By the way, nearly all product-related concepts seem to always be presented as either advertising or promotion, where everything is described under absolutely perfect, ideal conditions. In the case of windmills, that means windspeeds that rarely occur, but which are the greatest that their equipment could survive! If modern promoters were trying to sell that old-style farm windmill mentioned just above, they might overlook the fact that the AVERAGE windspeed was 10 mph and instead decide to describe the extremely rare condition of a 40-mph wind (which they would neglect to mention!) but where the absolute maximum amount of available electricity then would be 64 times as great, or 3800 Watts! OR they might decide to describe the maximum amount of energy in the wind, only exaggerating up to 20 mph wind (under the assumption that you build a 200-foot-tall tower to put it on, again, neglecting to mention this detail!) which could then legally claim a number of around 480 Watts. Both of those statements are technically true, but both are incredibly misleading, for a system which realistically would provide around 60 Watts most of the time. The owner of the newly bought and very expensive (in the 1980s, often around $15,000 for the windmill and tower) windmill and tower would then find that he could consistently only get around 60 Watts of electricity from it. This is actually a brief description of why the very popular wind power of the 1980s rapidly faded and disappeared! It seems to be an accepted part of modern advertising to make the most exaggerated claims that they would not get sued over! We think very differently, and so WE choose to use numbers which you ACTUALLY would be likely to get. Yes, on windy or stormy days, you might briefly get a lot more. Consider that to be gravy!
And so the product promotions and advertising always describe glorious amounts of production, such as electricity generation, but which is realistically only likely to occur one or two percent of the time! Our presentations, including this one, try to have a more practical and realistic approach. We present numbers that are NORMALLY TO BE EXPECTED! This actually results in our systems providing performance under those ideal conditions at far greater production than is generally described, which we see as a nice bonus. In any case, there can be real difficulties in trying to compare such realistic information with other approaches which only present absolute maximum capabilities. I guess it is nice to know that my Corvettes are CAPABLE of going 170 mph, although there is no practical need for that in my life. Our presentations tend to more focus on subjects akin to what the gas mileage is of the Corvettes at highway speeds (around 26 mpg) and whether it can pass a truck (it definitely can!)
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The enormous publicity from many people getting on TV and announcing that "wind energy is going to be the solution of the energy crisis" has caused two different approaches, large and small, to be aggressively pursued. Both have NOWHERE NEAR the potential that all the hype constantly claims for them! People need to have REALISTIC EXPECTATIONS and things can be fine! But with the ridiculous expectations of today due to all the hype, there are going to be a LOT of disappointed people who spent a lot of money chasing a questionable technology!
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 that 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 alternative energy devices, they seem to always be PEAK POWER RATINGS, meaning the greatest amount of electricity or power which can be created. That is entirely different than ratings for AVERAGE USAGE CONDITIONS, which would be realistic numbers of amounts of electricity or power which might NORMALLY be expected to be provided. The discussion and calculations included here will indicate that OFTEN the realistically expectable amounts of electricity or power 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 even for FUTURE giant windmills and hydrogen as a fuel. They invariably state PEAK POWER RATINGS, like that 495 horsepower engine in the car, numbers that may be technically true but are extremely misleading.
No one seems to have told those lawmakers or taxpayers that transporting electricity long distances is not very efficient! This has been known for a hundred years, and designers knew even then that there was value in sending the electricity at the highest possible voltage. Power is voltage times current (and some other complications such as phase-relationships), so it is beneficial to send electricity at the highest possible voltage to reduce the Current needed to transfer a specific amount of electricity. THAT is why there are High Tension Lines everywhere! Most of them operate at just over 100,000 volts. Really long lines are often operated at around 500,000 volts.
Even then, the wires pretty much are like the wires inside your kitchen toaster when carrying extreme amounts of electricity. In fact, the standard Industry design rule is to design everything so that around 90% of the electricity put in at one end of a 60-mile long stretch of high-tension lines comes out the other end. Ten percent of the electricity put in is therefore wasted, as heat, along that 60 miles. This also pretty much explains why virtually all electric power plants are built within around 60 miles of the center of a major city!
But consider a SECOND 60-mile stretch (for a total of 120 miles). We only had 90% get through the first section, and ten percent of the remainder will get wasted in the second section (or 9% of the original). We can also think of this as being (9/10) that gets through a section raised to the second power (because of two sections) (0.9)+2 which is 81%, as being the amount that actually gets through the 120 miles of high tension lines. Well, if we are talking about trying to carry electricity for over 2,000 miles, it turns out that very little actual benefit will really be obtained! If we say 1,980 miles, that is 33 of those 60 mile segments. That means that the fraction that would actually get to Southern California would be (0.9)+33. This turns out to only be 3.09% of the electricity created by the North Dakota windmills would ever actually be able to arrive in Southern California. The other 96.91% would have been lost along the way as heat by the hot wires!
So maybe the California investors will build enough giant windmills in North Dakota to produce an impressive amount of electricity. But they apparently do not know that only about 3% of that electricity created could ever get to Southern California!
Actually, there ARE a few people who realize this problem, and they present an interestingly speculative idea! They concede that they cannot actually get the electricity to Southern California, so they now claim to want to SELL electricity to people IN North Dakota, where they would then MAKE MONEY, by which they could BUY ELECTRICITY in Southern California! Does THIS seem to make sense to YOU? To spend billions of dollars building things in a distant State, only to SELL electricity to THOSE people, where an ultimate goal would be to have extra money in California to buy electricity with? What an I missing here? Couldn't they spend their billions of money in Nigeria in Africa, to then sell the resulting electricity TO NIGERIANS, and thereby get extra money into Southern California?
From an Accountant's perspective, DOES it actually make sense to choose to spend billions of dollars, where the ultimate goal is the hope that a few millions of dollars might eventually get back to the investors? ALL Accountants laugh at such bizarre thinking!
So what is the likely effect if we take really massive amounts of power out of winds? When a windmill is operating effectively, we will discuss below that the effect slows down those winds to around 2/3 their original speed. Is that a bad thing? NO ONE KNOWS because NO ONE HAS EVER EVEN INVESTIGATED IT!
Yes, with the rather limited power we now extract from winds, there probably are few serious side effects. But we are getting far less than 1% of the needed electricity from wind now. What will be the environmental, weather effect in the future when we have 20 times as many or 100 times as many of those giant wind farms in operation? No one knows. I have a suspicion that it will "surprise" the leaders in bad ways. If they decide that they do not then have to tell the public, we may then never even know that there could be this problem! Just like New Orleans leaders all seemed totally surprised that the levees broke during Katrina. (I happened to be one of many scientists who had tried to previously alert the Mayor and others of New Orleans regarding flooding consequences of hurricanes.) Duh!!! Is THIS the level of Design and Engineering and Planning we have sunk to? Only think about the consequences for the coming week, and assume that no future problems could ever arise?
