Aerodynamic flutter coefficients for subsonic, sonic and supersonic flow (linear two-dimensional theory)

Abstract

The solution is derived, in a convenient form for numerical evaluation, for a two-dimensional aerofoil oscillating with arbitrary downwash at sonic speed, and is shown to be the limit of both the subsonic and the supersonic solutions as the Mach number tends to unity. Linear theory is shown to be applicable at sonic speed for an oscillating aerofoil of zero thickness, but at near-sonic speeds consideration of the lift distribution shows that linearization is not permissible. Hence for near-sonic speeds the sonic solution gives a better approximation to the non-linear solution than does the linear solution for the actual speed. It is shown that interpolation of the force coefficients is more justifiable in the subsonic range than in the supersonic range. The physical validity of the linear solution is discussed ; certain singularities which occur in the transition to sonic speed are shown to have no physical significance. The four main aerodynamic force coefficients for an oscillating two-dimensional wing are presented in the form of tables and isometric graphs over the ranges 0 to 2 of Mach number and 0 to 1.4 of frequency parameter based on the wing chord; the present sonic solution and existing subsonic and supersonic solutions have been supplemented by interpolated values for Mach numbers between 0.7 and unity.