# Wind Speed Problem

1. Jan 20, 2008

### physixguru

A windmill power generator converts a fixed fraction of wind energy into electrical energy..

Supposing the wind falls on the windmill at a speed v...[wind speed=v]

What is the total electrical output proportional to..????

1.v^2
2.v^3
3.v
4.v^4

2. Jan 20, 2008

### kamerling

Find out how much air goes through the windmill each second and multipy by
the kinetic energy of that air.

3. Jan 20, 2008

### physixguru

hey bro..pls be a bit more specific...

what do ya mean by " how much air goes through the windmill'?

4. Mar 20, 2008

### physixguru

can someone guide me through pls.

5. Mar 20, 2008

### kamerling

Find the volume of air that will will go through the windmill in the next second. Assume for this that the windspeed is completely uniform, and the windmill won't influence it in any way. What shape is this volume? This volume will depend on the wind speed and the radius of the windmill
Now suppose we can convert all of the kinetic energy of this volume to electrical energy.

6. Mar 21, 2008

### physixguru

game.

7. Mar 21, 2008

### MacG

1D momentum theory:

T=0.5*rho*A*V^2*CT where CT=4*a*(1-a)
P=0.5*rho*A*V^3*CP where CP=4*a*(1-a)^2

rho: density of fluid kg/m^3
A: Area of turbine m^2
V: Free stream wind velocity m/s
a: axial induction factor, nondimensional. Axial flow velocity at rotor disc is V*(1-a).
T: Thrust force on rotor
P: Power form wind

a=1/3 maximizes power (for given A, rho and V), so this is usually close to what is aimed for on a wind turbine (below rated power).

So Trust force scales with V^2, and Power with V^3. (when running the turbine at the same design point, that is the same 'a')

-Mac G

8. Mar 22, 2008

Thx all.