Effect of Finite Span on the Airload Distributions for Oscillating Wings I : Aerodynamic Theory of Oscillating Wings of Finite Span

A formula is derived for the pres8ure distrib-!.lt:ion on an oscillatir,g HftinG surface of fini tiC; span unc.er the acsumpUon of a ratio of• span to average chord (aspect ratio) that is not too small.The ranGe of validity of this i'ormula, so far as aspect-ratio l~.mi tat~.om: are concerne•i, is not less than the rt.:0..ge of vali•ii ty of lifting-line theory for tho non-oscalating 1.rinG.It is found that the effect of three-dimensionali t~r of the flow may be incorporatec.in the results of the two-rlimensional theory by adding a correction factor cr to the basic function C (1;:) of the t.lo,...dimensional i.heory.The correction term cr is a function that depends o~ :form: .,ingdefiection function, and reduced fregD_ency k. naticn reCluires the solution of e.n inteGral e1uation .Ihich the integral eq,uation of lifting-line theory. vring plan Its determiis similar toThe present report cbncludes .Ti th an explici t statement of ~he form which the results of the theory assume for the s11amlise varia"i.:,ion:. of lift, total moment, and hinge moments on a wing ilhich is oscillating in uendin3, torsion, and aileron and tab deflection.Methods for the numerical evaluation of' the results obtained as well as numerical applications to specific problems are given in part II of this report.O