In recent years, our government has invested enormous amounts of (taxpayer) money in "windfarms" where large numbers of amazingly large windmills look like fields of daisies! Sadly, each of those installations I have visited have had only a few actually facing the wind and rotating as intended! Some are usually just stationary, and a few are usually pointed in wrong directions! For this and other reasons discussed below, it seems like a somewhat foolish investment of taxpayer money, although politicians want to "look good" with such projects because it seems like they are really caring about our future.
Somehow, many of those self-destruction windmill incidents never got to the attention of news Reporters, but there were quite a few such failures. Small scale installations have the same problems, but since they are small and lighter, the mechanical stresses are generally far less, and there seem to be fewer serious mechanical failures.
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 close to 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!
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.
For reference, the 1/6 horsepower that such windmills could make was equal to about 120 watts. After mechanical and electrical conversion losses are accounted for, even such a rather large windmill could only realistically produce a usable 40 to 70 watts of electricity, enough for one medium-sized lightbulb!
A technical detail: A factor called X, the turbine-tip speed ratio, for a farm-style windmill is generally roughly 1.0. This number can be multiplied by the air speed (feet per second) and divided by the overall radius to get the approximate speed of revolution in radians per second. For that ten foot diameter windmill just discussed, the radius is 5 feet, and if we say that the average windspeed at that 50 foot height is 14 mph or 20 feet per second, then we can estimate the spin rate of that windmill. 1.0 * 20 ft/sec / 5 ft is 4 radians per second, which is about 2/3 revolution per second or 40 rpm. This method can be used for any wind device, but the turbine-tip speed ratio is different for different types of devices. In this case, we could estimate that we would need to use pulleys or gears to multiply the shaft speed by around a factor of 20:1, to have around 800 rpm which is sufficient to turn a car alternator at an acceptable speed.
There seem to be thousands of web-sites where people describe their own unique ideas of harnessing wind power. From what I can tell, they are all nearly useless and worthless, primarily because the person who was trying to build and use such things had absolutely no education in Electrical Engineering or Mechanical Engineering, and no experience or ability in calculating any of the important things that must be known! I sometimes read such pages for entertainment! For example, a guy who spent five years in trying to produce wind-generated electricity (1995-2000) seemed to keep trying random thoughts! He clearly spent at least $20,000 during those five years, and his descriptions seem to suggest that he may not have gotten even ONE DOLLAR'S WORTH of electricity for all his efforts! He built a "triple-Savonius rotor" and kept building taller and taller towers to put it on! Since Savonius rotors rotate rather slowly, he decided to use a fan belt to make a car alternator spin at 20 times as fast (with a really tiny pulley). He found that it wouldn't even start! He (randomly) tried smaller and smaller pulleys, until he got it to turn. Since he was disappointed with the output, he decided to re-wire the alternator to make it create higher voltage, apparently believing there was some advantage in that! Eventually, he realized he was wasting his time and went back to standard 12-volt alternators.
But even after five years of serious and expensive effort, he still never got anything to work very well. At one point, he said that he got 20 amperes of electricity. However, that would be quite impossible with the setup which he had made, EXCEPT during a storm where winds were maybe 40 mph. Yes, at that time, he might have briefly produced 20 amperes, and if the storm lasted a couple hours, he may have produced TWO CENTS worth of electricity!
However, he presents his web-site as though he is an authority, and there are probably people who will try to duplicate the disasters he managed to do! It would help if he even knew something about the subject for his own use, but he feels that he can be telling others what to do.
Hundreds of other web-sites that claim to provide information on wind-generated electricity seem to have similar lack of knowledge! THIS presentation was created BECAUSE of that total lack of useful information! Below are the actual equations used that Rankine and others developed to understand the amount of power in moving wind, including math examples. If someone feels the need to show off their expertise, it may help to be able to know ahead of time whether there is any chance that it will work, or how much electricity it might actually create under different circumstances.
Personally, I feel that the farm windmill design is pretty useful, even though it only has an efficiency of around 30%, but it is certainly very well proven. But the cost of buying or building one today is so high that there is no chance of it ever paying for itself in money saved in reduced electric bills. There are many variants that can be incorporated, each of which increases the cost even more, which rarely make much sense regarding paying for itself. If an existing old farm windmill can be obtained, it might be economical to re-build it, and that could be quite desirable. But to spend $10,000 or $15,000 or more for a windmill and tower, counting on a salesperson to be both honest and knowledgeable, is probably a poor idea!
There are a variety of things that are called Savonius rotors, some of which actually are and some of which are simply VAWT devices of a hundred variants. Personally, I feel that nearly all of those variant devices are too expensive to buy or build, mostly because some genius decided that he knew how to improve the Savonius concept without actually knowing anything at all! Many of the more-expensive and more complex variants actually work WORSE than the basic Savonius does! And since the basic concept of the Savonius has pretty low efficiency to start with (around 13%), even IF someone knew how to greatly increase its performance, it better not require a lot of money to do, for the small amount of electricity that they will likely provide. I would NOT build most of them because I do not see how they would ever pay for themselves.
IF someone builds such things just to show off construction talents, fine. But if their intention is to actually save on electric bills, they are probably wasting their time and money. Especially if they follow the guidance of web-pages of people who had no idea what they were doing!
An exception could be for a really remote location, where access to conventional electricity is either impossible or ridiculously expensive. For such applications, it could make sense to build a LOT of crude Savonius rotor devices, which can realistically be counted on to produce roughly 7 to 10 watts each in average winds. (we will see this below). Since 55-gallon drum Savonius rotors are quick and easy and cheap to make, and if there are no neighbors, maybe making 20 or 50 of them could make sense! All this to get two or three hundred watts of electricity!
Persuasive salespeople are able to sell "complete systems" of tower windmills, including the parts for a tower. Such complete kits tend to sell for $15,000 or more. They tend to be more sophisticated than the home-brew attempts, and they tend to be better designed, but still, the chance that they will ever produce $15,000 worth of electricity to pay for themselves seems extremely unlikely. The salespeople always make spectacular claims regarding how much electricity you would get, but that salesperson has rarely ever used one to know the reality. As a ballpark, we will see below that a square foot of wind area commonly has around 5 watts of mechanical power in it. 23 A ten-foot-diameter windmill has 78 square feet of area, so it intercepts around 390 watts of wind power. A farm-style windmill generally has around 30% efficiency, so the amount of SHAFT power is now down to 117 watts. After belts, pulleys or gears and an alternator, figure around 60 to 70 watts of actual electricity made.
The more-expensive modern windmills generally have airfoil blades instead of the flat blades of a farm-style windmill. That generally increases the efficiency to around 39%. This increases the shaft power to around 150 watts, and the electricity production up to around 100 watts. Is that much electricity really worth spending $15,000 for a tower windmill? Of course if you BELIEVE the salesperson over the laws of science, go for it!
