Nonuniform propagation of sonic discontinuities through thermally conducting gases

Equations (8) and (10) are the present versions of Williams' results. The first gives the lift as an integral involving the loading induced by unit plunging downwash P , as Williams found. The second gives the nose-down moment about the airfoil center as an integral involving only P ( 7 ) ; the loading induced by a pitching downwash whose chordwise dependence is x. In both cases, the arbitrary motion of the airfoil is represented by the downwash w ( x ) , which appears in the integrals as w ( — x ) . In the present centered coordinate system, then, not only are lift and moment for arbitrary motion determined only by the loadings for plunging and pitching, but the lift depends only on the plunging loading and the moment only on the pitching loading. This seems to be a useful reformulation of Williams' results. We also note that for unit downwash, Eq. (10) gives