Wind turbine B has blades twice as long as wind turbine A. If they are subjected to the same wind, what is the relationship between the power from turbine A (PA) and the power from turbine B (PB) ?

The Power output from Turbine B with the doubled blade will be X4 of the power output from Turbine A.

Explanation:

The Power generated by a wind turbine is governed by the equation:

P=0.5ρAV³

Where ρ = Air Density

A = Swept Area of the Blade = πr²

V = Wind Velocity

If they are subjected to the same wind, Air Density and Wind Velocity will be equal

For both turbines,

Let Air Density=1

Wind Velocity=1

Power from Turbine A = 0.5X1XπX1²=0.5π

Power from Turbine B (radius=2) = 0.5X1XπX2²=2π

Power from Turbine B/Power from Turbine A = 2π/0.5π=4