On the construction and calculation of optimal nonlifting critical airfoils
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Numerical calculations are carried out in the hodograph plane to construct optimal critical airfoil shapes and the flow about them. These optimal airfoil shapes give the highest free-stream Mach numberM ∞ for a given thickness ratio δ and tail angle θ t (nonlifting) for which the flow is nowhere supersonic. A relationship betweenM ∞ and δ for various θ t is given. Analytical and numerical solutions to the same problem are found on the basis of transonic small-disturbance theory. These results provide a limiting case asM ∞ →1, δ → 0 and agree well with the calculations of the full problem. Using a numerical method to calculate the flow about general (subsonic) airfoils, a comparison is made between the critical free-stream Mach numbers for some standard airfoil shapes and the optimal free stream Mach number of the corresponding δ and θ t . A significant increase in the critical free-stream Mach number is found for the optimal airfoils.
KeywordsNumerical Calculation Mach Number Mathematical Method Free Stream Thickness Ratio
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