For these reasons, I tend to have a "lower-cost-approach" to wind-generated electricity! Specifically, there is one version of the Savonius rotor which is the ONLY one that I have ever built or used (maybe 15 or 20 of them over the years). When I refer to a Savonius Rotor, I therefore refer to ONLY the following: Get an old 55-gallon drum. Draw a line completely around it, to be able to saw it apart into two exactly identical half-drums (vertically). The two halves will then resemble two rocker baby cribs. I generally use a Sabre saw with a fine-toothed metal cutting blade, and it makes a LOT of noise!
The two halves are stood up (as though they were still actual drums) where their one cut edge is nearly touching each other (actually with about one inch space between the two, for a shaft to later fit between), but the two are facing opposite directions. You should see the INSIDE of one half drum and the OUTSIDE of the other, whichever side you look from. Then place a 36" length of 1x1x1/8 angle iron (or larger) on top of the two and across both. Drill some holes in the tops of the drum-halves and the angle, and use 1/4" bolts to securely attach the angle iron to the drum halves. I use lock washers to make sure the bolts will not loosen from vibration.
Flip it over and mount a second piece of angle iron on the other end of the drum-halves. THAT is pretty much it! How much did this cost? Well, I have always found drums for free, because a lot of people want to discard them. The angle iron and bolts might be around $4, so that is the total cost of the Savonius that I call a Savonius!
There ARE "high class" versions of this, which might be a lot prettier but also which seem to cost whatever the seller is able to get for them, often hundreds of dollars! Since I always look at such projects with the thought of how long it would take to pay for it from whatever benefit is obtained (amortization), I generally do NOT see that the high-classed Savoniuses could ever pay for their cost. These 55-gallon drum Savoniuses do NOT produce a lot of electricity! You will see below that the calculations show that in average winds, one Savonius can be expected to produce maybe 7 Watts of actual electricity (to charge a car battery at around half an ampere). The expensive products which are sold as Savoniuses ARE generally larger than my 55-gallon drums, so they do have the capability of collecting a little more wind power, but not enough to impress me! These numbers might also make it clear why I have never even bought really good shaft bearings for my Savoniuses, because that would just make the amortization time a lot longer!
I generally drill a 9/16" hole through the very center of both the top and bottom angle piece. There can be merit in using slightly larger angle, as my holes drill away nearly the entire flange of the angle! I then drive a length of 1" (or larger) water pipe into the ground, several feet. On the top, I get a pipe reducer down to 1/2" and I add a short piece of 1/2" water pipe, maybe a foot. I then get a 4 foot length of 1/2" solid steel rod. I put that rod into the 1/2" pipe at least 9 inches, and drill a small hole through the pipe and rod to secure it with a thin rod or screw or bolt. Two might be better.
There is now the larger water pipe sticking up maybe 10 feet above the ground (sturdy), with the 1/2" rod sticking about 3 feet above that. I then raise the Savonius assembly above it and lower the holes in the angles down over the vertical rod. I usually find salvage water pipe to drive into the ground, so this tower assembly often costs only around $5. The entire project therefore often costs around $10 total!
Yes, buying actual bearings can make sense, but this works fairly well as described, although it sometimes squeals due to metal friction! Given that the 55-gallon drum will likely only last two or three years before it rusts out, I found that my non-bearings never caused any of the angle irons to break from wear.
POINT: Since this entire assembly only cost me about $10, I never really needed to produce massive amounts of electricity before it paid for itself! Since virtually NO other wind-generated electricity system has ever actually paid for its own cost, right there is a real advantage, the way I see it! But you will see shortly that even with this bare-bones device, it still is likely to take about 10 months of it generating electricity before it even pays for just the $10 cost of materials!
POINT: Since this Savonius and tower is so simple, easy, quick, and dirt-cheap to make, I tended to save up all the old barrels I could find, and convert them all into Savonius Rotors! Yes, there is a serious UGLINESS factor! (I did not have any close neighbors in any of three different locations I made them.)
We show another drawing here which shows both the benefit of a Savonius as well as its greatest disadvantage! The two lower arrows show the wind that is caught INSIDE the concave half of the Savonius, which then forces it to rotate around its central (vertical) shaft. This shows why it has such great torque, even at very low wind speeds.
The upper two arrows show the disadvantage. The oncoming wind hits the convex half of the Savonius as well, and only its convex shape is what causes the air to be deflected sideways around it. If you think about it, the wind's effect on the two halves of the Savonius is not that different, same speed, same area, the only difference being the concave and convex shapes presented to the oncoming air. You probably see why a Savonius only has around 13% overall efficiency; much of the power that might be captured has to get used up pushing the convex half!
We will see below that such Savonius Rotors, combined with standard (used) GM car alternators, and the common 10 to 11 mph wind in the Midwest, can REALISTICALLY create maybe 7 watts (24 hours every day), then ten of these very cheap devices can produce 70 watts, or almost two kilowatt-hours per day. THAT is a useful amount of electricity! As long as you have two or three car batteries to store it!
However, it must be remembered that if electricity sells for 15 cents per kWh (nearly half of which is often delivery fees and taxes), that means that TEN of my ugly Savonius only produces maybe 30 cents of electricity per day! That is around $10 per month (for TEN of them operating!). When people get all excited about buying a $400 Savonius rotor, see why I can't share that excitement?
Regarding rotating rate, the factor called X, the turbine-tip speed ratio, for a Savonius is also around 1.0. Therefore, if you use standard 55-gallon barrels, with a radius of around 0.8 foot, and the windspeed is around 15 ft/sec, using the method we used before gives 1.0 * 15 / 0.8 or about 12 radians per second or around 2 revolutions per second or 120 RPM. A speed ratio of around 5 or 6:1 can get a shaft turning fast enough to drive a car alternator.
In virtually all practical devices, this rotation occurs at a rather low rate. Most devices therefore use some sort of gear train to get a rotation rate that is fast enough for electrical alternators.
Electricity is somewhat of an inconvenient commodity. It is extremely difficult to STORE in any substantial quantity. In fact, it can ONLY be stored as Direct Current (DC), as in batteries, and Alternating Current (AC), as in your house, cannot be stored at all. Wind is also somewhat inconvenient, because it is not constant or controllable. The consequence of these facts is that the need (or demand) for electricity seldom matches the supply available from a wind generator. Alternating current electricity (what supplies all of our homes and businesses) cannot be stored at all. These facts have caused an almost universal reliance on a direct current (DC) WECS system. A limited amount of direct current CAN be stored, usually in automotive batteries.
