Simulations were used to design ducted wind turbines with the objective of either maximizing power per rotor area (PPRA) or maximizing power per duct exit area (PPDA). When PPRA is maximized, any rotor position within the first half of the duct produces approximately the same PPRA. When PPDA is maximized, the optimal position of the rotor is at the rear of duct. In this case, the PPDA exceeds the theoretical power per unit area that can be produced by an open rotor.