Salient White Elephant

April 18, 2009

Pseudo-Lifting Fractal Turbine

When I first started learning about wind turbines, I wondered why a wind turbine with 2 or 3 blades was described as “aerodynamic”, or “highly efficient”.

Sleek, Highly Efficient, Modern HAWT
So much of the swept area seems unaffected by the blades. Surely adding more blades would allow for harvesting the energy in the wind that seems to be “escaping” through the large regions that are between the blades in the diagram above. This issue is discussed with the aid of the word “solidity”, which refers to the ratio of the area occupied by the blades divided by the total swept area. Surely the higher the solidity the better… no?

High solidity is a desirable feature with turbines that do not employ lifting surfaces. But a turbine that uses airfoils, like the one in the diagram above, is perfectly able to influence air “from a distance”. Imagine a long straight line of people dancing “the train”. Each has her hands on the shoulders of the person immediately before her. You’re standing there beside the line, and just as the last person goes by, you jump in line behind her. Then you put your hands on her shoulders and start dancing with the rest of the people in the train, but you kind of “drag your feet”. That is, you move more slowly than the rest of the train. Because the train is outrunning you, your arms will have to stretch out forward. And since you’re pulling back on the shoulders of the girl in front of you, she will have to slow down too. Her arms will have to stretch out forward, and so she slows down the guy in front of her, and so on. In this way, you cause the whole train to slow down, though you’ve only touched the girl immediately in front of you.

I think this is exactly how a lifting wind turbine manages to draw kinetic energy from air that has already “escaped” through the empty spaces between the blades:

Airfoil Exerting Influence From A DistanceYou may have heard that wind turbines with lifting devices are far more efficient than those that rely on drag forces alone. I can think of two ways of looking at this. First, the lifting force created by suction on the low pressure side of the airfoil is much larger than the lifting force created by ram air pressure on the other side. I read once that the suction force is 5 times greater than the ram air force. Second, most drag devices create turbulence. Why is this bad? Imagine the long line of air molecules “dancing the train” past the high-speed airfoil rotor. Their momentum is in the downstream direction, and their motion is very orderly. It’s hard for a molecule to make its way back toward the rotor because everybody is moving downstream. It’s kind of like trying to drive slow on a Los Angeles freeway when everybody else is barreling by at 90 mph. But turbulence is disordered motion. Imagine a crowd of people in a riot. Everybody’s running this way and that, banging into each other and so on. Now imagine the air molecules passing a turbine rotor in this chaotic fashion. Not only is it easier to make your way back to the rotor, but in fact somebody may bang into you and push you back toward the rotor. For this reason, the rotor cannot maintain low pressure on its downwind side. This eliminates the suction force that the rotor might otherwise generate, and therefore there is far less force to torque the rotor against the generator and generate electricity. Of course, we didn’t need to go through all this analysis to realize that the drag rotor turns less of the wind’s kinetic energy into electricity. All we had to do is consider all the chaotic energy in the “wind riot” that is left in the wake of the rotor. All of this chaotic energy is energy that was not converted into electricity, and it therefore represents an inefficiency in the system. We’d like to design a rotor that slows all of the air gently and evenly, leaving the least amount of disturbance in the wake.

Now let’s talk about thunder – what is it? When lightning pierces a region of air, it heats the air in the region tremendously. But lightning is only present for a very short time, and then it disappears. The air that was in the path of the lightning bolt is very hot, meaning it has expanded. But immediately after the lightning bolt is gone, this heat is dissipated into the surrounding air. Now the pressure of the air that was left in the wake of the lightning is very low because it is still expanded. So the surrounding air collapses into this evacuated space with a tremendous slap and a deafening roar. How does this relate to the issue of solidity and turbine rotors exerting influence from a distance? The fewer blades a turbine has, the lower the solidity. In order for a 2 bladed turbine to exert as much aerodynamic influence as a 3 bladed turbine, it must spin faster. But if it can exert influence from a distance, why does it need to spin faster? Because it can only exert influence from a limited distance. Unlike the human train, each molecule in the wind train exerts just a little less backward force on the molecule that is next in line downstream, until eventually molecules exert no backward force at all on their downstream neighbors. This makes sense. If turbines could draw kinetic energy from wind that is 100 miles downstream, we’d be powering entire nations with just a handful of wind turbines. A 2 bladed turbine spins faster than a 3 bladed machine so that the wind that passes through the “empty regions” between the rotor blades doesn’t have time to escape the region of aerodynamic influence before the rotor has extracted its energy. (Although not relevant to the Pseudo-Lifting Fractal Turbine, I may as well go ahead and explain why a turbine cannot extract all of the kinetic energy from the wind that passes through its rotor. If a rotor took all of the energy from the wind, then the wind would not be moving at all, and we’d be left with giant piles of air molecules lying around the turbine! The good news is that this renewable energy waste is not radioactive; the bad news is that we’d have to hire a bunch of truck drivers to haul it off to the official government renewable energy waste dump. If you want to learn more about this phenomenon, look up Betz’ law in Wikipedia.)