Since most common appliances only operate on alternating current (AC), it is therefore generally necessary to use an Inverter to convert the direct current into alternating current. The AC can then be used in the house, or even sent back into the Power Grid, for potential profit! This is an aspect (lure) that caused many people to spend the $7,000 plus installation cost back in the 1980s for small WECS systems. Sadly, as explained below, virtually none of those people ever received more than a dollar grand total for providing power to the Power Grid! The customers had been seriously misled, or, as I see it, lied to.
Therefore, a wind generating system will necessarily include: (1) a mechanism to convert wind power to rotary motion; (2) a gear train or the equivalent; (3) an alternator or generator; (4) a number of automotive type (or better) batteries; and an Inverter. Each of these components can be of various designs, but the function must be as described.
The efficiency of farm windmills is never above 30%, and that is only at a fairly narrow wind velocity range, with efficiency dropping off rapidly for both faster and slower windspeeds. This variety is technically called a slow-tip-speed wind-axis turbine. Most actual old farm windmills have flat blades and not airfoils.
So the giant windmills are generally shut down when the wind is slow, because there is little power then to be captured, and they are also shut down if the wind gets too strong, due to dangers that the rotor might self-destruct! We had mentioned that above with a few examples. This results in their being able to actually function to be less than 100% of the time. In fact, a commonly accepted number is a 34% Capacity Factor, meaning they only actually operate productively about 1/3 of the time!
The companies that manufacture such tower windmills seem extremely resistant to ever disclosing any information regarding the actual performance of their products! In Britain, due to a requirement to supply the figures to Ofgem in order to claim Renewables Obligation subsidy certificates, such information was disclosed for one installation, and the actual data showed a Capacity factor of around 21.6%, while the manufacturer argues that it was actually around 26.8%!
However, even those efforts at protecting their expensive windmills seem to be in vain, as per the regular news reports such as those mentioned above, of some tower windmills destroying themselves!
These very advanced and very sophisticated designs tend to be far too expensive for small residential installations, and they are almost universally used on giant towers on wind farms.
The Propeller style is what is called a high-tip-speed wind-axis turbine. Because of the high tip speed, the theoretical efficiency can be higher, around 43% to 45%. This higher efficiency explains the choice of Propeller-style turbines on those giant wind farms. However, it might also be a dumb choice due to the need to shut them down so much of the time! They virtually don't work at all in slow winds, because the power in wind is proportional to the CUBE of the windspeed. If the wind is half normal speed, that only contains ONE-EIGHTH the power in the wind. So the large tower windmills are never operated during slow winds OR fast winds!
Doing our usual calculation again, we have the factor called X, the turbine-tip speed ratio, at 6.0, which has the tip ends flying at around 190 ft/sec. For a tower windmill that is 200 feet in diameter, the circumference is therefore 630 feet, and so it rotates around once every 3.3 seconds, or about 18 rpm.
There are two varieties of the propeller-type which have been used, two-blade and three-blade. Nearly all modern wind farms use three-blade, rigid-rotor for medium sized turbines and two-blade, teeter-rotor for the very largest turbines. It does not seem appropriate here to discuss the relative design advantages of each.
On these large, expensive systems, often the individual blades are rotatable (teeter-rotor), like on a helicopter rotor. These variable pitch blades can be tilted to capture more or less wind power, in order to try to maintain fairly constant rotational speed, and to survive serious storms.
An interesting detail is that some of the modern tower windmills are SO large that the TOP of the windmill consistently experiences much faster winds than when the same blade passes the BOTTOM of its path. This causes enormous structural stresses in the blades! Another reason to shut them down when the wind picks up. Actually, even the weather patterns can be different at different areas of the windmill surface, and those implications are not yet fully known.
This design is technically called a low-tip-speed (or slow speed) cross-wind-axis turbine. No airfoil shape is involved, which is part of the explanation for the very low efficiency.
However, the Savonius design is by far the simplest of these various VAWT mechanisms. Nearly all of the others involve advanced airfoil shapes and complicated structures. The economy and simplicity of a Savonius Rotor cannot be matched. The 55-gallon drum construction described above emphasizes that fact.
This design is technically called a high-tip-speed cross-wind-axis turbine. The airfoils and the high airfoil velocities allows this style to have efficiencies as high as about 32%, over a fairly wide range of wind speeds.
A Cyclogiro is direction-sensitive and must be constantly configured for the specific wind direction. In operation, the individual rotor airfoils continuously vary in pitch, to maximize the effect at some points in the orbit and to minimize the wind drag in other places. Because of all this sophisticated technology, the efficiency of the Cyclogiro can be extremely high, around 60%. This is actually higher than the theoretical maximum efficiency of any fixed airfoil design (because of all the tweaking of airfoil orientation angles)! Unfortunately, the great complexity and cost of the control systems and mechanisms have tended to make Cyclogiros have minimal application.
In addition, physically large units have shown evidence of sometimes developing mechanical problems and becoming unbalanced, and a number of them have destroyed themselves as a result, even causing some accidental deaths. There might be some possibility of controlling the rotor blade pitch by a computer program, but this design still seems to have stability problems.
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 is an equation that Rankine derived long ago. Also note that the power 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 is the density of air.) (the last terms are just the circular area being considered).
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)
ρ is the air density or 0.00237 lbf * sec2/ft3.
For a ten-foot diameter (R=5) farm windmill in a 60-mph wind (88 ft/sec), this total Thrust calculates to be a maximum of 775 pounds, quite a horizontal load on the turbine rotor for the tower to have to withstand. (This calculation is based on an "ideal" efficiency where a = 1/3, something that is very difficult to approach for a farm-style windmill.)
In case you're curious, using that kinetic energy content equation presented above, we can see that a 60-mph wind (88 feet/second) has:
E = 0.5 * (0.00237) * (883) * 12
E = 810 ft-lb/sec, about 1.5 horsepower (which is also about 1,090 watts) of power per square foot of wind area!
You can probably see why really strong winds can knock buildings down!
A 10-mph wind has far less power in it, around 3.7 ft-lb/sec, or about 1/150 horsepower per square foot. For reference sake, a horsepower is 746 watts, so this 10 mph air has around 5 watts of power in it (per square foot of surface area). Only some of that power can be captured!
More precisely, if wind moving smoothly at exactly 10 mph, that is 14.67 ft/sec, so the Energy equation is 0.5 * 0.00237 lbf * sec2/ft3 * (14.67 f / s)3 * 1 ft2, which is 3.74 lbf/sec for a one square foot area. When converted into metric, that is 5.064 Watts/square foot of area. It can also be calculated directly in the metric system. Air density is 1.221 kg/m3. 10 mph wind speed is the same as 4.47 m/s. So we have 0.5 * 1.221 kg/m3 * (4.47 m/s)3. This is therefore 54.537 Watts PER SQUARE METER of wind area. Converting this to a square foot, we get 5.064 Watts/square foot of area. I generally just call that 5 Watts per square foot!
