Question

During the entry of the Apollo space vehicle into the Earth's atmosphere, the Mach number at a given point on the trajectory was M = 38 and the atmospheric temperature was 270 K. Calculate the temperature at the stagnation point of the vehicle, assuming a calorically perfect gas with γ = 1.4. Do you think this is an accurate calculation? If not, why? If not, is your answer an overestimate or underestimate?

Answer 1

The temperature at stagnation point is 78246K. The answer is an overestimate of the actual value.

Step-by-step explanation:

Given:

Mach number, M = 38

Atmospheric temperature, Tₐ = 270K

γ = 1.4

Temperature at the station point, Tₓ = ?

We know,

`Tx = Ta * [1 + M^2 * (gamma-1)/2]`

Tₓ = 270 X [ 1 + (38*38) X (1.4-1) /2]

Tₓ = 270 X [ 1 + 577.6/2]

Tₓ = 270 X [1 + 288.8]

Tₓ = 270 X 289.8

Tₓ = 78246K

Therefore, the temperature at stagnation point is 78246K which seems to be inaccurate because the assumption of a calorically perfect gas holds good up to M = 5.

The answer is an overestimate of the actual value.