic power to LIFT the assembly maybe five vertical feet, where an additional five vertical feet of wall could be added above the previously poured walls. That process could be repeated until the walls became the full 400 feet long and 100 feet tall. There are some important details involved in the Forms assembly, to enable it to efficiently be allowing pouring the concrete walls.
This system, providing electricity to be sold and used locally, could therefore be fully operational within about three months (in many locations). This system has very little that could ever deteriorate or fail for many years of reliable operation (it can be built with only one or two moving parts!) (Media reports have stated that the tower windmills have around 800 moving parts in them!).
If just the conservative 1.2 megaWatts of electricity is produced, around 2/3 of the time (when the prevailing winds blow), the electricity produced in EACH following year could therefore BE SOLD (at a conservative 15 cents per kWh, which includes significant amounts of Delivery costs and assorted taxes, and even without any future price increases,) FOR $1,050,000! In just a year or two years of operation, the entire construction cost and all the employees wages could be completely paid for! This is impressively quick amortization or ROI. This is true even separate from the government's PTC tax credits!
The details of this are different for each community, as in some places Prevailing winds are extremely reliable and in other places they are not. The system WILL work in any community, but the likely ROI and electricity production should be confirmed by a local Engineer using local weather data.
Therefore, it seems extremely obvious to me that a local Bank or a local business might see cause to get this done! It seems to be an OBVIOUS profit-making business, with guaranteed LOCAL customers, and absolutely minimal operating overhead costs!
In fact, it might make sense for one thousand home-owners to each put up $2,000 in a Co-Operative ($2.0 million total), where they would effectively pre-pay some of their electric bills, and thereby own the entire project! By having PRE-PAID their usual electric bills (with that initial $2,000), the homeowners might then be able to nearly entirely stop paying for electricity at all, and then forever after have essentially free electricity! (Essentially, because there ARE times when the wind does not blow, or blows from the wrong direction, where conventional electricity supplies would be needed!)
This presentation has used VERY conservative numbers in the calculations. A town may easily receive more than double the amount of electricity described in these calculations, but they will certainly not receive less! We could have used the far higher overall efficiency percentage, and also the far higher Capacity Factor, to present truly impressive numbers, but we like the idea of a town being PLEASED at getting MORE benefit than they had expected, rather than being disappointed by any utilities that perform more poorly than had been presented to them.
Since THIS system is intended to be built FAIRLY SMALL and within a few miles of each town, there are actually rather minimal losses due to the power grid.
THIS community-wind system (1) uses natural wind power [which is actually a version of solar energy]; (2) it captures that energy decently efficiently; (3) it creates the electricity rather near the destination where the electricity is needed; (4) it needs no future fuel for power; and (5) there are few moving parts that could ever break down in the future. MANY different aspects exist which each contribute toward very substantial electricity production and delivery at minimal costs.
Peak Power Rating vs. Average Power Rating|
You may drive a car which was advertised as having a 495 horsepower engine, and that may have even affected whether you bought that specific car. That engine rating can be called a PEAK POWER RATING, being the greatest amount of power that it is capable of producing. When creating that enormous amount of power, it is realistic to expect to get around one or two MPG gas mileage. But for AVERAGE driving on an Interstate Highway, your engine only produces around 40 horsepower, during which you may get 25 miles per gallon gas mileage. This AVERAGE situation is a far more accurate description of what YOU CAN ACTUALLY EXPECT, such as regarding gas mileage. Both situations are true, but they are extremely different. One is a situation which sounds very impressive, but which you will likely NEVER actually experience, except possibly rarely for a second or two at a stoplight! The other is a situation which you may experience every day of driving! IF you were only given ONE of the numbers, which would you consider more important to know?
Whenever electricity ratings are given for wind turbines, they seem to always be PEAK POWER RATINGS, meaning the greatest amount of electricity that COULD ever be created. That is entirely different than ratings for AVERAGE WIND CONDITIONS, which would be realistic numbers of amounts of electricity that might NORMALLY be expected to be provided. The discussion and calculations below will indicate that OFTEN the realistically expectable amounts of electricity is only around ONE-TENTH that of the PEAK POWER RATINGS. But no one bothers to mention this important fact! So advertising makes claims of spectacular performance numbers for photovoltaic solar-electric panels, and for solar roof panels, and for electric vehicles, and for Hybrid vehicles, and for windmill-electricity-generation, and for the giant tower windmills. They invariably state PEAK POWER RATINGS, like that 495 horsepower engine in the car, numbers that may be technically true but are extremely misleading.
The public is permitted to assume that future electricity would be less expensive because of those windmill towers. But ALL reliable sources agree that extensive use of tower windmills will cause SIGNIFICANT INCREASES in the cost of electricity! That is primarily due to the rather expensive construction of each wind tower ($15 million each is not unusual today) and the nearly continuous maintenance and repair expenses (not disclosed yet but some experts think around a million dollars each year is likely) AND the fact that the owners of such equipment bought it as INVESTMENTS in order to have guaranteed future profits. Some news reports in 2008 indicated that a tower windmill generally contains around 800 moving parts! Imagine a wind-farm of 1200 such tower windmills, where around a MILLION MOVING PARTS would certainly require a LOT of maintenance. That maintenance would have to be done at the top of 300-foot tall towers and by Technicians who had very specialized knowledge. Wanna guess at how expensive each repair figures to be?
The American public is also not generally informed that the actual OWNERS (investors) of such windfarms are often NOT even in America! So the relatively unregulated profits which will be created in the future by such windfarms will often be sending American money to foreign countries to pay for energy we use! Sound familiar? A similar situation has had us financing most Mideast countries and others based on the petroleum we buy now!
The American public is fed only very selective details regarding the single advantage that windfarms produce, a moderate amount of additional green electricity, without ever being told of these assortment of disadvantages. Reporters never seem to know enough to ask the right questions! People who happen to live near wind farms which already exist seem to universally complain about the peculiar sound which the rotating blades create. People who had moved out to rural areas to escape the noises of cities, now find themselves hearing a constant throbbing sound of the sonic shock waves of the rotating blades. Most existing windfarms are still fairly small and they are also rarely in full productive operation yet, but once 100 or 150 such giant windmills are each rotating and generating such sounds, it seems certain that many nearby residents will sell their houses to move to somewhere quieter. The sounds will eventually be 24 hours every day! And as a person might walk around in a nearby neighborhood, the fact that all the windmills are THE SAME DIAMETER, and that they will generally rotate AT THE SAME SPEED (both horribly dumb design considerations!), there will be intense RESONANCES in some locations. Some day, the manufacturers of such windfarms will learn that they MUST make different windmills with DIFFERENT diameters and other different parameters to minimize such resonances between different windmills, but for now they do not seem to know that! There is NO doubt that there will be some locations, possibly even miles away from the windmills where a home in an unfortunate location may constantly and continuously shake itself apart! Or the wineglasses in the cupboards will constantly dance around! This is vaguely related to the Physics effect of an opera singer singing a CONSTANT FREQUENCY note to cause a (distant) wineglass to shatter itself. The singer does not sing loud enough to shatter the glass. But the CONSTANT FREQUENCY of the note permits a wineglass which has a specific resonant frequency to self-destruct.
