The Maximum of the Theoretically Possible Exploitation of Wind by Means of a Wind Motor

Abstract

Considering the current shortage of coal, the exploitation of the energy of wind has generated considerable interest. For this reason, it is the ambition of the engineer to convert this energy into a usable form with the highest possible efficiency. Furthermore there arises the problem that for wind motors, the efficiency term is not as explicitly defined as it is for most other machines. Since the energy which is available in the wind is in reality infinitely big; in essence, it therefore depends on the size of the wind motor how much of this energy is converted. To obtain a reasonable measure for the efficiency, an energy parameter for input power must be introduced, which is proportional to the size of the motor (proportional to the area of the bladed wheel). We can consider for example the windmill as the inverse of a propeller by imagining that the wind wheel is moved through stagnant air at a speed corresponding to the wind velocity v in the axial direction, which has the same effect as the air blowing with this velocity against the wheel. With this concept of operation, it is implicity clear that this introduced energy is the same energy that is necessary for the axial movement of the wheel. If the wind pushes in an axial direction on the wheel with a force P, then the energy per second has the value P ⋅ v, and if the useful power ouput of the wheel at the shaft has the value L, thus this yields the efficiency.