Speed and Velocity

A car traveling at 60 mph northbound and a car traveling at 60 mph southbound have the same speed but opposite velocities. In most everyday contexts, the difference is trivial. In physics and energy systems, it is not.

Speed is the rate at which an object covers distance per unit of time, measured in meters per second (m/s). Velocity is speed with a direction attached. For energy calculations, the critical insight is not the distinction between speed and velocity; it is how speed enters the kinetic energy formula: KE = ½mv². Because velocity is squared, doubling speed quadruples kinetic energy. Not doubles. Quadruples.

This square relationship dominates wind energy. A 12 m/s wind carries four times the kinetic energy per kilogram of air as a 6 m/s wind. When you factor in that faster wind also delivers more mass per second (mass flow rate scales linearly with speed), wind power scales with the cube of wind speed. A site averaging 8 m/s produces roughly eight times the energy of one averaging 4 m/s. This cubic relationship is why wind farm siting decisions, measured to fractions of a meter per second at hub height, drive billions of dollars in investment.

Worked Example

Two proposed wind farm sites are under evaluation. Site A averages 6 m/s winds. Site B averages 9 m/s.

• Find the speed ratio. 9/6 = 1.5 times faster.
• Cube the ratio for power. 1.5³ = 3.375.

How much more power does Site B produce compared to Site A, all else equal?

About 3.4 times more. That single difference in average wind speed can determine whether a project is financially viable or dead on arrival.

This speed-energy relationship is the foundation for understanding kinetic energy in any moving fluid, from wind to water.

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