Watch the news in coming years to see Reporters going to people's homes near windfarms to videotape glassware dancing across a dinner table and other such things which will destroy the reputation of wind energy. A SINGLE windmill COULD have such an effect, if the target object happened to have a suitable resonant frequency (which will NOT include wineglasses because their resonant frequencies are too high). But there are many other things which will be found to have resonant frequencies that are affected by the frequencies produced by giant windmills. However, we are NOT talking about a SINGLE windmill, and the far more extreme effects will be due to RESONANCES BETWEEN WINDMILLS (since they all produce the same frequency). If something called the Damping Factor is minimal, then even two (identical) windmills could create a very localized resonance which could be hundreds of times as intense as either one could create alone! In Physics, this is called Destructive Interference of Waves. And with a field of 150 such windmills, the sensations for anyone living near them figures to be extremely strange and probably extremely annoying.
This brings up an additional important point. America and Europe are rushing ferociously into massive use of giant windmills to produce significant amounts of electricity WITHOUT HAVING EVER DONE EVEN BASIC SCIENTIFIC RESEARCH REGARDING UNEXPECTED SIDE EFFECTS. It may easily be that hundreds of billions of dollars is invested in building massive numbers of such tower windmills only to find in five years that no one will be willing or able to live within five miles of them! There is a similar unresearched area of possible consequences which could be even more dangerous. The human brain and nervous system operates on various low frequency rates, sometimes called alpha waves, beta waves, delta waves, etc. It can be really screwed up when an external source of some stimuli occurs at a related frequency. You might recall that a Japanese cartoon got in a lot of trouble a few years ago when they had the TV screen flash around three times per second. They SHOULD HAVE KNOWN that for more than thirty years, researchers have known that strobe flashing of around three times per second can cause very large numbers of people to suddenly have epileptic fits. My point here is that we are rushing into such massive use of those giant windmills that no one ever seems to have done any research regarding whether the frequencies produced by the windmills cause any adverse effects in the behavior of nearby residents or in their physical health. Such research seems critically important, as it is a terrible idea to have a situation where nearby residents are guinea pigs in such experiments!
As a Physicist, I am also concerned about another possible resonance, that of an extreme low frequency. It was learned in the 1980s that (much smaller) windmills were often destroying themselves due to resonant vibrations. As a windmill blade passed in front of or behind the supporting tower, the wind was momentarily blocked and a shock wave occurred in that blade, and a vibration developed which was repeated every time each blade passed by the tower. At the time, designers had apparently not studied much about resonances, and they often built towers and/or blades which happened to have resonant frequencies which matched what was naturally occurring. I tended to always wonder where they got their Degrees, as this issue became well studied around 1940 after the Tacoma Narrows Bridge self-destructed in a moderate wind. How could they not have known? Such windmills were disasters waiting to happen, and quite a few self-destructed within weeks of starting operation. Well, designers today (hopefully) know to avoid THOSE resonances! But the spinning of a 200-foot or 300-foot diameter windmill rotor, which weighs around 15 tons, certainly transfers some resonant energy into the tower, along with those unavoidable problems of resonances due to the blades passing the tower. This seems to me certain to be transferring extremely low frequency vibrations INTO THE GROUND by each of the towers. Now, with 150 such vibrating towers each causing these (sub-audible) vibrations in the ground, and the fact that the Interference Effects of such waves will certainly cause localized intense shock waves, it would be nice to know if such a windfarm could initiate an earthquake or landslide, wouldn't it? Rather than simply being blind and waiting for a disaster to happen and THEN trying to figure out why it happened?
Now, it would be nice to think that our leaders would not allow something that stupid to happen, right? But around 1970, the US government was merrily proceeding with a project where they intended to sequentially detonate several dozen nuclear weapons underground, in order to blast rocks out for a new railroad path through the mountains. The railroads have always complained that they have to use immense power to get every entire massive train UP one side of mountain chains, only to then be able to coast down the other side. The figured that blasting a groove through the entire set of mountains would save the railroads a lot of money! Why was this so insane? No one seemed to bother to have checked that they were already drilling the boreholes for the nuclear weapons exactly on the San Andreas Fault line in Southern California! No one seemed to have a clue that they would nearly certainly have TRIGGERED a horrific earthquake by their "brilliant"? idea of trying to make a cheaper railroad path! So we must stay vigilant.
The tower windmill manufacturers seem to be absolutely free to announce absolutely any specifications they wish, or more commonly, making sure to AVOID ever letting the public know any specifics at all! It is unbelievable! For eight years, a company has aggressively tried to get permission to install about 130 tower wind turbines off the coast of Cape Cod. They have extremely impressive web-sites, but they are amazing in never actually SAYING anything!
The Cape Cod group has one page which is titled "How much electricity do we use", which a reader might expect would actually answer their own question! But it never does. The ONLY bit of information they even present in that page is that whatever the usage now happens to be, it will increase by 17% in coming years! NO actual usage numbers from the Utility companies! No numbers regarding anything!
They do that for a selfish reason. Another page of their presentation announces that they expect to be able to provide 3/4 of the electricity for Cape Cod by 2020. Such a claim is a lot easier to meet if no one knows what the electricity usage actually is!
They also carefully avoid EVER saying the Rating of the turbines that they want to install. This is even MORE important to them! It turns out that the long-established Engineering formulas regarding such things, and the long-known patterns of wind-speed, pretty much establish that a 200-foot diameter turbine, on a significant height tower, would generally be in (average) winds of around 21 mph. That speed wind is easily shown by Rankine's formulas to contain around 45 watts per square foot area, or 1.45 megaWatts of power in that entire area of the rotor, IN THE UNDISTURBED AVERAGE WIND. The maximum mechanical efficiency of their design of windmill is around 43%, so we are down to 0.62 megaWatts of MECHANICAL power that can be realistically captured. After converting that to electricity, it drops to just under 0.5 megaWatts of electricity produced and supplied WHEN the wind is blowing at that AVERAGE speed.
