Fixed-pitch prop, same RPM, different power

[bravobravo74]

Hi everyone,

An aircraft with a reciprocating engine and a fixed-pitch propeller runs the engine/prop combo at a given RPM at two density altitudes. At the higher of the two altitudes less power will be produced.

Power = (force X distance) / time. Distance / time is speed and in this scenario relates to engine RPM. It therefore follows that Power = force X RPM whereby force is (pressure in the cylinder during the power stroke / piston crown area).

The only variable that can explain the difference in power produced at a given RPM for different density altitudes is the pressure in the cylinder during the power stroke. My question is:

With a fixed-pitch propeller, how does the crankshaft (and therefore the propeller) turn at the same RPM if cylinder pressure during the power stroke is different?

The only explanation that comes to mind is the assumption that at the higher density altitude the force that opposes the propeller's rotation is less for the same RPM. Is this even true?!

Many thanks and best wishes to you all.

[autoflight]

"With a fixed-pitch propeller, how does the crankshaft (and therefore the propeller) turn at the same RPM if cylinder pressure during the power stroke is different?"

Have to admit much prop time was variable pitch, like Winjeel, C130, DC3 & F27 but here goes:

Manual gradual increase adjustment of the throttle by pilot achieves the desired RPM during climb. At higher altitudes, finally full throttle will be insufficient for the same RPM that you could easilly select at sea level. Some aircraft might have a barometric sensor to assist in maintaining the desired RPM, but I guess training type light aircraft might not.

A turbocharger will increase the altitude where full throttle can maintain the desired RPM. Maybe this equipment might not be fitted to small training types.

[bravobravo74]

Thanks for the reply Autoflight.

I understand full-throttle altitude and the necessity to advance the throttle during the climb to maintain a given RPM; where I'm struggling is the idea that, for instance, 2300rpm at sea level produces more power than 2300rpm at a higher density altitude.

How does the engine physically turn at the same speed if the power produced is different? Let me put it another way - if power is the rate at which work is done and in both cases the RPM is the same, how is the engine at the higher density altitude doing less work?

[EEngr]

if power is the rate at which work is done and in both cases the RPM is the same, how is the engine at the higher density altitude doing less work?

Because density affects the amount of thrust (and drag) that a propeller produces at the same RPM.

The induced drag due to the prop's thrust (lift) plus the parasitic drag is seen at the shaft as a torque. Torque times RPM is proportional to power.

[Jan Olieslagers]

I'm afraid I may be over-simplifying things, yet here goes for all I have learned:
Even if the engine were not driving a prop, but a constant load such as a generator or a hydraulic pump, it would produce less power at altitude because less fuel/air mixture is loaded at each stroke. That's to say, if no pressure loading is applied through a turbo or such.

[bravobravo74]

Eengr - that's cleared it up for me, thanks.

So for a given engine/prop RPM a higher density altitude means that less power will be produced due to reduced cylinder pressure on the piston during the power stroke yet the RPM is maintained due to reduced propeller torque (engine torque and propeller torque being equal at a constant RPM).

[stickandrudderman]

It might also be argued that pumping losses are reduced at lower air density thereby facilitating increased RPM for a given power output.

[FlyingStone]

Originally Posted by bravobravo74

I understand full-throttle altitude and the necessity to advance the throttle during the climb to maintain a given RPM; where I'm struggling is the idea that, for instance, 2300rpm at sea level produces more power than 2300rpm at a higher density altitude.

If you maintain (or CSP maintains it for you) contant RPM during climb - in your case 2300 rpm and assuming full throttle, the volumetric flow of air into the engine is constant - the engine has a fixed volumetric displacement and if you turn it with the same speed, it will pump the same volume of air in a time unit, regardless of the density of air.

However, when you are climbing, the pressure and temperature of the air decrease, so does the density of the air. The mass is by the definition volume multiplied by density. If you add time dimension, you get that the air mass flow equals to volumetric air flow multiplied by air density. So basically, with increasing altitude, air mass flow into the engine reduces and since maximum power of the engine more or less depends on the density of the air entering the cylinders, you can see that even with constant RPM the power of the engine will reduce with increasing altitude.

[EEngr]

So basically, with increasing altitude, air mass flow into the engine reduces and since maximum power of the engine more or less depends on the density of the air entering the cylinders, you can see that even with constant RPM the power of the engine will reduce with increasing altitude.

Yep. Given the two effects, reduced torque load and reduced engine output at higher altitude, it could be toss up as to what a fixed throttle setting will do. Altitude compensation and/or turbocharging add a few more variables to the mix.

From what I understand, the preferred situation is to have the two curves (prop load and engine output) nearly match. But adding more throttle (to compensate for a bit of power loss) at increasing altitude is better. Or looking at it the other way around, you want more thrust as you descend without having to adjust the throttle. But I'm not the expert on that sort of stuff.

[bravobravo74]

Very well put FlyingStone

[Jan Olieslagers]

Seems I was less far off than I feared. Bravo for those who taught me!

[24Carrot]

This is probably a bit of a side-issue, but I wonder how much impact the ambient temperature has on air density as it actually enters the engine. Obviously the external air at altitude has a higher density the colder it is, but the intake air has to go through part of a hot engine to reach the cylinders, and so will be warmed.