You would think the rotor characteristics just discussed would lead us to select a 2 bladed rotor design in order to cut the cost of one blade from the cost of the turbine. Unfortunately, things are not that simple. A 2 bladed turbine makes more noise than a 3 bladed turbine. This is because a high speed 2 bladed rotor blade pierces the wind like a lightning bolt. Yes, the evacuated region on the downwind side of the airfoil is able to draw kinetic energy from wind that is already considerably downstream of the rotor, but the evacuated region that realizes this action subsequently collapses just like the collapsing air in the wake of a lightning bolt. The first large wind turbine I ever worked on was the 2 bladed Carter 300 kW machine. One fascinating aspect of this machine was that it was able to extract energy from wind traveling as fast as 40 miles per hour! Standing beneath this turbine in a 40 mph wind was like standing beneath a heavy military helicopter – VOP!!!… VOP!!!… VOP!!!… VOP!!!… VOP!!!… Although it belonged to the “featherweight class” of turbines, it produced the electricity of an expensive heavyweight champion. But a machine like this pays the penalty of noise. Such a turbine can’t be sited near places that have people – residential areas and so forth. And its high-speed airfoils are difficult for birds to see, so this further limits siting options.

Now that modern wind turbines have reached a scale of several megawatts, you can imagine the difficulty of designing a robust blade that’s 40 yards long. A wind gust hits a region of one blade at a point (say) 75% down its longitudinal dimension (near the blade tip), and not only must the 40 yard long slender blade dissipate the huge lifting force generated by this gust, but in fact that mechanical shock ripples throughout the entire slender turbine structure. It’s a little like trying to design a giant “stick man” using nothing but drinking straws, and requiring that he cannot be knocked down by even 100 mile per hour storm winds.

The Pseudo-Lifting Fractal Turbine

The Pseudo-Lifting Fractal Turbine proposes to solve many of these issues. It moves very slowly, and I think it should be extremely quiet. It won’t kill birds. It poses little danger in the case of an accident. (I can’t think of a way for this turbine to “run away” and fly apart like an unloaded traditional rotor.) It can’t impress an admiring green public with lightning flash signs of power, but it will just absolutely dazzle mechanical engineers with the simplicity of its scalable mechanical design characteristics. I am hypothesizing that this turbine delivers the efficient aerodynamic performance of a high-speed modern rotor, but with the low velocity of a drag rotor. I’ve prefaced its description with a long theoretical discussion because I developed this machine from that theory.

The turbine design begins by finding the “perfect” drag shape:

The Perfect Drag Shape

Now we fractalize this shape one iteration:

Fractalized Drag Shape
Now we approximate the small arcs with clamshell airfoils that can open up into the fractal shape, and that can close up into a shape that has a low drag profile:

Clammified Airfoils Approximate Ideal Drag Profile
(I’ve drawn the clamshells packed together like sardines. Not sure why I did this. If the rotor truly generates aerodynamic suction, then the long arguments presented earlier would seem to indicate that it isn’t desirable to have 100% solidity. But while thinking about this topic, I want to point out something interesting about the open clamshells above. Doesn’t it look like the ram air pressure would be higher than it would be were it only hitting a single angled airfoil!? And I wonder if the low pressure might also be augmented somewhat, since low pressure air can’t reach the high pressure side of the airfoil by zipping around its trailing edge.)

