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National Advisory Committee for Aeronautics, Technical Notes - Tables and Graphs of Normal Shock Parameters at Hypersonic Mach Numbers and Selected Altitudes

Tables and graphs of normal-shock parameters are presented for real
air in thermal and chemical equilibrium at conditions ahead of the shock
corresponding to six selected altitudes, and for temperatures behind the
shock from 2,0000 K to ll,000o K. The altitudes used are those repre-
senting the boundaries of the isothermal layers in that part of the
earth’s atmosphere considered applicable to aerodynamic flight; that is,
below an altitude of 500,000 feet. The altitude data and the real-air
thermodynamic data used are reliable for application to this rangewof
altitudes. Tabulated values at each altitude as a function of the tem-
perature behind the shock are presented of the normal-shock Mach numbers,
flight velocity, enthalpy behind the shock, and ratios of real to ideal
values of pressure, density, temperature, and velocity of sound. Graphs
are presented to show the variation of the normal-shock parameters with
flight Mach number and altitude, and some discussion of the dependence
of the parameters on the initial pressure and temperature is given. A
method for adapting the data to the case of oblique shocks is included.

It can be shown from the tabulated thermodynamic properties for
real air (for example, ref. 1) and the Rankine—Hugoniot shock relations
that the hypersonic shock parameters are strongly dependent upon both
temperature and pressure as well as on Mach number. This concept is
in contrast to that for ideal air in which no temperature or pressure
dependency is indicated because of the assumed constancy of the specific
heats, constancy of the molecular weight, and perfectness of the gas.
(See, for example, ref. 2.) Until the relatively recent advent of
hypersonic flight in the atmosphere, the assumption of near ideal air
has been adequate for flight, since the temperatures encountered were
moderate and hence the thermal properties of the air were near to the
ideal values. At high temperatures, however, the thermal properties of
air become greatly different from those of ideal air, and, in fact, the
air changes composition due to dissociation and ionization of the con~
stituent particles.