(There are few locations that have more than around 10 mph average windspeeds near the ground). Notice that only around 30% of this power can actually be converted to rotary motion by a farm windmill (the ideal value of a in the Rankine momentum equation above), so we are only talking about 1.5 watts of (mechanical motion) output for each square foot of wind area blocked. This explains why farm windmills were always quite large!
A ten-foot diameter farm windmill intercepts a maximum of 78 square feet of wind area, so that (10 mph) wind initially contained about 0.534 horsepower in it. At its maximum efficiency of 30%, the farm windmill could capture around 0.16 horsepower, a sufficient amount for pumping water. The 0.16 horsepower actually collected is around 120 watts. That is not really enough to seriously consider trying to make electricity! Such a (fairly large, ten-foot diameter on top of a fairly large tower) windmill might be able to provide a reasonably consistent 50 watts of electricity (when the wind blew), not even enough to light a single modern home light bulb! Of the 120 watts, there are many losses that cannot be avoided. There is gearing it up to a high enough speed to drive an alternator, which has a lot of frictional gear or belt losses, and then the alternator is only around 80% efficient at best, and then the battery has inefficiencies, which is why the 50 watts is actually somewhat optimistic.
There IS actually a useful new fact. Windspeeds higher up tend to be higher. Unfortunately, this effect generally needs really tall towers for significant benefits! On a 30-foot tall tower, around a 10% increase can be expected, 11 mph instead of 10 mph. On a 300-foot tall tower, it is common to expect about double the windspeed, or in this case 20 mph. Remembering that the power in wind is proportional to the cube of the wind velocity, such a tall tower can provide around 8 times the output power. This actually explains WHY they build such enormous towers for the giant wind turbines! On the 30-foot tower, around 30% greater output can be expected than at ground level. The cost of a 300-foot tall tower is too great for most applications except for the large scale wind farms. A 30-foot tall tower is commonly considered worth the cost for that extra 30% of output power. But since I tend to prefer the really cheap and crude Savonius rotor concept, I usually conclude that I could build at least 50 Savonius rotors with their car alternators for the cost of a single tower, so my Savonius have always been only five to ten feet above the ground. But for expensive windmill systems, which often cost $10,000 or more, the addition of another $5,000 for a 30-foot tower for it can sometimes make sense. In addition, that gets the rotating blades high enough up so no one is accidentally hit by one.
You probably know of people who announce that they will be Energy-Independent because they will make 2,000 watts or 5,000 watts of electricity from wind. Can you realize how large the turbine has to be for that level of production? Salespeople sometimes SAY such extravagant things, because they know it enormously increases the enthusiasm of the customer, especially regarding spending $7,000 or $15,000 or far more, as the salesperson sees a very attractive Commission for himself IF a sale gets made!)
And the salesperson is technically correct IF the wind is blowing at 40 mph or more! But virtually every customer has been told of 5,000 or 7,500 watt RATING (meaning the HIGHEST POSSIBLE output) and they immediately started dreaming of sugarplums in believing that they were going to get that performance! Just remember that since the power in wind goes as the THIRD POWER of the wind speed, if a 40-mph wind could produce a usable 6,400 watts, then a 10-mph wind for that same installation will likely produce about 100 watts! Customers are NEVER told such things by salespeople!
But they DO LOOK impressive!
A crude Savonius Rotor made from two halves of an old 55-gallon drum would intercept about 6 square feet of wind, which contains around 30 watts of wind-power in it. Its 14% efficiency would get about 4 or 5 watts from that 10 mph wind. If such a device was used to drive an automobile alternator, only around 3 watts of reliable power would likely be created. This can seem somewhat discouraging! But any salesperson for such products or systems will say spectacularly different things!
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.
In practical terms, there are swirls or turbulences in the wake that have not been accounted for, and there are 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 can never be very close to these theoretical numbers.
A farm windmill or a Darrieus Rotor only reduces the (average) wind velocity by a maximum of around 8% (16% total, including the wake slowing), and this accounts for their maximum 30% efficiency. For a Savonius Rotor, the reduction in net wind speed is around 3.5% (7% total) maximum for its 14% maximum efficiency. As noted above, the extremely huge new propeller turbines on wind farms can have efficiencies around 45% (when the wind is blowing, of course). A wind farm might cost $100 million to build and install, and it might realistically produce a total of 10 Megawatts of power when there is wind. IF the wind would keep going for all 8800 hours that are in a year, that would mean that it could provide 88 million kilowatts per year. At current large-quantity electricity prices, that would mean around $5 million each year. Of course, that would be gross income, having to cover all the employees of the site, and all materials and repairs. If such a wind-farm could generate even $1 million in net profits, it would not even come close to covering the Interest on the hundreds of million that was invested, much less EVER pay for itself. You might note that I do not see much cause to be a huge fan of large-scale wind-farms. Show me some actual Accounting numbers where there is a chance that they might pay for themselves ... then maybe!
However, SMALL-scale setups to provide electricity for an individual house, seems like a wonderful idea! Especially if the total cost for the equipment can be kept below around $20,000! (Your annual electric costs are probably around $1,000. If interest rates on an investment of $20,000 is no higher than 5%, that is also $1,000, which means that such a system would at least hold its own! If the system cost' LESS than $20,000, it might even have a chance of eventually paying for itself!
(You might see the special reason I really favor the dirt-cheap $10 Savonius described above, regarding being something that has a far better chance of quickly paying for itself/themselves)
This is the general logic behind this presentation. Simple, traditional farm windmills or modified Savonius rotors cannot make enough electricity to even be worth the trouble of building or buying (personal opinion). The dirt-cheap Savonius is an exception! But with some fairly simple improvements, their performance can be improved to several times as much output, and a simple and inexpensive (maybe under $500) system might actually be able to provide noticeable amounts 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 easily always solved that sort of problem. If the wind would ever be 400 mph, there may then 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 as long as a football field, around 300 feet! They also have considerable weight. as much as 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 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!
We addressed above that the X-factor of about 6 is good for improving the efficiency, but it also caused extremely high speeds in parts of the rotors! If a fairly normal storm causes 40 mph winds at the ground, and the tall height gives about twice the ground wind speed to the rotor, that is around 80 mph. And with an X-factor of 6, that means that the outer ends of the rotor blades are spinning at 80 * 6 or 480 mph! MANY TONS of rotor blades, spinning at such ferocious speeds, relatively close to the Speed of Sound, guess what can result?
There are other really serious problems that often apply to the home/commercial-sized propeller-style units. When those many people in the 1980s were paying small fortunes for their high-tech windmills, not only were they led to believe that they would make 2,000 or 5,000 watts for their own use, they were sold on the concept where they were going to be able to sell huge amounts of electricity back to the Utility Companies, a sort of revenge! Unfortunately, the designers of the systems had massive lack of understanding of what they were trying to design and sell!
