# CHAPTER12:LINEARIZED SUPERSONIC FLOW¶

## Example E01 : Pg 395¶

In [1]:
# All the quantities are expressed in SI units
from math import pi,sqrt
alpha = 5*pi/180;                    # angle of attack
M_inf = 3;                            # freestream mach number

# from eq.(12.23)
c_l = 4*alpha/sqrt(M_inf**2 - 1);

# from eq.(12.24)
c_d = 4*alpha**2/sqrt(M_inf**2 - 1);

print"The cl and cd according to the linearized theory are:cl =", round(c_l,2)
print"The cl and cd according to the linearized theory are:cd =",round(c_d,2)

The cl and cd according to the linearized theory are:cl = 0.12
The cl and cd according to the linearized theory are:cd = 0.01


## Example E02 : Pg 395¶

In [2]:
# All the quantities are expressed in SI units
from math import sqrt,pi
M_inf = 2.;                       # freestream mach number
rho_inf = 0.3648;                # freestream density at 11 km altitude
T_inf = 216.78;                  # freestream temperature at 11 km altitude
gam = 1.4;                       # ratio of specific heats
R = 287.;                         # specific gas constant
m = 9400.;                        # mass of the aircraft
g = 9.8;                         # acceleratio due to gravity
W = m*g;                         # weight of the aircraft
S = 18.21;                       # wing planform area
# thus
a_inf = sqrt(gam*R*T_inf);
V_inf = M_inf*a_inf;
q_inf = 1./2.*rho_inf*V_inf**2.;

# thus the aircraft lift coefficient is given as
C_l = W/q_inf/S;

alpha = 180./pi*C_l/4.*sqrt(M_inf**2. - 1.);

print"The angle of attack of the wing is:",alpha,"degrees"

The angle of attack of the wing is: 1.97493716351 degrees


## Example E03 : Pg 400¶

In [3]:
# All the quantities are expressed in SI units
# All the quantities are expressed in SI units
from math import sqrt,pi
# (a)
M_inf = 2.;                       # freestream mach number
rho_inf = 0.3648;                # freestream density at 11 km altitude
T_inf = 216.78;                  # freestream temperature at 11 km altitude
gam = 1.4;                       # ratio of specific heats
R = 287.;                         # specific gas constant
m = 9400.;                        # mass of the aircraft
g = 9.8;                         # acceleratio due to gravity
W = m*g;                         # weight of the aircraft
S = 18.21;                       # wing planform area
c = 2.2;                         # chord length of the airfoil
alpha = 0.035;                   # angle of attack as calculated in ex. 12.2
T0 = 288.16;                     # ambient temperature at sea level
mue0 = 1.7894e-5;                # reference viscosity at sea level

# thus
a_inf = sqrt(gam*R*T_inf);
V_inf = M_inf*a_inf;

# according to eq.(15.3), the viscosity at the given temperature is
mue_inf = mue0*(T_inf/T0)**1.5*(T0+110.)/(T_inf+110.);

# thus the Reynolds number can be given by
Re = rho_inf*V_inf*c/mue_inf;

# from fig.(19.1), for these values of Re and M, the skin friction coefficient is
Cf = 2.15*10**-3;

# thus, considering both sides of the flat plate
net_Cf = 2.*Cf;

# (b)
c_d = 4.*alpha**2./sqrt(M_inf**2. - 1.);

print"(a) Net Cf = ",net_Cf*1e3
print"(b) cd =",c_d*1e3

(a) Net Cf =  4.3
(b) cd = 2.82901631903