Fixed-pitch prop, same RPM, different power
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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.
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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!
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!
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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...
).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...
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.
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Was the original question prompted by an exam question?
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Originally Posted by 24Carrot
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.
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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.
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.
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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.
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.
Last edited by mm_flynn; 25th Feb 2012 at 06:06. Reason: fixed a spelling error and added the final paragraph
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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)
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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 a while ago, FWIW.
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 a while ago, FWIW.
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mm_flynn, I should start by saying I agree with practically everything you have written above. Just a couple of quibbles:
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.
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%.
the better MPG shown in most POHs for higher altitude operation are almost exclusively due to the lower IAS
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
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%.
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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
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.
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)
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.
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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.
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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.
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.
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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
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