(The 21 mph windspeed used for the top of a tower windmill is based on a number used by companies that sell those tower windmills! We will use it here, but the number might be a little optimistic on their part. It is generally accepted that windspeed can be reasonably predicted as being proportional to the 1/7 power of the height above the ground. If you do the math, you can see that the windspeed actually DOUBLES over the winds that we normally encounter at around 400 feet height. Yes, their large tower windmills DO reach to that height at the very top of the rotor blades movement, so they are not exactly lying. But the AVERAGE windspeed encountered by an entire tower windmill rotor is certainly somewhat less than is commonly claimed, because most of the time the rotor blades are only 200 feet or 300 feet high. Is that deception? Hard to say, but we think it is! But we are still willing to use that claim of theirs, that the windspeed at the height of their tower windmill rotors is DOUBLE what exists near the ground, as we do not really want to beat up on them more than they manage to do on their own!)
That particular sized windmill is often cited as having a Rating of 1.8 megaWatts. That number is generally referred to as a PEAK POWER RATING. It does NOT refer in the least to AVERAGE power that could be expected! It describes a situation of FASTER winds than usually actually would occur! It is essentially just saying what the MAXIMUM the device could handle before burning out! This seems likely to be very deceptive. Readers and investors and Legislators see a figure of 1.8 megaWatt rating and they are likely to conclude that means that it WILL PRODUCE 1.8 megaWatts of electricity! That is not remotely true! IT CAN PRODUCE that amount of electricity, true, but only in much stronger than normal wind conditions. It turns out that their actual (future) performance will certainly even be worse than even the 0.5 MegaWatts calculated above! A discussion below explains why their windmills cannot be allowed to operate at high windspeed and are not practical to be used at low wind speed, and that there is therefore a Capacity Factor of around 34%, where that 1.8 megaWatt RATED (PEAK POWER) windmill is actually likely to consistently SUPPLY around (0.50 * 0.34) or 0.16 megaWatts (in AVERAGE WINDS), less than 1/10 what their Rated (PEAK POWER) claim seems to imply. Someone needs to start carefully checking the accuracy and likelihood of their claims!
It is easy to calculate that the 1.8 megaWatt PEAK POWER RATING would actually only be true if the wind was actually moving at around 33 mph. Essentially all that rating says is that the MAXIMUM PERFORMANCE can only occur at a wind speed of around 33 mph, without admitting that the ACTUAL AVERAGE windspeed expected is around 21 mph. That is akin to advertising a Corvette as having a PEAK SPEED of around 160 mph. That might be a true statement, but it is essentially irrelevant for practical purposes.
It turns out that winds that are much slower than that have VERY little power in them (half as fast a wind contains only ONE-EIGHTH the power in it), so such tower windmills are rarely operated when the winds are slow. However, when the winds are much faster, the mechanism comes into great danger of destroying itself (if it should be allowed to spin much faster, noting that each of the three blades on many of those towers weighs around five tons! Imagine if such large mass would start spinning wildly!) (During the 1980s, many such tower windmills destroyed themselves in such ways) So those tower windmills are also shut down when the wind is fast!
These tower windmills are of a design called a high-tip-speed wind-axis turbine. These have a factor called X, the turbine-tip speed ratio, at around 5 or 6 to one. We just discussed a common windspeed at the top of a tower of about 21 mph or 32 feet per second, this means that the very ends of the propeller blades are traveling at around 32 * 6 or 190 feet per second or around 130 mph. When five ton propeller rotors are spinning that fast, immense centrifugal forces exist which try to cause the propeller to destroy itself! This fact explains why the very large tower windmills have to be shut down if the wind starts blowing faster! The propeller blades on the very largest tower windmills often weigh around 5 tons apiece, and you can probably imagine if that massive weight hundreds of feet high in the air would start spinning at 400 mph or more! In the 1980s, there were some tower windmills that built up so much centrifugal force that they self-destructed! Therefore, nearly all modern tower windmills are shut down if the wind starts rising! Funny, isn't it?
The result of these limits is that such tower windmills only actually operate when the winds are in a fairly narrow speed range, therefore with around a 34% Capacity Factor. The operators can only have them connected to make electricity around 1/3 of the time (34%) Therefore, the consumers of that electricity can realistically expect to receive an AVERAGE of around 0.16 megaWatt of electricity and not the cited 1.8 megaWatts PEAK POWER. That is less than 1/10 what the public is led to believe! "Ideal" performance is generally cited, which IS relatively impressive. It is too bad that real life is likely to be only 1/10 of that! Such numbers would chase away most of the possible investors and also the politicians who are needed to support such projects. So the turbines are INFLATED into having an alleged "Rated Capacity" of 1.8 megaWatts, more than ten times what they can realistically be expected to supply!
So when the Cape Cod people announce 130 future turbines, each allegedly rated at 1.8 megaWatts (PEAK POWER), they ALLOW readers to believe that means that (130 * 1.8) 234 megaWatts of consistent electricity would be provided to the citizens and businesses on Cape Cod. And that SOUNDS very attractive and desirable! But AFTER it is all installed, and paid for, and the people then learn that the whole project only supplies 1/10 of that, (130 * 0.16) an AVERAGE of around 21 megaWatts, what could they do then? Not much.
So a project that was expected to have a 2001 cost of $1.2 billion dollars, has a likelihood of ACTUALLY supplying only an average of around 21 megaWatts of electricity (in average winds) but with the capability of producing a PEAK POWER of 234 megaWatts (during a storm, and just before being shut down for over-speed!). Better than nothing, true, but is it worth investing $1.2 billion dollars to be able to receive about $3,100 worth of electricity in most hours? No one also ever mentions that many millions of dollars worth of maintenance and repairs would certainly be necessary every year for those 130 complex devices spinning at fairly high speed. Media reports indicate that each of those 130 windmills will have around 800 moving parts in them, for a total of over 100,000 constantly moving parts that will wear out and break and require maintenance.
Such projects ARE of value, but they are not even close to what they are promoted as being!
Yes, IF the wind could be guaranteed to ALWAYS blow at around 33 mph, AND the turbines can be built strong enough to not self-destruct at such windspeeds, those turbines then COULD produce their claimed output. It ain't gonna happen! (Windspeed near the ground is usually around 10 mph, and at 300-feet altitude, it is about double that, 21 mph. To EXPECT it to always be tremendously faster than that, is nearly Easter Bunny or Tooth Fairy level expectation!
We mentioned above that the tower windmills are very complex systems, they are on very tall towers, and they include moving blades which can weigh as much as 5 tons and which could wind up moving at around 480 mph (if a fairly normal windstorm occurs, where ground wind speeds are around 40 mph, then the wind speed at the top of the tall tower would be about double that, as we have discussed, or 80 mph. And since propeller-type tower windmills have that X-factor of about 6 from their design, that means the outer ends of the rotor blades would be moving at around [80 * 6] or 480 mph) . Does this sound at all dangerous to you? It should!
