Wind: How energy resides
The cube law, and why wind farms need so much land
What this tab covers The physical form in which the energy is held or carried, where it comes from, the chain of transformations that put it there, and how concentrated it is.Wind is the kinetic energy of moving air, set in motion by pressure differences that uneven solar heating creates. Its power rises with the cube of wind speed, but per square metre of land a wind farm delivers only about 0.5 W.
Form Kinetic energy of moving air Origin Indirect solarHow it got there
Fusion in the Sun Sunlight Uneven heating of land, sea and air (tropics more than poles, land more than sea) Pressure differences between warm and cool air masses Air flows from high to low pressure, deflected by the Earth's rotation WindHow concentrated it is
| Measure | Value | Note |
|---|---|---|
| Power carried by the flow at 5 m/s | about 77 W per m2 of swept area2 | Calculated as 1/2 x air density (1.225 kg/m3) x speed cubed. Before any turbine losses. |
| Power carried by the flow at 10 m/s | about 610 W per m2 of swept area2 | Same calculation (612.5 W/m2); doubling the speed gives eight times the power. |
| Power density of operating onshore wind farms | 0.50 W of electricity per m2 of land3 | Mean of 411 US wind plants in 2016; earlier estimates span 0.3 to 47 W/m2. |
| Same measure for solar farms, for comparison | 5.4 W of electricity per m2 of land3 | Mean of 1,150 US solar plants in 2016. |
The Sun heats the tropics more than the poles and land faster than sea. Warm air rises and expands, cool air sinks, and the resulting pressure differences push air around the planet, turned into great swirling patterns by the Earth's rotation. Wind is therefore solar energy converted once more, into the motion of air.
Because the power in moving air rises with the cube of its speed, a site with 10 m/s winds carries eight times the power of one with 5 m/s. This makes siting decisive. But air is light (about 1.2 kg per cubic metre), so turbines must sweep huge areas, and they must be spaced several rotor diameters apart so that each one is not starved of wind by its neighbours. Measured over the whole site, a typical US onshore wind farm yields only about 0.5 W per square metre, about one tenth of a solar farm, although nearly all the land between turbines remains usable.
Sources
- Power in the wind (power = 1/2 x density x swept area x speed cubed; air density about 1.225 kg/m3) Electrical and Mechanical Services Department, Hong Kong SAR Government (HK RE Net), 2026
- Observation-based solar and wind power capacity factors and power densities (Miller and Keith, Environmental Research Letters) Harvard Kennedy School, 2018