The formula
α (alpha) is the wind shear exponent, which depends on how rough the ground is. The classic "one-seventh power law" uses α = 1/7 ≈ 0.14 for open land.
Worked example
A weather station reports 5 m/s at 10 m. Over farmland (α 0.2), at a 15 m hub height: 5 × (1.5)0.2 = 5.43 m/s. That's 8.5% faster wind, but because power follows the cube of wind speed, about 28% more power.
Limits of the power law
The power law is a good rough guide over flat, open terrain. Near buildings, trees, cliffs and hills, the airflow is turbulent and the law doesn't hold, so measured data at your site is always better.
Frequently asked questions
How much does a taller mast increase wind turbine output?
Over open farmland, going from 10 m to 20 m raises wind speed by about 15% and power by about 50%.
What wind shear exponent should I use?
0.10 over water, 0.14 for open flat land, 0.2 for farmland with hedges, 0.25 for woodland or suburbs and 0.3–0.4 in towns.