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. 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, γ {displaystyle gamma } , equal to 1.4. The upstream Mach number, M 1 {displaystyle 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 γ {displaystyle gamma } to be 1.4 over the entire Mach number range leads to errors over 10% beyond Mach 5. Given an upstream Mach number, M 1 {displaystyle M_{1}} , and the ratio of specific heats, γ {displaystyle gamma } , the post normal shock Mach number, M 2 {displaystyle M_{2}} , can be calculated using the equation below. The next equation shows the relationship between the post normal shock pressure, p 2 {displaystyle p_{2}} , and the upstream ambient pressure, p 1 {displaystyle p_{1}} . The relationship between the post normal shock density, ρ 2 {displaystyle ho _{2}} , and the upstream ambient density, ρ 1 {displaystyle ho _{1}} is shown next in the tables. Next, the equation below shows the relationship between the post normal shock temperature, T 2 {displaystyle T_{2}} , and the upstream ambient temperature, T 1 {displaystyle T_{1}} . Finally, the ratio of stagnation pressures is shown below where p 01 {displaystyle p_{01}} is the upstream stagnation pressure and p 02 {displaystyle p_{02}} occurs after the normal shock. The ratio of stagnation temperatures remains constant across a normal shock since the process is adiabatic.