OK, letīs imagine a comparison between the ecact same airplane in two conditions. Say, Phoenix in Arizona, at about 1000 feet above sea level - and the air temperature happens to be 52 Celsius or 125 Fahrenheit. Which should be about ISA+40 - or is it called ISA+72... Anyway, the density altitude should be about 6000 feet.
Now, compare it with conditions at actual altitude of 6000 feet, say around Denver, and in ISA conditions, which means 5 Celsius or 41 Fahrenheit there.
Airplane at 1000 feet and 52 Celsius and airplane at 6000 feet and 5 Celsius should encounter exact same air density. They ought to stall at exact same TAS and therefore need exact same TAS and ground speed to unstick.
The fans ought to meet the same mass flow, and therefore ought to produce equal thrust at equal N1. Correct?
So, the difference should be that the mass flow entering the engine at 1000 feet and 52 Celsius would be less effective in cooling the turbine? And therefore, the engine would have to operate at lower rpm and thrust to prevent overheating - thus requiring longer takeoff roll to reach the same Vr?
Correct?