klemmi85
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Why Is An A/c Engine Only Efficient At High Alt?

Mon Apr 20, 2009 2:40 pm

Hi there,
I was just wondering why an aircraft engine isn't fuel efficient in low altitude but much more at high altitudes.

I don't have exact figures now, but I think I read somewhere, that i cruise, the fuel burn is only a quarter of the amount used during takeoff. Of course, in cruise your're not at maximum takeoff thrust, but there has to be something else?!
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packcheer
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Mon Apr 20, 2009 2:52 pm

Basically, the air is thinner, the engine doesn't work as hard (intakes less fuel to move same amount through thinner air)
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PolymerPlane
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Mon Apr 20, 2009 4:33 pm

I don't know about more or less efficient (efficiency measured as thrust/fuel ratio).

Airplane is more efficient because at higher altitude it encounters thinner air, thus less drag. It needs less thrust to move the airplane as compared to lower altitude.

Cheers,
PP
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klemmi85
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Mon Apr 20, 2009 5:45 pm

So it's all about the thinner air and thus resulting less drag ?

Okay, if that's what it's all about, thank you very much guys  Wink
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Soku39
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Mon Apr 20, 2009 5:59 pm

No, that's not it, much of it has to do with how much colder it is. Generally they try to fly right up until the tropopause, once you get into the stratosphere it starts to warm up again. All combustion engines are more efficient at colder temps.
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LHRjc
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Mon Apr 20, 2009 6:33 pm

In a jet aeroplane fuel flow is directly related to the thrust produced. Jet thrust is limited by 2 things, the TGT (Turbine Gas Temperature) limit and RPM limit. As the throttles are advanced both RPM and TGT increase, whichever limit is hit first will dictate how the maximum thrust varies with temperature. Therefore, when the air is hot, the TGT limit is hit 1st, whereas when the air is cold, the RPM limit is hit 1st. Jet thrust will decrease in the lower density air found at higher altitudes.

So, we want to operating in the most efficient RPM range, (80%- 97%) and by flying up high for low temperatures and the best thermal efficiency which is helped by the low intake temperature.

In the cockpit we can see 1 of 2 (or both) gauges, EPR and/or N1. EPR is the ratio of jet pipe pressure to inlet pressure, whereas N1 is the speed of the fan. In an A320 for example, the IAE engine is controlled by EPR changes, the CFM controlled by N1 changes.

Hope that helps...
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planewasted
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Mon Apr 20, 2009 7:48 pm

Isn't jet engines less efficient when the airplane is flying at slower speeds? Planes usually fly slower at low altitudes...
I know that the Concorde's engines actually were the most efficient of all jet engines when the plane was new. But only at supersonic speeds.

Edit: Or is the the cold temperatures that make the engines more efficient? According to the thermal physics I've studied larger temperature differences between intake air and engine core gives higher efficiency.

[Edited 2009-04-20 12:51:55]
 
tdscanuck
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Tue Apr 21, 2009 1:17 am



Quoting Klemmi85 (Thread starter):
I was just wondering why an aircraft engine isn't fuel efficient in low altitude but much more at high altitudes.

It's considerably less efficient at high altitudes. Several posts above are mixing efficiency, thrust, and fuel flow. At high altitudes the engine is less efficient, producing less thrust, and has much lower fuel flow. The overall fuel burn for a particular trip is minimized at high altitude because you can go faster for a particular amount of thrust due to lower drag.

Quoting Klemmi85 (Thread starter):
I don't have exact figures now, but I think I read somewhere, that i cruise, the fuel burn is only a quarter of the amount used during takeoff. Of course, in cruise your're not at maximum takeoff thrust, but there has to be something else?!

The major change with altitude is thrust...as you ascend, density and pressure are dropping, so thrust drops. Fortunately, drag drops off faster than thrust, so your overall burn drops off considerably at altitude. This isn't because the engine is gaining efficiency, it's because the engine isn't sucking as much fuel because required thrust is dropping.

Quoting PlaneWasted (Reply 6):
Isn't jet engines less efficient when the airplane is flying at slower speeds?

If you're going very very slow, the pressure at the fan face is is lower than atmospheric because the fan has to suck air in. As you speed up, you start to get "ram pressure" in the inlet. However, for subsonic aircraft, ram pressure is a fairly negligible effect up until you hit the transonic region.

Quoting PlaneWasted (Reply 6):
Edit: Or is the the cold temperatures that make the engines more efficient? According to the thermal physics I've studied larger temperature differences between intake air and engine core gives higher efficiency.

This is complicated by the fact that they Brayton cycle, as implemented in a jet engine, isn't actually closed. The temperature recover happens outside the engine (as the exhaust returns to atmospheric). But you're absolutely right that any thermodynamic cycle gets better as the difference between the hot and cold temperatures goes up.

Tom.
 
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Tue Apr 21, 2009 8:44 am

Aaah  Wink I knew there was more than just thinner air  Wink Thank you guys for explaining.
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vinniewinnie
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Wed Apr 22, 2009 9:54 am

So could manufacturers make more environmentally friendly aircraft by optimising the design for lower altitudes?

