# CHAPTER14:ELEMENTS OF HYPERSONIC FLOW¶

## Example E01 : Pg 440¶

In :
# All the quantities are expressed in SI units
from math import sqrt,pi,sin,cos
M1 = 8.;                    # mach number
alpha = 15.*pi/180.;        # anlge of attack
theta= alpha;
gam = 1.4;
# (a)
# for M = 8
v1 = 95.62*pi/180.;
v2 = v1 + theta;
# from Appendix C
M2 = 14.32;
# from Appendix A, for M1 = 8 and M2 = 14.32
p_ratio = 0.9763e4/0.4808e6;
# from eq.(11.22)
Cp2 = 2/gam/M1**2*(p_ratio - 1);
# for M1 = 8 and theta = 15
b = 21*pi/180;
Mn_1 = M1*sin(b);
# for this value of Mn,1, from appendix B
p_ratio2 = 9.443;
# thus
Cp3 = 2./gam/M1**2.*(p_ratio2 - 1.);
c_n = Cp3 - Cp2;
c_l = c_n*cos(alpha);
c_d = c_n*sin(alpha);
L_by_D = c_l/c_d;
print"The exact results from the shock-expansion theory are:"
print"Cp2 =",Cp2
print"Cp3 = ",Cp3
print" cl =",c_l
print"cd =",c_d
print"L/D =",L_by_D
# (b)
# from Newtonian theory, by eq.(14.9)
Cp3 = 2.*sin(alpha)**2;
Cp2 = 0;
c_l = (Cp3 - Cp2)*cos(alpha);
c_d = (Cp3 - Cp2)*sin(alpha);
L_by_D = c_l/c_d;
print"\n(b) The results from Newtonian theory are:"
print"Cp2 =",Cp2
print"Cp3 =",Cp3
print"cl  =",c_l
print"cd  =",c_d
print"L/D =",L_by_D

The exact results from the shock-expansion theory are:
Cp2 = -0.0218681754368
Cp3 =  0.188459821429
cl = 0.203161244164
cd = 0.054436891307
L/D = 3.73205080757

(b) The results from Newtonian theory are:
Cp2 = 0
Cp3 = 0.133974596216
cl  = 0.129409522551
cd  = 0.0346751770605
L/D = 3.73205080757