Detailed Analytical Solution for Performance Prediction of Ideal Horizontal Wind Turbines

Abstract

The actuator disk method developed by Rankin, Froude and Betz has shown good assumptions of the aerodynamic performance of wind turbines, especially if it has been combined with blade element theory. However, given the non-linearity of the resulting equation that estimates the efficiency of wind turbines, numerical integration is used as an alternative to give an approximation to such a problem. This work presents an analytical solution of the maximum attainable power coefficient <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$C_{p}$</tex> to be extracted by an ideal horizontal axis wind rotor at a given tip speed ratio <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\lambda$</tex> as derived from the axial momentum theory improved by Betz. This paper does not consider the Blade element theory.