I am disregarding changes in fuel flow due to variations in how much you can lean the engine at different altitudes
I think that one is worth looking at.
The mixture setup is based on mass flow of air and mass flow of fuel.
The mass flow of fuel is hardly temp dependent – 0.1% expansion per degC.
The mass flow of air is very temp dependent. At low levels (say below 20k) and ISA profile, it should be 2 degC per 1000ft, which is what % mass change?
So the fuel flow is different for different air temps, at the same air pressure (same pressure altitude), no? It should be lower at lower air temps, because fewer fuel molecules are required in warmer (thinner) air. I hope I got that right…
And less fuel = less power!
look in your POH performance tables/graphs.
I don’t have any of those 
Edit: I found this:
where the note at top left says a 1% change in power for every 10F change from ISA, if I understand it right. What I don’t know is whether this is best-power or best-economy (peak EGT).
Peter wrote:
So the fuel flow is different for different air temps, at the same air pressure (same pressure altitude), no? It should be lower at lower air temps, because fewer fuel molecules are required in warmer (thinner) air. I hope I got that right… And less fuel = less power!Yes, but you were asking for difference in cruise speed for a fixed fuel flow. The same fuel flow will give the same power — as long as the same leaning procedure is used.
Really? My TB20 POH does.look in your POH performance tables/graphs.I don’t have any of those
Edit: I found this:
where the note at top left says a 1% change in power for every 10F change from ISA, if I understand it right. What I don’t know is whether this is best-power or best-economy (peak EGT).
That is for a fixed MP and rpm. If the temperature changes, you will have to change the engine settings to maintain the same power (and thus fuel flow) — just as you have to do when changing altitude.
Maybe @bookworm might have ideas here… intuition tells me this is not trivial.
At any altitude above about 8k, one is already flying with a wide open throttle. So the fuel flow is probably not literally fixed at x USG/hr. I think, with colder (denser) air at a given air pressure, you can use more fuel to achieve peak EGT. So there will be more power in colder air. But will the plane go faster, given the air is denser? There will be more lift (because lift is produced by redirecting the mass air flow downwards, one molecule at a time) so the AoA can be smaller, so there is less induced drag, but more parasitic drag…
Peter wrote:
At any altitude above about 8k, one is already flying with a wide open throttle.
Depends on your power setting. With 75%, yes. With 65% it shouldn’t happen until around 11k. 65% is my standard power setting and at FL100, I don’t have WOT.
A while back I looked at the C172 POH max climb rates.
Air density accounted for most of the variation, as you would expect, but there was a roughly 20% unexplained variation between the -20 degree data and the +40.
If you plot climb rate vs air density, the higher temperature lines come out above the lower temperatures.
I don’t know causes the effect, but as the speed of sound rises with temperature only, and propeller tip speed (TAS) depends on RPM, perhaps propeller efficiency causes the non-density variation.
Peter wrote:
intuition tells me this is not trivial
It’s not trivial but I don’t think it’s too bad.
For a given thrust or power, it’s density altitude that determines ceiling or speed at a particular level. So certainly speed for a given fuel burn should be dependent on DA alone.
If available thrust/power fell off in a way that depends only on density altitude, that would be all there is to it. However, as you’ve observed, in a normally aspirated engine the full throttle MP depends on pressure, not density. So, at the same DA, on a cold day you actually have a lower pressure of air, and less power available. So the ceiling will be slightly lower in terms of DA, though of course higher in terms of pressure altitude.
Can we do a ballpark check on David’s 20%. At ISA-20 the SL temp is 268K. At ISA+40 the SL temp is 328K. So if you get 27"of MP of manifold pressure at SL density on an ISA-20 day, you’ll get 33" of MP on an ISA+40 day (though you’ll have to dig a mile-deep mineshaft to find SL density on an ISA+40 day!). I think that could explain a 20% difference in climb rate.
Peter wrote:
Huv’s formula above of 8C = 1000ft seems about right in reality for the ceiling.
Not only. It’s commonly used for a quick DA calculation. Use it all the time.
Airborne_Again wrote:
Depends on your power setting. With 75%, yes. With 65% it shouldn’t happen until around 11k. 65% is my standard power setting and at FL100, I don’t have WOT.
Some don’t like to rev their normally aspirated engine so high to maintain power with increasing altitude. I cruise with full throttle at 7500 or 8500 ft, at 65% power or lower. I don’t worry about the exact percentage. For me (and maybe my engine), lower rpm makes for a more pleasant cruise experience.
Weight mainly affects climb rate. My main concern there is that I run the engine rich until altitude lowers power below 75% with full throttle/2500 rpm, so lower climb rate means more fuel burn at the beginning of a given flight, until MP drops to 23 inches and I start to lean.
So certainly speed for a given fuel burn should be dependent on DA alone.
I remain confused, because the fuel burn itself varies with the air density i.e. temperature.
I should have phrased the question with an additional qualifier: at the best economy setting.
That would be applicable to practically all non-turbo Eurocontrol IFR flight in Europe.
My feeling is that a higher TAS is achieved in sub-ISA conditions, but I don’t know how to work it out.
Peter wrote:
I remain confused, because the fuel burn itself varies with the air density i.e. temperature.I should have phrased the question with an additional qualifier: at the best economy setting.
That would be applicable to practically all non-turbo Eurocontrol IFR flight in Europe.
My feeling is that a higher TAS is achieved in sub-ISA conditions, but I don’t know how to work it out.
I don’t see why that should be the case. Assuming that you’re working at best economy and burning fuel at a given rate, the power output should be constant. So the speed will depend on the density altitude.