Now we use two clamshell airfoil fractals to make a reciprocating rotor. (The following diagram is zoomed out to the extent that you can’t see the smaller arcs… only the large ones.)

Pseudo-Lifting Fractal Turbine
When the clamshells on one side close, the clamshells on the other side open, and vice versa. I am hypothesizing that if this rotor is carefully designed to avoid the generation of turbulence, and if the rate at which the clamshell airfoils open and close is just right, then this turbine should use aerodynamic suction to siphon kinetic energy from the wind in a manner that is very similar to the action of a high-speed modern turbine rotor.

How is the machine yawed? Both the tower and the tube at the top of the tower reciprocate as the machine produces power. (The ring and the generator are at ground level.) But the tower-top tube is also able to rotate with respect to the tower. Its motion is fixed to the motion of the tower whenever a brake that connects the two is activated. When the controller detects a change in wind direction, it simply releases this brake at the appropriate time and for the appropriate duration to cause the tower-top tube to rotate with respect to the tower to the correct yaw angle.

The turbine is shut down during high winds by closing all clamshells and releasing the brake that controls the yawing action.


I guess there are a lot of variations on the ideas presented here. Here’s an example:

Reciprocating Savonius-Like Turbine

Earlier I asked whether the high pressure and low pressure might be augmented by the open clamshell airfoil shape. Here’s a diagram that examines this issue in different way:

Clamshell Airfoil

And if this works, then why not something along the lines of the following?

Staggered Clamshell Airfoil

Maybe if the staggered clamshell airfoil produces lift, then maybe it would additionally provide the advantage of mixing air of different energy levels. If so, it might eliminate the “dead air” that is present with some airfoil designs. Another interesting question is what kind of vortex activity might be generated by this device? On the one hand, I can see how it might make zillions of vortices, but on the other hand I wonder if they would mostly cancel each other?

I wonder if anybody has ever tried to think of ways to use fractal shapes to make a wind turbine. Seems like there might be some amazing new possibilities there doesn’t it?



  1. hi,

    your whole elaboration is very intriguing and thorough but having read a bit about the actual low efficiency and practical uselessness of VAWTs (particularly as opposed to HAWTs), I tend to be a lil’ bit cautious before jumping high in joy of a new, breakthrough invention. Obviously, I am by no means knowledgeable in terms of aerodynamics but the first question that comes to me is: have you estimated the theoretical efficiency of this thing? I’m sorry to maybe drag you down to earth but the reality is that if sth is not better than what we have now (ie. HAWTs) and at the same time (!) has no better ROI (think $$$) then it’ll forever remain a theoretical design. Regretfully, because just reading your article it seems to me a beautiful idea!

    good luck, max.

    Comment by max — May 4, 2009 @ 5:32 am

  2. Thanks for your comment max. I pretty much agree with what you have said, but I would just make one comment about the psychological nature of this problem. When I read that the “efficiency” of a VAWT is less than a HAWT, it tends to bias my judgment. I mean who wants an inefficient machine? But I think you hit the nail on the head when you said “think $$$”! Suppose I can build a VAWT for $1,000 that has an efficiency of energy conversion of 20% and that produces 1,000,000 Megawatt hours a year. And suppose that as an alternative I can build a HAWT for $2,000 that has an efficiency of energy conversion of 50% and that produces the same 1,000,000 Megawatt hours a year. As an engineer, I am psychologically biased in favor of the HAWT because it has an “efficiency” of 50% whereas the VAWT has an efficiency of only an engineeringly embarrassing 20%. But if I take your advice, I notice that the VAWT lets me buy 1,000,000 Megawatt hours for $1,000 while the HAWT requires I pay $2,000 for the same energy. So clearly the VAWT is superior.

    As for the numbers, I have not crunched any numbers for this blog for two reasons. The first is I don’t have any tools. The second is that I don’t have a strong enough technical background. I figure I am good at coming up with new ideas, so I’ll just focus on that. There are plenty of people with the skills, money, and interest to evaluate the ideas I present here.

    Thanks again, and good luck to you too…

    Comment by Salient White Elephant — May 4, 2009 @ 6:41 am

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