Hypersonic blunt body flow

• $\delta$ = shock stand-off distance
• $R$ = radius of sphere/cylinder
• $\beta$ = limiting angle to which the curved bow shock is asymtopic
• $R_c$ = radius of curvature at the vertex of the hyperbola

Shock shape is given by the equation

$$x = R + \delta - R_c \cot^2\left[\beta \left( \sqrt{1+(y^2 \tan^2\beta )/R_c^2}-1 \right) \right]$$ (1)

where, for sphere-cone

$$\frac{\delta}{R} = 0.143 \exp\left( \frac{3.42}{M_\infty^2} \right)$$ (2)

and for cylinder-wedge

$$\frac{\delta}{R} = 0.386 \exp\left( \frac{4.67}{M_\infty^2} \right)$$ (3)