I thought about this while skiing at 8,000 ft amsl last week. As I left the ski locker room to go outside, the ambient temperature dropped by 30 degrees C, and I thought to myself that at least the air was 10% denser outside. Later, I realised that all the relevant air was inside my lungs at 37C, so it didn't make any difference indoors or out, the air pressure was the key variable.

I accept that the vast surface area of the lungs will be far better at warming air than an inlet manifold, but it made me think. Does anybody know the answer?

[gasax]

Lots of approximations but on a standard day if you increse the temperature from 15 to 25 deg C the density will decrease by about 3.5%.

So your 10% guess has a real ring to it....

I suspect if I had a CRP6 handy I could just read it off.....

[mm_flynn]

A couple of more answers

1. On the limited number of fixed pitch props I have flown behind I have always had to advance throttle to maintain an RPM as I climb.
2. The predominate effect of climbing is (as many others have said) a reduction in the mass of air going through the combustion chamber. This requires a reduction in fuel flow to maintain a consistent mixture and results in a reduced power output for any RPM
3. If one does not reduce fuel flow while climbing the power will decline even more (unless one is climbing LOP in which case you have the instruments and training to ignore this post)
4. The thrust produced by the prop is broadly determined by RPM,pitch and air density. The first two of which are fixed in this example (one would expect this to pretty much exactly balance the reduction in power but see the next point)
5. The power needed to generate a given thrust increases as your true airspeed increases - so for any given prop thrust you need more power the faster you are going (which generally means the higher the density altitude). This results in the need to further advance the thrCottle to create the additional power needed to generate the reduced thrust (which should be very close to the reduced power generated by the higher density altitude) need because you will have a higher TAS when you try and generate the thrus (sorry the English is pants on this point)
6. finally to the OAT point. Generally the intake air enters the plumbing at the air filter at the front of the engine compartment and then moves at quite a rate. There will be very little heat transfer to the intake air so the temperature will be clost to OAT. This is not true for turbocharged engines where they may be quite a lot of heating in the compressor.

[bravobravo74]

I have no problem admitting that I'm still slightly confused - even after all of this input.

At the higher density altitude and at the same engine RPM less power is being produced because of the reduced mass flow of air, even though the volumetric flow is the same. Because of the reduced mass flow of air the fuel flow will also be less, meaning that fuel flow is proportional to power. The throttle will be further advanced for this given RPM than it would be at the lower density altitude.

So we have a situation wherein the throttle butterfly is more open, the volumetric flow of air is the same but the mass flow of air is reduced. What has the opening of the throttle actually done at the higher density altitude?

[mm_flynn]

For a given rpm, the volumetric flow remains constant regardless of density altitude, temperature, throttle setting, etc.

To achieve say 2300 RPM at sea level you throttle the engine. That is introduce a restriction in the intake that results in a lower manifold pressure and hence reduced mass flow and further hence reduced power.

As you climb the mass flow further reduces because the intake air pressure reduces. Openning the throttle offsets this pressure reduction by causing less pressure reduction across the throttle.

[Jan Olieslagers]

Your confusion might well come from tackling two subjects at the same time: CS props and increasing altitude. I already tried to separate them, for clarity's sake and also because CSP's are not my cup of tea.

Your fuel system, whether carburettor or injection, adds the appropriate amount of fuel to whatever quantity of air available, creating an optimal mixture for the given conditions. That's why carburettors have a mixture regulator knob.
At increasing altitude, the air becomes thinner, so the same volume of air contains less molecules.Thus, less air, or rather less air/fuel mixture, will be available to be sucked into the cylinders at each inlet stroke. Weightwise, that is. Opening the throttle will allow a larger part of the available mixture to enter the engine, but it will not increase the availability. To make things worse, a non-turbo engine relies on ambient pressure alone to pushload the mixture into the cylinders; with increasing altitude there will be less atmospheric pressure, hence poorer loading.
Again, I am not saying anything about prop behaviour. All I said equally applies to vehicle and stationary engines. If you have driven several generations of mid-to-heavy weight vehicles at high altitudes, you will have had occasion to appreciate the advantages of turbo loading.
HTH,

[Jan Olieslagers]

For a given rpm, the volumetric flow remains constant

Shouldn't that read "for a given output power" ?

[24Carrot]

I think mmflynn had it right.

Volumetric flow is swept cylinder volume times cylinder strokes per second.

The first is constant, and the second is strictly proportional to rpm.

[bravobravo74]

Shouldn't that read "for a given output power" ?

No - it's the mass flow which is constant for a given power output.

As you climb the mass flow further reduces because the intake air pressure reduces. Openning the throttle offsets this pressure reduction by causing less pressure reduction across the throttle.

I'm sure that this is true but this suggests that you're maintaining manifold pressure as you climb by opening the throttle, as is the procedure when you have a constant-speed unit at your disposal.

In the fixed-pitch case, 2300rpm produces less power at a higher density altitude than it does at a lower density altitude and therefore the manifold pressure must be less (even though we don't have a MAP guage to tell us this). The MAP is less but as has been discussed the throttle is further advanced for 2300rpm at the higher density altitude.

So in the CS case you advance the throttle to maintain the MAP as you climb but with a fixed-pitch prop you advance the throttle to maintain the RPM but the MAP reduces (less power at the same RPM).