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.

, and
, “
Design of Optimum Propellers
J. Propul. Power
), pp.
Wilson, R. and Lissaman, P., 1974, “Applied Aerodynamics of Wind Power Machines,” Oregon State University, NSF-RA-N-74-113, PB 238 595, Corvallis, OR.
Robison, D. J., Coton, F. N., Galbraith, R. A. McD., and Vezza, M., 1995, “The Development of a Prescribed Wake Model for Performance Prediction in Steady Yawed Flow,” Proceedings of ASME Wind Energy, Houston, TX, Jan 29–Feb 1.
Chattot, J.-J., 2002, “Design and Analysis of Wind Turbines Using Helicoidal Vortex Model,” Computational Fluid Dynamics Journal, 11(1), pp. 50–54.
Prandtl, L. and Betz, A., 1927, “Vier Abhandlungen zur Hydrodynamik und Aerodynamik,” Gottingen Nachr., Gottingen, Selbstverlag des Kaiser Wilhelminstituts fur Stromungsforschung.
Chattot, J.-J., 2002, “Optimization of Propellers Using Helicoidal Vortex Model,” Computational Fluid Dynamics Journal, 10(4), pp. 429–438.
Fingersh, L. J., Simms, D., Hand, M., Jager, D., Cotrell, J., Robinson, M., Schreck, S., Larwood, S., 2001, “Wind Tunnel Testing of NREL’s Unsteady Aerodynamics Experiment,” AIAA paper No. 2001-0035. NREL data base,
Drela, M., 1989, “XFOIL: An Analysis and Design System for Low Reynolds Number Airfoils,” Conference on Low Reynolds Number Airfoil Aerodynamics, University of Notre Dame, also in Low Reynolds Number Aerodynamics, T. J. Mueller (editor), Lecture Notes in Engineering No. 54, Springer Verlag, 1989.
Giguere, P., and Selig, M. S., 1999, “Design of a Tapered and Twisted Blade for the NREL Combined Experiment Rotor,” Subcontract XAF-4-1407-03, NREL/SR-500-26173.
You do not currently have access to this content.