Is there a possibility that hasnt been searched for/discovered?
 
tdscanuck
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Thu Apr 23, 2009 1:48 am



Quoting Vinniewinnie (Reply 9):
So could manufacturers make more environmentally friendly aircraft by optimising the design for lower altitudes?

I'm not sure that would work. Going lower requires more thrust, which means more fuel...the change in fuel flow with thrust is a lot bigger than the change in fuel flow with efficiency. The fundamental problem comes about because of the thrust range that's required...enough thrust for takeoff will always be vastly overpowered for cruise, which means the engines are running off-maximum at cruise with the related efficiency hit.

Flying slower could have fairly huge benefits, since drag goes with speed squared, but there are other costs involved that go up with decreasing speed (crew time, asset utilization, etc.).

One interesting option would be much longer runways, which would reduced the amount of thrust required, which would allow the engines to run harder at cruise, which would improve their efficiency. That that's probably a logistical nightmare.

Tom.
 
ZBBYLW
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Thu Apr 23, 2009 2:08 am

Your example mentioned take off vs cruise. Due to the acceleration of take-off the engines would be creating alot more thrust and burning more fuel because of that. While in level flight the engines do perform better at higher elevation and that was already covered.

Another little thing of info is that in some aircraft it may be more fuel efficent to cruise around at say 18,000 feet then at 36,000 feet for instance because the fuel required to climb from 18,000 to 36,000 may be more then the extra fuel burned at a less efficent altitude. This only happens on shorter flights. After any signifigant cruise this is no longer a factor.

[Edited 2009-04-22 19:11:31]
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jetmech
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Thu Apr 23, 2009 4:51 am



Quoting Klemmi85 (Thread starter):
I was just wondering why an aircraft engine isn't fuel efficient in low altitude but much more at high altitudes.



Quoting Tdscanuck (Reply 7):
Several posts above are mixing efficiency, thrust, and fuel flow. At high altitudes the engine is less efficient, producing less thrust, and has much lower fuel flow.

I think there are two seperate entities at play that combine to give overall "efficiency", these being thermal efficiency and propulsive efficiency.

Thermal efficiency in simple terms is the useful work output divdied by the energy input from combusting fuel. Propulsive efficency with respect to aerospace vehicles propelled by reaction type engines is the vehicle velocity divided by the exhaust gas velocity.

Thermal efficiency can be estimated from either the compression or temperature ratio across the engine. I seem to remember that the thermal efficiency tops out at around 40% when calculated by either method for the following reason;

Quoting Tdscanuck (Reply 7):
This is complicated by the fact that they Brayton cycle, as implemented in a jet engine, isn't actually closed.

Below is the diesel cycle plotted on Pressure vs Specific volume and Temeprature vs. entropy diagrams.

http://www2.cemr.wvu.edu/~smirnov/mae320/figs/F9-5.jpg

The area inside the curves represents the amount of useful work that one has the potential to extract from the process. The larger the area, the more work one can get out of the cycle. However, as the amount of cycle work increases, one would find that the thermal efficiency of the cycle starts to decrease towards zero.

Alternatively, one could make the area inisde the curve smaller in an attempt to increase the thermal efficiency, but then the cycle work would approch zero. Either extreme is of no practical use, thus we must choose the optimum balance between thes two mutually exclusive factors to get the best compromise. Unfortunately, this means we have to accept less than 100% thermal efficiency and maximum cycle work. I suspect the Brayton cycle may have similar characterisitcs.

Propulsive efficiency may be affected by the engine / airframe combination. An airframe with high drag not only slows the aircraft, but also demands a higher exhaust gas velocity from the engine to make more thrust to hold a given aircraft velocity, which decreases propulsive efficiency. A streamlines airframe may have the opposite effect.

A compromise where the combination of thermal and propulsive efficiencies are optimum would probably give the best overall "efficency" that one is seeking. Again, the extremes are of no practical use. One may have a 100% thermally efficent engine, but if it stays at idle for an extended period whilst the airrcaft sits with the park brake set at the end of the runway, the propulsive efficency will be zero, and all the enrgy will be going to waste.

Regards, JetMech
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DocLightning
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Thu Apr 23, 2009 5:07 am



Quoting JetMech (Reply 12):

Below is the diesel cycle plotted on Pressure vs Specific volume and Temeprature vs. entropy diagrams.

AAAARRRGH!!!!!! *goes into a seizure of flashbacks from HS physics class*
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baroque
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Thu Apr 23, 2009 2:13 pm



Quoting DocLightning (Reply 13):
Quoting JetMech (Reply 12):

Below is the diesel cycle plotted on Pressure vs Specific volume and Temperature vs. entropy diagrams.

AAAARRRGH!!!!!! *goes into a seizure of flashbacks from HS physics class*

The trouble with those diagrams is that they induce large slugs of entropy within the brain of the physicsophobes.

But keep going Jetmech, there is probably a (faint) hope of educating us mechanically unwashed.

Remember:

Heat won't flow from the cooler to the hotter,

You can try it if you like,

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DocLightning
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Thu Apr 23, 2009 4:46 pm



Quoting Baroque (Reply 14):

The trouble with those diagrams is that they induce large slugs of entropy within the brain of the physicsophobes.

