Max efficiency altitude for a Jet Engine

[compressor stall]

Ignoring pressurisation problems, (and coffin corner aerodynamic issues) what would be the maximum altitude for efficiency for a jet aircraft (say 744).

As I understand it, as altitude increases, the increasing difference between the EAS and the TAS mean that the aircraft can travel further (ie more efficient in this context). When would this stop? At the tropopause when the temperature becomes constant?

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Those who restrain desire do so because theirs is weak enough to be restrained.
William Blake

[This message has been edited by compressor stall (edited 27 January 2001).]

[HotDog]

The effect of altitude on thrust output is a function of density. The higher you go the less air pressure there is and the colder it gets. As pressure decreases thrust decreases, but as temperature decreases thrust increases. However, the pressure drops off faster than the temperature so that there is actually a drop off in thrust with altitude.

At about 36,000ft (tropopause) the temperature stops falling and remains constant while the pressure continues to fall. As a result, the thrust will drop off more rapidly. This makes 36,000ft the optimum altitude for long range cruising, just before the rate of thrust fall off increase. Lighter weights can offset thrust lapse rate and retain optimum conditions at higher flight levels as shown in cruise performance data.

[SKYYACHT]

There are a number of considerations, and most of these are associated with the "Design RPM" of the engine, which lies somewhere between 85% and 96% of Max Permissible. As has been noted on some of the other replies, it is the MASS FLOW through the engine core that is a contributory factor to efficiency. A good thermal gradient through the engine core is needed, and the greater the thermal difference between intake and exhaust, the greater the power for each kg of fuel burnt. The limiting factor here is the max temperature that the tailpipe can withstand without becoming a liquid, (which is embarrassing, and frightens the pilots!)
Therefore it is prudent to get as much altitude as possible, where the Ambient OAT is very low, -56.5°C at ISA. The reduction in density as altitude increases, is virtually negated by the ram air effect of traveling through the air at high TAS.

Therefore, it is difficult to say exactly what altitude would be best for a 747 to get max range, but the optimum would take some of these factors, and probably a heap more that I dont know about into account.

Tailwinds

[Cuban_8]

CS,

I remember doing this theoreticaly in Uni, so for what it's worth, will add my thoughts.

Efficiency with altitude comes in two parts. Firstly, as you stated, the higher you climb, the greater your TAS - as the atmosphere becomes more rarefied, the aircraft has to travel faster to stay up there! Thus, you are covering more range for unit fuel burn.

The second aspect is that of turbine efficiency. The higher you go, the more efficient the turbine cycle becomes due to the difference in the OAT and the trubine temperature becomeing grater (turbine entry temp stays essentially constant). Thus, you get a greater SPECIFIC thrust due to TSFC (Thrust Specific Fuel Constmption) being greater. However, SPECIFIC thrust is the thrust generated per unit mass flow of air through the engine. As you climb, the mass flow through the engine decreases and thus the thrust drop off. It is stated by some that the "ram effect" of travelling at the higher speed reverses the effect of the lower density - this is not really true as the dynamic pressure id greater flying at lower altitudes.

On that note, what HD said is correct. After the tropopause, the temperature remains constant (hence no further increase in engine efficiency) whilst the density continues to fall. Thus, the point of greatest efficiency is not too far away from the tropopause.

Hope you can de-code my ramblings!

Cuban_8

[Bellerophon]

compressor stall

When Hotdog talked about the tropopause being at 36,000 ft, he was referring to the height at which the tropopause is deemed to exist under standard conditions, as defined by the International Standard Atmosphere (ISA), and as SKYYACHT said, the temperature assumed at the tropopause is -56.5°C.

We should bear in mind however, that conditions are rarely standard, and also that the tropopause is subject to seasonal and geographical variations.

To give examples, on the North Atlantic Track System, in Autumn through to Spring, it is pretty much where it should be, in Summer it drifts a bit higher. Over the Poles it can be down at 27,000 ft and over the Equator up to 55,000 ft.

Likewise the temperature variations from ISA can be substantial. On my current (!) type, which is very temperature sensitive in cruise, I’ve had temperatures ranging from an OAT of -77°C (ISA -20.5°C) at FL600 en-route to Barbados (very welcome), with an OAT of -82°C not unheard of in those latitudes, to the other side of the coin, an OAT of -22°C (ISA +15°C) at FL260 whilst trying to accelerate over North East Canada (most unwelcome)!

So, in practice where the tropopause actually is, on any given day, may be a completely different matter!

[Capt Claret]

As a perhaps interesting aside, the Significant Wx chart for Australia on Friday evening showed the Tropopause over Southern Australia in the low FL500's. A result I guess of the High causing heat wave conditions over much of Southern Aus.