These devices are really huge! The rotor on a single windmill is often nearly as large in diameter as an entire football field is long! Since there are either two or three blades, mounted on a tower that is generally around 30-stories (300 feet) tall, these are VERY large, VERY heavy objects moving around up there, sometimes 50-stories high at the top! Obviously, they use really good bearings on all those many hundreds of such windmills, but it has to figure that some day some bearing will fail or some bolt will fall out. We can only hope that no people or animals are down below when that happens, when all those tons of materials fall all that distance to the ground!
It seems that every few days, one of these tower windmills self-destructs! Here are some still photos from a movie made as one in Denmark destroyed itself in fairly normal winds in a storm. A 10-year-old Vestas turbine near Århus, Denmark, spins out of control during a storm on Feb. 22, 2008. It effectively explodes when one of the blades hits the tower. According to a Feb. 25 report by Kent Kroyer in Ingeniøren, "large, sharp pieces of fiberglas from the blade rained down over the field east of the turbine, as far as 500 meters from the base of the turbine". Another collapse occurred in Sidinge [Vig?], Denmark, 2 days later: "one of the heavy blades flew 100 meters through the air and crashed to the ground with a boom". Kroyer continues: "It has not even been a month since a similar Vestas turbine at Nås in Gotland, Sweden, lost a blade in the same way as in Sidinge. In that case the blade flew 40 meters and hammered down in a field. A neighbor described the bang as 'a sonic boom or a car accident'. Before the New Year, a Vestas turbine in Northern England collapsed, and a month earlier a Vestas turbine collapsed in Scotland." Note that this is a 10-year-old 600-kW model and much smaller than today's behemoths.
The rotation rate shown in the video suggests that the ground wind speed as it destroyed itself was probably around 60 mph. This was a fairly small unit, around 100 feet in diameter (where many recent ones are around 300 feet in diameter) and it was fairly new (around eight years old). Using the mathematical analysis presented in this page, we know that the windspeed at the top of that 200-foot tower was probably around double or 120 mph. We also know that the X-factor for that design of propeller blades is around 6.0. This means that the tip speed of the rotor blades in this video was probably around 6 * 120 or 720 mph! This is essentially above the speed of sound, so there is no wonder that it disintegrated!
Click here (1.4 MB)
or here (1.2 MB)
to view the MP4 videos.
Click here (0.8 MB)
or here (1.1 MB)
to view the very similar Flash videos.
Or click here to see the newscast which presented it.
Reports of several that destroyed themselves in the British Isles in early 2009 were also in the news. "Turbines in Britain - there are 2,000, almost all of which are onshore - aren't immune from failure. A 200ft turbine at a wind farm in Kintyre collapsed last November (2008) in a 50mph wind. Following that, 26 wind turbines across Scotland were shut down as a precautionary measure while the broken structure was examined. Then the following month in Cumbria, a 100ft steel turbine crashed to the ground."
Others: June 24, 2007, one on fire near Palm Springs, CA, USA. July 12, 2007, one on fire near Villarcayo. Feb. 24, 2008, (two days after the one in the video here), one disintegrated at Nordtank. Sept 13, 2008, one on fire in Spain. An accident in Wayne County, PA, USA.
It seems that a lot of people keep their videocameras handy, as during 2007, 2008 and 2009, there have been an amazing number of videos uploaded to You-tube and similar Internet web-sites. A number of the videos show the mechanisms on fire, while others show them becoming imbalanced and disintegrating.
As the government is getting more and more aggressively supporting wind-energy projects, there are getting to be truly outrageous numbers thrown around, 300 megaWatts, 500 megaWatts, and no one seems to be blinking an eye regarding having any doubts regarding the accuracy and therefore future benefits of such installations. But if some installation is bought and paid for on the assumption that it will SUPPLY a consistent 300 megaWatts of electricity, and when that installation is built and operational in five or ten years and it turns out that it actually only SUPPLIES 30 megaWatts of electricity, that might be beneficial, but isn't that still essentially a shell game, outright deception of the public and the government?
IF there is a giant wind-farm about to be built near you, INSIST on seeing the RESULTS of an INDEPENDENT STUDY of a year's operation of ANY other completed wind-farm in the world! No one seems to have noticed that NO such documentation is ever available, because the performance of such wind-farms is so pitiful as compared to the CLAIMS made for them. Obtain data on ACTUAL DELIVERED ELECTRICITY PER YEAR and also the COST OF CONSTRUCTION PER WINDMILL. Do NOT accept a manufacturer's evidence that under ideal conditions their system can produce a certain PEAK amount of electricity! Then YOU could do the math regarding the actual benefits of what is being proposed to you!
Yes, if the Cape Cod promoters would be more honest and state that they could eventually provide A RELIABLE 21 megaWatts of electricity, that would be a useful and significant accomplishment. They don't seem willing to do that (be honest) because they know that there is no one (apparently except us!) that is going to challenge any claims they make, especially since there is such universal enthusiasm for wind-power. But they also know that they have to be giving impressively large numbers, to try to cause awe in politicians and investors and in the public, where they can then have nearly unlimited budgets to build their expensive projects.
Let's explore some general numbers. We discussed above that each popular tower windmill currently costs around $15 million in construction and the 130 tower windmills realistically can produce an average of $3100 worth of electricity every hour. That is around $25 worth of electricity per hour per windmill. If we ignore any cost of maintenance, that implies that the windmill would have to operate continuously for roughly 600,000 hours, (the one divided by the other) just to amortize the cost of the initial construction. That is 25,000 days or 70 years! A rather important DETAIL, eh? Assuming that it never needed any maintenance or repairs for 70 years, it would only then actually credibly even pay for its own construction cost. AFTER that, it might have a chance of actually producing electricity at a savings!
For comparison, we might examine the amortization of the old-style farm windmill from the late 1800s. In our other wind presentation, we presented the analysis where such a 10-foot-diameter windmill could produce around 1/6 horsepower to pump water up a well or it could be set up to produce an average of around 60 watts of electricity. That is about a penny's worth of electricity every hour, which is around $100 per year. Depending on how expensive the small tower was to construct and the simple rotor of a non-airfoil farm windmill, if it could be built for $500, that implies that it might amortize its construction cost in around 5 years. Not too impressive, but at least it could eventually actually be in the black!
During the 1980s, a lot of people were talked into buying impressive tower windmills for $7,000 to $15,000 construction cost. You can probably see that even if such windmills had continuously operated for the past 30 years, even if they performed well and provided $300 or $400 worth of electricity every year, they would only now be starting to have paid for their initial construction cost. Unfortunately, virtually all of them had mechanical or electrical failures late in the 1980s and I doubt if any of them are still operating. If there is one, which has operated smoothly and continuously for the past 30 years, without needing any expensive maintenance or repairs, that MIGHT be a unique tower windmill that may have finally amortized itself!
For the record, the many attempts at solar energy have also dismally failed at amortizing themselves, again with the exception of very simple and very inexpensive devices like swimming pool heaters and such.
