Question

For a given chamber pressure, the thrust of a rocket engine is highest when

• A. the rocket is operating at its design altitude
• B. the rocket is operating in vacuum
• C. the rocket is operating at sea-level
• D. there is a normal shock in the rocket nozzle

Hint:

Lower external pressure increases rocket nozzle exit velocity and thrust.

Answer 1

The Correct Option is B

For a given chamber pressure, the thrust of a rocket engine is primarily influenced by the pressure differential between the ambient pressure and the exhaust pressure at the nozzle exit. The thrust can be expressed by the equation:

\(F = \dot{m} \cdot V_e + (P_e - P_a) \cdot A_e\)

where:

• \(\dot{m}\) is the mass flow rate of the exhaust gases
• \(V_e\) is the exit velocity of the gases
• \(P_e\) is the pressure at the nozzle exit
• \(P_a\) is the ambient pressure
• \(A_e\) is the exit area of the nozzle

The second term \((P_e - P_a) \cdot A_e\) indicates the contribution of the pressure differential to the total thrust. In a vacuum, \(P_a\) is zero, maximizing this term and thus maximizing total thrust:

• Operating at design altitude: This refers to when the rocket engine is optimized for specific ambient conditions, but \(P_a\) still exists, reducing potential thrust.
• Operating at sea-level: The ambient pressure \(P_a\) is highest, significantly reducing thrust due to a smaller pressure differential.
• Presence of a normal shock: Normal shocks within the nozzle decrease exit velocity and increase exit pressure significantly, adversely affecting thrust.
• Operating in vacuum: Here, ambient pressure \(P_a\) is zero, allowing the nozzle exit pressure to fully contribute to back pressure thrust. This maximizes the performance due to the absence of atmospheric pressure interference, leading to the highest possible thrust for a given chamber pressure.

Therefore, the correct answer is: the rocket is operating in vacuum.