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 very special equipment required to please the power companies is VERY expensive! It virtually NEVER pays for itself in any tiny rebates from the power company.
Related to that, I have a request! There has long been immense publicity regarding people allegedly selling electricity back to the power companies from their home WECS investment, for close to 30 years. But I have NEVER seen anyone SHOW any monthly utility bill that shows such rebates! My suspicion is that the best a person might hope for might be maybe a dollar a month max. I would think that ANYONE who actually received any massive rebate would have immediately called Reporters and SHOWN THE BILL ON TV! I am not aware that that has ever happened! So I hereby ASK anyone to photocopy any electric bill that shows such rebates from the power company, and I am willing to present them in this presentation on wind power! I would love to think that even ONE person has received say $50 from any electric Utility! I just have grave doubts that it has ever yet happened!
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, probably so much so that you would never sell enough excess electricity to ever pay for that extra equipment. Better to simply think about providing electricity for your own house, and maybe a very dear neighbor!
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. News reports in 2008 indicated that modern large wind turbines contain around 800 moving parts! Seems to be that that is lots which can break down! 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.
If the entire cost of an installation is added up, including the turbine, the tower, labor, the electronics and control system, and all other costs, it is likely that around $3,000 will need to be spent for each Nameplate kilowatt. So for a system that would have the maximum capability of 5 kw, this is around $15,000 of investment. However, the wind does not always blow at the high speed needed for maximum performance! In fact, when all conditions are considered, a Capacity Factor defines what average performance can be expected. For a turbine that is mounted on a 50-meter (160-foot) tall tower, in a consistently windy location, the Capacity Factor can be around 20% to 25%. This means that the $15,000 investment just discussed could realistically be expected to produce an actual average of just over one kilowatt of electricity. You could only use a toaster (1.5 kw) when it was especially windy and you were using no other electricity! At the current common 15 cents per kwh (nearly half of which is often delivery fees and taxes), in a year of 8700 hours, around 9,000 kWh of electricity could be expected to be created, worth around $900. If there were no need for maintenance or repair, that would mean that it would take around 16 years to pay back the original investment, but actually at least twice that long to also make up for the interest expense on that borrowed money.
Regarding the government-financed projects, they all have tremendous drawbacks that no one seems to notice! Above, we noted Southern California's heavy investing in wind farms in North Dakota. Assuming they manage to generate a million watts of electricity from all those giant propeller-type wind turbines. They would then have to use inverters and transformers to convert it to high voltage alternating current to be sent along high-tension powerlines. (There is loss in doing these conversions.) Instead of 1,000 kW actually created by the windmills, only around 20 kW would actually arrive, nearly enough for one city block of homes! Definitely NOT worth the millions of dollars of investment in such a silly project! And, in even attempting it, the other 980,000 watts of electricity put into the wires would simply heat up the atmosphere, one of the worst possible side-effects!
This also should all make clear why I tend to focus on small-scale LOCAL electricity production, for a single household!
I prefer to concentrate here on potential improvements to some of the low-expense designs, specifically the farm windmill and the Savonius Rotor. In both cases, there are seemingly obvious ways to greatly improve their low performance efficiency, and I have been surprised at not seeing the following improvements regularly used.
In both cases, these devices are best suited for small-scale mechanisms, not being suitable to scaling up to giant versions, and therefore the government and power companies seem to have little interest in refining them. However, improved versions of either of these small-scale technologies make electric power generation for an individual home very realistic in many areas where there are reasonable winds. This is the thrust of these suggestions for improvements.
Two obvious levels of improvement seem possible. Both somewhat defeat the non-directionality advantage of the Savonius, but they greatly improve efficiency to a point at or above other technologies.
A large enclosing cylindrical 'shroud' surrounds the whole Savonius Rotor, and this shroud is mounted on bearings on the vertical shaft so it can independently rotate around the Rotor. It is only slightly larger than the Savonius Rotor, so there is relatively little clearance between the inside of the shroud and the moving outer edges of the Savonius rotor cups.
This shroud has a 'tailfin' to always orient it in a specific way to the wind. This is very much like the idea of a weathervane, which therefore always points directly into the wind.
Roughly half of the 'front' of the cylindrical shroud is cut away, exposing the catching 'cups', while the remaining half of the 'front' of the shroud blocks the wind from hitting the back side of the returning 'cups'. At least half of the rear side of the shroud is also cut away, to allow the air to leave after it has given up its power to the Savonius Rotor.
This simple improvement roughly doubles the net efficiency of a Savonius Rotor, essentially to the level of other technologies. It also tremendously increases the starting torque.
Begin with the same cylindrical shroud described above, but add an intake chute to the front, and possibly an exit chute to the rear (which is not shown in this drawing). The front of the shroud would therefore be extended several feet forward. This forward section would have a funneling effect, where the very front of the shroud would extend the full width of the entire Savonius/shroud width, but the airpath would taper to about half of that width where it entered the original shroud opening to feed pressurized air to the productive 'cups'. Basically, this now captures the air over the entire frontal area of the Savonius/shroud, virtually twice as much air, and therefore nearly twice as much available power (doubling the performance, and actually better).
Appropriate aerodynamics is important here, both inside the air funnel and exterior to it, to reduce turbulence losses in both areas. For example, the intake tunnel should ideally not be a constant taper but it should have the shape of what is called an Exponential Horn, to better match the acoustic impedance of the Rotor intake with that of the ambient surroundings. (Advanced Loudspeaker engineering concepts are used here, for the exponential horn design.)
This Acoustic Impedance match essentially means that any possible turbulence is virtually eliminated, and the pressure and velocity of the air is changed very smoothly and evenly along the exponential horn. The air very smoothly ACCELERATES as it goes through the intake horn, nearly doubling in speed, as the twice-area initial intake of the horn is funneled into the once-area exit of the intake horn into the actual Savonius.
The benefit of an exponential horn regarding creating a good acoustic impedance match depends on the LENGTH of the exponential horn. It it were extremely short, you can see that the oncoming wind would essentially just run into a nearly flat surface, and create enormous new turbulence. Toward the other extreme, if that intake horn was 100 feet long, then the airflow would be incredibly smooth, and the acoustic impedance match would be ideal. (There are labyrinthine loudspeaker enclosures which create a folded path of as many as 20 to 30 feet for a loudspeaker, to create truly pure sound production, but few people can afford the $20,000 or more price tag of such speaker equipment!)
In our case, we have a different complication! Since this exponential horn needs to be able to face into the wind, that means that the entire horn shroud has to be able to rotate around the axis line of the Savonius rotor. Any extremely long intake horn would take up far too much space and even represent a possible danger when the wind direction shifted!