For all the hype, alternative energy devices have had a truly disappointing record of never (yet) actually paying their own way! The system described in this presentation is very different regarding this. The construction cost is only about 1/8 that of a tower windmill, and it has far higher average efficiency, where amortization is easily shown to be quite attractive, commonly in around two years of operation! Even the fact that our set of exponential horns intercepts around seven times as much air as a much more expensive tower windmill does, contributes toward greatly improving amortization of the system.
And the concept presented here? The numbers presented above indicate that it is designed to (very conservatively) provide roughly $80 of electricity every average hour for a community. (Actually, the 1.2 megaWatts we designed this for means 1200 kWh per hour, and if that electricity can all be sold at 15 cents per kWh, that is even more attractive at $180 of electricity for every average hour for the community!) Doesn't sound like much! But $80 per hour is $2,000 per day or $750,000 per year of produced electricity. In about two and a half years of operation, that amortizes the entire $1.8 million construction cost we project. Instead of taking 70 years before any actual benefit regarding electricity would begin, as with the tower windmills, two and a half years is very attractive! THAT is the main reason why we think this is such an excellent concept! (Using the higher number, the $180/hour, that amortizes at about $1.6 million per year, even faster yet!)
Since we will neglect to mention this later, we note here that the SOUND created by our system is all INSIDE the concrete enclosure, and is therefore greatly reduced for any nearby residents. Our system is NOT a high-tip-speed turbine, but an entirely different design which is a Momentum device. In fact, it is NOT an aerodynamic (lift-based) rotor at all, and instead is a momentum (drag-based) system. This means that the factor called X, the turbine-tip speed ratio, is generally nearly always around 1.0. Where we saw above that the tower windmills have their propeller tips flying at around 190 ft/sec, ours can only move about the same speed that the wind is blowing, in our case, initially just 24 ft/sec, but increased to somewhat faster airspeed by the Exponential Horn shape. Still, NEVER remotely near the speeds that the high-tip-speed tower windmills always operate with. This greatly reduces (air) noises, but it also allows our system to operate over a much wider range of windspeeds, greatly increasing the Capacity Factor for greater electrical output. It would also be easy to add external sound insulation around that fairly small circular enclosure to eliminate sound and noise completely!
The turbine-tip speed ratio also provides us with an estimate of the rate of rotation of our rotor. As the air is funneled into 1/4 the cross-sectional area in the Exponential Horn, we can expect the air to speed up to nearly four times the initial average windspeed of 24 ft/sec. With the X ratio of 1.0, this means that the perimeter of the rotor is likely to move at around 96 ft/sec. Since the circumference of our rotor is around 315 feet, this tells us that the rotor will likely rotate at 96/315 or 0.3 revolutions per second, or just over 18 RPM. THIS speed would be for an unloaded situation, where no electricity was being produced. When large amounts of electricity is being produced, the rotor speed is slower, being dependent on just how much electricity was being produced at any moment, but 10 to 12 RPM is a realistic expectation when in full operation, with average wind speed.
These concrete walls are relatively straight but designed to vaguely resemble the curved shape of a Public Address loudspeaker, but only very slightly curved. Technically, the shape is called an Exponential Horn. This drawing is to show prevailing winds coming from the right hand side of the drawing, and then being funneled into a smaller space after it has passed between the (curved) concrete walls, leaving to the left of the drawing.
In this drawing, the width of the end opening (on the left) we will define as being 50 feet, and we will call it A0. The equation at the top gives the dimensions of an Exponential Horn, where A is the width (vertical in the drawing) of the horn at any location, x is the distance along the horn centerline (from the plus mark at the left hand side of the drawing, at the center of the exit opening). e is the base of the natural logarithms, 2.718281828. m is a constant which we choose to determine the taper rate of the horn. We choose 0.0034657.
By choosing this constant, we can see that at a distance x = 400 feet along the centerline, the width of the horn has increased to exactly four times the 50 feet (left side) width, or therefore, the OPENING of the horn (to the right) is exactly 200 feet wide.
So, for construction, it is only necessary to carefully mark out the centerline, and a scale of feet beginning at the x = 0 point at the cross, and it is then very easy to be able to calculate the exact width of the horn, and therefore mark the exact positions of the concrete walls, at every point. For example, at the point 127 feet from the left end point in the drawing, we have:
A = 50 * e.0034657 * 127
Which is 77.65 feet total width there, meaning the inside surface of each wall is half that distance, or 38.82 feet from the centerline, which is 38 feet 9 and 7/8 inches.
That is essentially all the major design work needed for the shape of the concrete walls of the Exponential Horns!
So the "mouth" (or opening) between a pair of such walls would be built so they are facing relatively west (in the Mid-West US) or slightly north of that, whatever the direction that the Prevailing winds come from. The oncoming wind would then flow into that 200-foot-wide space between the two tall concrete walls and gradually get "funneled" into a narrower path, eventually just 50 feet wide.
We strongly recommend using re-bars in the concrete, to be able to make the walls less thick and still be durable, which can greatly reduce the cost of the concrete and the labor to mix and install it.
(Many people seem to think this design is to create higher PRESSURE, which is technically true, but that is barely the case! Yes, it creates SLIGHTLY higher pressure (by about one part in 1400), but the central advantage here is regarding MOMENTUM of the air. Primarily, this is related to as an increase in the VELOCITY of the air, increasing as it becomes funneled into the narrower path.
The minimal increase in air pressure is not even noticeable by any person or any animal, which might be inside the exponential horn. The higher speed of the winds in there ARE obvious. The end of the horn IS covered by chain-link fencing or other methods to keep any children or pets out of the rotor assembly, which COULD be dangerous, although birds should be able to fly entirely through the entire horn and rotor without any danger to them!
All the same air is then in that smaller space, but now it is moving faster and has slightly higher air pressure in it. At the rear end of the curved concrete walls, that now-faster-moving air enters into an (enclosed) mechanism that resembles the revolving door of many office buildings. But the function is rather different here, where the speed and pressure of the wind (actually, the Momentum) really has no choice but to "force its way" through that assembly, which forces that assembly to rotate. (This is actually a variant on a long-used vertical-axis-wind-turbine (VAWT) called a Savonius Rotor).
Obviously, THIS "revolving door" is a lot bigger! It is 100 feet tall and 50 feet wide for each fin or paddle or 100 feet wide overall, and is welded up of standard structural steel materials available locally. There are four fins or paddles, such that at any instant, at least ONE paddle blocks off the entire outlet airflow from the Exponential Horn structure. Another, fairly small partial semi-circular enclosing wall is also needed here (like the enclosure of a revolving door) which traps all that air into forcing its way through the fin/paddle/door.