I completely dominated physics (and calculus). And despised every second of it.
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FredT
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RE: Why Is An A/c Engine Only Efficient At High Al

Wed Apr 29, 2009 7:16 pm

You must consider the design point for the engines. They're designed to operate efficiently at a relatively high RPM. At a high RPM at sea level, they produce a lot of thrust in order to enable the aircraft to take off and climb. Flying straight and level at this high RPM setting would mean overspeeding, or at least blasting through the skies at a speed much higher than the speed for aerodynamically economical cruise. Reducing the RPM by throttling the engines would mean taking them below the design RPM where they are the most efficient and a severely increased specific fuel consumption.

What to do, what to do?

Bring the engines to a higher altitude, where the thinner air will make them produce the right amount of thrust for level flight at or near the design RPM. You want to find that sweet spot where you have the minimum amount of aerodynamic drag (in actual truth, a bit more to find a good compromise between speed and efficiency), and where this drag corresponds to the thrust generated by running the engines at their most efficient RPM setting.

High also mean a lower EAS for a given TAS, converting to less drag at a higher speed and less energy used per track mile to overcome drag.
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Wed Apr 29, 2009 11:35 pm



Quoting Tdscanuck (Reply 7):
The major change with altitude is thrust...as you ascend, density and pressure are dropping, so thrust drops. Fortunately, drag drops off faster than thrust, so your overall burn drops off considerably at altitude.

No, drag doesn't drop. When cleaned up and flown at a resonable speed, then drag is always around 5 or 6% of the weight of an airliner. That is when flown at the speed at which the plane has the best L/D (lift to drag ratio).

Drag will be roughly the same going M=0.8 at 35,000 feet or M=0.4 at sea level, and you will need the same thrust for level flight.

But since you go twice as fast at at 35,000 feet on the same thrust, then you save half of the fuel up there.

Quoting Tdscanuck (Reply 10):
Flying slower could have fairly huge benefits, since drag goes with speed squared, but there are other costs involved that go up with decreasing speed (crew time, asset utilization, etc.).

No, it's a lot more complicated than that. If you fly an ordinary airliner at, say, M=0.6 at cruising altitude, then you will need to fly it with a very high angle of attack and your, drag will be very high, and your fuel efficiency goes to hell. You will need a much larger wing to fly it efficiently at such a slow speed, and then your drag would still be 5-6% of the weight.

Airliners are designed to cruise with best fuel efficiency around M=0.75 to M=0.8 give and take a little depending on load (payload and fuel load) and assigned flight level. Up to 10% slower for some RJs, especially the BAe-146/ARJ.

That speed was chosen because going much faster, then transonic airflow will be present at certain places as air is acellerated around the plane. and totally different and very unfavorabble drag rules apply.

When RJs are optimized for slightly slower speeds, then it is because they mostly have a generously sized wing to boost short field performance. In addition, for sinplicity they often do away with the most efficient high lift devices. Instead the have a wing airfoil section which has a high lift without high lift devices. Such airfoil sections will encounter transonic drag at slower speed than airfoils sections used on long range planes.

Airliners generally have a max sea level thrust which is 25 to 33% of MTOW, which is roughly five times what is needed for level flight. At 35,000 feet most turbofan engines will have lost three quarters of that thrust due to the thin air. So there isn't much power left for further climb until you have got rid of some fuel and that way become less heavy. Fortunately fuel flow at max thrust will also be cut by roughly 75% maintaning roughly the same SFC (specific fuel consumption) which is some 0.5 lb fuel for one lb thrust in one hour give and take a little depending on engine type and operating conditions.
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tdscanuck
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Thu Apr 30, 2009 3:46 am



Quoting Prebennorholm (Reply 17):
No, drag doesn't drop. When cleaned up and flown at a resonable speed, then drag is always around 5 or 6% of the weight of an airliner.

Yes, drag drops. The weight-dependent part of the drag is the induced drag, but that's only one piece of the overall drag. Form drag and skin drag are also in there, and they drop with altitude (at equal speed).

Tom.
 
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Thu Apr 30, 2009 4:15 pm



Quoting Tdscanuck (Reply 18):
Quoting Prebennorholm (Reply 17):
No, drag doesn't drop. When cleaned up and flown at a resonable speed, then drag is always around 5 or 6% of the weight of an airliner.

Yes, drag drops. The weight-dependent part of the drag is the induced drag, but that's only one piece of the overall drag. Form drag and skin drag are also in there, and they drop with altitude (at equal speed).

Tom.

No, if you fly the same L/D and the same weight at FL150 and FL350, the drag in units of force is the same since:

D = Weight* (D/L)

An advantage you have of being at the higher altitude is the higher TAS for the same EAS as Prebennorholm says.

Of course, it may be a bit difficult to get an exact L/D match between the two altitudes but you'll come pretty close if you fly the same CL (same EAS) for a relatively incompressible Mach (say below 0.75M).

My problem with Prebennorholm's statement is that it's unlikely you'll get the same L/D for 0.4M and 0.8M because at the higher Mach you may be into the drag rise so the Drag term will now include a Dcompress term that won't be there at 0.4M
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ANITIX87
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Thu Apr 30, 2009 4:45 pm



Quoting OldAeroGuy (Reply 19):
No, if you fly the same L/D and the same weight at FL150 and FL350, the drag in units of force is the same since:

D = Weight* (D/L)

Yes and no. If you are the same L/D, then yes, but when you are cruise, your L/D changes since the air is thinner and your lift remains the same. You may be confusing maximum L/D with actual L/D for a given real-world flight dynamic.

