Wind turbine design and wind farm operation are likely to improve with the advent of a physics-based mathematical model devised by MIT engineers. The aerodynamics model explores how wind interacts with rotor blades and can be applied to analyze the forces, flow velocities and power of a rotor.

The approach overcomes the limitations in older momentum theory equations, which fail to predict the amount and the direction of changes in thrust force at higher rotation speeds or different blade angle. When designing the profile of rotor blades or the layout of wind turbines in a farm, engineers have typically relied on ad hoc adjustments added to these formulas, based on some wind tunnel tests and experience with operating wind farms, but with no theoretical underpinnings.

The unified momentum model described in Nature Communications eliminates the need for complex corrections on older mathematical models and can accurately predict power production, thrust force and wake dynamics of rotors under arbitrary inflow angles and thrust coefficients. The theoretical analysis-based model was validated it using computational fluid dynamics modeling; additional validation is now being pursued in wind tunnel and field tests.

Design and operating issues related to controlling both individual turbines and arrays of turbines can be implemented without requiring any modifications to existing hardware in place within wind farms.

The study could have a significant impact for wind turbine manufacturers and operators by improving the efficiency of individual turbines and, by implication, of entire wind farms. In addition to enhancing wind energy efficiency, the model is also applicable to aircraft and ship propellers, and to hydrokinetic turbines.

The formulas can be downloaded from GitHub.