The rotating shaft of this assembly is on very large thrust bearings. It rotates fairly slowly, around six to twenty-five times per minute (rpm), and so it then drives a gear train and then a relatively commonly available alternator to produce the electricity to send to nearby houses. If the alternator produces 11,000-volt electricity, of about the same voltage that the existing utility poles carry to your house, then each alternator would only need to have an output of around 11 amperes, where extremely thin and inexpensive wires can be used (just like on the utility poles now). The ten different alternators could each supply a different sets of maybe 100 houses each. Alternately, the power could be combined together from all ten alternators and then transferred to the town in a more conventional manner, possibly because that might be much more compatible with usage of the power grid when the wind did not blow.
NONE of this is very complicated, and NONE of it requires any technology that has not long been proven and used! The laborers hired to erect the wooden forms for the concrete would do the same that has been done millions of times before, so their training would be minimal. The employees in a local welding shop would use conventional MIG or sub-arc welding to build the needed assemblies. It might be most practical to have the rotor fins built in IDENTICAL 50-foot by 8-foot sub-assemblies, so that any local welding shop could build them. Such sub-assemblies would each weigh less than 4,000 pounds and therefore easily be moved around and onto flatbed trucks, and they could then be easily hauled from the welding shop(s) to the site on standard flatbed trucks. A standard crane could raise each 4000-pound section from the truck on top of the previous stack to be bolted, riveted or welded on. (A total of around 50 of these sub-assemblies would need to be welded up and hauled out to the site and stacked to form each four-finned rotor.)
The workers would build a row of ten of these complete identical systems, adjacent to each other, where they would eventually cover most of the 20 acres of land. From their point-of-view, it would not be that different from building a series of identical homes in a subdivision, one after the other. Well, concrete homes! At the same time, the welding shops would be welding up the many (around 500 total) identical sections of the fins.
All of the work is extremely standard and mundane labor.
Since this installation would likely be within a few miles of the town that would use the electricity, there is probably not even significant benefit in having to install high-tension electric lines, although generating the electricity at maybe 11,000 volts might be beneficial. At that voltage (which is currently the voltage used in nearly all the power lines we see across our neighborhoods), standard utility poles are fine. A single standard thin 12 gauge wire, capable of carrying up to 20 amperes in normal use, would therefore be able to carry (11,000 volts * 20 amperes) 220,000 watts of electricity from the facility to the hundred homes in the town that were to receive the electricity from that particular alternator. Between the 10 separate alternators, that is an ability to deliver around 2.2 megaWatts of electricity to the thousand destination homes. This is to indicate that even very common and inexpensive wiring could handle DOUBLE the normal (conservative) electricity production of this system.
A central point in all this is that NO exotic alternator would be needed or even desired, and an off-the-shelf alternator would be excellent; the concrete construction is both very economical and very well proven; by using air-entraining concrete, there can be great resistance to freezing and thawing, and the steel construction is also both very economical and very well proven. There is NO POSSIBLE WAY that there could be any cost over-runs! AND, the fact that in the first three years of operation, at least two million dollars of electricity would be produced and supplied and sold, the entire system would pay for itself within less than three years of use! After that, the many years of use would all just be gravy!
Undisturbed wind contains power from kinetic energy (energy flux) equal to:
E = 0.5 * ρ * V3 * π * R2.
Note that this is a simple application of the kinetic energy definition. It includes the (moving) mass of air, which involves its density and also a third velocity factor. It is an equation that Rankine derived long ago. Also note that the power in the wind is dependent on the THIRD power of V, the wind speed. A 20-mph wind has about 8 times as much power as a 10-mph wind, and a 40-mph wind has about 64 times as much power. (ρ (rho) is the density of air.)
The analysis of momentum by Rankine produced the following equation for the axial thrust (force) applied to a turbine:
T = 2 * π * R2 * ρ * V2 * a * (1 - a)
Notice that: π * R2 is just the frontal area, for a circular windmill that Rankine was then considering. All we actually care about is the area itself.
ρ is again the air density or 0.00237 lbf * sec2/ft3.
For ONE of our funnel-arrangements, we have an undisturbed initial area of natural wind of 100 feet tall and 200 feet wide or 20,000 square feet. We can see that Rankine's formula above now becomes:
T = 2 * (20,000 square feet) * (0.00237 lbf * sec2/ft3) * V2 * a * (1 - a)
Many locations in the US have average windspeeds of around 10 mph at ground level. This airspeed tends to increase higher up, with the windspeed often being at around 18 mph at 100 feet high. For the height of walls we have chosen, the average windspeed is often around 60% faster, and so we will use a conservative value of 16 mph (23.5 feet/second) as the base average windspeed in these calculations.
The best value for a is 1/3, so the a * (1 - a) factor is 1/3 * 2/3 or 2/9 or 0.2222 We therefore have:
T = 52,000 pounds (due to the initial undisturbed wind, and not yet considering the efficiency of any device).
After accounting for the interference factor, Thrust = 11,500 pounds (for each one of our ten assemblies).
Because of our funneling effect, the wind actually increases in speed before it gets to the turbine that we cause it to move, so the Thrust or Force applied to that mechanism to turn it is actually somewhat greater than this. We will not go into that mathematics here, as it is a little complex.
You can probably see that since we arrange it so wind applies a force of around 11,500 pounds thrust to the paddle on the rotating mechanism, it WILL turn, AND it will turn a geartrain and alternator as well!
We can also calculate the available energy flux initially in the undisturbed wind, using that kinetic energy content equation presented above. For the conditions just described:
E = 0.5 * (0.00237) * (23.53) * 20,000
E = 306,000 ft-lb/sec, about 557 horsepower, or about 415,000 watts of actual power in that wind area! We propose building ten of these, so the total of them would be 4,150,000 watts or 4,150 kiloWatts, or 4.15 megaWatts. This is NOT electric power but simply the AVALIABLE power in the wind.
Rankine first showed that simple analysis of energy and momentum establishes that the MAXIMUM theoretical efficiency of any wind turbine is 4 * a * (1-a)2, where 'a' is the fractional reduction in wind speed (called the interference factor) from the original free flow to the location at the plane of the turbine blade. This suggests a theoretical maximum at a = 0.3333, where the efficiency would be 59.3%. If the free wind velocity was reduced by one third at the plane of the turbine blade (and reduced by another third immediately behind it, the theoretical maximum efficiency could be had. (Regarding our system, this means that a theoretical maximum of around 2.5 megaWatts of mechanical power might be extracted from the wind.)
In practical terms, there are swirls or turbulences in the wake that have not been accounted for here, and there are some minor radial pressure gradients (centrifugal effects) that are also not accounted for, in this simplistic analysis. More thorough equations exist that better account for these matters, which are beyond the scope of this article, and they fairly accurately represent the performance of the various turbine technologies. But they make clear that ACTUAL performance of ROTARY windmill devices can never be very close to the (59.3%) theoretical numbers.
