I know a fellow who, when discussing of wind power, always reminds people that the modern three bladed wind turbine is built wrong. He claims that it should have many more blades because that would catch the wind better.

Then he goes on to show photograps of old pumping mills that have dozens of large sheets suspended from a metal ring and tilted at an angle towards the wind, or jet aircraft compressor wheels that have hundreds of blades filling the entire disc. That's his idea of what the optimal windmill should be. He even has a small conspiracy theory about how Danish engineers play down the merits of the old farm type windmill to sell more of their cheap "rubbish mills" and how the Betz' law doesn't really apply for wind turbines.

His rationale: the larger the blade surface area, the more wind it catches and the more torque it generates, and the more blades there are, the less wind escapes between them and goes to waste. His idea of a windmill blade is like that of a sailboat sail - the bigger it is, the more it pulls.

Now I've tried to explain to him about the idea behind the sweeping motion of the blade, and how the wind that "leaks through" will still have an effect on the rotor, but I have no direct way to prove my point, so I deviced a simple experiment:

1) Take a circular piece of cardboard
2) Put a bolt through the middle for weight
3) Drop it and measure the fall time
4) Cut the cardboard into four relatively narrow blades but don't twist them
5) Drop it and measure the fall time
6) Drop it again and this time spin the rotor
7) Compare and contrast

If I am correct in my assumption, the fall time of the spinning rotor should start to approach that of the disc the faster it is spun because the sweeping motion of the blades catches more air than the stationary wings. Notice that the flat blades do not produce lift from the spinning motion, so the only variable in fall time should be caused by how much "wind" the rotor catches as it falls.

The point is, that you don't need more blades to make an effective wind turbine. You can even do it with just one blade as long as it spins fast enough to catch the wind that is coming at the sweeping circle of the windmill. This may be counterintuitive, but it's true.

I tried to prove it myself, but I only have a digital camera that does 30 blurry low-resolution frames per second, and I don't have a working release mechanism for the spinning rotor or any way to spin it other than by hand.

Could you help me, please?

If you want to make a longer segment of it, you could also build small windmills with different number of blades and see how they fare at different wind speeds. See which mill makes the most power.

If you are really interested in wind powered objects, you might want to peruse this forum:

http://www.talkrational.org/showthread.php?t=19434

If you ask your question there, you are very likely to get replies from several very learned people with extremely good credentials. There is however a major quack on that site by the name of humber. For the sake of your sanity, ignore everything he says!

Your friend is both right and wrong in this case. The most efficient windmill will have a large number of thin blades; however, this efficiency will not exceed the Betz limit. The Betz limit is actually an extreme case of an infinite number of infinitely thin blades that have 0 drag. The only other assumptions made for the Betz limit are purely axial flow, and that the flow is incompressible and adiabatic...all of which are ideal conditions that are better than you can expect from reality.

Now, why do we want a bunch of thin blades instead of a few big barn doors? Drag on a windmill is lost energy that is put into stopping rotation (part of the drag vector points opposite the rotation direction). It acts both axially, trying to push the windmill over, and opposite the blades rotation. Just like an airplane wing, induced drag is inversely proportional to aspect ratio. So thin blades are more efficient at producing lift (the force that rotates the windmill blades). This means thin blades achieve a high L/D which is exactly what we want in a windmill blade. A barn door would generate a lot of lift, but also a lot of drag. Practically speaking, we can't make a windmill with an infinite number of infinitely thin airfoils...structural integrity, high speed vibrations, bird strike are all things that are problematic with high blade counts. Also, adding more blades beyond a point becomes ridiculous. Blade count and efficiency follow diminishing returns. While increasing from one blade to 2 will net you around a 6% increase in efficiency, the jump from 2 to 3 will only give you only a 3% increase and so on and so on. All these tradeoffs correlate to having 3 blades be the most efficient design for today's technology.

Wind turbines have become a highly competitive business with companies like GE behind the designs. GE arguably has the most sophisticated gas turbine design teams and tools in existence.

You can count on the fact that modern wind turbines are highly optimized designs not just for aerodynamic considerations, but also many practical considerations such as manufacturability, strength, economics of construction, transportability, ability to withstand inclement weather conditions, and many more. I believe a long, continuous blade would likely fail many of these considerations, not to mention potentially be inefficient due to excess drag from so much surface area.

The old farm and Danish windmills are likely flat and large because it was more practical to fabricate flat shapes, placement was less ideal, masts were much shorter, and thus average wind velocity substantially reduced.

There are good examples of modern day air handling machines that have a very high density of blades as you mention. Look at any turbofan aircraft engine. Turbofans usually have much higher working pressure and velocity than a wind turbine, spin considerably faster, are ducted, have very strict size requirements, and are designed to work in conjunction with static blade sets.

quote:

Your friend is both right and wrong in this case. The most efficient windmill will have a large number of thin blades; however, this efficiency will not exceed the Betz limit. The Betz limit is actually an extreme case of an infinite number of infinitely thin blades that have 0 drag.

The Betz assumption does not actually represent a most optimal windmill. He simply imagined an infinitely thin disc that extracts energy out of the flow to simplify the problem. Whether an infinitely large number of infinitely thin spinning blades matches this assumption is a matter of debate. More modern calculations have showed that the Betz limit is not exactly "right", but very close anyways.

