Wind and Air: Available Wind Power

Calculate energy flow without promising turbine output.

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Kinetic power carried by air through area A is P_air = rho A v^3/2 for uniform speed and density. It is not the electrical output of a turbine. Conversion limits, losses, control settings and cut-out operation matter.

Worked example

Using rho = 1.2 kg/m^3, A = 10 m^2 and v = 5 m/s gives P_air = 750 W. At 10 m/s, the same calculation gives 6000 W, eight times as much available air power.

For fixed density and swept area, doubling wind speed increases available kinetic power by eight. The diagram compares speed ratios 1 and 2 with air-power ratios 1 and 8, not turbine electrical outputs.

Would you believe it?

At fixed air density and swept area, doubling wind speed gives eight times the available kinetic power in the air. That does not mean a real turbine delivers eight times the electricity.

U.S. Department of Energy: wind power basics

Question 1 What is P_air for rho = 1.2, A = 10 and v = 5 in SI units? 750 W 150 W 1500 W

Question 2 At fixed density and area, doubling speed changes P_air by what factor? 4 2 8

Question 3 At fixed speed and density, doubling area changes P_air by what factor? 1/2 2 8

Question 4 Can a turbine deliver all 750 W as electricity just because 750 W crosses its area? No, conversion limits and losses apply Yes, always Yes, if no measurement is taken

Question 5 Why might actual output stop increasing in very strong winds? Wind contains no energy when fast The cubic formula changes to a promise Controls or safety shutdown can limit operation

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