Parasitic drag is a function of air density, velocity, area, and drag coefficient.

D = (1/2)*(rho)*(v^2)*(A)*(Cd) where "rho" is air density. Therefore, as density decreases, the drag force will decrease. And you therefore need less thrust for a given velocity than you would at ground level.

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OldAeroGuy
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Thu Apr 30, 2009 5:56 pm



Quoting ANITIX87 (Reply 20):
Yes and no. If you are the same L/D, then yes, but when you are cruise, your L/D changes since the air is thinner and your lift remains the same. You may be confusing maximum L/D with actual L/D for a given real-world flight dynamic.

Parasitic drag is a function of air density, velocity, area, and drag coefficient.

D = (1/2)*(rho)*(v^2)*(A)*(Cd) where "rho" is air density. Therefore, as density decreases, the drag force will decrease. And you therefore need less thrust for a given velocity than you would at ground level.

No, I'm not confused.

For an incompressible drag polar (Mach below 0.7), for a given CL there is a given CD that is virtually invariant with altitude. [I say virtually since as altitude increases the skin friction Cd (part of Cd parasitic) increases due to decreased Reynolds number.]

For best efficiency, an airplane wants to fly at (L/D)max. On an incompressible drag polar, there is a unique CL for (L/D)max and a corresponding CD. For best range, fuel mileage etc, the airplane wants to always fly at the constant CL for (L/D)max.

To fly at the same CL for the same weight at various altitudes, dynamic pressure must be constant. This introduces the concept of Equivalent Airspeed or EAS.

The relationship between True Airspeed (TAS) and EAS is:

TAS = EAS * (1/rho)^.5 where rho is the ratio between the actual density and sea level density.

If the airplane is at FL150 or FL350 and flying at an incompressible Mach no at the CL for (L/D)max for the same weight, then dynamic pressure (and EAS) is the same for both altitudes.

Since CD will be the same and dynamic pressure is the same, then Drag will be the same.

However, at F350, TAS will be higher because rho is lower at FL350 than at FL150 and airframe efficiency will increase due to the higher airspeed. See the Breguet range equation.

This discussion is a bit simplified since best efficiency for high speed aircraft is obtained when flown at (M(L/D))max but the general principles still hold.

Airplanes climb not to reduce drag at constant weight but to gain airspeed when flying at the same drag.

Concurrently, airplanes climb as weight reduces to operate at the CL that produces the best L/D or ML/D. Drag does drop under these circumstances, but only because weight (ie lift) is also reducing.
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ANITIX87
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Thu Apr 30, 2009 6:51 pm



Quoting OldAeroGuy (Reply 21):
No, I'm not confused.

Apparently not. Sorry, haha. I understand what you meant now. I thought you were simply stating that drag is always the same since it's a function of L/D regardless of speed or altitude.

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OldAeroGuy
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Thu Apr 30, 2009 6:56 pm



Quoting ANITIX87 (Reply 22):
Quoting OldAeroGuy (Reply 21):
No, I'm not confused.

Apparently not. Sorry, haha. I understand what you meant now. I thought you were simply stating that drag is always the same since it's a function of L/D regardless of speed or altitude.

No problem. It's an interesting topic to discuss.
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Thu Apr 30, 2009 10:42 pm



Quoting OldAeroGuy (Reply 19):
No, if you fly the same L/D and the same weight at FL150 and FL350, the drag in units of force is the same since:

Yes but, as you noted, you can't practically fly at the same L/D at two altitudes that different so it's not a realistic comparison. At the same speed, you definitely won't have the same L/D at the different flight levels.

Tom.
 
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Fri May 01, 2009 2:57 am



Quoting Tdscanuck (Reply 24):
At the same speed, you definitely won't have the same L/D at the different flight levels.

I don't agree with you here. It's quite possible to have nearly the same L/D at different altitudes if you're operating at the same CL. It may entail wing loadings that are lower than you'd normally like to fly but it doesn't invalidate the basic premise.
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Fri May 01, 2009 5:16 am



Quoting OldAeroGuy (Reply 25):
I don't agree with you here. It's quite possible to have nearly the same L/D at different altitudes if you're operating at the same CL. It may entail wing loadings that are lower than you'd normally like to fly but it doesn't invalidate the basic premise.

I think he's saying that at airliner airspeeds (IOW, IAS=250+kts), that at the higher levels (FL350 was mentioned), that you're almost certainly pushing into Mach effects, relative to 250kts indicated at 15,000ft, which will impact your L/D.
 
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Fri May 01, 2009 3:29 pm



Quoting Rwessel (Reply 26):
I think he's saying that at airliner airspeeds (IOW, IAS=250+kts), that at the higher levels (FL350 was mentioned), that you're almost certainly pushing into Mach effects, relative to 250kts indicated at 15,000ft, which will impact your L/D.