A tremendous advantage of the Exponential Horn structure of this system is that many turbulences are eliminated. If a SECOND Exponential horn is provided at the rear, to enable the air to again expand out wider and slow down, the benefits can be even greater. A crude traditional Savonius Rotor causes a reduction in net wind speed of around 3.5% (7% total) maximum, which limits it to its 14% maximum efficiency. This system is a very distant second-cousin to the Savonius concept, and makes many improvements to the Savonius. In fact, this system actually operates on an entirely different basic approach, of FORCING the wind to have to go THROUGH the VAWT mechanism in order to get past the obstructing walls. It is therefore a system which creates a slight PRESSURE against the forward surface of the turbine paddles, and the air has no alternative but to force the turbine paddle back in order to finally get past our obstruction!
This fact enables this BASIC system (without any Exponential Horn funneling walls) to have at least 35% overall efficiency. If well-built Exponential Horn infeed structures are also provided, then an overall efficiency of greater than 50% may be realistic. So the system described here might certainly be able to capture around 2.5 megaWatts of power from this area of air, but we choose to use a very conservative approach to the calculations where we know that around 1.4 megaWatts of captured mechanical power will be captured from that 4.2 megaWatts of power available in the wind. The alternators to convert this mechanical power into electricity is not quite perfect efficiency, and we arrive at a very reliable 1.2 megaWatts of reliable electricity being created. In principle, a really well-built system might easily produce twice this usable output of electricity.
One spectacular problem that occurred many times in the 1980s and early 1990s was where the designer had not taken into account the design factors of forced vibrations, and specifically the Strouhal number calculations! As a result of such Engineering blunders, when the wind would be at a certain speed to cause the turbine to rotate at a specific speed, that speed would be a resonant frequency of the tower structure! The tower would start violently shaking and destroy itself. This problem has been well known for at least 60 years, as many early tall smokestacks would destroy themselves in surprisingly moderate speed winds, and you may have seen the popular movie of the Tacoma Narrows Bridge which vibrated and twisted itself into destruction around 1940.
Another related problem also occurred many times in large windmill installations. Each time a blade would pass behind or in front of the tower structure, there was a brief loss of thrust and great change of local forces on that blade. Some large windmills wound up having the rotors wildly vibrating, and at the time, no one seemed to even know why! Same thing, a simple application of the Strouhal number could have identified potentially dangerous rotation rates, and simple stiffening of the tower and the blades easily always solved that sort of problem. If the wind would ever be 400 mph, there may then still be a vibration problem, but the entire system would probably have fallen over first in such ridiculous winds.
There are a number of other serious Design / Engineering issues in the truly huge devices now being made. Some are so large that the diameters of the rotor blades are the size of a football field, around 300 feet! They also have considerable weight, in some cases, each individual blade weights around five tons. When such massive and huge objects are expected to reliably rotate for years on end, many complicating surprises often show up. One of the more interesting (to me) is that the rotors are now so huge that the weather / windspeed for one portion of the rotating motion is different than for a different area! This can cause immense mechanical stresses on the structure of the blades, the rotor shaft and bearings and the tower. Since no one has ever built anything of that size that is intended to move and survive intense storms, designers are often at a disadvantage! The common procedure is to simply shut the entire windfarm down any time the wind started to rise! They also do not work when the wind is going really slow, so the practical situation today is that those giant wind farms really only perform well for a rather narrow range of windspeeds! If you have driven past many of them (and I have) it is extremely rare to see all the windmills turning! Yes, the TV promotional commercials always show them all merrily rotating, but the reality is that it is not that common in real life!
In fact, some of the wind farms I have driven past, have only had one or two of the entire field of windmills actually turning! Some of them are usually even pointed in the wrong direction! For something that the promoters have assured the American public that they can rely on, it is not very comforting to see such disappointments. Actually, I cannot recall EVER seeing ALL the windmills in any windfarm actually spinning properly! For all our billions of taxpayer dollars, one would think we could expect more than that!
There ARE some potential complications to consider. IF such an installation was intended to somehow hook into the Power Grid, then the inexpensive alternators referred to above may not be suitable.
One of the most severe problems was / is that the electrical generators commonly used are poorly suited for this application. Nearly all of the home/commercial-sized windmills sold in the 1980s and 1990s used either synchronous or induction generators, because the cost of such types of generators is moderate enough to be able to sell the systems! However, synchronous generators are great IF the spin rate is exactly controlled and constant. When the spin rate changes, such generators create very large harmonic voltages in the Power Grid!
One popular supposed solution to this over the past 20 years has been to use a control system that included a synchronous inverter to convert created DC voltage into AC. This control system generally is of very reasonable cost, and fairly simple, and it works fine for an individual home, but when it tries to feed into a power grid, it has power quality and harmonic injection problems, and there are resulting inductive LOADS on the Power Grid, and they generally wind up DRAWING MORE inductive (volt-ampere) power FROM the grid than the watts they are (resistively) putting into it! Utility companies also did NOT like the fact that their power lines were then having undesirable and destructive resonant voltages in them. As a result, Utility companies today insist on only accepting certain types of WECS systems for providing power to their Power Grid lines. Nearly no home-sized systems qualified.
The other kind of generator, the induction generator, is generally more expensive, and it can tolerate a SMALL range of frequency variations but it had its own set of problems. The point here being: You should probably not really count on your local Utility Company agreeing to pay you for excess wind electricity that you want to put onto their Grid. When they agree to such an arrangement, they now usually insist on extra electronic controls that are quite expensive.
One consistent problem that seems to show up in all of the larger-sized WECS installations has to do with the vibrations and stresses in the equipment. Some is due to wind gusts and turbulences, while others are due to the vibrations of the rotating turbine and other components that have to be able to move. Over time of operation of such systems, it has been sadly common that various fasteners become loosened from the vibration and stresses. Depending on which fasteners come loose (and usually fall out) the range of the bad things that then happen is pretty broad.
The wind does not always blow at a speed in the narrow range needed for maximum and safe performance! In fact, when all conditions are considered, a Capacity Factor defines what average performance can be expected. For a tower windmill turbine that is mounted on a 50-meter (160-foot) tall tower, in a reasonably windy location, the Capacity Factor can be around 35%. That means that, for tower windmill windfarms, OTHER sources of electricity would likely be needed MOST (65%) of the time!
But since this system is so simple and inexpensive, AND it would certainly provide hundreds of local laborers with good-paying jobs, and it would certainly solve a great need regarding supplying our electricity, it seems inconceivable to me that THOUSANDS of towns all over the USA wouldn't immediately start such programs up. (There are over 6,000 towns in the US which have populations greater than 5,000 people, so certainly 10,000 should easily be able to decide whether or not to build this system to provide their own electricity.) The only real complication has to do with the great weight of the tall concrete walls and whether foundation caissons would need to be made to make sure that the walls did not settle in following years. But even that technology is long known and proven, so it would only add some expense to the construction (but therefore also some additional jobs!)
