Variational approach to conical bodies having maximum lift-to-drag ratio at hypersonic speeds
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An investigation of the lift-to-drag ratioE attainable by a slender, conical body flying at hypersonic speeds is presented under the assumptions that the pressure distribution is modified Newtonian and the surface-averaged friction coefficient is constant. The length of the body and the elongation ratio of the cross section α are prescribed, and the values of the free-stream dynamic pressure, the factor modifying the Newtonian pressure distributionm, and the surface-averaged friction coefficientCf are knowna priori. The indirect methods of the calculus of variations are employed, an it is found that, for any given value of the length and the elongation ratio, the optimum transversal contour is a diamond shape. As the elongation ratio increases, the maximum lift-to-drag ratio increases, tending to the limiting valueE=0.529\(E = 0.529^3 \surd (m/C_f )\) when α → ∞.
KeywordsFriction Coefficient Pressure Distribution Indirect Method Ratio Increase Dynamic Pressure
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