Normal shock tables

In aerodynamics, the normal shock tables are a series of tabulated data listing the various properties before and after the occurrence of a normal shock wave. With a given upstream Mach number, the post-shock Mach number can be calculated along with the pressure, density, temperature, and stagnation pressure ratios. Such tables are useful since the equations used to calculate the properties after a normal shock are cumbersome.
The tables below have been calculated using a heat capacity ratio, formula_1, equal to 1.4. The upstream Mach number, formula_2, begins at 1 and ends at 5. Although the tables could be extended over any range of Mach numbers, stopping at Mach 5 is typical since assuming formula_1 to be 1.4 over the entire Mach number range leads to errors over 10% beyond Mach 5.
Normal shock table equations.
Given an upstream Mach number, formula_2, and the ratio of specific heats, formula_1, the post normal shock Mach number, formula_6, can be calculated using the equation below.
The next equation shows the relationship between the post normal shock pressure, formula_8, and the upstream ambient pressure, formula_9.
The relationship between the post normal shock density, formula_11, and the upstream ambient density, formula_12 is shown next in the tables.
Next, the equation below shows the relationship between the post normal shock temperature, formula_14, and the upstream ambient temperature, formula_15.
Finally, the ratio of stagnation pressures is shown below where formula_17 is the upstream stagnation pressure and formula_18 occurs after the normal shock. The ratio of stagnation temperatures remains constant across a normal shock since the process is adiabatic.