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, $$\gamma$$, equal to 1.4. The upstream Mach number, $$M_1$$, 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 $$\gamma$$ 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, $$M_1$$, and the ratio of specific heats, $$\gamma$$, the post normal shock Mach number, $$M_2$$, can be calculated using the equation below.
 * $$ M_2 = \sqrt{\frac{M_1^2\left(\gamma - 1\right)+2}{2\gamma M_1^2 - \left(\gamma - 1\right)}}$$

The next equation shows the relationship between the post normal shock pressure, $$p_2$$, and the upstream ambient pressure, $$p_1$$.
 * $$ \frac{p_2}{p_1} = \frac{2\gamma M_1^2}{\gamma + 1} - \frac{\gamma - 1}{\gamma + 1}$$

The relationship between the post normal shock density, $$\rho_2$$, and the upstream ambient density, $$\rho_1$$ is shown next in the tables.
 * $$ \frac{\rho_2}{\rho_1} = \frac{\left(\gamma + 1\right)M_1^2}{\left(\gamma - 1\right)M_1^2 + 2}$$

Next, the equation below shows the relationship between the post normal shock temperature, $$T_2$$, and the upstream ambient temperature, $$T_1$$.
 * $$ \frac{T_2}{T_1} = \frac{\left(1 + \frac{\gamma - 1}{2}M_1^2\right)\left(\frac{2\gamma}{\gamma - 1}M_1^2 - 1\right)}{M_1^2\left(\frac{2\gamma}{\gamma - 1} + \frac{\gamma - 1}{2}\right)}$$

Finally, the ratio of stagnation pressures is shown below where $$p_{01}$$ is the upstream stagnation pressure and $$p_{02}$$ occurs after the normal shock. The ratio of stagnation temperatures remains constant across a normal shock since the process is adiabatic.
 * $$ \frac{p_{02}}{p_{01}} = \left(\frac{\frac{\gamma + 1}{2}M_1^2}{1 + \frac{\gamma - 1}{2}M_1^2}\right)^\frac{\gamma}{\gamma - 1}\left(\frac{1}{\frac{2\gamma}{\gamma + 1}M_1^2 - \frac{\gamma - 1}{\gamma + 1}}\right)^\frac{1}{\gamma - 1}$$

Note that before and after the shock the isentropic relations are valid and connect static and total quantities. That means, $$p_{total}\neq p_{static} + p_{dynamic}$$ (comes from Bernoulli, assumes incompressible flow) because the flow is for Mach numbers greater than unity always compressible.