Apparent-Wind Aerodynamics and Lift-Drag Optimization in Wind Turbines and Hydrofoil Sailcraft

Wind-turbine blades and hydrofoil sailcraft operate through the same fundamental inter-action between free-stream wind and system motion. For a horizontal-axis wind turbine (HAWT), aerodynamic lift is resolved into a tangential force that produces rotor torque; correspondingly, in sailing, the forward component of sail lift provides the driving force that propels the craft. This paper develops a comparative apparent-wind framework for these rotating and translating aerodynamic systems. Velocity and force-vector analysis re-lates apparent-wind velocity, apparent-wind angle, angle of attack (AoA), lift-to-drag ratio (L/D), and useful-force production. For hydrofoil sailing, a force balance gives the speed ra-tio U/V = (L/D) sin θ − cos θ – K, where U is craft speed, V is true-wind speed, θ is the true-wind angle relative to the course, and K represents normalized aerodynamic and hy-drodynamic losses, and the associated velocity made good, VMG = U cos θ. For vertical-axis wind turbines (VAWTs), the corresponding relative-wind angle varies cyclically with blade azimuth and tip-speed ratio, requiring rapid pitch adjustment to control AoA, dynamic stall, torque, and fatigue loading. Sail trim performs an analogous function by adjusting sail angle, twist, and camber to maintain favorable AoA and L/D, although its objective is maximum speed or VMG rather than maximum power coefficient. The comparison shows that apparent-wind velocity and angle provide a common basis for understanding tangen-tial-force generation, pitch or trim control, and system-level aerodynamic optimization. The results show that sailing faster than the true wind arises from the combined high lift-to-drag performance of the sail and the low-drag lift and lateral resistance provided by the hydrofoil. Finally, the potential for apparent-wind power generation aboard a high-performance sailing craft, scaling approximately as ½ ρ Asail V³ (L/D)², is also explored.