On Similarity Rules for Transonic Flows
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The hypersonic similarity law as derived by Tsien has been investigated by comparing the pressure distributions along bodies of revolution at zero angle of attack. In making these comparisons, particular attention was given to determining the limits of Mach number and fineness ratio for which the similarity law applies. For the purpose of this investigation, pressure distributions determined by the method of characteristics for ogive cylinders for values of Mach numbers and fineness ratios varying from 1.5 to 12 were compared. Pressures on various cones and on cone cylinders were also compared in this study. The pressure distributions presented demonstrate that the hypersonic similarity law is applicable over a wider range of values of Mach numbers and fineness ratios than might be expected from the assumptions made in the derivation. This is significant since within the range of applicability of the law a single pressure distribution exists for all similarly shaped bodies for which the ratio of free-stream Mach number to fineness ratio is constant. Charts are presented for rapid determination of pressure distributions over ogive cylinders for any combination of Mach number and fineness ratio within defined limits.
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The author first sets forth some observations about the theory of models. Then he established certain general criteria for the construction of dynamically similar models in water and in air, through reference to the perfect fluid equations and to the ones pertaining to viscous flow. It is, in addition, pointed out that there are more cases in which the analogy is possible than is commonly supposed.
Drag tests at zero lift have been made at Mach numbers from 0.7 to approximately 0.95 in the high speed wind tunnel of the Institute of Aerodynamics, ETH, Zurich, on a group of untapered wings of aspect ratio 3.25, having sweep angles of 0 degree and 35 degrees. For each sweep angle, a series of geometrically similar models was tested at a constant Reynolds number to provide a verification of computed tunnel blocking corrections. Tests were also made for wings having thickness ratios of 0.09 and 0.12 and the results compared with results predicted by von Karman's similarity law.