Hybrid Exact-Approximate Analytic Hypersonic Aerodynamic Relations for General Vehicle Shapes

Abstract

This study investigates the creation of hybrid exact-approximate, analytic hypersonic aerodynamic relations for a wide range of vehicle classes to support conceptual design. This is accomplished by performing exact, analytic integrations of the Newtonian pressure coefficient over the unshadowed surface of the vehicle where possible and analytically approximating the remaining terms. Comparisons with a panel method validate the analytic solutions formed for arbitrary bodies of revolution with profiles described by second-, third-, or fourth-order Bezier curves as well as non-axisymmetric geometries described by constrained second-order Bezier surfaces. The computational and design advantages provided by the analytic relations enable the rapid design of vehicle shape within conceptual studies in manner that is not possible with traditional panel methods.Nomenclaturê n in inward normal vector Bcontrol node location, m P Bezier function, m r position of differential surface element, mcoefficient n order of Bezier curve N u number of discrete elements along u N v number of discrete elements along v p ∞ freestream pressure, Pa u arclength, surface parametrization variable v surface parametrization variable V ∞ freestream velocity magnitude, m/s ρ ∞ freestream density, kg/m 3 θ inclination angle, rad