# How to calculate power necessary generated from wind turbine to run a motor

I was making a small/cheap wind turbine, and I am stuck on how to calculate the power needed (speed of wind) to run a brushed motor (since I figured that would be the easiest to run with rotor blades of the turbine made out of plastic). The dimensions of the length of one rotor blade is 6 inches

• In principle this is a very good question, but it seems like we will need quite a bit more information. Like, angle of the rotor with respect to the wind, weight of the rotor, torque required to move the brushes, etc. – levitopher Feb 6 '16 at 2:36

The power generated by wind turbine goes approximately like

$P={1\over 2}C_p\rho A v^3$

Where $\rho$ is the density of air, $A=\pi r^2$ is the area swept by the blades, $v$ is the velocity of the wind and $C_p$ is a power conversion factor that is around 0.3-0.4 for the best wind turbine designs and will probably be on the order of 0.1 for your rotor. Putting it together we get roughly the following numerical expression for your design:

$P\approx 0.5\times 0.1\times 1.225{kg\over m^3} \times 3.14 \times ({6\over 39.37} m)^2 \times v^3 \approx 0.0045 {kg\over m} v^3 = 0.0045 {kg \over m}{m^3\over s^3} ({v\over m/s})^3\approx 0.0045W ({v\over m/s})^3$

At 1m/s (light air) your wind generator may produce approx. 4.5mW, at 10m/s (strong breeze) it may go up to 1000 times that much, i.e. theoretically 4.5W. And there you can see why wind turbines have to be so large to produce significant amounts of wind power and why, even more so, strong winds are essential.

• how do you calculate voltage from this? – user510 Feb 9 '16 at 2:41
• The voltage will depend on your generator and the rpm at which the blades are turning. Wind turbines have gearboxes to adjust that ration for the max. power efficiency. Since I don't have the details about your generator (dc motor), I couldn't tell. You should measure it with a voltmeter. – CuriousOne Feb 9 '16 at 3:28
• okay I thought there was a way to calculate voltage also theoretically using the power equation you provided above. Thanks! – user510 Feb 9 '16 at 3:53
• Is there a theoretical way to calculate voltage that a wind turbine will produce based on given speed of wind? – user510 Feb 9 '16 at 4:19
• Only if you know the characteristics of the generator and a few other things. Importantly, though, voltage is not important. Voltage can be changed without losing much power. What's important is always the power. Whether you generate 4.5V and 1A or 9V and 0.5A, that's all the same, a little bit of electronics can convert that into anything you like. The hard part is to generate the power in the first place. – CuriousOne Feb 9 '16 at 6:18