Jet Aircraft Fuel Burn Variations with Altitude

[Ledhead27]

Hi everybody,

Was wondering if anybody would be able to help me with my query, it's part of a university assignment I am currently trying to complete.

For a typical jet aircraft, for instance the Boeing 737-400, why do aircraft not fly at relatively low cruise altitudes?

As far as I understand a jet engine works more efficiently at higher altitudes, also as fuel payload is burnt off throughout the flight the optimum altitude can be increased (met by conducting step altitudes).

However, is there any factors that would cause fuel burn at lower altitude to be lower in comparison to high altitude (excluding the effects of jetstreams). I was hoping the effects of Specific Air Range may factor into it but if anyone could help that would be greatly appreciated.

Regards,
Dan

[PDR1]

It's not that the engines are more efficient at higher altitudes; it's that the higher altitudes have lower air density and so the airframe drag is [much] lower so you go faster for a given thrust = faster for a given fuel burn.

PDR

[Ledhead27]

I was led to believe that because of the greater temperature differential at higher altitude between the OAT & temperature within the turbine, this made for a more efficient thrust output? And of course air density decreases which alters the fuel/air mixture ratio.

[tdracer]

The Thrust Specific Fuel Consumption (TSFC) is actually worse at higher altitudes - basically the compressor has to 'work harder' with the thinner air. The lower temperatures do help, but not enough to offset the loss of compressor efficiency.
As PDR notes, it's the lower drag at high altitude that normally makes it more efficient.
Note also that cruising at a higher altitude doesn't always give better fuel burn - there are optimum cruise altitudes dependent on aircraft weight - go lower or higher and you'll burn more fuel at the same cruise speed. This is all programed into the Flight Management Computers to assist the crew in optimizing their flight plan.

[Ledhead27]

That all sounds very interesting, it seems that the typical trend of information on the Internet states that TSFC improves with an increase in altitude because of the reduced thrust setting. However, are they failing to describe that the compressor does not work as efficiently at higher altitudes?

Also if anyone has any available sources that might assist in further improving my understanding that would be greatly appreciated.

[DaveReidUK]

I was hoping the effects of Specific Air Range may factor into it

Specific Air Range is a derived parameter, not a factor.

[CaptainProp]

Some good stuff in these documents from Airbus.

http://www.smartcockpit.com/download...erformance.pdf

http://www.smartcockpit.com/download...el_Economy.pdf

http://www.smartcockpit.com/download...Cost_Index.pdf

CP

[DaveReidUK]

Originally Posted by wondering

It´s not one single factor affecting efficiency. 'Aerodynamics for Naval Aviators' (although somewhat dated now) explains some of the physics and is not just stating the facts. There´s a free online version somewhere.

http://www.faa.gov/regulations_polic.../00-80t-80.pdf

Not for the fainthearted: 434 pages

[CallmeJB]

Here's an (over)simplification of where to start:

Fuel burn (lbs/hour) for a given Indicated Air Speed is essentially constant, even as altitude changes.

For a given Indicated Air Speed, True Air Speed increases with an increase in altitude.

[grounded27]

Really simple, same equates in a similarity to automotive fuel efficiency, drag really increases. 45-65MPH seems like a sweet zone, anything over the force of air increases exponentially as drag. To add a personal note, I found my fuel efficiency better in my motorhome (really high drag) at higher altitudes even though I was climbing and descending grades.

This is why airliners have been built to fly at altitudes up to 420, smaller pressure tubes in the exec-jet upwards of 50k as they can achieve a higher DP.

[Wizofoz]

The question asked is if there was a reason a jet might fly at a lower altitude. One obvious one is wind. The actual optimum altitude may be significantly lower than it would be in still air if flying lower nets a lower head wind or (less typically) stronger tail-wind.

Keeping out of an en-route jet-stream head wind might mean an optimum altitude ten thousand or more feet lower than it would be in nil wind.

[standardset]

ISA deviation can make a huge difference especially if there is a large height band at high deviation. It made sense to fly lower and faster out of the band. Logging the temperature every 5000 ft soon gives you a clue to the best altitude for temperature to compare with actual winds. This worked well in B757 and B767 in Europe, I often found high 20000 to low 30000's would be better than optimums around 37000.

[pattern_is_full]

@ledhead27

I think your are seeing conflicting information because you are not clearly and tightly defining your frame of reference.

Take a jet engine off the airframe and put it in a test chamber where you can change the ambient air pressure/density, and "climb" the atmosphere to simulate high-altitude engine performance. You will get one set of results.

Put the engine back on the airframe and fly it in an "ideal world" in which there are no winds or temperature changes (except ideal lapse rate with altitude), and no particular place to go, but there is drag, and you will get a different set of answers.

Put your 747 into the real world, with real-world changes in all kinds of factors, from winds to baro pressure to air temperature to flight distance to aircraft weight - and you will get yet another set of answers.

As to the first - engines burn two things, fuel, and air. One won't burn without the other. At an altitude where the air is 0.25 the density of sea level, you will "burn" 1/4 as much fuel, and get approximately 1/4 as much thermodynamic output. You can pump in as much fuel as at sea level, but 3/4s of it won't burn, and becomes as (in)effective as water - a cold fluid that doesn't burn, cools the "fire," and provides a bit of reaction mass.

That isn't necessarily more "efficient" - since you also get ~1/4 as much power. Try to run an engine in a vacuum, and you will get zero fuel burn (very efficient) and zero power (not efficient at all).

