Temp has less affect than air density or altitude
Ke but in fact the real issue is the colder air into the engine. (Standard temp drops with altitude doesn't it?) The engine has no idea how far above the ground it is.
You know much more about these hings than I, so if you have another thought I would be interested.
Take this example:
21"/2400 rpm , at sea level std day (59F) and 8,000' at std day (30.5F)
Sea level (59F) = 62.4% pwr
8,000 ft (30.5F) = 71.4% pwr
Now take the 8,000 ft case and at temp (59F) = 69.4% pwr
The altitude changed power 9% (71.4%-62.4%); Temp alone was only worth 2% (71.4%-69.4%).
Why the difference?
One, Throttle pumping loss - At sea level to maintain 21" you need to close the throttle (a lot). At 8,000 ft the throttle is wide open or near WOT. The engine has to suck past the closed throttle at sea level but not at 8,000 ft. This extra effort to suck past the closed throttle butterfly costs HP. This is called PUMPING LOSS.
Two, exhaust back pressure (pumping loss). As someone mentioned the exhaust backpressure is less at altitude. Depending on exhaust design this can be a small advantage or none. The problem is you can only optimize the exhaust for one altitude (air density) and RPM. Variable exhaust geometry would be cool but too complicated for our RV's purpose. So the affect of this can vary depending on exhaust.
Three, in the above example the temp was 2% of the added power, but
really there's more air going into the engine at 8,000' even if the MAP's & RPM & Temp are equal. The MAP gauge is a dumb vacumn gauge. It does not compensate for temp or mass air flow. In cars they have
mass air flow sensors, as well as a MAP sensor for a reason. So your indicated power is lower than actual power as you climb. Lycs power curves probably has correction built in.
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The normal situation as you climb is not constant MAP. Usually as you climb MAP drops since you're at or near WOT. Even with the temp drop pressure drops (MAP) so you have less air and less power. Temp has less affect on PISTON engine power than air density. Higher altitude = less air density. Less air density = less air for the engine to breath.
Your engine knows what altitude it's at.
When piston engines need to make more power they put a turbo or blower on to compress the air (increase air density), not an ice box to cool the air. However when you compress air you do make the air hotter, which is a draw back. So some turbos have inter-coolers to cool the air back down. That's a little about making more power, but its also about not detonating the engine and melting it (hot air + more power = possible detonation). Some turbos don't use an inter-cooler, The engine makes more power even despite the hotter induction air temp. Engines never have have a problem getting fuel into them. The problem has always been getting more airflow. That is why cars or plane engines use tricks like "angle valves", 4-valves per cylinder, nitrous oxide and turbos. The more AIR you can pump the more power you make.
Temp has a huge affect on Jet engine power. Jet engines have no breathing problem, but they do have thermal issue. As you climb the air-frame has less resistance, but the jet engine can still breath in thin air, with it's extra "lung capacity". An extra bonus for a jet is the cooler temps as you climb, which helps the engines thermal limits. The jet engine needs oxygen as well, but its breathing capacity is like a Kenya Olympic marathon runner. The runner can run fast as long as they are cool. A piston engine makes all the power it can at sea level and starts to wheeze as soon as it starts climbing to altitude, colder temps or not. Cooling is important to the piston engine but its ability to breath is the limiting factor.
Colder temps does affect air density a little and engine HP, but the affect is also on the prop and wing. The prop makes more thrust and the wing makes more lift. On a cold day takeoff you get the bonus of more prop thrust, wing lift and HP. All three give the impression of more performance, but only part is just from a HP increase.