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National Advisory Committee for Aeronautics, Technical Notes - Accuracy of Approximate Methods for Predicting Pressures on Pointed Nonlifting Bodies of Revolution in Supersonic Flow

The accuracy and range of applicability of the linearized theory,
second-order theory, tangent-cone method, conical—shock-expansion theory,
and Newtonian theory for predicting pressure distributions on pointed
bodies of revolution at zero angle of attack are investigated. Pressure
distributions and integrated pressure drag obtained by these methods are
compared with standard values obtained by the method of characteristics
and the theory of Taylor and Maccoll. Three shapes, cone, ogive, and a
modified optimum body, are investigated over a wide range of fineness
ratios and Mach numbers.

It is found that the linearized theory is accurate only at low values
of the hypersonic similarity parameter (the ratio of free—stream Mach
number to body fineness ratio) and that second-order theory appreciably
extends the range of accurate application. The second-order theory gives
good results on ogives when the ratio of the tangent of maximum surface
angle to the tangent of the Mach angle is less than 0.9. Tangent-cone
methods cannot be widely applied with good accuracy. In general, the
conical-shock-expansion theory predicts pressure and drag within engineer-
ing accuracy when the hypersonic similarity parameter is greater than 1.2.
Although Newtonian theory gives good accuracy, except for cones, at the
highest values of the hypersonic similarity parameter investigated, it is
less accurate than the conical-shock-expansion theory.

Various methods have been proposed for predicting pressure distribu-
tions on bodies of revolution at zero angle of attack in supersonic flow.
The method of characteristics, which can be carried to any degree of
accuracy, is too time consuming to be practical for many engineering needs.
Other methods, although requiring less time, involve varying degrees of
approximation which limit their accuracy and range of applicability. This
investigation was undertaken to ascertain the range of applicability and
accuracy of a few of the approximate methods. Pressure distributions
determined from the method of characteristics and from the theory of
Taylor and Maccoll are used as standards for determining the accuracy of
these approximate methods. Wide ranges of Mach number and fineness ratio
are investigated in order to determine the range of values of the hyper—
sonic similarity parameter, the ratio of Mach number to body fineness
ratio, for which each of the various approximate methods is useful.