Question

Since the engine power changes with altitude, we would like to have a way to model the behaviour of engine power with altitude.

Give an equation which can model this altitude effect. Explicitly indicate division with a / symbol. Indicate a subscript using _ (e.g. is written as a_0). Greek letters are to be written out ( becomes alpha), and powers can be indicated with ^ (e.g. becomes x^a).

Answer 1

To model the effect of altitude on engine power, we can use a simple equation that reflects the relationship between engine power, sea-level power, and the altitude. A commonly used approximation is:

P_h = P_0 × (1 - (alpha × h))^beta

Where:
- P_h is the engine power at altitude h
- P_0 is the engine power at sea level
- alpha is a constant that represents the rate at which power decreases with altitude (in per unit per meter)
- h is the altitude (in meters)
- beta is an exponent that can account for non-linear effects, often close to 1 for small altitudes

This equation indicates that as altitude increases (h increases), engine power (P_h) decreases. The constants alpha and beta can be determined experimentally or through manufacturer specifications.