It seems to me that if just 10,000 small towns each decided to SELF finance this system, and then a few months later have unlimited free electricity for those homeowners, that would be 12,000 Megawatts of FREE electricity that would never again need to use up any fossil fuels! That happens to be about the same output of a dozen very expensive (and potentially dangerous) nuclear power plants!
Which would YOU want in your back yard? (NIMBY???)
The location of those footers are determined by the formula given above, where the walls are relatively straight but have a very slight curvature.
The concrete walls are intended to have re-bar inside them, with the standard re-bar spacing for that climate regarding freezing, thawing, moisture and wind loads.
The very top of the walls can be joined with light wideflange H-beams, in order to stabilize the verticality of the walls over future years. However, those bridging beams should have provision regarding thermal expansion and contraction of their own length, or else they would contribute toward causing the walls to very slightly rock back and forth with the heating and cooling of day and night. The problem is not significant, and the footers can tend to simply rock a few thousandths of an inch, and the value of adding these bridging beams seems greater than that of leaving the walls to settle and possibly tilt over coming years.
These walls are designed to taper from a two-foot thickness at the ground level to less than a one-foot thickness at the top. These dimensions may certainly be altered if local conditions suggest different Engineering guidelines.
As always with tall concrete structures, only a few feet of height should be poured before waiting a suitable time for strength curing to begin. Again, standard concrete construction procedures for that climate should be followed, unless Engineering suggests some variance.
As the air is funneled into a narrower path, it speeds up and it also slightly increases in atmospheric pressure. The pressure change is very minor, where even if the air was moving at 65 mph at the end of the concrete walls, the local pressure will only be about 1/1400 higher than natural, around 0.02" higher in barometric pressure. That difference has no safety issues and virtually no operational issues that are of much significance. Airspeed near ground level would be less.
But such a structure would be rather large (20 feet tall and covering a ground area comparable to a large house) and fairly expensive to build (200 tons of concrete + ), and whether it makes sense for a particular (rural) house might be debatable. This system SCALES UP WELL, where the larger version seems to amortize faster and perform better.
Given this smaller size structure, creative people may find different construction procedures. One that seems to have potential is in using standard pole-barn construction. Such as installing a curved line of 11 standard pole-barn posts, every eight feet. Then standard corrugated metal pole-barn siding can be nailed to them, but with one important difference. Normally, the corrugations are aligned vertical, but that would cause severe turbulence in the air movements! So the corrugations would have to be HORIZONTAL. And the metal surface must be on the INSIDE of the poles, again, for smoother air flows. So the outside would look fairly ugly, unless you add a second entire surface of the metal to hide the posts.
However, there can even be solutions to that! It would be a lot more complicated and take up more space, but imagine creating a set of such Exponential Horns which were facing Southwest and a SECOND set of them which were facing Northwest. I suspect that the simplest and least expensive approach would be to simply build completely independent systems, where only one of them would sometimes be operating in making electricity. But the point would be to still be able to produce great deals of electricity even if the wind was coming from some different direction for a few hours or days. In fact, if enough vacant land was available to build FOUR complete systems, they could be faced all four directions, so that at least one of them would be able to produce electricity as long as there was any wind at all. The fact that the systems are fairly inexpensive to build, and construction is rather traditional, and the electricity produced can be sold for good profits, it might even make sense that a town might EVENTUALLY build four like that.
There are many other variants of what could be built. I chose reinforced concrete construction, because it is already familiar to millions of workers, it is not very expensive, the materials are available in nearly any region, and the construction is very durable. But alternative construction is certainly possible. Imagine using well-drilling equipment to bore a series of 50-foot deep holes every ten feet along the Exponential Horn Plan line. Then a series of oil-drilling pipes are lowered down into those holes and screwed together in conventional methods, to result in a series of 100-foot-tall sturdy iron pipes which are very securely mounted in deep soil. Then, flat sheets of material could be welded to those poles or bolted to them, to essentially create "pole-barn" construction. Only the one (interior) side of the Exponential Horn needs to be smooth, and the outer side could probably be left unfinished, except for appearance reasons. Corrugated materials cannot be used for this, as they cause too much turbulence, unless possibly the corrugations were horizontal, with the wind motion.
There are also (slight) potential advantages in adding a roof structure over the top of the Exponential Horn. This becomes more important if a smaller scale structure is involved, for complex reasons. The actual air pressure increase in the (large) Horn as described is very minimal, and little air should be lost upward if no roof is added. However, and especially if the Exponential Horn tapers to an even narrower end width, where the air velocities and local pressures became even higher, there might be value in trapping the air in the Horn into having to push the VAWT paddle in order to escape. That variant slightly modifies the design concept from being a velocity/momentum system into a pressure-based design, and it reduces the overall efficiency. Both can work fine. The roofless version seems easier, cheaper and simpler to build and so is my preference.
A local Engineer needs to examine the Weather Bureau's wind records to determine whether an adjustment might be appropriate. For example, in western Kansas, winds are generally strong and the system might be built with fewer than ten segments. In southern Georgia, winds are generally light and more than ten may be appropriate. The system has immense flexibility about such variables.
If the town then later decides to install a second or third systems, the same arrangement would apply.
I built a small scale-model of one of the ten assemblies, at 1/50 scale. 8 feet long a horn, with a mouth that is 4 feet wide and two feet tall. The total volume of air inside the horn at any instant is about 40 cubic feet, and since about 13 cubic feet of air weighs one pound, there are about THREE POUNDS OF AIR inside the horn at any time. A roof IS necessary for such a scale assembly, because three pounds of air can easily get re-directed upward, which would avoid having to pass through the rotor.
But the scale of the horn that I Engineered for this system is 50 times longer, 50 times wider and 50 times taller, so that it contains 125,000 times as much air as the scale model. This means that there are around five million cubic feet of air, weighing 375,000 pounds of air, inside the horn at all times!
The scale is such that, in order for that air to avoid having to pass through the rotor, an immense amount of force and work would be necessary to cause 375,000 pounds of air to all move upward by 100 vertical feet! Yes, a small fraction DOES get lost upward due to the lack of a roof, but Engineering calculations show that it is a rather small fraction. The cost of building a very large roof for each of the ten horns would never amortize themselves even over many years. But any town is free to build such roofs if they wish!
I DO recommend that at least three TRUSSES be mounted atop the concrete walls (near the front, near the middle and near the rear) to fix the spacing between the concrete walls. As the foundations settle over many years, the walls cannot be allowed to ever tilt. Three trusses should be sufficient to maintain their correct position and orientation.
C Johnson, Theoretical Physicist, Physics Degree from Univ of Chicago