Analytical Prediction of Vortex Lift

Abstract

General integral expressions are derived for the nonlinear lift and pitching moment of arbitrary wing planforms in subsonic flow. The analysis uses the suction analogy and an assumed pressure distribution based on classical linear theory results. The potential flow lift constant and certain wing geometric parameters are the only unknowns in the integral expressions. Results of the analysis are compared with experimental data and other numerical methods for several representative wings, including ogee and double-delta planforms. The present method is shown to be as accurate as other numerical schemes for predicting total lift, induced drag, and pitching moment. b c c CL CD Cm CT Cs cc, ccd E2 Nomenclature = aspect ratio = wing span =chord = reference length = lift coefficient = drag coefficient = pitching moment coefficient = thrust coefficient = suction coefficient = section lift coefficient = section induced drag coefficient = section suction coefficient = pressure loading coefficient = drag = proportionality constant, Eq. (32) = proportionality constant, Eq. (53) = chordwise function, Eq. (44) ff(rj) = span wise f unction, Eq. (28) K = potential constant L =lift loading constant, Eq. (5) S = suction force SR = reference area s = suction force per unit length T = leading edge thrust, Eq. (7) T' = leading edge thrust per unit length V = freestream speed Wj = downwash velocity component, Eq. (11) a. = angle of attack F = vorticity p = freestream density £ = nondimensional chordwise coordinate 77 = nondimensional spanwise coordinate A = leading edge sweep angle Subscripts P = potential flow E =edge / = induced VLE = leading edge vortex VSE = side edge vortex