On SEP airplanes, why does the fuel consumption decreases with temperature, pressure and airspeed being equal?

Looking at the cruise performance tables in the POH of the C150, C172 or C182, one can see that for the same pressure altitude, the same RPM and the same true airspeed, the fuel consumption is reduced at higher temperature.

For example, a 1976 C150 POH indicates, at 2500 RPM, at 2000 ft pressure altitude,

• at -5°C: 97 KTAS, 5.3 GPH
• at 15°C: 96 KTAS, 4.9 GPH
• at 35°C: 95 KTAS, 4.6 GPH

(yes, there is a 1 kt difference each time, but interpolating the values gives very similar results)

But thermodynamics tells us that the efficiency is proportional to the difference of temperature between the isothermal expansion at Th and the isothermal compression at Tc in the Carnot cycle, thus efficiency = (Th-Tc)/Th.

I cannot reconcile the consumption data with that theory, since apparently the output power is the same (true airspeed, with identical parasitic and induced drag forces) for an apparently higher efficiency at higher Tc temperature.

What other factor am I missing?

• true airspeed, with identical parasitic and induced drag forces Why would the drag be identical? Same TAS in lower density air means lower IAS and less drag. Commented Nov 27, 2017 at 21:41

In the examples cited, there is a slight increase in Density Altitude (DENALT), which results in a slightly higher TAS. As the air becomes thinner, fewer molecules pass by the aircraft per mile, resulting in a lightly less loss due to drag. Increased temperature does not have the same range of change as altitude, however, it is nonetheless a higher DENALT, which is thinner air.

As an aside, in practice, you will note that the throttle becomes wider open with less dense air, until it is fully open. (Note that RPM is not the primary measure of power, rather fuel burn is. RPMs will become higher at higher DENALT for the same power.) At that point there will be no more available power, and any increase in temperature or altitude cannot be compensated for by increasing the throttle setting.

You will also note that less energy is expended per mile at higher DENALT, not factoring in the cost of a climb to that altitude.

Finally, a different practical example of this: When flying in icing conditions, conditions (and the POH) may call for continuous carburetor heat at altitude. When this is done, the engine should be releaned, as the DENALT will be higher, and if uncompensated for, will result in a rich mixture which could foul spark plugs.

• Very clear and thorough explanation, thanks! I was neglecting the impact of temperature on parasitic and induced drag (as others also helpfully remarked). Commented Nov 28, 2017 at 9:50

As the temperature increases the air expands becoming less dense. In a normally aspirated engine, the less dense air means less oxygen is drawn into the cylinders and less fuel is required to maintain the proper air/fuel ratio. Thus, fuel consumption is reduced.

This also results in less power and a lower IAS. But the higher temperature helps offset that resulting in only a small decrease in TAS.

• Exact, thanks a lot! Commented Nov 28, 2017 at 9:51
• The drag is also another important factor. Commented Dec 2, 2017 at 10:09