Second-Order Theory for Unsteady Supersonic Flow Past Slender, Pointed Bodies of Revolution

An analysis is made of the second-order effects of thickness on the unsteady aerodynamic forces on a slender pointed body of revolution in supersonic flow. The theory is restricted to harmonic oscillations for small angles of attack. The solution is obtained by approximating the nonlinear terms in the second-order potential equation by their first-order values and solving the resulting inhomogeneous partial differential equation, subject to more refined boundary conditions. The pressure equation is likewise refined and integrated to give the second-order corrections to lift and pitching moment coefficients. The analysis can be considered as an extension of the second-order, slender body theory of Lighthill to the case of unsteady flow. The results indicate appreciable reductions in unsteady lift and damping moment coefficients when applied to slender cones. The present theory is estimated to be reliable provided that Mb is less than 0.7.