Optimum Altitude and Temperature
 

The flight planning manual for the Global Express states that the optimum altitude for a given mach number is independent of temperature (as long as within the cruise thrust limit for the speed).

I can't get my head around why optimum altitude is a pressure altitude and not density related. Can anyone explain?

Mach is a function of temperature.

By maintaining Mach you are negating the effect of temperature on lift and drag.

With an increase in temperature, maintaining Mach Number, your TAS will have to increase and the air density will decrease. Your Specific Air Range (SAR) will decrease (your fuel economy will become worse.) The question the optimum altitude calculation is asking is: can this situation be improved by changing Flight Level?

The drag profile of the aircraft is based on your Mach Number/IAS (OK, EAS) and this relationship will not change with temperature, so changing Flight Level will not improve the situation, hence the Optimum Altitude doesn't change (things are worse with the increasing temperature, but won't be improved by changing Flight Level.)

Optimum altitude is the altitude for the best possible fuel efficiency in cruise i.e. fuel miles (distance covered against a specific amount of fuel).

In other words

Fuel Miles = TAS/Fuel Flow

The optimum altitude determined by FMC is based on aircraft gross weight and cruise speed in still air.

Optimum altitude varies with weight, lower if aircraft is heavy and higher if aircraft is light.

Temperature does not have much effect on optimum altitude. Why?

Mach No = TAS/LSS

Increase in temperature = Increase in LSS (local speed of sound)

In order to maintain a constant mach no TAS will have to be increased.

Increase in TAS = Increase in Fuel Flow

Since Optimum Altitude was all about Fuel Miles

and Fuel Miles = TAS/Fuel Flow (as mentioned above)

Increase in both TAS and Fuel Flow = No change in fuel miles.

No change in fuel miles = Temperature not considered for optimum altitude calculations.

Checkboard:
Your explanation is mostly correct, but this part is not. At given weight, altitude and Machnumber Specific Air Range and thrust-specific fuel consumption (tsfc) do not change with temperature.