Two-Dimensional Airfoils at Moderate Hypersonic Velocities

Abstract

Expressions for lift, drag,' and pitching moment coefficients are derived for a large number of airfoil sections in two-dimensional hypersonic flow. These expressions, differing from those obtained using linearized, second-order, and third-order theories, can be used throughout a moderate range of hypersonic Mach Numbers. The fundamental parameter of these formulas is the two-dimensional hypersonic flow similarity parameter, K = M0d. To obtain these expressions, the shock-wave and expansion-wave equations for pressure ratios across such waves are expanded in powers of K. Following this, it is shown that the first three terms so obtained for both wave types are practically identical for values of K less than about 1.0. Further, it is shown that they closely approach the exact pressure-ratio expressions. The application of the expressions thus derived to various airfoil sections is then demonstrated, and a table of airfoil coefficients is presented. It is shown that the airfoil formulas can be applied to finite wings with reasonable accuracy for design estimations.