Effect of weight and temperature on operating ceiling and speed

Power required is drag * v or proportional to rho v^3 at a given L/D (say, best glide). So if the density is 3% lower you get 1% more speed per power. And the density goes down by about 3% per 1000 ft. So it’s about 1% of speed/power or distance/energy per 1000 ft of density altitude.

Peter wrote:

I remain confused, because the fuel burn itself varies with the air density i.e. temperature

Actually there is a direct correlation between fuel burn and power. For the same MP/RPM fuel burn will be lower with higher temperature (for same mixture setting e.g. best economy), i.e. power output will be lower. In other words you will need higher MP (or RPM) to compensate for the less dense air and obtain the same power as at ISA.

Peter wrote:

So, let me get this right… you reckon 1% extra distance flown for every 8C above ISA?

At the same fuel flow, yes.

In a jet aircraft the specific range ( Nautical air miles / lbs of fuel ) is independant of the temperature ( same altitude and same speed ) – TAS and fuel flow will vary with temperature.

bookworm wrote:

Power required is drag * v or proportional to rho v^3 at a given L/D (say, best glide). So if the density is 3% lower you get 1% more speed per power. And the density goes down by about 3% per 1000 ft. So it’s about 1% of speed/power or distance/energy per 1000 ft of density altitude.

I think this is wrong. Let me think about it and reply when I have some time.

In Peter’s example, flying WOT at peak EGT, assume that OAT suddenly goes up. Air density and thus dynamic pressure/CAS would decrease. What would happen to the aircraft?

The immediate effects would be that

• Engine power would decrease. This would tend to decrease TAS. The mixture would have to be leaned more to maintain peak EGT so fuel flow would also decrease.
• Parasitic drag would decrease. This would tend to increase TAS.
• Induced drag would increase as AOA would have to be increased to maintain lift. This would tend to decrease TAS.

So the question is which effect would be dominant?

Engine power would change approximately proportional to the change in air density. Assuming the change in propeller efficiency caused by any CAS and/or blade angle change is negligible, thrust would also change proportional to the change in air density. So would dynamic pressure and thus parasitic drag. The changes in thrust and parasitic drag would cancel. The remaining effect would be the increase in induced drag, so TAS should decrease.

Does this analysis make sense? I’m making a lot of assumptions and simplifications, and it seems to disagree with bookworm’s analysis.