Estimating Maximum Power from Wind Turbines with a Simple Newtonian Approach

Recent findings in action mechanics showing torques result from rates of variation in impulsive action motivated this more fundamental approach to estimate maximum power from wind turbines. Newton’s third law of equality of action and reaction provides a strictly causal mechanism of wind power from the deflection of wind momentum by twice its angle (θ) of incidence on rotor blades. The lateral reaction needed to conserve wind momentum provides the turning moment for the turbine rotors. This direct approach challenges the current continuum mechanism for generating power from flows of kinetic energy in wind passing through the areas swept by rotating blades. Action mechanics integrates the rates of impulsive wind action on turbine blades as torques (∫mrvdθ/dt ≡ mv2) exerted on rotor surfaces at decreasing radii. Windward torque (Tw) is estimated from rotor dimensions, the angle of wind incidence and radial action of wind impulses on the blade surfaces (also ∫mrvdθ/dt ≡ mv2). A leeward torque (Tb) for back reaction of turbine blades on air mimics drag exerted parallel to the plane of rotation of the blade. Net torque is then converted to potential power (Tw - Tb)Ω by the angular velocity (Ω) of the turbine rotors, a function of tip speed ratio to wind speed. New contributions from action mechanics for managing wind power include larger estimates of its possible magnitude by including vortical energy, much larger than the kinetic energy. Better predictions of limits to wind power can be made, by including control of optimal wind angle and blade length. An analysis of the equivalence of deflected air momentum on turbine blades or air foils for aircraft reveals that even the lifting action on air foils can be explained by the normal reaction to the momentum in an air stream, also deflected by an angle twice that (2θ) of incidence, validating application of action mechanics to airflight. A mechanism for release of vortical field energy from laminar flow of air in anticyclones is predicted in turbulent downstream wakes, possibly assisting achievement of maximum power output by wind farms. Significant heat release by downwind turbulence from vortical energy requires care for their location. Diligence demands that use of windfarms as major sources of renewable energy should minimize any environmental impacts, such as drying of landscapes.