These devices are really huge! A single blade on a single windmill is often nearly as long as an entire football field! Since there are either two or three of those blades, mounted on a tower that is generally around 30-stories (300 feet) tall, there are VERY large, VERY heavy objects moving around up there, sometimes 50-stories high! 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!
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 energy put in is therefore wasted, as heat, along that 60 miles. This also pretty much explains why virtually all electric power plants are build 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!
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.
The large scale devices are extremely susceptible to a real problem. Each time a windmill blade crosses in front of or behind the tower that is holding everything up, the wind get blocked for an instant. So suddenly the tower is no longer being slightly bent from the force of the wind! The tower therefore tilts forward into the wind, only to be immediately bent back. Also, the force on the blade is also affected by the fact that the wind is momentarily not able to smoothly continue past the blades. These things can cause RESONANT FLEXING of both the towers and the blades. During the 1980s, there were many of the larger windmills where towers either completely broke off and fell, or stress fractures formed in either or both of the tower and/or the rotor blades, or even more commonly, the constant flexing caused bolts to loosen and fall out! (This is vaguely related to the short movie you probably saw in High School science where the Tacoma Narrows Bridge started vibrating in a rather constant wind and eventually destroyed itself from resonant vibrations that got so intense that the Bridge cables and structure could not support it. Also, many tall chimney towers would start vibrating and then collapse, from resonance issues.)
Somehow, many of those self-destruction windmill inicidents 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 mechanical failures.
In a related presentation, we present a far more logical and far less expensive approach to capturing wind power and converting it to electricity. Not only that, the construction is NOT full of exotic devices but instead would all be constructed BY A COUPLE HUNDRED LOCAL LABORERS in and near the community that would receive the electricity. On top of that, our approach gives every indication of FULLY AMORTIZING ITS COMPLETE CONSTRUCTION COST in only two to three years! The presentation is at An apparently far better approach to the wind farm concept.
Small Scale Devices
From about 1870 on, farm windmills were extremely popular. Many were installed on towers that were about 50 feet tall, and they were about ten feet in diameter. This is being noted here because FEW attempts at building and installing small scale devices are anywhere near that large. We will see below that those farm windmills generally could capture about 1/6 horsepower of the wind's power (at average windspeeds). That was enough power to raise water up a well, which was the ONLY function that those windmills were ever used for!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. 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!
What I Consider to be a Savonius Rotor!
(Drawing is a top view of a completed Savonius)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 nearlly 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!
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!
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 Savonuis 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!
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.
Several technologies have existed for a number of years that use the power that is present in wind movements to create electric power. In general, the wind movement causes some sort of rotary motion.
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.
Mechanism
There are two main categories of mechanisms.
Horizontal-Axis Wind Turbines (HAWTs)
This category includes all mechanisms where the axis of rotation must be oriented to face directly into the wind.
- An extremely early version of this mechanism was the big Dutch-style
windmill, which was used primarily for milling grain. We do not know
the overally efficiency of Dutch-style windmills, but it figures to be
rather low.
- Another early style of this mechanism was the windmill that was on most all
farms in the early part of the Twentieth Century. It was a rather simple
(and somewhat inefficient) design, but it was only intended to pump water up
a well. Its extremes of performance were of little importance, as were
its low efficiency in converting the power in the wind to useful work.
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.
- An improved version is called the multi-blade wind-axis turbine.
This version uses airfoils instead of flat surfaces, which improves
its maximum efficiency to around 39% or 40%.
The factor called X, the turbine-tip speed ratio, is greater for these
airfoil-bladed windmills, commonly around 2.3 when the blade airfoils
are well-made. This means that the speed that the ends of the blades
commonly move is around 2.3 times the wind speed! If we consider
a tower windspeed of around 20 ft/sec, this means that the circumference
of the windmill rotates at around 46 ft/sec. If the windmill is 10
feet in diameter, or a circumference of 31.4 feet, this indicates
that that windmill should rotate around 1.5 revolutions per second
or about 90 rpm. A gearing ratio of around 8:1 should be fine
to spin an automotive alternator appropriately fast. Otherwise, the
operation is relatively similar to farm windmills.
