Consider two different aircraft using the same propulsion system (air-breathing), so both aircraft deliver the same amount of thrust and have the same mass flow through the engine. Aircraft A is aerodynamically completely optimised, while aircraft B has a lot of excrescences. Therefore, aircraft A has a higher cruise speed than aircraft B.

Which of the two aircraft has the highest propulsive efficiency when operating at cruise speed.

Aircraft A

Aircraft B

They have the same propulsive efficiency

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 months ago

To determine which aircraft has the highest propulsive efficiency at cruise speed, we need to consider the concepts of propulsive efficiency and how it is influenced by aerodynamic design and drag.

Propulsive efficiency (\( \eta_p \)) is defined as the ratio of the useful work done by the thrust produced by the aircraft to the power used by the engines. It can be expressed as:

\[
\eta_p = \frac{V}{V + \frac{T}{\dot{m}}}
\]

where:
- \( V \) is the true airspeed of the aircraft,
- \( T \) is the thrust produced,
- \( \dot{m} \) is the mass flow rate of the air through the engine.

In this scenario:
- Aircraft A has a higher cruise speed due to its optimized aerodynamic design, which results in lower drag.
- Aircraft B has more excrescences (protrusions, irregular shapes, etc.), leading to higher drag and a lower cruise speed compared to Aircraft A.

Since Aircraft A has higher speed (and assuming thrust produced and mass flow rate remain constant), its propulsive efficiency will generally be higher due to the lower influence of drag, allowing a greater proportion of the thrust to do useful work.

In conclusion, **Aircraft , with its optimized aerodynamics and higher cruise speed, will have the highest propulsive efficiency when operating at cruise speed compared to Aircraft B.