Yes, if you include compressibility effects at the higher altitude, you may get a decrease in L/D. But if weight is the same, then Drag will increase, not decrease.

The statement made was that Drag will decrease if you fly at a higher altitude.

Quoting Tdscanuck (Reply 18):
Yes, drag drops. The weight-dependent part of the drag is the induced drag, but that's only one piece of the overall drag. Form drag and skin drag are also in there, and they drop with altitude (at equal speed).

The key question to Tdscanuck's statement is what is meant by equal speed. If it's equal TAS, then the equivalent airspeed is less at the higher altitude, CL is higher so you're flying at less than L/Dmax. At the same weight, Drag would go up, not down.

If it's equal EAS, see my statement above.

This is not to say that even with compressibility drag included you won't get an efficiency improvement at the higher altitude even if Drag is higher. Remember for high speed flight the figure of merit is M(L/D).

If you could design an SST with a cruise L/D of 7 while flying at M3.0, the airframe would be more efficient than the best subsonic airliners flying.

SST: L/D = 7; M = 3.0; M(L/D) = 21.0

Subsonic Airframes: L/D = 21; M = .85; M(L/D) = 17.85

Unfortunately, SST cruise L/D's are more on the order of 4.0 so M(L/D) = 12.0 which is another reason (besides the environmental ones) that you don't see any SST's in service today.
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Fri May 01, 2009 6:36 pm



Quoting OldAeroGuy (Reply 27):
If it's equal TAS, then the equivalent airspeed is less at the higher altitude, CL is higher so you're flying at less than L/Dmax. At the same weight, Drag would go up, not down.

You're saying at a given true airspeed and weight, total drag is higher at higher altitude? The same airliner, at the same weight, at, say, 460 knots TAS, has more drag at ... FL350 than at FL 250?

If that example has the wrong numbers for your contention, can you give us some right numbers?
 
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Fri May 01, 2009 10:10 pm



Quoting OldAeroGuy (Reply 25):
I don't agree with you here. It's quite possible to have nearly the same L/D at different altitudes if you're operating at the same CL.

Yes, but if you're operating that the same Cl then you're *not* operating at the same speed. The translation from Cl to L is q, which is proportional to density and to speed squared. If you've got the same L and the same speed, but density changed, you must necessarily be at a different Cl.

Tom.
 
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Sat May 02, 2009 5:03 am



Quoting Timz (Reply 28):
You're saying at a given true airspeed and weight, total drag is higher at higher altitude? The same airliner, at the same weight, at, say, 460 knots TAS, has more drag at ... FL350 than at FL 250?

Please see the table below:

FL000 FL250 FL350
Press 2116.2 785.32 497.96
Density 0.002377 0.001065 0.000737
a - kts 661.47 601.95 576.42
delta 1 0.3711 0.2353
rho 1 0.4480 0.3101
TAS - kts 256.14 382.66 460
EAS - kts 256.14 256.14 256.14
Mach 0.3872 0.6357 0.7980
q - psf 222.1 222.2 222.0
CL 0.45 0.45 0.45
L/D 21.0 21.0 20.06
CD 0.02143 0.02143 0.02243
M(L/D) 8.132 13.35 16.01

The table doesn't look as good now as it did when it was created. Sorry


In this example, I've used your value of 460 kts @ FL350 and assumed you meant it to be in terms of TAS. Note that this gives you a Mach number of about 0.80 for this condition, well into the compressible region where you have to start adding an additional drag increment due to compressiblity effects.

You'll note that I've also computed a 256.14 kts EAS for this condition. See Reply 21 for the relationship between TAS and EAS.

I then applied this value of EAS for FL000 and FL150. At these altitudes, TAS for constant EAS is 256.12 and 382.66. There should be no surprise about the Sea Level condition since EAS relates back to SL equivalent density. Also per the definition of EAS, dyanmic pressure (q) is the same for all three altitudes.

Mach drops to .3872 and .6357 at FL000 and FL250 respectively. This is important for the situation we are discussing since there are essentially no compressibility effects below 0.70M. Therefore the drag polars for FL000 and FL250 at the conditions being discussed are essentially identical.

Let's chose a typical design CL of 0.45. This will apply to all three altitudes since airplane weight is assumed to be the same per the discussion and q is the same for all three altitudes. At the same time, we'll say the incompressible polars have a modern L/Dmax at this design point of 21.0. CD for FL000 and FL250 be .02143. At FL350, the higher cruise Mach requires that a CDcompress term be added to the basic drag polar. An optimistic value for the increment would be .0010. At FL250, CD is now .02243 or about 5% higher than at FL000 or FL250. Since q is the same, the Drag in units of force will be about 5% higher at FL 350 than at FL000 or FL250. L/D also drops about 5%.

You'd still want to fly at FL350 rather than FL250 though. Remember that for high speed flight, M(L/D) is an important efficiency indicator. M(LD) for FL250 and FL000 drops by 17% and 49% relative to M(L/D) at FL350.

Quoting Tdscanuck (Reply 29):
Yes, but if you're operating that the same Cl then you're *not* operating at the same speed.

