VAWT calculations

[Maarten Jacobs]

Hello everyone I'm new to the forum. I'm making a vertical axis wind turbine of the Lenz2 type as a school project and I also have to do some calculations about it.

I found this formula to calculate the power: p=1/2*rho*A*v^3

In this formula the "A" is called the frontal area but i don't really understand what it is and how to calculate it

[Rob Beckers]

Maarten, "A" is the area that intercepts the wind in square meters. For a VAWT it's simply the width x height, or to put it another way, imagine a light shining on the turbine and it's the surface area of the shadow at its largest.

That equation is just the power in the wind, it is not the power coming off the rotor. For that you have to multiply it with the efficiency of the rotor, how good it is at capturing power from that wind. A guy named Betz figured out that no rotor can be more than 59.3% efficient, the "Betz limit". Most rotors are far less efficient than that.

-RoB-

[Maarten Jacobs]

Thanks for explaining. Do you know if there is a way to calculate the RPM of a VAWT?

[Rob Beckers]

There should be papers on Lenz-2 type turbines that go into TSR (Tip Speed Ratio) and RPM, my own knowledge is largely about HAWTs. If I remember right the Lenz design is somewhat between a drag-type and a lift-type device. Turbines relying on drag don't go over a TSR of 1 (the tips of the blades move no faster than the wind speed), good lift devices (mostly HAWTs) run at a TSR of 5 - 7, I suspect yours would run best somewhere in between.

-RoB-