Question

1. Using the equations describing the standard atmosphere, plot the speed of sound (in m/s, ft/s and knots) in the altitude range sea level – 32 km. You can use Matlab or Excel (10 points).


2. An airfoil has a critical Mach number of ??? = 0.65. The wing is swept back at 30°. a) What is the design flight Mach number for this wing? (2 points)

b) What is the design flight speed in knots at an altitude of 30,000 ft? (10 points)


3. A supersonic passenger plane is traveling at an altitude of 60,000 ft. A normal shock forms in front of the nose of the plane. A pitot-static system on the nose (behind the shock) measures the pressure ratio between stagnation pressure and static pressure to be 1.2256. a) Calculate the flight Mach number of the aircraft (12 points).

c) Calculate the required wing sweep for minimum wave drag. (4 points)


3. A fighter jet passes over you at Mach 1.6 at an altitude of h = 10000 m. What is its horizontal distance x from you when you hear the sonic boom? (6 points)

Answer 1

Kindly upload different questions separately. Thank you! Answer to the first question is here:

Note that the speed of sound depends on temperature of air which, in turn, depends on altitude.

MATLAB CODE:

h=0:0.1:32; % Height range in Km
T0=288; % Standard sea level temperature in K
L=6.5; % Lapse rate in K/Km
R=287; % Gas constant for air in m2/s2/K
r=1.4; % Ratio of specific heats for air

T=T0-L.*h; % Temperature in K at height h
V_m_s=sqrt(r.*R.*T); % Speed of sound in m/s
V_f_s=V_m_s.*3.2808; % Speed of sound in f/s
V_knots=V_m_s.*1.9438; % Speed of sound in knots

plot(h,V_m_s)
xlabel('Height range in Km');
ylabel('Speed of sound in m/s');
grid on

plot(h,V_f_s)
xlabel('Height range in Km');
ylabel('Speed of sound in f/s');
grid on

plot(h,V_knots)
xlabel('Height range in Km');
ylabel('Speed of sound in knots');
grid on