ATPL Performance Question

[Mr Irons]

As static temperature increases at the same altitude with N1 held constant:

A: TAS increases and SFC decreases.
B: TAS and SFC both increase.
C: Neither TAS nor SFC will be affected.
D: TAS decreases and SFC increases.

Does anyone know the answer and why?

Thanks

[Keith.Williams.]

Specific Fuel Consumption (SFC) is the mass of fuel that is used per hour to produce each unit of thrust (for a jet engine) and each Brake Horsepower (for a piston engine).

SFC is at its minimum value when:

a. The engine RPM is within an ideal band (typically 90% to 95% for jet engines.
b. The throttle is fully open (for piston engines).
c. The air pressure and density are high.
d. The air temperature is low.

So increasing ambient air temperature will increase SFC.


Increasing ambient air temperature will reduce the air density. This will have the following consequences for the engines:

a. Mass airflow rate through the engine at any given N1 will decrease.
b. Reduced mass flow will decrease thrust and power available.

It may be tempting to think that the IAS will remain constant, in which case the deceasing air density will cause TAS to increase. To investigate this idea we need to look at power available and power required.

To maintain constant TAS in level flight we must have power available = power required.

But as stated above the decreased air density will decrease power available.

And

Power Required = Drag x TAS.

Drag is proportional to TAS squared, so power required is proportional to TAS cubed.

So if our TAS increases then our power required would increase with the cube of the TAS.

But our Power Available is actually decreasing because of the reduced air density.

So our TAS will actually decrease.

So the answer to this question is TAS will decrease, SFC will increase.