So, for these practical reasons, I felt that if the exponential intake horn was of a length of about two times the diameter of the Savonius rotor (in my case, around six to seven feet long for each of the shrouds that I built, for 55-gallon drum Savonius rotors, and from my calculations, I felt the acoustic impedance benefits were fine enough.) (The drawing above shows an intake horn that is around 1.3 times the diameter of the Savonius rotor, which is about as short as I would ever suggest making one.)
The traditional 13% efficiency of a Savonius is significantly improved to roughly 22% by eliminating the need to force the convex side of the returning cup into the oncoming wind. (THAT was the First Improvement). Then THAT amount is nearly doubled up to around 38% by actually USING that air that would have hit the convex cups and smoothly adding that air to the air that would have originally gone into the concave cup. It turns out that there are some losses that exist as well, and my actual measured performance was always at least 28% and sometimes around 32%. The result is that the simple and cheap 55-gallon drum Savonius can have about MORE THAN DOUBLE the standard performance! More than TWICE AS MUCH ELECTRICITY can be produced! If a really good exit horn is also used, that improves even more up to around 38%. In my experiments, I tended not to add the exit horn, except on one of the units, although that might have been due to laziness!
Keep in mind that these improvements in efficiency were even with really crude 55-gallon drum Savonius Rotors and "quick and dirty" construction techniques!
Notice that there are also exterior shroud walls (top and bottom lines in the drawing) which keep the oncoming wind from being turbulently affected by the motion of the returning convex surface. Notice also that there is an odd shaped area near the top right of the drawing which is actually a dead-air space (enclosed).
You can see that ALL the air that is caught by the full-width opening of the exponential horn HAS TO hit into the concave cup of the Savonius. Actually, because of the shroud, the concave shape is not actually even that important any more! I have made some of these which had FLAT surfaces instead of concave, and FOUR of them instead of two. As the air is forced into contact with the rotor, the additional blades actually help direct the air against the desired blade for the greatest torque generation!
A number of people have shown interest in this concept, but are not familiar with the sophisticated concept of an exponential horn. And, without a lot of drawings, I guess it is hard to visualize this intake chute. The following description is meant to help!
Again, begin with a cylindrical shroud just slightly larger than the width and height of the Savonius rotor itself, just big enough so nothing rubs when either rotates. (we only see about 1/4 of this structure in the upper right of the drawing, as the inner wall of the dead-air space.) And slightly less than half of the front surface of that shroud is removed. When it is operating, only the inside of one of the rotor cups would be visible through that opening. Now, extend the OUTER wall STRAIGHT (flat) ahead, say 6 feet, with the full height of the shroud. That piece is therefore rectangular, right? (It is the bottom line in the drawing).
Next, there is another rectangular piece, also with the full height of the shroud, and maybe also 6 feet in the other dimension. This piece should not be too thick, because it has to be curved, flexed. It will also attach to the cylindrical shroud, but at the edge of the opening that is near the middle of the front, initially also sticking straight forward. (this is the curved inner wall of the intake horn in the drawing.)
Now, make another rectangular piece exactly the same as the FIRST, flat outer wall. Mount it on the opposite side of the cylindrical shroud from where the first piece was attached, and it also points forward. (this is the TOP straight line). There is NO hole in the shroud anywhere near this piece! Its function is only to allow air passing nearby to not be disturbed by the irregular shape of the exterior of the structure.
The assembly should now have three vertical panels sticking forward from the cylindrical shroud. Now, the middle one of these is now bent, bowed, so that it's outermost edge meets the frontmost edge of the third piece described. They would be attached together, at least temporarily. There should now be an empty space trapped in front of the non-open side (the dead-air space we have mentioned), and there should be a funnel-shaped opening into the rotor itself (most of the right half of the drawing).
Top and bottom (flat) surfaces are then added to enclose those two spaces and to add structural strength to the three surfaces.
Now that you understand the five pieces that are necessary, you can pre-plan building it. The middle vertical panel must be curved in a specific exponential shape. It is easiest to create the correct shape by first attaching a 2x10 to the floor and roof pieces. One edge of these 2x10s is cut to follow a curved shape. Once those backing plates are mounted to the top and bottom surfaces, the inner surface can be very easily and smoothly bent against them in getting its front edge to meet the other front edge.
(See the drawing nearest above to see what these dimensions are describing, the WIDTH of the tapering space on the right-hand side of that drawing.) A simple way to do this is to draw out on the floor and roof panels, the curve that will be necessary. For an intake chute that is to extend three feet in front of a six-foot diameter shroud, the outer side walls would be the (3 + 3) 6 foot dimension mentioned above. The initial width of the chute would be the 6 feet of the full shroud width and it would narrow down to slightly less than half of that, slightly less than 3 feet wide. The following chart could be used to draw the curved line:
|Dist.Forward||Width inches||Width as a decimal|
The last column is straight from a standard exponential chart from any math book. The middle column is simply 35" times that number, and represents the distance from the OUTER edge of the chute. These numbers can be different depending on the width of the intake and outlet of the exponential intake horn. We have obviously given dimensions here which are larger than those appropriate to a 55-gallon drum!
The top line indicates that the chute width would be 35" as it releases the air into the rotor. The bottom line indicates that it is 72" wide at the very front, so all the air that would have hit the Savonius is now re-directed to go through the rotor.
This chart could be used for any size Savonius rotor, and any length of intake extension. Just start with the width of the opening that will feed the Savonius cups (taken here as 35", slightly less than half the 72" width of the actual rotor to provide for the center vertical axle shaft). Multiply the value in the last column by that measurement to get each width value.
As to other lengths of the intake extension, consider this: In principle, the intake chute could be made 1" in length! But then, the curved inner wall would essentially be flat against the wind. It would technically be an exponential horn, but the air wouldn't have enough time to adjust for its tapering shape.
On the other hand, consider a 50-foot long intake extension. The incoming air would have plenty of time to move sideways the couple feet to adjust for the tapering shape, and it would have extremely high overall efficiency. However, the outer shroud, including this intake extension, must be able to rotate to face the wind! Imagine the tail structure that would be necessary to swing such a huge intake horn into a strong wind! And imagine that it would knock down anything or anyone that was in the way!
As long as the intake extension is at least as long as the width of the final output, as in the example above (both 3 feet), the air generally has adequate time to adapt and the efficiency will be greatly improved. However, a six-foot long extension on the example system above would increase performance efficiency by several percent. It may or may not be worth considering! In general, our attitude is that, if a few percent more output power is a serious concern, just make the Savonius rotor a couple inches bigger in diameter, or taller, or both. In any case, the actual effect of any length of exponential horn intake can be calculated, although it is fairly messy to do. Our experience is that an extension length equal to the full-width of the Savonius rotor seems to provide about as much of improvement as is practical without having a really long extension swinging about! An intake chute extension length equal to double the whole-width of the Savonius rotor seems to give around 2% or 3% higher overall efficiency and significantly better performance.
