Piston engine power at altitude

[bookworm]

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!]

[ShyTorque]

I don't have access to your data, but the answer is already in your post.

Efficiency = Useful energy got out / energy put in.
Or, in this case, Efficiency = Power achieved / fuel put in.

Yes, the efficiency of the piston engine does increase with altitude, due to lower pumping losses. With a reduction in ambient atmospheric pressure, the piston has less work to do to on the exhaust stroke to clear the combustion chamber of spent gases. More combustion energy goes into turning the prop, (which is where you would measure "power") rather than moving the piston against atmospheric pressure. To think of it slightly differently, the exhaust gas is more "willing" to leave the cylinder, allowing the engine to achieve the same power/rpm at a lower throttle setting, which equates to a lower fuel flow.

Of course the ACTUAL power output may be less, as you realise, due to the reduced charge density, either as soon as a normally aspirated engine starts to climb, or in a supercharged engine, once it has reached full throttle altitude and then starts to climb.

The mixture must be "leaned off" as required to take full advantage of higher altitude effects (actually it's more correct to say "kept at the same a/f ratio").

The other gain in "efficiency" is the IAS / TAS relationship benefits of higher altitiude, albeit not directly relevant to your question as that is really an airframe consideration.

A likely reason your manual doesn't give any data on reducing fuel flow at altitude is just because the sea level data errs on the safe side and the manufacturer didn't actually bother to produce any more data. More flight testing = more time and expense for the manufacturer.

[bookworm]

Thanks for that ShyTorque

The likely reason your manual doesn't give any data on reducing fuel flow at altitude is just because the sea level data errs on the safe side and so the manufacturer didn't actually bother to produce any more data. More flight testing = more time and expense for the manufacturer.

Well it's Lycoming data, so I imagine the engine was bolted firmly to the ground. :)

Given only my post above, I can see why you'd think that might be the case. But I'm doubtful, because of the level of detail of the data provided. It would be surprising if they just didn't bother to measure the fuel flow, as they have clearly measured the power as a function of MP, RPM and altitude.

If our model is correct, shouldn't the fuel flow simply depend (neglecting temp for a moment) on the actual MP, which determines the charge, and the RPM, which determines the rate at which it is burnt.

So the two models seem to be:

1) Fuel flow is determined only by MP and RPM

2) Fuel flow is determined only by output power (BHP) and RPM

The procedure Lycoming shows for calculating fuel flow is considerably more complex than would be the case for model 1. It is clearly more conservative. I could understand that if the truth were somewhere between the two models, but not if it were much closer to model 1 as we believe.

[ShyTorque]

Although it is quite simple to measure the fuel flow on the ground, on a rig, I can see practical problems with precisely measuring it in flight at the various altitudes. The test aircraft would need to contain telemetry and the data would presumably only be valid for that particular aircraft type. It would perhaps need to be repeated for each type of aircraft the engine was installed in.

Or perhaps I am missing something more obvious here. I would be intrigued to know the answer from the manufacturer.

[E1453]

The cooler temperature of the air above implies that, for a given pressure, it's density will be greater.

For a given power setting, 65% for example, the fuel flow should be the same at all levels, for a given RPM. However, as we climb, the temperature drops, so, for a given manifold pressure, the air density increases. The consequence is that, to mantain the same percent power with the same RPM as we climb, the MP should be reduced.

I made the emphasis at the "RPM" because, the higher the RPM for a given power, the lesser the efficiency. My protest to Cirrus Design for protecting its marvelous planes from intelligent pilots.

[411A]

Keep in mind for your calculations that, altho ambient temperature does indeed reduce with altitude (ignoring inversions here), the intake temperature of the fuel charge may well be much higher than ambient, with supercharged engines, unless intercoolers are used, and even then, they are certainly not 100% efficient.
Generally however, the less 'backpressure' at altitude is quite important, for optimum power output of piston powerplants.

[palgia]

Correct me if I'm wrong, but I was under the impression that piston engines are less efficient at altitude. For this reason, the max range decreases with cruising altitude (technically max range stays the same if we ignore the fuel it takes to climb, if we factor it in, you will see that the lower you cruise, the farther you go with a fixed amount of fuel).

