Propeller-wing integration for minimum induced loss

An analysis of propeller-win g combinations in inviscid incompressible flow reveals some of the fundamental interactions which affect the performance of an installed propulsion system. A generalized version of Munk's stagger theorem is used in a rapid, approximate calculation of optimal lift distributions and installed efficiency. Results indicate that the distribution of lift over the wing which maximizes overall efficiency differs markedly from elliptic loading. Swirl recovery by the wing leads to increments in net propeller efficiency of 6% in example cases. The maximum installed efficiency is computed for single-rotation (up-inboard and up-outboard designs) and counter-rotating systems. Results suggest that some of the performance advantages attributed to counterrotation may be less dramatic for well-integrated wing-propeller designs than for isolated systems. Nomenclature An = amplitude of nth harmonic of wing lift & = wing aspect ratio b = wingspan c =wing chord CL =wing lift coefficient CT = thrust coefficient, =ir2T/pw2R4 D =drag IU,IW = definite integrals, Eqs. (10) and (11), respectively / = advance ratio, = irU00/uR I = section lift L =lift N = number of blades Obj = objective function Q = propeller torque R = propeller radius r - radial coordinate T = thrust Uw = freestream velocity u = axial perturbation velocity V = induced velocity vt = tangential induced velocity w = induced downwash x = stream wise coordinate y = spanwise coordinate .Vprop = spanwise location of propeller F = circulation 6 =dimensionless spanwise coordinate K =Goldstein's radial velocity correction X =Lagrange multiplier p = density Subscripts int = interference component = wing w = propeller