Power-on channel wing aerodynamics

A theory is developed for lift developed by semicircular channel wings with a pusher propeller at the trailing edge. The theory assumes that the lift on the inside (or top) of a channel airfoil can be determined by using standard airfoil pressure coefficient data but with an effective freestream velocity and an effective freestream static pressure equal* to those values just in front of the propeller plane. The lift on the outside (or bottom) of a channel airfoil is assumed to be the same as that calculated by present-day standard methods. Good correlation was found between the theory and wind-tunnel and flight- test data. Both the theory and test data indicate extremely large values of lift coefficient can be obtained with channel wings. Nomenclature A = area of propeller disk Ae = streamtube area of infinity c = wing chord length Ci = lift coefficient/unit span Cu = ideal lift coefficient/unit span CL = power-on lift coefficient, L/qmS CL* = unpowered lift coefficient, L/qmS CT = thrust coefficient,-T/qmA L = lift m = mass flow rate n = number of engines P = power p = pressure T — thrust/engine Tc = thrust coefficient, nT/qmS q = dynamic pressure, JpF2 R = channel radius S = total horizontal projected wing area Sc = horizontal projected channel wing area, 2 Re V = velocity x = distance from leading edge along chord line a. — angle of attack a = average sectional angle of attack in the channel /*7T/2 = COS"1 I COSO! COS = COS~1[a Cota]^, = 0 J o