Aerodynamically blunt and sharp bodies

Computational fluid dynamics studies at supersonic and hypersonic speeds have resulted in an improved understanding of the meaning of aerodynamically, as opposed to geometrically, sharp and blunt shapes. An analytic investigation using Newtonian theory was conducted to support the computational results. Based on this work, a new criterion for the definition of an aerodynamically sharp shape is proposed. Defining the power-law shape to be the relevant gauge function, one can classify bodies with it > 2/3 as aerodynamical ly sharp, even though the initial body slope dr/djc is 90 deg. The paper describes the analysis that resulted in the new sharp and blunt shape criteria for aerodynamics. Nomenclature A = constant in power-law body equation defining fineness ratio Cp = pressure coefficient / = fineness ratio for the Sears-Haack body, Eq. (9) / = length of the body in definition of von Karman ogive and Sears-Haack body n = exponent in power-law body definition, Eq. (1) R = longitudinal radius of curvature, Eq. (2) R (0) = longitudinal curvature at x = 0, the leading-edge radius RK_O = longitudinal radius of curvature for a von Karman ogive RS-H = longitudinal radius of curvature for a Sears-Haack body r =body radius at a given x location TK-O =body radius for a von Karman ogive rs-H =body radius for the Sears-Haack body S = cross-sectional area SK-O =cross-sectional area of the von Karman ogive s =arc length along the surface from the leading edge, x = 0 V - volume of Sears-Haack body x = axial distance from leading edge £ ^transformed independent variable for the Sears-Haack body, Eq. (7) 0 =body slope angle, tan"1 (dr/dx)