DDWFTTW energy feedback loop for windmill?

A variation on the Directly Down Wind Faster Than The Wind (DDWFTTW) Boat. First the drawing by Andrew Bauer from 1969 of a cart or boat. Bauer-Faster-Than-The-Wind.pdf

Click on image below for larger / sharper image.

Now a fixed windmill version. Can V C (Velocity of Car) be replaced by V B (Velocity of air Between airscrew & turbine)? See formulas by Thin Air Designs. Click on image below for larger / sharper image.


The airscrew "pulls" in a larger column of flowing wind, than a windturbine. (In the diagram below the wind direction is left to right.)

Will this generate more power than the turbine by itself that utilizes a smaller cross-section of the wind that is flowing by? (Betz law).

Thin Air Designs who made a Faster Than The Wind cart say:
The only use we *intend* for it to have is:
1) to keep us occuppied during the non-windy season.
2) To demonstrate that it's a bad idea to try and substitute intuition for science.

However, it does have some interesting aspects. One such aspect is the somewhat bizarre outcome that you can theoretically harness an unbounded amount of energy from the wind - if your windmill is allowed to move through the wind. A traditional windmill has a very definite limit to the amount of power it can produce for a given amount of wind. However, a moving windmill can continue to produce more power as it moves itself through the wind.

It's hard to say whether this will become any sort of practical reality, but there are folks using the principle - including our sponsor Joby Energy.

Discussion added october 22: E-mail from Professor Mark Drela of MIT:

Ansgar,

> If you put a Prop in front of a stationary windturbine, do you get a
> similar effect ?

I don't know what "similar effect" you are referring to.

> Using your terms in the Power Analysis: Instead of V-W and V-W+ΔW for
> the prop, you have W and W+ΔW.

OK, but the prop will require power to do this.

> For the turbine the prop wake is the input: instead of V you have W
> +ΔW , I am not sure what the speed would be behind the turbine... is
> ΔV then equal to ΔW ?

The dW_t behind the turbine simply depends on how much power it's
producing, and can be almost anything.
The maximum power is produced when
dW_t = W * 2/3,
in which case the wind behind the turbine is
W-dW_t = W - W*2/3 = W/3
This case is the Betz limit.

> Is it more effective than a standard wind turbine because it utilizes
> a larger streamtube than one dictated by Betz law?

Sure, blowing on the turbine will allow it to make more power. But this
blowing itself requires power, and the net power will be less than
without the propeller.

MD

Close, but wrong way around to be turbo windmill XKCD 2012 http://xkcd.com/1119/

Comments, questions or E-mails welcome: ajbrenninkmeijer (a) gmail.com