A New Theory for Estimating Maximum Power from Wind Turbines: A Fundamental Newtonian Approach

A novel method for calculating power output from wind turbines using Newtonian mechanics is proposed. This contrasts with current methods based on interception rates by aerofoils of kinetic energy to estimate power output, governed by the Betz limit of propeller theory. Radial action [mrωrδφ =@, J.sec] generates torques from impulses from air molecules at differing radii on rotor surfaces, both windward and leeward. Dimensionally, torque is a rate of action [(mrωδφ)/δt, MLT, Nm]. Integration of the windward torque [Tw, Nm] is achieved numerically using inputs of rotor dimensions, the angle of incidence (θ) of elastic wind impulse [δMv] on the blade surface, chord and blade lengths and the tip-speed ratio with wind speed. The rate of leeward or back torque [Tb , Nm] in the plane of rotation is estimated from radial impulses from the blade’s rotation on material particles, with magnitude varying with the square of the blade radius and its angular velocity. The net torque (Tw Tb) from these rates of action and reaction is converted to power by its product with the angular velocity of the turbine rotors [P = (Tw Tb)Ω, Watts or J sec], considered as an ideal Carnot cycle for wind turbines; its design should assist optimisation of the aerodynamic elements of turbine operation. A matter of concern must be predictions for a significant rate of heat production by wind turbines, represented partly by the magnitude of the leeward reaction torque but also by a greater release of heat downwind caused by a turbulent cascade in the wake of air flow following its impacts with the blades. Given the widespread occurrence of wind farms as sources of renewable energy and a need to minimise environmental impacts this new method should promote improved theory and practice regarding wind energy.