Optimum Planforms

Optimum Planforms



Design Tools



Planar Planforms

Biplane Rigs

"A" Frame Rigs

It is widely believed that an elliptical span loading produces the minimum induced drag for a lifting surface. In general, the optimal span loading is quite different and the elliptical loading is only optimal for the restricted case of an isolated planar wing in uniform flow. The correct conditions of optimality, as derived by Munk for minimum induced drag for a given span and by Jones for minimum induced drag with a moment constraint, are applied by means of an inverse lifting line technique. Validation of the method by comparison with test data and classic theoretical results is shown.

Design charts showing optimal span loadings, planform shapes, induced drags, and centers of effort are derived for isolated surfaces, single sails in ground effect, twin sail biplane rigs, and hydrofoils operating at high speed near the water surface are presented. The application of the method to the design of optimal keel winglets is also shown. 

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