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]

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 :D

[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

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.
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
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)
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)
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)
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).

[24Carrot]

Was the original question prompted by an exam question? Much of my stuff below is repeating what has already been said, but I am trying to go for the whole picture.

Assuming for simplicity we are talking about two aircraft with the same weight, cruising S&L at the same Lift/Drag ratio, at the same rpm, but with different altitudes in a standard atmosphere:

1) Both aircraft have the same aerodynamic Drag, because it is the same fraction (L/D ratio) of their identical weights.

2) Because the higher aircraft flies in a lower air density, it must have a higher Drag Coefficient or higher True Airspeed, or combination.

3) The engine has a suck-squeeze-bang-blow cycle. Unless we are at the limit, the throttle can be opened so the suck cycle delivers as much fuel/air as required to maintain the RPM. The blow cycle actually works better at altitude, as the exhaust faces a lower ambient back-pressure.

4) Turning to the propeller, the higher aircraft flies through lower air density, at the same RPM, but its thrust has to match the same drag as the lower aircraft. It can only do this if the blade angle of attack is higher. As the blade pitch is fixed, it can only do this if the TAS is lower. So going back to 2, the higher aircraft's Drag Coefficient must be higher.

5) The higher Drag Coefficient, the lower airspeed and the lower air density suggests the higher aircraft is flying at a higher angle of attack.

But if the aircraft are flying at different angles of attack, the L/D ratios are unlikely to be the same, and we should drop that assumption. The higher aircraft will probably have a higher Drag, and a lower TAS, and it is their uncertain product which determines the power consumption.

I think the question as stated cannot be answered.


---
There is a different question that I think can be answered. With optimum power settings you get better miles per gallon at altitude (you can see it in e.g. the C172 and R22 performance charts) and I believe that is because of the more efficient blow cycle. I learned this from a truly ancient PPrune thread involving (if memory serves) BEagle, ShyTorque and bookworm!

[peterh337]

All sorts of interesting things appear in flight dynamics e.g. if you fly peak-EGT or LOP throughout a flight, then climbs and descents don't cost you anything in range (to a 1st order approximation, of course ;) ).

But some effects are not at all obvious e.g. my TB20 does almost the same IAS regardless of weight (maybe a 2% change from min to MTOW). This has to do with varying elevator AoA as the loading varies, presumably. There is no straightforward explanation for this.

There is similarly no obvious explanation for why a TB21 does at least 10% less MPG than a TB20. Should the turbonormalising not overcome the lower compression ratio of the engine?

I think, very often, what are supposed to be 2nd order effects are definitely not 2nd order effects...

[Big Pistons Forever]

There is similarly no obvious explanation for why a TB21 does at least 10% less MPG than a TB20. Should the turbonormalising not overcome the lower compression ratio of the engine?

.

Probably because more fuel is scheduled for any give power output in the turbocharged engine to provide additional cylinder cooling. The pressurized induction air is hotter than what a non turbocharged engine would experience.

[bravobravo74]

Was the original question prompted by an exam question?

No it wasn't, I just realised that my knowledge about piston engines isn't comprehensive enough.

[FlyingStone]

There is a different question that I think can be answered. With optimum power settings you get better miles per gallon at altitude (you can see it in e.g. the C172 and R22 performance charts) and I believe that is because of the more efficient blow cycle.

My bet would be on reducing pumping losses, since at "optimum" altitudes (6000ft and above for normal aspirated engines) you are flying WOT (wide open throttle) instead of closing the throttle at lower altitudes to remain RPM below the 75% of rated power, where you can lean to peak EGT, which in turn gives you somewhat best economy.

[funfly]

You can get too complicated with this;

Every rev takes in the same volume of air because the piston goes up and down the same amount on each rev.

As the air pressure decreases the mass of air (and thus the number of oxygen molecules) in a specific volume decreases.

With less oxygen taken into the pot at each stroke it is obvious that each stroke will produce less power.

[mm_flynn]

My bet would be on reducing pumping losses, since at "optimum" altitudes (6000ft and above for normal aspirated engines) you are flying WOT (wide open throttle) instead of closing the throttle at lower altitudes to remain RPM below the 75% of rated power, where you can lean to peak EGT, which in turn gives you somewhat best economy.

NO, the better MPG shown in most POHs for higher altitude operation are almost exclusively due to the lower IAS (and hence lower drag). You would achieve virtually the same MPG at sea level and at 10000 feet if you flew at the same IAS. (there will be some pumping loss difference but they are minimal).

Interestingly to achieve the same IAS at altitude requires more power so your fuel burn rate will be higher, but you are going faster and these two effects balance out. (note the physics are totally different for jet engines vs propeller engines)


Peter, I believe (but am not sure) that the TB21 engine has a lower compression ratio (and I also thought it was turbocharged not turbo normalised ). This lower compression ratio makes detonation less likely but does make the engine intrinsically less efficient.


RE the questions on the manifold pressure part of my list. regardless of CS or FP prop or the presence/absence of a MP gauge - there is a manifold pressure in all piston engines and when the engine is turning and the throttle is partially closed this manifold pressure is less than the local atmospheric pressure (ie a partial vacuum). This reduced pressure means there is less airmass going through the engine and less power. This is fundamental to the principle of throttling an engine.

[mm_flynn]

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

I looked at your original question again and noticed this paragraph, which is not correct.

