Abstract
Munk's theorem specifying the downwash condition for minimum drag is generalized to include lifting surfaces operating in proximity to solid boundaries. A simple method for finding the optimum lift distribution on a wing above an infinite flat plane is developed. The optimum configuration for a ram wing in a tube is found, and by means of a simple transformation this is mapped into the previously obtained solution for a wing in ground effect. An expression for the induced power required is calculated, and it is shown that there is a favorable effect on this requirement for the case of tube vehicles which have significant blockage ratios. Experimental results are presented which demonstrate that at very small clearances the theory must be modified to include viscous effects, and because of these effects ram wings in tubes usually have lower induced power requirements than the inviscid theory would indicate. Nomenclature AR = aspect ratio A t = cross-sectional area of tube b = wing span = vehicle width Cof — induced drag coefficient CL = lift coefficient Di = induced drag F = volume flux
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