The Newtonian impact theory is valid at high angles of attack. The wall inclination for a blunt body gradually decreases along the free stream direction. For such cases, when this angle is less than \(35^{\circ}\) the Prandtl-Meyer expansion is applicable. Solve Problem 1.14 using the Newtonian impact theory together with the Prandtl-Meyer expansion to obtain the surface pressure for the half circle.

Problem 1.14

Find the surface pressure for the frontal region of the capsule during its reentry. Assume the shape of the frontal region as a half circle and comment on the region of validity of your result.