You are if the same speed is EAS. It's not true if you're talking about TAS. See the preceding discussion.
Airplane design is easy, the difficulty is getting them to fly - Barnes Wallis
 
baroque
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Sat May 02, 2009 3:27 pm



Quoting OldAeroGuy (Reply 30):
The table doesn't look as good now as it did when it was created. Sorry

But lovely if you copy it to word, insert tabs and convert to table. Fascinating!  bigthumbsup 
 
tdscanuck
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Sat May 02, 2009 4:46 pm



Quoting OldAeroGuy (Reply 30):
You are if the same speed is EAS. It's not true if you're talking about TAS.

I'm talking TAS. Should have made that clear from the beginning. For the purposes of this initial discussion, I'm not sure why you'd ever want to use EAS.

Tom.
 
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Sat May 02, 2009 4:54 pm



Quoting Tdscanuck (Reply 32):
I'm talking TAS. Should have made that clear from the beginning. For the purposes of this initial discussion, I'm not sure why you'd ever want to use EAS.

You use EAS because the main theme of this discussion is Efficiency as described by the thread title. For best efficiency, you want to operate near the design CL for any altitude as this will be near (L/D)max. TAS for operating at a constant CL (and constant EAS if weight is a constant) is a fallout of the particular altitude you're operating at.
Airplane design is easy, the difficulty is getting them to fly - Barnes Wallis
 
tdscanuck
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Sat May 02, 2009 9:23 pm



Quoting OldAeroGuy (Reply 33):
You use EAS because the main theme of this discussion is Efficiency as described by the thread title.

I agree we're talking efficiency, but all of your major efficiency measures (L/D, SFC, range, time to destination, fuel to destination, etc.) are pegged off TAS, not EAS.

Tom.
 
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Sat May 02, 2009 9:56 pm



Quoting Tdscanuck (Reply 34):
I agree we're talking efficiency, but all of your major efficiency measures (L/D, SFC, range, time to destination, fuel to destination, etc.) are pegged off TAS, not EAS.

Actually, it's a mix.

Design CL and its associated L/D are keyed to EAS. SFC is also related to EAS as q at the fan face is a factor in this term.

The other factors you list are a fall out of flying at constant CL at the best possible altitude to maximize M(L/D).

For our discussion on why it is advantageous to fly at higher altitudes, the use of EAS and its attendent constant CL is a necessity. If you fly at the same TAS between at two different altitudes, one may be at the CL for best L/D while the other is at a higher or lower CL that yields a degraded L/D.

To understand the true altitude effect, you need to compare the best L/D condition for both altitudes. Constant EAS allows you to do this. Constant TAS does not.
Airplane design is easy, the difficulty is getting them to fly - Barnes Wallis
 
timz
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Sat May 02, 2009 11:15 pm



Quoting OldAeroGuy (Reply 27):
...what is meant by equal speed. If it's equal TAS...
...At the same weight, Drag would go up, not down.

I'll try the question again. An aircraft at 460 knots TAS at FL250, compared to the same aircraft at the same weight at 460 knots TAS at FL350. At which altitude is total drag greater?
 
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Sun May 03, 2009 2:05 pm



Quoting Timz (Reply 36):
An aircraft at 460 knots TAS at FL250, compared to the same aircraft at the same weight at 460 knots TAS at FL350. At which altitude is total drag greater?

Its very much dependant in the aircraft as they all have different drag polars but I would say that it would have higher drag at FL 250 as the EAS would be a lot higher here and the drag more dominated by the lift independent factors.

Fred
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Sun May 03, 2009 11:47 pm



Quoting OldAeroGuy (Reply 19):
My problem with Prebennorholm's statement is that it's unlikely you'll get the same L/D for 0.4M and 0.8M because at the higher Mach you may be into the drag rise so the Drag term will now include a Dcompress term that won't be there at 0.4M

If we talked 0.45M vs. 0.9M, then sure that effect would be huge.

But I doubt that compression is a noticeable issue at 0.8M on a well designed modern airliner. I cannot "prove" that in a scientific way, but all long range planes are made to cruise efficiently at 0.82 to 0.85M. That wouldn't be the case if already 0.80M created a noticeable compression issue.

But sure, if every detail of an airliner isn't shaped with compression drag in mind, then 0.8M will create a huge compression drag issue.

There is, however, one thing which could improve a low level 0.4M airliner compared to present day airliners. An unswept wing would give a slightly higher Cl. Therefore slightly less wing area would be needed meaning less parasite drag. We saw that on older propeller airliners as well as present day turboprop RJs. Still that wouldn't anywhere near outdo the enormous performance gain by going twice as fast with roughly the same drag at FL350 compared to skimming the sea.

When efficiency of relatively slow and low flying turboprop planes compare well to high flying turbofan airliners, then it is mostly due to the efficiency of the propulsion system. In reality a turboprop is an unducted turbofan with a "100:1 bypass ratio". And another huge advantage is that it can keep the "fan" tip speed subsonic all the time. The turbofan engine loses a lot of efficiency by always having a supersonic fan tip speed. Still that disadvantage is overcome by going twice as fast with equal drag.
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Mon May 04, 2009 12:24 am



Quoting Timz (Reply 36):
I'll try the question again. An aircraft at 460 knots TAS at FL250, compared to the same aircraft at the same weight at 460 knots TAS at FL350. At which altitude is total drag greater?

