Engine performance under best economy vs best power mixtures and how it relates to TAS on a fixed pitch propeller?

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):

1. 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.
2. 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?

• I agree that these charts seem to disagree with each other on the surface. "75% best economy mixture" doesn't make much sense either since you're forbidden from operating above 75% power at a lean mixture. Jul 31, 2023 at 23:12
• Yes I've read the same re: operating above 75% on a lean mixture. But couldn't you still have a theoretical max power achievable on a leaned mixture with which to cut new 55, 65, and 75% baselines for a separate best economy mixture engine performance chart? I agree, the POH clearly does not want you doing that seeing as pg. 102 stops at 75%, but is it fair to think of a separate engine performance charts for both best power and best economy mixtures, each with a different max baseline? That would make significantly more sense to me! Aug 1, 2023 at 11:03
• No doubt there is such a power, but I'm not sure why a pilot would care what that power is. Honestly I wouldn't worry about it much- it's not like the plane has a "powermeter" so it doesn't really make a difference to the pilot if they're running at 73% or 75% power or anything like that. Aug 1, 2023 at 15:48
• Hmm on a second look you are allowed to operate the engine leaned above 75% power for brief periods, so maybe it is that after all. Aug 1, 2023 at 15:52

For the fuel flow part: imagine you are leaned for best economy, at 75% power. You change the mixture control to best power. This makes it so you are producing more power, so you throttle back to 75% power.

You now are producing the same amount of power as before, but with less air and more fuel. So the fuel flow is different.

My suspicion for the charts is that you should read the best economy charts as if you start out leaned for best power and lean for best economy without touching the throttle. That is, "75% power" means more like "the throttle position is set to where it would be for 75% power, if you were leaned for best power."

It makes sense if you read it this way- your cruise speed goes down a few knots when you lean since you are losing a bit of power by leaning.

• Thanks, this makes sense as a possibility for achieving the lower stated airspeed, but as I've linked in another comment, there are some cruise performance charts that do contain "best economy mixture," which leaves me still suspecting my original confusion is due to a typo. But your framework still ties out, as I think it agrees with my suspicion that economy mixture yields a totally different (shifted) engine performance chart (pg. 98 in the original PDF). What do you think of that hypothesis? Aug 1, 2023 at 10:58

I think there are a few things that you have confused.

First, Figure 5-15 on pdf p. 98 is not associated with any particular airspeed. In fact, it is also independent of the propeller and the airplane in general. It simply a chart describing the behavior of an engine at altitude.

At a given altitude and airspeed, a fixed pitch prop will absorb more power as RPM is increased. (I think you were forgetting airspeed in the description above).

There may be some conditions under which the propeller fully stalls -- such that it stops delivering more thrust as the RPM is increased, but that is usually associated with such a large increase in power that it is not really achievable. However, it is important to keep in mind that airplanes fly on thrust (or propulsive power), not shaft power. The propeller efficiency is the difference.

Power required to fly at altitude at a given airspeed (and therefore the RPM) depends on the weight of the aircraft. When you do your first solo, you will be surprised how sporty the aircraft feels without all that induced drag sitting in the other seat.

• This misses the issue- that the two performance charts supposedly have everything equal except the mixture. Propeller efficiency is not going to be different just because the mixture control is different unless the power has changed. The weight is also the same for both charts. Jul 31, 2023 at 23:10
• @Chris-RegenerateResponse No, the first chart does not specify aircraft weight. It also does not specify cruise conditions (thrust equal to drag). The first chart is independent of the airplane (engine only). The two charts have little in common with one another (not 'supposedly everything equal'). Aug 1, 2023 at 1:17
• I'm referring to the two cruise charts on page 101 and 102, where the only difference is the mixture. I agree with what you say about the first chart on page 98. Aug 1, 2023 at 1:23
• @Chris-RegenerateResponse Sorry for the confusion re: p98. Aug 1, 2023 at 2:12
• Rob, thanks for the reply. I agree engine RPM is not always associated with specific airspeed: you could be in a challenging climb at full power for example, but at a low airspeed. My point was, if you are constantly trimming for level flight as you increase power (and for local ranges of power/altitude/etc), then the RPM is a monotonic function of % engine output; and, due to the level flight assumption, a monotonic function for airspeed. This is clearly a subset of configurations, but I was setting up a framework for interpreting the cruise charts (which are by definition for level flight). Aug 1, 2023 at 10:45

I overlaid the figures from p. 101 and 102. No great insight here, but I figured I would go ahead and share it.

Best economy in blue, best power in black.

I believe the confusion now arises from the use of the words "75% best power mixture" in the example on the middle of the chart on page 102 (the best economy chart).

I have no explanation for that, I tend to agree that the example should read 75% best economy mixture.

• Thanks, nice chart. I managed to find another POH that does include "75% best economy mixture"...pg. 99 in the below. That said, pg. 100 is also a Best Economy Cruise Performance chart but is back to "75% best power mixture" -- but for a different subset of serial numbers. I wonder if this is just a repeated typo, or whether the leaning procedures/interpretations of what best economy actually is changed for these serial numbers. Unfortunately all POHs so far are completely silent on this issue. montereynavyflyingclub.org/Other%20Docs/… Aug 1, 2023 at 10:52
• Once a chart like this is approved for a POH, it is much easier to duplicate than it is to change. Aug 1, 2023 at 16:47

If we were talking about true power then the resulting airspeed would be identical, with either a fixed or a constant speed prop. Assuming a fixed air density. (And prop governor setting)

But the operating manual is probably talking about a proxy for power like the absolute manifold pressure setting. The mixture ratio will change the true power output for a given manifold pressure setting.

• Therefor the RPMs are not the same. Aug 5, 2023 at 10:54
• Thanks, makes sense. The POH is using "engine RPM" as the power output proxy. But I agree that for fixed inputs of throttle (not RPM!), the mixture changes the true power output. Aug 7, 2023 at 14:39