Page:Threeshockwaves.pdf/5

 Returning to the configuration of shocks depicted in Fig. 3, since $$\zeta_{1,2}$$ is assumed known,

Hence, for the region in front of the shock

For the Mach shock the appropriate value of $$\sigma_\perp^{(1,4)}$$ is $$|\alpha|$$.

But the equality of the pressures in regions $$3$$ and $$4$$ requires that

The quantity $$\zeta_{2,3}$$ has been plotted by von Neumann as a function of the angle of incidence $$\alpha$$. Accordingly the intersection of the curve $$\zeta_{2,3}(\alpha)$$ with $$\zeta_{1,4}/\zeta_{1,2}$$ determines the angle $$\alpha_M$$ at which we have what we might call the. In this manner it is found that

respectively.