The question is kind of like asking "How long is a piece of string". The answer needs to be qualified with the statement "It depends". In this case the dependent variable that needs to considered is airplane weight.

It also makes me work harder to illustrate the answer. If you interested, I'll be posting a couple of tables in the next day or two.
Airplane design is easy, the difficulty is getting them to fly - Barnes Wallis
 
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Mon May 04, 2009 1:42 am



Quoting Prebennorholm (Reply 38):
But I doubt that compression is a noticeable issue at 0.8M on a well designed modern airliner. I cannot "prove" that in a scientific way, but all long range planes are made to cruise efficiently at 0.82 to 0.85M. That wouldn't be the case if already 0.80M created a noticeable compression issue.

Compression is absolutely noticeable at M 0.8. There's a gap between when compressibility effects start to show up and when shock waves start to show up. The latter is the critical Mach number (Mcr), which is typically right around cruise speed.

Quoting Prebennorholm (Reply 38):
And another huge advantage is that it can keep the "fan" tip speed subsonic all the time. The turbofan engine loses a lot of efficiency by always having a supersonic fan tip speed.

Many turbofans only go supersonic tips at or near maximum thrust. There's no inherent reason you can't build a turbofan with subsonic tips all the time, but you pay an economically unacceptable weight penalty.

Quoting OldAeroGuy (Reply 39):

Quoting Timz (Reply 36):
I'll try the question again. An aircraft at 460 knots TAS at FL250, compared to the same aircraft at the same weight at 460 knots TAS at FL350. At which altitude is total drag greater?

The question is kind of like asking "How long is a piece of string". The answer needs to be qualified with the statement "It depends". In this case the dependent variable that needs to considered is airplane weight.

You lost me there, OldAeroGuy...he specified equal weight. There's nothing wrong with the formation of his problem that I can tell...obviously one of those points is much farther from the optimum configuration than the other, but figuring the total drag differential isn't that big a deal.

Tom.
 
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Mon May 04, 2009 3:29 am



Quoting Tdscanuck (Reply 40):
Compression is absolutely noticeable at M 0.8. There's a gap between when compressibility effects start to show up and when shock waves start to show up.

I've read several texts that suggest one should start accounting for compressibility as early as Mach 0.3!

Regards, JetMech
JetMech split the back of his pants. He can feel the wind in his hair :shock: .
 
tdscanuck
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Mon May 04, 2009 3:45 am



Quoting JetMech (Reply 41):
I've read several texts that suggest one should start accounting for compressibility as early as Mach 0.3!

Agreed. There's three major "break points" of interest...when the compressible and incompressible solutions start to diverge (typically somewhere in the M 0.3-0.5 range), when they get different enough to matter for many practical problems (something like M 0.7), and when you start getting local shockwave formation (typically M 0.8-0.9).

Tom.
 
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Mon May 04, 2009 4:24 am



Quoting Timz (Reply 36):
I'll try the question again. An aircraft at 460 knots TAS at FL250, compared to the same aircraft at the same weight at 460 knots TAS at FL350. At which altitude is total drag greater?



Quoting Tdscanuck (Reply 40):
You lost me there, OldAeroGuy...he specified equal weight. There's nothing wrong with the formation of his problem that I can tell...obviously one of those points is much farther from the optimum configuration than the other

The question though is what equal weight? And you're right that the key question is how close you're to optimum conditions.

Please see the two following tables. Both are based on constant TAS = 460 kts. The first table assumes that airplane weight is such that Design CL is achieved at FL350. I've changed the Design CL to 0.5 for these examples but this is mainly a function of airfoil technology. I'm still assuming that the imcompressible L/D at this point is 21.0.

Altitude FL250 FL350
Pressure 785.3 498.0
Density 0.001065 0.000737
a - kts 601.95 576.42
delta 0.3711 0.2353
rho 0.448 0.3101
TAS - kts 460 460
EAS - kts 307.9 256.1
Mach 0.7642 0.7980
q 321.0 222.0
CL 0.346 0.500
L/D 17.72 19.76
CD 0.01951 0.02531
Cd0 0.01479 0.01479
Cdi 0.00442 0.00902
Cdcomp 0.0003 0.0015
M(L/D) 13.54 15.77

I've used AR = 9.0 and span efficiency factor = .98 to compute Cdi. Cd comp is higher for the FL350 case since the cruise Mach is higher and the CL is higher.

Clearly drag is higher at FL250 for this case since L/D is 11.5% higher at FL350 than at FL250.

Now let's assume that weight is increased so Design CL is achieved at FL250.

Altitude FL250 FL350
Pressure 785.3 498.0
Density 0.001065 0.000737
a - kts 601.95 576.42
delta 0.3711 0.2353
rho 0.448 0.3101
TAS - kts 460 460
EAS - kts 307.9 256.1
Mach 0.7642 0.7980
q 321.0 222.0
CL 0.500 0.7231
L/D 20.05 17.07
CD 0.02493 0.04235
Cd0 0.01479 0.01479
Cdi 0.00902 0.01886
Cdcomp 0.00113 0.00870
M(L/D) 15.32 13.62

For this case, the drag is clearly less at FL250 since L/D at Fl250 is 17.5% higher than at FL350. In fact, the CL for this weight at FL350 is so high that the airplane might have insufficient maneuver capability.

