The basic theory of the induced lift and drag of nonplanar, circulation lifting systems is developed, and methods are evolved for determining the span force loading intensity necessary for minimum in¬duced drag. It is shown that the aerodynamic efficiency of such optimally loaded systems can be expressed in terms of an effective aspect ratio which depends in value upon the spatial distribution of the vorticity of the system. Methods for determining the maximum effective aspect ratio of arbitrary lifting systems of given span by use of conformal transformation and electrical potential-flow analog techniques are developed and illustrated. The value of the induced-drag efficiency factor is determined for the families of circular, semiellipse, and com-plete-ellipse arcs and for several more complex forms.
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