The problem with the formulation may be that with blade bending the blade has to move downwind to produce work. Then it must move upwind to reset, at low blade lift.
If you do not take this into account your calculations will not directly match the starting point of the Betz limit calculations. So you are calculating something else. It has been shown for yoyo that the betz limit is lower for kites moving downwind. So maybe that is the answer you would eventually find also, considering that the blades are moving downwind.
The other problem with this theory is; how useful is it? Because for any rotary windmill, depowering the blade to unbend it is wrong in a lot of ways.
I wish we could find an example to discuss that was very concrete. Right now I am not following you at all
Yeah, I’m not following him at all either, and I don’t see why this “analysis” is taking place. Sure there is potential energy stored in a blade that is bent backward. and when it recovers, you will get recovered energy, just as a bird flapping its wing gives energy. But so what? You just lost the same energy bending the blade back. There is no free lunch here. Wind energy newbies are so far from even approaching the Betz coefficient that they are better off not even knowing about it. All it does is distract them and give them a new talking point to show off their general ignorance when they tell everyone how invalid it is and how they are going to beat it. You might as well just factor in a 16/27 multiple of the kinetic energy in the wind and realize that is what is available to extract on a continuous basis, period, full-stop, end-of-story. Yes you can extract more for a moment - by stopping the air flow, then after that, you get less energy. It is all way above most peoples’ heads and something most wind energy people have no reason to even think about. Build a decent turbine, and you will get a decent amount of power. Not all that difficult. Making power is easy. Controlling it at the top end is the challenge. The perpetual-know-it-all-newbies will always argue over that fact, while never experiencing it to find out the hard way that it true. As I’ve been saying for many years now: Overspeed protection - it’s not the MAIN thing, it’s the ONLY thing! :).
Yes. I am figuring out the same, though not wanting to dismiss the post too harshly or without understanding what was meant. But then, mostly unrelated to the latest few posts, I will introduce Tallaks corollary to Betz Law:
If someone new to wind energy does not embrace Betz law but rather wants to improve on it, that someone is maybe not that good at soaking up the experience of those who worked with wind prior. They will not be standing on the shoulders of giants, rather on their own. Chance to come across something revolutionary: slim to none.
I should get that in a text book. And guess what - maybe I just improved on Betz law there, by including the corollary…
Of course, it used to be that a turbine of a given diameter could only make a certain amount of power at a given wind speed. SuperTurbine™ changed that. The amount of power available from a turbine of a given diameter can be multiplied many many times over now.
I used to joke that it was a Betz-beater, but I was careful not to take it too far. I would quickly qualify it and say I was only joking.
The thing that amazes me is Betz figured it out on paper from first principles.
Ahh, he probably just got lucky…
Meanwhile leading science magazines are saying we still can’t agree on how lift actually works.
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