The problem of the design of a wind turbine for maximum output is addressed from an aerodynamical point of view. It is shown that the optimum inviscid design, based on the Goldstein model, satisfies the minimum energy condition of Betz only in the limit of light loading. The more general equation governing the optimum is derived and an integral relation is obtained, stating that the optimum solution satisfies the minimum energy condition of Betz in the Trefftz plane "in the average." The discretization of the problem is detailed, including the viscous correction based on the 2-D viscous profile data. A constraint is added to account for the thrust on the tower The minimization problem is solved very efficiently by relaxation. Several optimized solutions are calculated and compared with the National Renewable Energy Laboratory (NREL) rotor using the same profile, but different chord and twist distributions. In all cases, the optimization produces a more efficient design.