Question

At some point on its trip a Concorde aircraft flies 520 m/s at an altitude where the temperature is -56 degree C. Determine the Mach angle (in degrees) of its shockwaves at that instance. Determine the Mach angle (in degrees) of its shockwaves at that instance.

Answer 1

To determine the Mach angle of the shockwaves, we need to use the formula:

Mach angle (θ) = sin^(-1)(1/Mach number)

The Mach number can be calculated using the formula:

Mach number (M) = velocity/speed of sound

First, we need to calculate the speed of sound at an altitude where the temperature is -56 degrees Celsius. The relationship between temperature and the speed of sound is given by:

Speed of sound (v) = √(γ * R * T)

where:
γ = ratio of specific heats = 1.4 (for air)
R = gas constant = 287 J/(kg*K)
T = temperature in Kelvin = -56 + 273 = 217 K

Plugging in the values, we get:

v = √(1.4 * 287 * 217)
v ≈ 294.8 m/s

Next, we can calculate the Mach number:

M = 520 / 294.8
M ≈ 1.764

Finally, plugging the Mach number into the formula for the Mach angle:

Mach angle (θ) = sin^(-1)(1/1.764)
θ ≈ 38.9 degrees

Therefore, the Mach angle of the Concorde's shockwaves at that instance is approximately 38.9 degrees.