Propellers, Wind Turbines, etc.

$$\text{Windmill Day}$$

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Today (May 10) is Windmill Day! It is a day to commemorate these incredible feats of machinery that helped shape technology and the world we know today.

Modern wind turbines can produce a power, converted from the wind into rotational energy, that's given by the equation: $$P=\frac12\rho Av^3C_p$$

Rho, $\rho$, represents the air's density and is approximately $1.225\text{ kg/m}^3.$

Area, $A$, is the area of of the circle that one of the blades creates. The average length of a turbine blade is $52\text{ m}$.

The wind speed, $v$, is, well, the speed of the wind. Assume it is measured to be $12\text{ m/sec}$.

Finally, $C_p$ is the power coefficient. It is essentially how well the turbine can extract the energy carried by the wind. Assume it is $0.4$.