The result of the equation is that the efficiency depends on the ratio of flow speeds before and after the windmill. The more blades you put in a real windmill, the faster it needs to turn in order to -not- slow down the wind too much as the wind picks up speed. As the blade speed to wind speed ratio grows too much, the efficiency of the blade drops and so does the efficiency for the windmill.

In other words, windmills with large number of blades tend to perform badly in high winds. Their efficiency peaks out very early and falls off before the wind speed picks up. However, as the available power in the wind increases at the cube of its velocity, the most available power and subsequently, energy is usually had at high wind speeds regardless of the fact that high winds happen less frequently.

The original thesis and the myth is that a windmill with more blades should produce more. The antithesis is that a windmill that has less blades will do more work. Intuition says that more blades indeed means more force and therefore more work done, which is why it is so counterintuitive to claim that reducing the number of blades would actually yield you more.

What the experiment I suggested is supposed to prove is, that a windmill with less blades effectively acts as a windmill with more blades when you put a spin to it. I'm trying to provide some tangible evidence in a form that he might understand, because he basically denies the validity of Betz' law, so I can't use mathematical proofs.

Betz model predicts a power coefficient of 0.593 and is independent of tip speed because of its assumptions. The Glauert's wake rotation model asymptotes to the Betz limit as tip speed ratio increases (ie the rotation in the wake goes to zero). The third model is the GGS model that takes into account non-uniform pressure distribution and curvilinear flow across the rotor plane. This model predicts an power coefficient of 0.301 which is substantially lower than the other two. Peak efficiency, however, matches very close between these models. For the Betz model, the efficiency is a maximum at 66% flow through and for the GGS model at 61% flow through. (you're going to have to explain to me how the Betz model isn't the most optimal case of a wind turbine. It seems to me to be the best case where flow remains axial and no losses are incurred to drag.)

In reality, the GGS model is too low and the Glauert model is too high. Actual wind turbines fall somewhere in the middle with power coefficients between 0.301 and 0.593. Likewise, the most efficient windmill will be those that allow between 61% and 66% flow through. You also want higher tip speed ratios so that the angular momentum in the wake is low. That said, for a given airfoil, efficiency will eventually drop as tip speed is increased. The rotor will also act as a wall if tip speed is too high (essentially the axial induction factor increases so the flow is moving at an angle relative to the rotor area vector). And finally as tip speed and blade count increase, there is increased loses due to blades interacting with each others wakes. It's an extremely complex problem and there is no generality to cover all bases. Whether 3 blades is better than 5 is dependent on the situation and design.


Personally, I'd just give up trying to explain windmill design to your friend. But, the simplest way I can put it for him is that too many blades acts like a wall. It blocks the flow and lowers incoming wind speed. If wind speed is reduced before it hits the rotor, then you've already lost a bunch of energy that could have been extracted.

Probably the simplest method to prove it to him is to actually make some crappy small windmills that raise a weight and put them in front of a fan. Time how long each design takes to raise the weight. Heck, if you really want to hurt his pride, make it a competition. Let him build a 9 blade monstrosity...after all...he seems to know more about windmill design than GE or Vestas.

Einomies and TaurusSW, you should pop into the site that I listed for an entertaining and enlightening discussion of a wind powered device, namely one that can go directly downwind powered only by the wind and able to go faster than the wind that is powering it. A counter-intuitive concept and one that Mythbusters is apparently considering doing an episode on.

This has been on the web for the last four years and has generated some very interesting and sometimes astoundingly wrong physics arguments have been presented. My first exposure to this was on this forum last year.

Watch this video if you're interested:
http://www.youtube.com/watch?v=aJpdWHFqHm0

quote:

Originally posted by oldguy1:
Einomies and TaurusSW, you should pop into the site that I listed for an entertaining and enlightening discussion of a wind powered device, namely one that can go directly downwind powered only by the wind and able to go faster than the wind that is powering it. A counter-intuitive concept and one that Mythbusters is apparently considering doing an episode on.

This has been on the web for the last four years and has generated some very interesting and sometimes astoundingly wrong physics arguments have been presented. My first exposure to this was on this forum last year.

Watch this video if you're interested:
http://www.youtube.com/watch?v=aJpdWHFqHm0

The discussion sure is entertaining. I definitely got a few laughs from it. Thank you for the link.

As for the machine, it's quite an elegant design. I don't foresee it gaining any practical applications, but I wouldn't mind designing and building one myself. It'd be a fun project.

I have one of the small carts and have learned a lot of interesting things from it and the discussions around it. I mostly missed aerodynamics in my self-directed education but I think I have made up some ground because my participation in that topic. I contemplated designing and building a non-prop version just for the sake of doing so but soon realized the uphill battle involved with that task. There are plans available for the small cart and a large scale cart is presently being built:

http://www.fasterthanthewind.org/

No practical application, although there is the intriguing concept of a moving wind turbine encountering a much larger volume of air to harness energy from in a specific amount of time.

I've been fascinated with wind turbines for years and kept up on some forums. One of my degrees was in Electronic Engineering (circuit design, compared to large Electrical design). From looking at this the whole topic can turn into a design forum about wind turbines. How fast they can turn. Limits of weight, strength of material and an entire Engineering background in Aerodynamic design. With the push at a National level for energy I know there are going to be some engineering firms fighting for $$$ claiming their design is best. I see there is an ongoing interest here, though I wonder if the theories ever stop without some serious CAD/CAM software and a good build team. RJF