At constant TAS, the weight at FL250 would need to be 44.6% higher than at FL350 for both conditions to operate at Design CL. The question might be asked if this degree of change weight is realistic.

Using the 773ER as an example, MTOW is 775,000 lb. Weight at start of cruise is about 2% less or around 760,000 lb. If we use 760,000 as the weight at FL250, the weight at FL350 would be about 526,000 lb. With a OEW of 376,000 and an all passenger payload of 76,700 lb, there would be about 73,000 lb of fuel left on the airplane. With standard international reserves, this would be sufficient to fly more than 1500 nm. Therefore the weight range covered in these two examples appears to be realistic.

As this example shows, it's difficult to draw conclusions about the impact of cruise altitude on total drag unless you control some of the variables. My previous example that used constant EAS rather than constant TAS between altitudes made the comparison easier since both altitudes were operating at Design CL.

Quoting Tdscanuck (Reply 40):
but figuring the total drag differential isn't that big a deal.

It depends on how much spare time I have to lay out the examples. Please forgive me, but I do appear to be the only one trying to quantify altitude effects on drag.

Quoting Tdscanuck (Reply 40):
Quoting Prebennorholm (Reply 38):
But I doubt that compression is a noticeable issue at 0.8M on a well designed modern airliner. I cannot "prove" that in a scientific way, but all long range planes are made to cruise efficiently at 0.82 to 0.85M. That wouldn't be the case if already 0.80M created a noticeable compression issue.

Compression is absolutely noticeable at M 0.8. There's a gap between when compressibility effects start to show up and when shock waves start to show up. The latter is the critical Mach number (Mcr), which is typically right around cruise speed.

I agree with you here Tdacanuck.
Airplane design is easy, the difficulty is getting them to fly - Barnes Wallis
 
OldAeroGuy
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Mon May 04, 2009 4:31 am



Quoting JetMech (Reply 41):
I've read several texts that suggest one should start accounting for compressibility as early as Mach 0.3!

Compressibility effects at 0.3M are usually only important at angles of attack near stall. Near stall, you can have upper surface sonic velocities with low freestream Mach's.
Airplane design is easy, the difficulty is getting them to fly - Barnes Wallis
 
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jetmech
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Mon May 04, 2009 7:42 am



Quoting OldAeroGuy (Reply 44):
Near stall, you can have upper surface sonic velocities with low freestream Mach's.

Interesting! I suppose that this would be more apparent on thinner airfoils with smaller leading edge radii?

Regards, JetMech
JetMech split the back of his pants. He can feel the wind in his hair :shock: .
 
OldAeroGuy
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Mon May 04, 2009 3:45 pm



Quoting JetMech (Reply 45):
Interesting! I suppose that this would be more apparent on thinner airfoils with smaller leading edge radii?

Sonic upper surface velocities can occur on both thin airfoils with small nose radii and thick airfoils with large nose radii.

The difference is that the thin airfoils have sonic flows at lower angles of attack and this limits their CLmax capability.
Airplane design is easy, the difficulty is getting them to fly - Barnes Wallis
 
tdscanuck
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Mon May 04, 2009 4:02 pm



Quoting OldAeroGuy (Reply 43):
Please see the two following tables.

Fantastic analysis! Always good to put facts and data to the discussion. Thank you very much for this.

Tom.
 
timz
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RE: Drag

Tue May 05, 2009 6:33 pm



Quoting OldAeroGuy (Reply 43):
Now let's assume that weight is increased so Design CL is achieved at FL250.

Altitude FL250 FL350
Pressure 785.3 498.0
Density 0.001065 0.000737
a - kts 601.95 576.42
delta 0.3711 0.2353
rho 0.448 0.3101
TAS - kts 460 460
EAS - kts 307.9 256.1
Mach 0.7642 0.7980
q 321.0 222.0
CL 0.500 0.7231
L/D 20.05 17.07
CD 0.02493 0.04235
Cd0 0.01479 0.01479
Cdi 0.00902 0.01886
Cdcomp 0.00113 0.00870
M(L/D) 15.32 13.62

(I inserted spaces to make the table readable-- if they're in the wrong places, speak up.)

Quoting OldAeroGuy (Reply 43):
Using the 773ER as an example, MTOW is 775,000 lb. Weight at start of cruise is about 2% less or around 760,000 lb. If we use 760,000 as the weight at FL250...

So you're saying the table applies reasonably well to a 777-300 at 760,000 lb at 460 kt TAS? How different would it be for, say, a 747-200 at 460 kt TAS, at ... whatever weight you choose to make the table fit?
 
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RE: Why Is An A/c Engine Only Efficient At High Alt?

Tue May 05, 2009 6:45 pm



Quoting OldAeroGuy (Reply 44):
Quoting JetMech (Reply 41):
I've read several texts that suggest one should start accounting for compressibility as early as Mach 0.3!

Compressibility effects at 0.3M are usually only important at angles of attack near stall. Near stall, you can have upper surface sonic velocities with low freestream Mach's.

... i.e. when rushing to the bar after last orders are called.  duck 

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