Wind Turbine Blade Design Using Wilson's Method: Aerodynamic Optimization Approach

Wilson's method is a widely used aerodynamic optimization approach for wind turbine blade design, which balances momentum theory and blade element theory to determine optimal aerodynamic blade shapes. The core concept involves calculating axial and tangential induction factors - key parameters that directly govern the blade's aerodynamic performance.

When implementing Wilson's method in MATLAB, engineers typically utilize the fmincon optimization function from the Optimization Toolbox. This constrained nonlinear minimization function proves particularly effective for solving aerodynamic optimization problems by minimizing power losses or maximizing power coefficient through iterative calculations. The implementation requires defining an objective function that encapsulates the aerodynamic performance criteria, often formulated as a power efficiency maximization problem.

Several critical aspects require attention during the design process: First, establishing accurate mathematical models that describe the relationship between induction factors and blade geometric parameters; second, properly configuring optimization constraints, including physical limits for induction factors; finally, careful selection of initial values significantly impacts optimization convergence and results. The algorithm typically handles constraints on induction factors (0

The complete optimization workflow can be summarized as: objective function formulation → constraint definition → algorithm selection → optimization execution → result analysis. Through iterative computations using gradient-based optimization methods, the process converges to optimal induction factor combinations that satisfy design requirements. This methodology effectively balances aerodynamic performance with structural integrity, serving as a practical tool for modern wind turbine blade design engineering.