Prediction of the aerodynamic characteristics of wings of arbitrary plan form

I n our present effort t o fly i n and through the transonic-npeed range we have resorted t o widely diversified plan f o r m .' Ranges of sweep, espect r a t i o , and taper r p t i o a r e being considered which extend f e r 'oeyond those considered p r a c t i c a l several years ago, and the e f f e c t of wide variations i n those pai-te~s on the ~u b s o n i c aerodynamic characteristics of wings i s a0 yet largely unknown.The multiplicity of posaible plan form preclLide9 an inveeti&ation of each experimentally.A s a result,considereblc e f f o r t has been directed towslds developirq a theoretical method of predicting the loading over the wine since, once t h i s loading has been deterained, not only can' s t r u c t u r a l loads be estimated but values of the various aercx5ymmi.c-chamcteristicssuch a s lift-curve slope, aeroa-mamiccenter location, m d induced drag can a l s o be found, The investigation of several theo:%tical methods f o r the grediction of loading and the applicatzon of one of these methods t o 8 wide range of plan forme i s the subJect of t h i s paper.The theoretical methods studied were those developed by Falkner, b;r Mutterperl, and by Weissinger.I n each of these meth0d.s the wing is replaced by a diatribution of vortices.The strength d i s t r i b u - t i o n of these vortices i s fixed by the bounbry condition which requires that the induced velocities of these vortices produce no flow through the plane of the wing.The difference among the method6 lie's i n differences i n physical location of the vortices, i n the disposition of the control points where the boundary condition 1sapplied, and i n the reathematical manipulation.F i w e 1 compares the layout of vortices end control points f o r the msthods.Falkner replaced the wlng with a distribution of f i n i t e horseshoe vortices, both spanwise and chordnlse.He likewise distributed the control points both spanwise and chordwlse, hence h i s method is c l a s s i f i e d as a lifting-eurface method.A s a r e s u l t of his work Falkner has recommsnded a particular vortex and ccmtrol point diatribution which was followed i n our studieo.I n contrast t o the Falkner l i f t i n gsurface method, both the Weissinger and the Nutterperl methods a r e l i f t i n g -l i n e methods; that is, the loading 13 concentrated on the q~mrter-chord l i n e , and the control points a r e distri'outea along the three-quarter-chord l i n e , The Weissinger and Mutterperl methods d i f f e r i n the spanwise location of the control points and i n the mathematical development.