Any thoughts :confused:

palgia

[RatherBeFlying]

Turbo/Super-charging enable more power output at altitude where TAS gains can be made, but remember that the thinner air means less cooling which may necessitate enriching the mixture which pulls down efficiency.

Watch those CHTs.

[ShyTorque]

Palgia,

Don't forget that a PROPELLOR is less efficient at higher altitude, which is not necessarily the same as the efficiency of the actual engine itself.

[Tinstaafl]

I think they're taking a relatively simple 'FF proportional to HP' and leaving it at that. The efficiency gain is revealed elsewhere in TAS &/or range tables for the %HP.

[ShyTorque]

Tinstaafl,

Yes it would make sense because what is really important is the overall effect on the aircraft, i.e. taking into account the increased efficiency of the engine and the decreased efficiency of the prop.

[Lu Zuckerman]

These theories reflect small engines used in light civil aircraft but they go all to hell when you address large radial engines with pressure density carburetors. The pilot or flight engineer will set the mixture, which in effect establishes the maximum flow rate through the carburetor. But the ultimate control of how much fuel reaches the engine is an aneroid device that senses air density much like an altimeter and another section of the carburetor that senses impact air much like a pitot tube and an airspeed indicator.

Gleaned from my memory bank and what I remember from my mechanics training back in 1949.

:E :E

[E1453]

All small engines carburators or injection systems do the same that the old big radials did. The mass of the fuel delivered to the engine is proportional to the mass of air passing thru the induction system, for a given mixture ratio.

That's the reason why, as I explained above, the cooler the air temperature, less manifold pressure will be needed for a given power setting.


:8

[ShyTorque]

Lu, I'm sure you're right, but a 5 litre Lycoming ain't a large radial! No-one has yet given Bookworm his answer...... :\

[bookworm]

The cooler temperature of the air above implies that, for a given pressure, it's density will be greater.

For a given power setting, 65% for example, the fuel flow should be the same at all levels, for a given RPM. However, as we climb, the temperature drops, so, for a given manifold pressure, the air density increases. The consequence is that, to mantain the same percent power with the same RPM as we climb, the MP should be reduced.

I like the line of thought, but I don't think it quite explains the numbers. Try these:

18" 2400 at sea level (ISA temp 288 K) produces 75 BHP
18" 2400 at 12,000 (ISA temp 264 K) produces 97 BHP

97 BHP has an "equivalent sea level MP" of 21" (i.e. 21"/2400 produces 97 BHP at sl).

If it were purely a density effect, I'd expect to see an equivalent of 288/264 * 18" = 19.6". So it explains about half of the effect. Is it possible that the rest is pumping loss?

[ShyTorque]

Bookworm,

I do think a decrease in pumping losses could well be at least part of the answer. I understand that some engines used for pumping water use the weight of the "falling" water to cause a low pressure extraction effect in the exhaust, which is like the altitude effect we are looking at here.

Similarly, a well tuned exhaust pipe can have a very significant effect on power and / or economy on any piston engine. This occurs because a low pressure pulse in the exhaust port can be timed to occur in conjunction with the exhaust valve opening.

In a way, it's a little like a "negative supercharging effect", at the opposite end of the engine.

Interesting topic! :ok:

P.S. Try this link for some bedtime reading:

http://naca.larc.nasa.gov/reports/1920/naca-report-45/naca-report-45.pdf

[ft]

IIRC, for a constant MAP, the air going into the cylinders will for typical compression ratios be at a higher temperature due to a higher degree of compression, even though the ambient temperature is lower. I will have to redo the calculations to be certain. This would explain the fuel flow as the the air mass will be lower, i e a lower fuel flow for the same mixture.

The higher degree of compression will likely (as in 'I don't know but my educated guess is...') mean a higher amount of HP eaten by the compressor even in a supercharged engine. For a turbo, this would definitely be the case as the RPM would be higher, resulting in a higher backpressure against the turbine.

Then, as most people point out, the big gain is in not having to push the exhaust out against sea level ambient pressure.

Why some people talk about flying above the throttle full open altitude is beyond me, as the MAP will then drop off...

Cheers,
Fred