[n86121]

The weight of the airplane is 'constant' (at any instant)
That weight W requires an equal amount of lift L to stay aloft
To produce that lift induces a certain amount of drag D

The most efficient flight is in thin air when lift L is 'just enough' to hold the airplane up,
and drag is least (the 'coffin corner' for jets. Efficient but scary).

As throttle opens, airflow becomes more 'laminar'
So at max throttle engine breathes most air/fuel with least disturbance

As one climbs the engine as an air pump cant get enough air
So for fuel/air to remain stochiometric, reduce fuel to match less air

As throttle opens, airflow becomes more 'laminar'
So at max throttle, engine breathes most air/fuel with least disturbance

That's why most non-turbo cruise best around 7-9k feet
Throttle is full open but still getting enough air for available fuel flow
Adding more fuel wont add more power from burn, just richen mixture
Fly higher up and fuel must be reduced to available 02, so HP output drops off

Except for turbo.
But even turbo increases internal combustion 'drag' (energy to spin the turbo is not free).

Most efficient wing moves a lot of air just a little bit
A 'flat' blade at low RPM moves a lot of air a little distance per rotation
So prop efficiency better 'flat' as in takeoff
But delta V across blades (front to back) a function of cruise speed
The idea is to 'paddle' the air with least disturbance

And of course, internal engine friction a function of RPM
Turn the engine two times and it that produces two times the friction per unit of time.

If you can solve all those, you get an 'A.'

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The only lower limit consideration I have read has to do with the internal harmonic balancing of the engine. Spin too slow and harmonics increase vibration in some manner. Which of course consumes energy as heat, not output.

E=MC^2
F=Mass x Acceleration
K=1/2 Mass *Velocity ^2

Those aren't just good ideas, they are the law.