Shock compression ratio
= Shock compression ratio
{title2=$\chi$}
The shock compression ratio is the downstream-to-upstream density ratio. For a strong perfect-gas shock,
$$
\chi=\frac{\rho_1}{\rho_0}=\frac{\gamma+1}{\gamma-1}.
$$
In the upstream rest frame, the downstream velocity is $2V_s/(\gamma+1)$ and its pressure is $2\rho_0V_s^2/(\gamma+1)$.