- The third common version of wind-axis turbine is the high-tip-speed
or Propeller-style. These can have that factor called X, the turbine-tip
speed ratio, at around 5 or 6 to one. If the windspeed at the top
of a tall tower is 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. This fact explains why the very
large tower windmills have to be shut down if the wind starts getting
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 300 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?
These 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.
Vertical-Axis Wind Turbines (VAWTs)
This category includes wind turbines where the axis direction is at a right angle to the wind direction. In practical terms, this virtually always involves a vertical axis (VAWT or vertical axis wind turbine). There is a wonderful bonus from this situation. It works identically well, no matter what direction the wind comes from! So no provision for aiming the mechanism is necessary, as is critically important with HAWTs.
- An early style, from centuries ago, is generally called a Savonius
Rotor. The spinning part of a weatherman's windspeed device
(anemometer) is a variant of a Savonius Rotor.
Sideways mounted cups catch the wind and cause the vertical shaft to spin.
A Savonius Rotor has an advantage over the farm windmill in that it
does not have to be pointed into the wind. It works equally well
with wind from any direction. However, a Savonius Rotor has the
negative characteristic of having to "push" the back side of its
returning cups INTO the oncoming wind. This causes a
rather low maximum efficiency, around 14%. That efficiency does
not drop off as rapidly as most other designs (only the propeller
style has a wider range of windspeeds for high efficiency). In addition, the
Savonius Rotor has tremendous starting torque where most other
designs have very little torque at low rotational velocity.
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.
- A very sophisticated VAWT (vertical-axis wind turbine) is the Darrieus
Rotor. This design looks something like an egg-beater (and is sometimes
called that), with usually either two or three curved airfoils.
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.
Another, Technological Design
There is another design that does not fit in either of our main categories, called the Cyclogiro. This design vaguely resembles the Darrieus Rotor but the operation is extremely different. The Cyclogiro spins like a Darrieus, but its airfoils are vertical and straight instead of curved. Those airfoils are individually constantly controllable as to pitch orientation.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.
Actual Functionality
Any moving material carries kinetic energy and momentum. The basic laws of kinematics allow an easy analysis of a first approximation of performance. Essentially, any wind-power mechanism captures energy by slowing down the speed of the wind involved. The famous Rankine was the first to develop the equations for it. In simple terms, he determined the momentum in the wind to start with; then recognized that the air becomes pressurized just forward of the restriction of the turbine, which converts kinetic energy into pressure energy, which slows the air down by an amount called the interference factor; the air then loses more energy to the turbine itself, which slows the air down again. An analysis of the Conservation of Momentum establishes an equation. Then, applying the fact that Conservation of Energy must also apply, we arrive at reliable equations that show the theoretical performance of any wind turbine.
Undisturbed wind contains power from kinetic energy (energy flux) equal to:
E = 0.5 * r * V3
* p * 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. (r 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 * p * R2 * r * V2 * a * (1 - a)
r is the air density or 0.00237 lbf * sec2/ft4.
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
or
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).
(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 high tower can provide around 8 times the output power. 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.
Problems In Larger Systems
It turns out that there are MANY problems in the larger versions of these devices. A scary fact is that the DESIGNERS of the huge wind turbines on those wind farms often wind up GUESSING about certain design characteristics! There has not been a long enough history of usage to actually know many things yet!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 lengths of the rotor blades are as long as a football field, around 300 feet! They also have considerable weight. 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!
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 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, 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. 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 10 cents per kwh, 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.
These Suggested Improvements for SMALL-SCALE, Low-Expense Windmills
In general, very little research is being done on small-scale wind-power capturing techniques. What IS being done is financed by the government and the big power companies, and is virtually exclusively associated with the two known methods of highest efficiency, the Propeller-style HAWT and the Cyclogiro VAWT. Even the Cyclogiro has been getting little attention due to a number of catastrophic failures of equipment due to stability problems. These two technologies are both best suited to very large-scale mechanisms, which explains the government and power company interest as related to significant electric power generation.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.
