We already have a few questions and answers about the qualitative effects of altitude on fuel economy:
- How do I determine the best altitude to fly for fuel economy?
- Why does fuel consumption decrease with increasing aircraft altitude?
- What is the relation between an airplane's altitude and the drag it is experiencing?
- Why do jet engines get better fuel efficiency at high altitudes? (contains formula for thermal efficiency)
I am interested in understanding how the changes in pressure and temperature at different altitudes affect the fuel economy of a turbofan powered aircraft quantitatively. In the end, I would like to make a plot of relative fuel economy vs. altitude that takes all of these effects into account, but I don't know how to quantitatively combine these effects.
- By fuel economy I mean fuel required per distance traveled, not time.
- I am not interested in absolute numbers for the fuel per distance, which would require specifying a particular aircraft. I am only interested in how the fuel per distance figure would relatively change with altitude, e.g. normalized to 1 at sea level.
- I assume ISA (International Standard Atmosphere) profiles for pressure and altitude.
- I assume the no wind case. Different winds at different altitudes will of course have an effect on the result, but it is easy to take this into account after the no wind case is understood.
Let's assume a typical climb profile for a short- to medium-haul jet airliner: 250/280/0.78
You can see that the TAS increases until reaching Mach 0.78, then decreases due to the lower temperatures causing a lower speed of sound and then remains constant above the tropopause. I am particularly interested in how the fuel economy will behave around these altitudes.