Wind Power Density

Wind power density measures how much kinetic energy is passing through each square meter of a wind stream, and it's dominated entirely by wind speed cubed: the base formula is P = 0.5 × ρ × v³, meaning doubling wind speed multiplies available power by eight, not two — the single biggest reason wind-site selection is so sensitive to small differences in average speed. This calculator computes that instantaneous figure directly from your average wind speed and air density, but wind never actually blows at one constant speed — real sites have a distribution of speeds around that average, described by a Weibull distribution shaped by the parameter k (k=2, the Rayleigh distribution, is the typical default for most locations). Because power scales with the cube of speed, gusty/variable sites with the same average speed as steady ones actually carry more average power — captured here by a correction factor Γ(1+3/k) / Γ(1+1/k)³, computed via a Lanczos approximation of the gamma function.

That correction is multiplied into the average power density figure, which then gets mapped to NREL's standard 7-tier wind resource classification (Class 1 "Poor" up to Class 7 "Superb," based on published W/m² thresholds), and used to estimate annual energy density by multiplying by the 8,760 hours in a year. The sample turbine output assumes a small 3-meter-diameter rotor (about 7.07 m² of swept area) at 35% real-world efficiency — well below the 59.3% theoretical Betz limit that no real turbine can exceed, since some kinetic energy must remain in the wind downstream for it to keep flowing through the rotor at all.