Piston engine power at altitude
It's well known that the same manifold pressure and RPM produces more power at altitude than at sea level. Engine nomograms from Lycoming (and probably other manufacturers) are constructed to allow an interpolation between the power at sea level and the power where that MP represents full throttle.
My understanding was that this was due to pumping losses in the engine when the throttle is closed. At sea level, the engine has to help to pump, say, 22"Hg pressure air into a cylinder with 30"Hg on the other side of the piston. At altitude the pressure it pushes against is less. Thus the increase in power with altitude would be "free", i.e. the fuel flow should be the same for both the sea level and the full-throttle-altitude case.
But in calculating the fuel flow, the engine nomogram instructs the user to take the equivalent MP from the sea-level power chart in calculating the fuel flow. This implies that the cost, in fuel, of producing the power is independent of altitude.
An example from the O-320-B manual, point labels (A to G) indicated for those who have access to the chart:
24.5" 2350 RPM (point B) produces 118 BHP (point C) at sea level, 128 BHP at full throttle alt of 4500 ft (point A). Interpolate to 2000 ft gives 122 BHP (point D), and a correction for temp gives 126 BHP (point E). So far so good.
But now, transfer back to the sea level power chart, point F, 25.5" 2350 RPM, which gives 126 BHP at sea level. Now down to point G, on the fuel flow chart, which suggests that 25.5" (termed the equivalent sea level manifold pressure on another chart) 2350 RPM burns 10.8 US gph and so that is the fuel flow.
On the O-320-A/E charts, a separate fuel flow chart is provided, plotting FF vs MP and RPM. The note says "to obtain fuel consumption at altitude, enter this curve with the equivalent sea level manifold pressure for actual power, see point 'G' of example on altitude performance chart". So the FF for a given power and RPM is independent of altitude.
That doesn't tally with my understanding of the physics.
So, for a given power output at a given RPM, does the fuel flow vary with altitude? [I know the MP required to produce that power falls with altitude -- that's not the question!]