I am currently training on a very basic PA-28-161 (it has a single reciprocating air-cooled engine with fixed pitch propeller). I have a rather involved question on mixture as it relates to power as it relates to TAS, and have searched extensively for insight on both this website and others yet have struggled to find an explanation. My suspicion is that a POH issue/error has been the issue, but I would like an expert opinion. I hope my detailed thoughts and subsequent discussion help others with the same problem. For this question I will reference performance charts from the below POH link:
First, two priors I had going into this (and if these are wrong, then perhaps we can cut this discussion short):
- For a fixed pitch propeller, given a density altitude, the RPM is a monotonic function of the engine power output, since this is the only way the engine can "express" itself to the outside world. Using the POH's example from pg. 98 (titled Engine Performance; page number is expressed as that of the pdf document), given a 5000 ft pressure altitude and 15 C OAT, a 2625 RPM is associated with 75% power. A lower power output at the same altitude will always show up as a lower RPM and vice versa. Additionally, these RPM values as they relate to the proportion of power output are fixed, i.e. pg. 98 is an immutable property of the airplane. As an aside, the max power the engine is rated for may not be achievable at higher altitude (this is not a turbocharged engine after all): this makes sense and indeed, the "iso-power lines" slope up and to the right on pg. 98.
- Given an altitude and fixed pitch propeller RPM (presuming steady-state level flight is possible at the combination provided), there is only one airspeed that can possibly be obtained (everything here assumes there is no wind).
Now, notice on pg. 98 there is a box that compares gallons per hour fuel flow for a best power or best economy mixture at each level of power, 55%, 65%, or 75%. This is where I'm getting at my issue, namely that we can have different levels of fuel flow for a specific level of power...but a specific level of power (given an altitude) is associated with a specific RPM...which should be associated with a specific airspeed. Different fuel flows resulting in the same airspeed would intuitively be odd.
The POH examples demonstrate my confusion: looking at pg. 101 (Best Power Cruise Performance), we are operating at 75% power, which using the same environmental assumptions as before implies an RPM of 2625...and this is associated with a TAS of 122.5 kts. Now jumping to pg. 102 (Best Economy Cruise Performance), we are again operating at 75% power, but because the fuel mixture is optimized for efficiency the airplane flies at just a TAS of 118 kts. This is the issue: what does "operating at 75% power" mean on pg. 102, namely for Best Economy mixture assumptions? Because if my priors are correct, that 75% power should be associated with a specific RPM which should yield a specific airspeed...yet the airspeed on best economy is lower.
One way I have come up with to reconcile all this is that engine performance (and specifically the mapping of RPM to % power) has to account for the mixture setting (and so my first prior must be amended to include mixture setting). So in reality, pg. 98 Engine Performance looks totally different if re-done with a Best Economy mixture at every point (but the POH has only included the Best Power version). I would assume that RPM under a Best Economy mixture would be shifted lower in each case of 55%, 65% , or 75% power settings. Or more succinctly, the maximum power (and therefore RPM) one can achieve is higher when providing the engine with a best power mixture vs a best economy mixure...so the whole mapping shifts. In other words, this is a three dimensional relationship of RPM (or TAS) = f(g(% power, mixture), altitude). I suppose in that case that pg. 102 has a typo and it should read "Cruise Power: 75% best economy mixture" rather than best power mixture.
Is this the right way to think of this? Has all my trouble been due to a lack of exhaustive (no pun intended) engine performance charts and a POH typo? Is the right way of thinking about my theoretical Best Economy Engine Performance chart as a leftwards shift of the Best Mixture chart?