New directions in lifting surface theory

Abstract

speed of sound, dimensionless aspect ratio of planar lifting surface wing semichord, ft chordwise dimension of area element in supersonic and transonic theory local wing chord, ft reference chordlength, ft 2L/PxU*S = lift coefficient coefficient of pitching moment (p — ?>oo)/(pooM/2) = pressure coefficient depth of x-y plane below free liquid surface, ft or dimensionless depth below free surface, referred to I U/(gl) = Froude number gravitational constant, ft/sec height of wing midspan above ground plane, ft; also downward bending or heaving displacement, ft reference value of bending displacement at wingtip ( —1) /2 = complex unit wk/U or tal/U = reduced frequency kbi/b = reduced frequency based on areaelement size kernel function of subsonic integral equation reference length, ft upward normal force or force per unit span acting on lifting surface chordwise and spanwise coordinates of receiving area element, dimensionless flight Mach number static pressure distance between points, dimensionless {(x £) + (1 M)[(j/ T?) + (z 2o(i?))]) /2 = elliptical distance curvilinear coordinates measured spanwise along and normal to surface, dimensionless E S/STIP = normalized s projected cylindrical lifting surface area, ft or dimensionless; also spanwise distance on cantilever wing, measured in semispans. time coordinate, sec fluid velocity components, dimensionless flight speed, f ps velocity component normal to S, dimensionless function describing wake surface rectangular Cartesian coordinates, dimensionless, see Fig. 1 height of S above x-y plane, dimensionless displacement of wing above its projected surface, dimensionless angle of attack measured from zero lift : (M — 1) = cotangent of Mach angle discontinuous jump in a quantity, passing from lower to upper surface of wing