This second improvement also greatly improves the net efficiency of a Savonius Rotor. With well-designed and engineered exponential horns for acoustic impedance matching, this improved Savonius Rotor version can produce enough power to supply a substantial portion of a household's electrical needs. Because of the intake horn, the 10-mph wind is traveling at (nearly) 20-mph as it gets to the rotor cups, so it contains eight times as much power per square foot, in accordance with the equations above.
With the shrouds, even a single 55-gallon-drum sized Savonius can realistically create around 25 watts of relatively reliable electricity in moderate winds. More in stronger winds, of course. Bigger ones obviously could provide even more. However, with the extreme universal availability of surplus 55-gallon drums, it seems logical to just make ten of these assemblies to be able to provide a consistent 250 watts of electricity. In an average day, that would be around 6 kilowatt-hours, around 2/3 the total daily electricity consumption for an average American family. And it really does not take too long to make ten Savonius rotors and not too much more time to make all the shrouds for them.
Yes, and if there is a storm and there are 40-mph winds, you could capture over 7,000 watts of electricity then!
Regarding bigger ones: A simple Savonius Rotor with two six-foot-high by three-foot-wide cups would intercept about 36 square feet of wind area. With that 10 mph wind speed of our previous examples, that represents more than 0.9 horsepower of initial wind power. After losses for the Savonius mechanism, friction in bearings, pulleys/gears and losses in the alternator, this might realistically
create around 400 watts of reliable electricity.
Such a Savonius and (fiberglass? plastic? aluminum?) shroud could be constructed quickly, easily and inexpensively, and could be hooked up to drive an automotive alternator hooked to some car batteries. At very low initial expense, a reasonably consistent source of electricity for (some) house lighting could be provided!
(I still prefer the 55-gallon drum approach, especially for remote locations. In case future repair/maintenance is needed, replacement drum halves can probably be found.)
If the shroud is reasonably close fitting around the rotor, a cup-shape for the rotor blades is really not necessary. Once the air has entered into the intake funnel, it really has no choice but to push the rotor blades through. The latest version resembles the rotating doors on big department stores. A person (or air) cannot get by without pushing the door (blade). As to the number of these new flat blades, I am still experimenting. Two seems like a bad idea, because if the blades happened to be aligned with the wind, it would never self-start. Three would always start, but construction and static and dynamic balancing are harder. Four seems to be a currently attractive number. The air path is always blocked by either one or two blades, so it would always self-start, and that structure is naturally symmetric so static and dynamic balancing should not be too difficult.
One reason why this actually improves the overall performance has to do with the exiting air. The cup shapes have a tendency to keep air in the bottom, so some of the air is somewhat sucked over to the returning side, causing substantial turbulence. Flat blades, instead, do not have such a sucking action, and so the air is freer to continue to travel relatively straight. There is still turbulence generated, but far less than with the cup-shaped blades.
This design, too, can benefit from several different levels of improvement.
This improvement essentially places the farm windmill turbine inside of a large (horizontal) cylindrical shroud. Technically, this is called a 'ducted turbine'.
A normal farm windmill has its turbine upwind of the tower it is mounted on. There are a variety of stability reasons why it seems better to have the actual turbine wheel rearward of that axis with a shroud surrounding it. The shroud is basically a tube that is collecting and enclosing wind (and wind pressure). Once air is within the shroud, it has no choice but to eventually pass through the turbine wheel in order to escape. In the process of this, we are developing a 'stagnation pressure' inside the shroud just forward of the turbine wheel. This modification somewhat changes the concept from being a 'momentum' capturing device to one that also uses this dynamic pressure differential to rotate the turbine wheel.
The presence of the shroud slightly increases the maximum efficiency, but it also greatly widens the windspeed range for high efficiency operation. The result is a much greater actual average power output during the natural variations in wind speeds.
As with the Savonius, aerodynamic design considerations can GREATLY improve acoustic impedance matches for both intake and exhaust. Again, versions of exponential horns are very close to ideal choices.
A simple solution exists! Each of the (flat, not airfoil) blades of the turbine wheel would be mounted to the turbine structure slightly differently. Rather than being rigidly mounted (at a specific angle) to that structure, only the front (leading) edge of each blade would actually be attached to the structure, and that would be on a hinged mounting. Pressure from the wind (inside the upstream shroud) would therefore act to 'feather' the blades and greatly increase their tilt angle. A simple tensioning spring (like a screen door spring) would normally hold each blade in its 'preferred angle' position.
Operation would be as follows: At low windspeeds, the blades would remain very flat with the plane of the turbine wheel surface, very much resembling a normal farm windmill. At higher windspeeds, the greater stagnation pressure in front of the turbine wheel would cause each of the blades to stretch its spring and feather back, basically opening up and allowing much of the air to pass right through without further increasing the stagnation pressure. At extremely high windspeeds, like our 60 mph example, the blades would be pressed back completely 90°F so the high speed wind could pass fairly freely through without applying any significant pressure on or doing damage to the structure.
This improvement has an additional advantage of representing a sort of automatic speed control for the turbine. With very low speed wind, the blades are very closed and thus capture a substantial portion of the available power. As wind speeds would increase, the blades would automatically tend to open up, to minimize the effect of over-spinning the turbine wheel. And, as mentioned, at extremely high wind velocities, the blades would open up completely, which essentially stops the system from trying to capture any significant portion of that great wind power.
There are several parameters that are pre-settable with this configuration. Stop blocks would keep the individual blades from closing completely (due to the spring action) and establishes the performance efficiency at low wind speeds. The spring lengths and strengths can be chosen to allow the blades to open up at any desired rate. The local wind history for an area, and the size and construction of a specific turbine and shroud, would determine these choices, and experimental trials would probably be necessary to establish the ideal choices for a particular installation. For example, if a turbine structure was made of light, thin materials, it might be more susceptible to damage from high windspeeds, so weaker springs would be chosen, to allow the blades to feather in lower speed damaging winds.
For example, in this last Improvement, there is actually an additional 'drag coefficient' that exists in the calculations. Since our blades were normally virtually flat facing the wind direction, we assumed a drag coefficient of around 1.18 that applies to such situations. As the blades feather, this drag coefficient drops to near zero, which explains the stoppage of useful power production at very high windspeeds. At intermediate windspeeds, or with airfoil shaped blades, that drag coefficient can be modified. For the purposes of these inventions, it did not seem critically important to absolutely maximize the ultimate performance at massive financial expense in construction. I am saying this here in the event that some engineer wants to further refine these designs.
C Johnson, Theoretical Physicist, Physics Degree from Univ of Chicago