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bottums up !

[mustafagander]

Stallie,
Don't forget that the B747 series engines can equate to big turboprops and they hate high altitudes. The efficiency of the blades dies in the bum but is partially offset by the tip shrouding fortunately provided by the nose cowl. :)

Turbojets on the other hand, love high altitudes.

As has also been posted, the tropopause is all over the place depending on the location of the jet streams among many other factors. Pull the sigwx charts from Aust BoM and look at them over a few weeks.

[Bullethead]

That's a double barreled question Stallie. In the title you say jet engine and in the text jet aircraft. The jet engine bit appears to have been covered pretty well so I'll put in my two bobs worth, specifically in relation to the B744.
Optimum altitude for cruise is that altitude at which the engine and airframe are operating at maximum efficiency. Airframe efficiency is maximized by selecting a cruise speed which corresponds to the most efficient angle of attack and engine efficiency is maximized by operating in the design rpm range around 90% to 95%. If you climb at the best angle of attack with the engines operating at their design optimum and you reach a point where you are climbing at 300fpm or less then you have reached, for practical purposes, the optimum altitude. To operate either faster or slower than the optimum speed will be less fuel efficient as will operating higher or lower than the optimum altitude. So for any given aircraft weight and set of environmental conditions there is one optimum altitude at which you have maximumefficiency. For a RR powered B744 taking off at close to maximum all up weight (MAUW) of around 400 tonnes, generally, the initial optimum altitude is around FL290.
There are three cruise speed schedules used and they are ECONomy or minimum cost cruise, long range cruise (LRC) and maximum range cruise (MRC).
ECON is a variable speed schedule starting off at about M.85 and decreasing as fuel burns off and is a function of aircraft weight, cruise altitude and headwind component. Faster in a headwind and slightly slower in a tailwind.
MRC is also a variable speed schedule starting at about M.83, with speed decreasing, which gives maximum range though not necessarily maximum efficiency.
LRC is 99% of MRC (not speed, fuel efficiency) and starts at around M.86 and decreases. No wind corrections are applied to either MRC or LRC.
For the B744, ECON is midway between LRC and MRC! That’s right, LRC is faster than the normal cruise speed. The optimum altitude increases with fuel burnoff at around 100' every eight minutes.
It's confused me, I hope it helps you. Now I need a cold Crownie after that lot and what do you know there's one right here!
:) :) :)

[V2Climb]

Bellerophon: that's some machine that can cruise at F600!!! What is it?? :)

[Trident Sim]

Tricky question V2Climb, now let's see! :)

FL600, no clue there; temperature sensitive, not much help, en route to BGI...hmm, well, just a wild guess you understand, but how about:

http://www.airliners.net/open.file?id=124314

[twistedenginestarter]

Efficiency means different things.

As regards how much power you get for a specific input of fuel it's probably true what people are saying - above the tropopause you gain nothing.

As regards how much power you get per euro of capital investment - it probably gets more expensive as you go up beyond the tropopause. Less air means a bigger engine to get enough power.

As regards how many passenger kilometers you get per kilo of fuel I still think this leads you to go as high as other things will let you. Temperature may start to rise but pressure (=air resistance) continues to drop all the way out to Pluto. I still think if you could solve speed of sound and depressurization constraints, Boeing would immedately stick 4 GE90s on a 747 and have you TCASing up with the Concordes.

[jonno]

From my point of view, the man mentioned 'efficiency', well, that means nothing but 'tonnes burned per n/mile'.
With this in mind, as it always should be, climb until you attain your advertised best just starts to decrease, usually around 96 or 96% N1, and there you have it, easy eh!
Chears.

[Checkboard]

Ahh... Stallie, I go away for three months, and everybody forgets all my good work! ;)

Have a look at this topic from the Tech Log archive:
Why are jet engines more fuel efficient at high altitude? (http://www.pprune.org/ubb/NonCGI/Archives/Archive-000002/HTML/20000905-3-000980.html)

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Tech Log forum moderator

[This message has been edited by Checkboard (edited 13 February 2001).]

[twistedenginestarter]

Too many people here are captivated by the bleedin' obvious. We realise if you slide into your 747-436b that the best altitude is the one on the piece of paper marked best altitude.

The interest in this discussion is why isn't the RB211 bigger/smaller, designed with more/less stages to spin faster/slower with a higher/lower by-pass ratio etc etc etc.

My take is still this:

1 pressure differential on the hull
2 exhaust gas temperature
3 mach effects

And ... fuel efficency is not the same as efficiency which is normally outputs divided by inputs. Fuel only accounts for about half the (financial) inputs for a jet which is why you don't normally fly at the most economic cruise speed.