Estimating Maximum Power from Wind Turbines with a Simple Newtonian Approach

Abstract

Action mechanics showing torques result from rates of variation in impulsive action motivated a new method 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 transverse reaction needed to conserve deflected wind momentum provides the turning moment for turbine rotation. Action mechanics integrates impulsive wind action on turbine blades as differing torques (ʃmrvdθ/dt ≡ mv2 ) exerted on rotor surfaces at each radius. Windward torque (Tw) is estimated from rotor dimensions, the angle of wind incidence and radial action of wind impulses on the blade surfaces (also ʃmrvdθ/dt ≡ mv2). A leeward torque (Tb) is exerted as back reaction on turbine blades 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. 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. Release of vortical field energy from laminar flow of air in winds as heat is predicted in turbulent wakes, possibly affecting achievement of maximum power output by wind farms. Significant heat release by downwind turbulence from vortical energy requires their careful location. Diligence demands that use of windfarms as sources of renewable energy should minimize any environmental impacts, such as drying of landscapes.