# Why do piston engines have a lower fuel consumption with higher temperatures?

It is very common to find in the AFM/POH, Section 5 of most piston engine airplanes (C152, C172, PA28, BE76, etc) charts that indicate the fuel consumption for cruise/economy power settings.

You will notice that in all cases, for a given set of pressure altitude, RPM and manifold pressure (if constant speed propeller) the fuel consumption will depend on the OAT. The question is: why does the fuel flow (in PPH or GPH) decrease for higher temperatures?

I should make sense to me that higher temperatures (hot atmosphere) would decrease the overall performance of the engine, as we all know, since the air is less dense which directly impacts in the engine's operation. If the engine's performance is degraded in a hot day, why does it burn less fuel?

All manufacturers publish similar results, but I can't figure out a physical explanation to it. If you could point out an official reference in any textbook I would really appreciate.

• You still need to maintain the Fuel/Air mixture to get the optimal burn. If you are running hot and there is less air (oxygen) for a given cycle, it follows that you would need less fuel to maintain the same a/f ratio. It may be less fuel but it is also producing less power too. – Ron Beyer Jan 12 '17 at 19:30
• Please define "better". I guess all you see is a lower consumption at the same power percentage, but the reference for that percentage goes down with rising temperature, so the consumption/power ratio gets actually worse. – Peter Kämpf Jan 12 '17 at 19:47
• I just modified the title to properly address the question: "better fuel consumption" I meant "lower fuel consumption". – Francesco C Jan 13 '17 at 22:57

I don't have a reference, but the physics behind is not that complicated.

The key is that you have constant RPM, constant pressure altitude and constant manifold pressure.

A motor sucks in lots of air, but since the throttle restricts the air flow in the intake, the air pressure between throttle and motor is low. This is the manifold pressure1. At idle, i.e. almost closed throttle, the pressure is very low, while at full throttle, it ideally equals ambient pressure. And in turbocharged motors, it is even higher than ambient pressure.

Finally, manifold pressure together with RPM and displacement of the motor is a measure of how much air volume is aspirated by the motor per time interval.

Since you keep everything constant, this volume also is constant. But warmer air is less dense and contains less oxygen molecules per volume. Less oxygen molecules means less fuel can be burned. This is why fuel consumption is lower.
But it also means less power. To compensate, the throttle could be opened a little more to let in a little more air volume. This would also increase the manifold pressure. But if the throttle is already fully opened to get max. power, you can't open it further. So, max. power is lower at higher temperature.

1) NOTE: For simplicity, I'm speaking about absolute pressure here. The gauge in the cockpit displays the under-pressure with respect to ambient pressure, so a high displayed value means a low absolute pressure. And since ambient pressure changes with altitude, manifold pressure does, too, even if the displayed value is constant. The benefit of this is that the displayed value is a good measure of the power with respect to the max. power achievable at that altitude.

• maybe you should add that a higher ambient temperature means that the thermodynamic cycle is less efficient. The physics is quite the same as that for turbo machines. So relative to power, fuel consumption even goes up with temperature. – Peter Kämpf Jan 14 '17 at 1:21
• The problem is, those performance tables show that the airspeed is the same while the fuel consumption and the power is lower. This means that the same amount of work is performed in the same time interval, thus the same net power is output by the engine with better energy efficiency (at least at first glance, fuel consumption), while the thermodynamics tells us otherwise. – RedGlyph Nov 26 '17 at 18:36