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A method has been developed to analyze the flow and predict the lifting characteristics of vertical axis wind turbines. Blades are modelled by a number of discrete bound vortices located on the airfoil mean camber line; the wake is modelled by a number of discrete vortices shed from the blade trailing edge. Application of the flow tangency boundary condition and the Kutta condition permit a numerical solution for the strengths of the bound vortices. Blade forces are then determined from potential theory. This vortex model faithfully reflects the important phenomena of flow unsteadiness and wake/blade interaction. Wake details and energy extraction efficiency are analyzed for single and multi-bladed turbines. A comparison of experimental data to analytical predictions shows elose agreement for the maximum power coefficient and the tip speed ratio at which it occurs. A numerical procedure for estimating the theoretical maximum attainable power coefficient suggests that vertical axis turbines may exceed the Betz limit for horizontal axis machines.