def sigmaMax(Mach, gamma=1.4):
""" computes the MAXIMUM shock angle (always subsonic downstream flow)
"""
M2 = np.square(Mach)
ka = (M2-1.)*(1.+.5*(gamma-1.)*M2)
kb = .25*((gamma+1.)*M2-(3.-gamma))*M2 + 1.
return degree.atan(np.sqrt((kb+np.sqrt(kb**2+ka))/ka))
def strongsigma_Mach_deflection(Mach, deflection, gamma=1.4):
ka = (1. + .5*(gamma+1.)*Mach**2)*degree.tan(deflection)
kb = 1. - Mach**2
kc = (1. + .5*(gamma-1.)*Mach**2)*degree.tan(deflection)
kd = (ka**2/3. - kb)/3.
ke = 2.*ka**3/27. - ka*kb/3. + kc
if ke**2 - 4.*kd**3 > 0:
print "no strong shock wave solution"
return 90.
else:
phi = math.acos(-.5*ke/math.sqrt(kd**3)) + 4*math.pi
kf = 2.*math.sqrt(kd)*math.cos(phi/3.) - ka/3.
return degree.atan(1./kf)
