The Power (P) with which the wind operates is the product of the Force (F) of resistance to its movement by its velocity (V):

P = F * V

F better defined by “Aerodynamic Resistance Force” changes proportionally to the type of surface exposed to the wind (Frontal section D by coefficient of form Cx), the air density (p), by the law of kinetic energy, changes in proportion to the wind velocity (V) squared

F = 0,5 * D * p * Cx * V ²

Aerodynamic resistance is a force and only by multiplying it by the velocity, does it become the power produced by the wind. Combining the two formulas reveals how Power (P) is altered by the wind velocity to the third power.

P = 0,5 * D * p * Cx * V ³

Power P is expressed in Watt per square metre, frontal section D is expressed in square metres, air density (p) is expressed in Kg per cubic metre and air velocity in metres per second.

The coefficient of form (Cx) is the measure of aerodynamic penetration of the surface exposed to the flow and varies based on its geometric shape; some general examples are shown in the illustration.

Air density (p) decreases with altitude and changes from a value of 1.225 g/m³ at sea level to 1.112 g/m³ at an altitude of 1 km.

Wind power is related to wind velocity to the third power; slight increases in wind velocity therefore produce large increases in power; each time wind power is doubled, available power is increased by a factor of 2×2x2= 8; if wind power is tripled, energy will be 3×3x3=27 times greater.

Wind velocity does not increase steadily as we increase altitude; if at ground level velocity is practically absent, at levels immediately higher and up to 20-40 metres variations in velocity are irregular; velocity increases rapidly up to 500-600 metres and continues to increase at a slower rate for the next 200 metres.

Engineering calculations frequently apply the empirical mathematical formula known as “empirical law of power” (shown above) that, starting from wind velocity (V2) measured at altitude h2, computes wind velocity (V1) predictable at altitude h1. Coefficient c takes into account ground roughness and starts from 0.40 in city centres and goes up to 0.16 for plains or the open sea.

Above an altitude of 800 metres, the wind blows at an average speed of 7.6 m/s about 6000 hours a year compared to the average 4.6 m/s for 3000 hours a year at an altitude of 80 metres, where traditional wind power generators are deployed.

Wind velocity is a crucial factor in the efficiency of wind power generators and it increases with the distance from the ground. Traditional wind power generators based on a horizontal rotation axis design are structurally limited in the diameter of the blades (max 80-100 metres) and in the height of the tower (max 130-180 metres). Increased vertical height of the structure and the implementation of large diameter blades create complications in the static equilibrium of the structure itself which is put at risk by sudden gusts of strong wind.