Improved Savonius Rotor
(I invented these two improvements during the 1980s and first presented them in this web page in March, 1998. Extensive earlier experimentation with Savonius rotors began around 1972.)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.
Improvement 1 - Simple Rotatable Shroud
The greatest source of inefficiency of a Savonius is the need to push the back side of one 'cup' INTO the wind while the other 'cup' is catching the wind, creating useful power. This is essentially like a waterwheel that has water randomly coming down at it from all points. Such a waterwheel would still work, but much of the productive action of the filled 'cups' would be wasted in pushing the upward returning 'cups' up against the down-flowing water there. A waterwheel is far more efficient by selectively having the water ONLY hit the downward moving 'cups'. This is the concept of this improvement.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.
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:
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° 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.
Improvement 2 - A Far-Better, Fully Aerodynamic Shroud
The shroud described above greatly improves the performance of
a Savonius Rotor, but there are two problem areas that would
remain. Half of the area that is presented to the wind is blocked
off by the presence of the shroud covering the forward-moving
'cups' (so the power in that air is not captured), and a LOT of
turbulence occurs in the wake of that non-aerodynamic
configuration. This leads to the second level of improvement.
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).
Dist.Forward Width inches Width as a decimal 0" 35.0" 1.000 3" 37.2" 1.062 6" 39.4" 1.127 9" 41.9" 1.197 12" 44.5" 1.271 15" 47.25" 1.350 18" 50.2" 1.433 21" 53.25" 1.522 24" 56.5" 1.616 27" 60.0" 1.716 30" 63.75" 1.822 33" 67.75" 1.935 36" 72.0" 2.054
The rear chute of the shroud would also be extended several feet
(rearward). The exiting funnel shape is more complicated
here, but an exponential horn shape is pretty close to the
best shape to match the existing acoustic impedances. It obviously
starts with the half-width and widens to the entire width of the
whole shroud at the end exit.A Later Revision!
In late 2002, I discovered that this version of a Savonius and
this shroud can be substantially simplified, and it even
improves the performance!Improved Farm Windmill
(I invented these improvements, as a 'Duct-Axial Wind Generator' in 1975.)Improvement 1 - Another Shroud! (Actually, a Surrounding Duct)
The greatest efficiency loss of a farm windmill is due to air
that hits the blades doesn't all have time enough to continue on
through the slots between the vanes, and much of it 'spills'
radially outward to go past the turbine structure and be wasted.Improvement 2 - A Better Shroud
This improvement CAN also be enhanced by modifying the shroud into
being a short and simple Exponential Horn, as discussed for
the Savonius. Such a horn has less benefit for a farm-type windmill
because it is not easy to make it long enough to have significant
value. But it IS possible, and even a very short Exponential Horn
could have noticeable improvement effects.Improvement 3 - Avoidance of Self-Destruction!
A ducted turbine design is SO efficient at developing the desired
pressure gradients, that this can represent a problem. In extremely
strong winds, a LOT of pressure can develop inside the shroud, pressing
against the turbine wheel structure. Using previous examples, if our
shrouded farm-style windmill is ten-feet in diameter, in a 60 mph wind,
there is about 9.2 pounds per square foot of force pressing against the turbine
structure, or 720 pounds of total (static) pressure pushing on it.
This represents around 115 horsepower present there. Such huge forces could
bend or break the mechanism.
Additional engineering and design is possible on each of these
improvements. They have all included various assumptions,
in order to keep the mechanisms as simple and low-expense as
possible, while still giving high performance and efficiency.
We have concentrated on the 'Mechanism' in this article. The
other necessary parts of the system, the gear train or pulleys,
the alternator or generator, the batteries, and the inverter,
are all well-established technologies that are at the point of
being proven, economical items. Any of the
'improved' versions could be arranged to spin an automobile
alternator (which often includes a voltage regulator inside it)
to keep half a dozen generic car batteries charged. Then, either
low-voltage (12 volt) wiring and lights could be installed or a
standard inverter (12 volt DC to 110 volt AC) could be used to
provide the desired lighting or electricity. If you build the
mechanism ($200 materials), you get a rebuilt alternator ($50),
you get six $30 new batteries ($180), and a standard inverter
($100), you will only have spent around $500 to have a wind-powered
electric system. Depending on whether you could mount it on a
garage roof or a utility pole, or if you have to buy a strong tower,
there's another expense that could range from near zero to several
thousand dollars. In any case, there's the possibility that you
could create an inexpensive wind-powered electric system.
