How much more power is available from wind when the wind speed doubles?

The power generated by wind is proportional to the cube of the wind speed. This relationship can be represented mathematically by the equation for wind power, which states that power is equal to a constant multiplied by the area swept by the wind and the cube of the wind speed.

When the wind speed doubles, you can observe the effect on power as follows:

If the original wind speed is ( v ), the power generated at that speed is proportional to ( v^3 ). When the wind speed doubles to ( 2v ), the new power becomes proportional to ( (2v)^3 ).

Calculating this gives:

[ (2v)^3 = 8v^3 ]

This means that the power generated at double the speed is eight times the power at the original speed. Thus, when the wind speed doubles, the increase in available power is indeed eight times greater than the original power. This makes the correct answer evident, as it reflects the cubic relationship between wind speed and power.