THE THEORY OF INDUCED LIFT AND MINIMUM INDUCED DRAG OF NONPLANAR LIFTING SYSTEMS

The basic theory of thP induced lift and drag 0.f nonplanar, circulation lifting systems i s developed, and methods are e d c e d for determining the span force loading intensity necessary for minimum induced drag.I t i s shorn that the aerodynamic e$iciency of such optimally loaded systems can be expressed in terms of a n egective aspect ratio which depends in value upon the spatial distribution of the rorticity of the system.Methods for determining the maximum eflective aspect ratio of arbitrary lifting systems of given span by use of conformal transformation and electrical potential-$ow analog techniques are deitlopec?and illustrated.T h p value o.f the induced-drag efficiency factor i s determined for the families of circular, semiellipse, and complete-ellipse arcs and f o r several more complex forms.The results of the theory are interpreted in terms of the physical airjbil requirt metLta ILecesmry jw SZLCcessful realization of the theoretical induced-drag reductions.The practicnl application aspects of nonplanar wing systems are hrit$y considered.