Back in the 1980s, many people were generally charged around $7,000
for wind-generating systems that did not perform much better!
Worse, they tended to include unique circuitry and unique parts, so if
anything broke or failed, the owner was up a creek! The approaches
described here all use very commonly materials. If the automotive
alternator you use fails some day, you would just find a different one!
I invented the Ducted Axial Fan version around 1972 and built an experimental
prototype in 1975, around four feet in diameter, which worked very well.
I invented the acoustic-impedance-match, exponential shroud for a
Savonius made from an old 55-gallon drum around 1985 but only first actually
built one in early 1998. This presentation
was first placed on the Internet in April 1998.
A different web-page provides a lower-tech approach to using Savonius
rotors to produce massive amounts of electricity for a house that
aspires to be self-sufficient!
A Simple, SUBSTANTIAL and Reliable supply of Electricity
A different web-page provides far larger-scale approach to using modified Savonius rotors inside of such a shroud and Exponential Horn, to produce massive amounts of electricity for hundreds of houses of a community. An Inexpensive, Fairly Simple, and Fairly Quick SUBSTANTIAL and Reliable supply of Electricity
Energy-Related presentations in this Domain:
Global Warming Calculated by a PhysicistStrict Scientific Analysis of Consequences of Fossil-Fuel Burning
Global Warming and Climate Change - Possible Physics Solutions
Unlimited Hot Water FOR FREE, while Solving Global Warming! (biodecomposition)
Heat Your Whole House FOR FREE, while Solving Global Warming! (biodecomposition)
Two Systems: to (1) collect sunlight heat and (2) store it for a winter, for ANY building!
Published Current Energy Resources Remaining in the Earth (Scary!)
Making all (Black) Asphalt Roads, Rooftops and Parking Lots White can reduce Global Warming!
Global Warming Issues Regarding HEAT Sent into the Atmosphere
Global warming Issues Regarding Carbon Dioxide, and Sealevels Rising
Hydrogen as an Fuel-source Replacement
A 100%-Solar Home Heating System For Virtually Any Climate
Solar Electricity from PV Photovoltaic Cells
An Absolutely GREEN Transportation and Freight System Which Is 20 times More Efficient than Cars and Trucks and Airplanes, Cheaper and Faster (200.0 mph)! (invented in 1989)
Batteries or Hybrids as an Fuel-source Replacement
Wind-Power for Making Electricity (Residential, some Watts)
Wind-Power for Making Electricity (Community, MegaWatts) (a million construction jobs and 12,000 MegaWatts of electricity)
The Earth's Wobbling (Precession) as a Source for around 63,000 MegaWatts of Energy
The Earth's Rotation as a Source for Energy
Waste Nuclear Power For Making Electricity And Heat?
The Physics of Efficiency In Electric Power Plants
Individual Ways of Reducing Your Energy Usage
Methods of Storing Energy for Later
How Much Energy Comes From the Sun? And Why is there Global Warming?
How does the Sun create so much energy?
Inventions Which Might Help Deal With Coming Energy Catastrophes
An Invention to Efficiently Make Electricity from Solar
Enormous Heating of the Atmosphere by the Alaska Pipeline
Air Conditioning without Huge Electric Bills and GREEN, without Freon
A Method of Storing Summer Heat to (Nearly) Entirely Heat a House all Winter
The Sophisticated Woodstove I Invented in 1973
The Physics of Wood as a Heating Fuel
Why is the North Pole Heating Faster than the rest of the Earth?
Scientific Explanation of Airplane Flight
A Possible way to greatly reduce Aerodynamic Drag of Airplanes
Link to the Index of these Public Service Pages
( http://mb-soft.com/public/othersci.html )
E-mail to: Public1@mb-soft.com
C Johnson, Physicist, Physics Degree from Univ of Chicago