The power dissipated by a propeller is a very complex equation and the velocity parts of that equation are definitely not propeller RPM. You can deduce the power dissipated in flight by determining the drag of the aircraft (the prop force must balance this in straight and level flight) and multiply by the TAS of the aircraft (this gives the power needed to overcome the drag and by implication the power being dissipated by the prop to produce the thrust)

[peterh337]

Yes I did say the TIO540 has a lower CR than the IO540 (ref. the specific variants) but I wondered if the turbo (it is "normalisation" BTW, IMHO, because the max rated HP is still 250 so I think the max MP is still sea level) compensates for that. I suspect it doesn't and the efficiency (SFC) of an engine is in fact still directly related to the CR - even if "something" is stuffing the air into it for free. It is IMHO obvious that increasing the MP does not improve SFC; it merely gives you more HP.

There are loads of 2nd order factors e.g. at high altitude, wide open throttle, you can use a lower RPM and a lower RPM (say 2200) goes well with LOP operation in that the slower burn is well timed for the slower RPM, which is how I can get ~1350nm range out of my TB20.

I wrote this (http://www.peter2000.co.uk/aviation/engine-management/index.html) a while ago, FWIW.

[24Carrot]

mm_flynn, I should start by saying I agree with practically everything you have written above. Just a couple of quibbles:

the better MPG shown in most POHs for higher altitude operation are almost exclusively due to the lower IAS

Is that true? I thought the optimum power setting at altitude gave you an airspeed with a good Lift/Drag ratio, comparable to what you got at the lower altitude.

Then the energy expended over a given distance is:
Drag x Distance,
which is just:
Weight / LDratio x Distance.

If the performance improvement is aerodynamic, then the L/D ratio would have to improve with altitude, compared to sea-level cruise.

there will be some pumping loss difference but they are minimal
All I know about engines came from the Trevor Thom books or similar, so I am not any kind of expert, but isn't the engine power related to volumetric flow times BMEP (Brake Mean Effective Pressure), and the blow-stroke saving related to volumetric flow times the change in atmospheric pressure?

So at maximum power, and a BMEP of say 10bar (is that reasonable?) and sea-level versus 10,000ft giving a pressure difference of around 0.3bar we get a 3% power improvement.

But at 10,000ft the engine is not producing anything like maximum power. The optimum RPM will likely still be quite high, so it isn't the volumetric flow which drops, it is the BMEP. So now we compare our 0.3bar with a lower BMEP, indicating a higher percentage power saving. From memory the POH savings were around 10%.

[24Carrot]

mm_flynn, I just noticed point 6 in your earlier post re the OAT. Thanks for that.

[mm_flynn]

24Carrot,

I don't have POH for normally aspirated aircraft to hand. However, what you should see is a table for a given cruise power setting (say 75% Best Power Mixture)

The tabulated values should have the following pattern of change with regard to altitude up to about 6000 feet

RPM should increase (as per the lengthy posts that you need more rpm to dissipate the same power in the propeller because it is spinning in thinner air)
Fuel flow should remain the same (because we remain at 75% power)
TAS should increase (but not by quite as much as one would expect -see next point)
IAS should decline. This is the important one - power = drag * speed (At higher altitude you TAS will typically be higher therefore the drag must be decreased. The way this is achieved in cruise is a reduction in IAS and a corresponding drop in parasitic drag (with a small offset due to increased induced drag)

So the range is improving with altitude, but it is almost exclusively due to the reducing IAS and the corresponding reduction in drag.

As a note we all cruise at speeds way above optimal L/D (Vy) and therefore slowing down (no wind) will invariably reduce drag and improve MPG.


Range is determine by energy consumption which is drag*distance travelled
Power is determine by drag *velocity (TAS in this case)

above 6000 feet or so you should see no change in rpm (as you are already max achievable power), a more rapid decline in IAS and a less rapid increase in TAS until the IAS gets low enough that the increasing induced drag becomes material)

finally IAS will reduce to Vy and you are at your ceiling.

[miroc]

I suspect it doesn't and the efficiency (SFC) of an engine is in fact still directly related to the CR - even if "something" is stuffing the air into it for free. It is IMHO obvious that increasing the MP does not improve SFC; it merely gives you more HP.Efficiency of theoretical (ideal) Otto cycle is lower with lower compression ratio.

Otto cycle - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Otto_cycle)

Miroc

[Crash one]

You can get too complicated with this;

Every rev takes in the same volume of air because the piston goes up and down the same amount on each rev.

As the air pressure decreases the mass of air (and thus the number of oxygen molecules) in a specific volume decreases.

With less oxygen taken into the pot at each stroke it is obvious that each stroke will produce less power.


Perfect, shimples. And the prop does the same, same volume but less molecules, less molecules = less pull/push.

[24Carrot]

mm_flynn, I agree with all of that.

I just blew an afternoon with a spreadsheet looking at the POH cruise performance figures for a C172SP. I matched the CAS (and so Lift Coefficient) at two altitudes, so any performance differences would have to be prop or engine related.

There were no differences! Range performance does indeed seem to depend only on CAS, at least for this C172! I have no idea whether this is clever design by Cessna, or some grand principle is at work here.

I don't know how to do tables on pprune, so I put it here: twododecacarrot (https://sites.google.com/site/twododecacarrot/)