With small piston planes, you get the same effects. The only difference is, in small planes the fuel flow is adjusted to the ideal ratio with the ambient available air by the pilot leaning the mixture by hand, whereas jets have automatic fuel metering. If your piston engine gets too hot and threatens to start detonating, you can cool it by adding MORE (excess) fuel (richen the mixture) - some of which goes out the exhaust unburnt, but which cools the engine as it passes through (low initial temperature, plus evaporative cooling).

You lean for maximum efficiency (fuel flow best matched to available air molecules) by watching the EGT (exhaust temperature): maximum EGT (hottest "fire") = "perfect" ratio of fuel to air, with all the intake air and all the fuel going into combustion, with no waste of either.

Back to jets - lower fuel burn is not more efficient if you lose something else as well, i.e. thrust or power. But once you put the engine back on the aircraft, and fly it at high altitudes, then you get a benefit in terms of reduced drag. Your reduced thrust can push you as fast or faster through the air, and you still get the benefit of reduced fuel use. The whole system is more efficient, even if the engine itself is not.

Up to a point, where there is not enough air to hold the plane up at even the highest achievable speed, without so much nose-up pitch that your (induced) drag skyrockets. Self-limiting.

As to when flying lower is more "efficient" - efficient meaning total flight efficiency in terms of time and total fuel burn, not engine SFC/thrust ratio at a given moment:

Winds and temperatures have been mentioned as reasons. Trip distance is also important. An A320 will ideally always sip fuel more efficiently at 36,000 feet than at 24,000 feet - yet BA flies Paris-London at ~24,000. Why? Because it is a short trip, and the fuel costs to fight gravity and climb the extra 10,000 feet (and immediately start down again) are higher than the additional fuel burn from staying low. BA's dispatchers and bean-counters have studied the curves and determined that 24,000 or thereabouts (depending on the day's weather) is the most cost-effective altitude, all factors considered.

[Escape Path]

Originally Posted by pattern_is_full

Trip distance is also important. An A320 will ideally always sip fuel more efficiently at 36,000 feet than at 24,000 feet - yet BA flies Paris-London at ~24,000. Why? Because it is a short trip, and the fuel costs to fight gravity and climb the extra 10,000 feet (and immediately start down again) are higher than the additional fuel burn from staying low. BA's dispatchers and bean-counters have studied the curves and determined that 24,000 or thereabouts (depending on the day's weather) is the most cost-effective altitude, all factors considered.

Great explanation PIF, found it quite helpful myself.

That last bit was what I was also thinking. In Colombia we get a lot of short trips, several of our routes are sectors of less than 35 minutes. We don't go higher than 22 or 24 thousand ft on those, and that usually even involves either taking off or landing at Bogota (elevation is 8360 ft). We even have one particularly flight with cruise at 18000 ft, flight time is 23 min.

The FMGC can give an optimum altitude higher than that, particularly if the aircraft is light, but the trip is so short we usually don't change more than +/-2000 ft (for a light/heavy aircraft, respectively) of our usual cruise altitude for that particular route, because it would be going up and straight back down again.

So there you go, another scenario in which is preferable to fly lower than usual.

[N1EPR]

Jet fuel burn

Jets normally fly at a fixed Mach. Since TAS decreases above FL240 when flying a fixed Mach number the FL240 you are using provides a much higher TAS as well compared with FL 360.

[FE Hoppy]

Here is the answer I wrote to this question about 5 years ago here on pprune:

why do we fly high in jets?

It's to get the maximum miles per gallon.

This is know as the Specific Air Range or SAR

the formula for SAR is TAS/GFC

GFC is Gross fuel consumption (gallons per hour)

GFC = Thrust*SFC

SFC is pound of fuel per pound force of thrust per hour.

We can derive the following formula for SAR if we realise that in steady flight Thrust = Drag.

SAR = (1/SFC)*(TAS/Drag)

Now we have 2 factors that we need to optimise to get the maximum SAR:

1/SFC is purely engine related.

TAS/Drag is purely airframe related.

To get the highest value of 1/SFC we need SFC to be as low as possible. This means we need the engine to be producing it's maximum thrust per pound of fuel and this occurs by design when the engine is operating around max continuous. Any lower trust and you are wasting fuel.

So 1/SFC is largest at @max cont

now lets look at TAS/DRAG

that's pretty easy really isn't it? If we think about the drag curve then this must be @1.32Vimd (max range speed)

so now we have 2 conflicting requirements

a) max cont thrust

and

b) 1.32 Vimd

so how can we match the two?

the last thing we have at our disposal is air density so we can climb to reduce the density of air entering the engine, and therefore the mass flow of air at a fixed RPM and intake size. This of course means we are reducing the thrust. We climb until the thrust is such that we equal the drag at +.32Vmd and we have found our optimum altitude.

As the aircraft weight reduces with fuel burn we could continue to climb to match thrust to the reducing drag (less lift required means less induced drag). This cruise climb is the theoretically optimum way to operate a jet but as the ATC environment generally prohibits cruise climbs we step climb instead.


in summary we fly high because it allows us to operate both the engines and the airframe in their respective optimum bands.

afterthought:

In my old days on maritime patrol we had a spanner in the works when it came to optimising fuel use. We were often required to fly around at low level.
Solution: shut down some engines to keep those running as close to optimum as possible.

Sometimes we were more interested in loitering rather than getting from A to B and for this the reference speed was a gnats chuff above Vmd rather than max range.

It's still valid ;-)

[Ledhead27]

Thanks for the help everyone so far, unfortunately the assignment descriptive was quite vague which has meant I've not really been able to specify my question properly.

As an additional question, would the application of using the ECON mode within the aircraft's FMC have any further effect time and/or fuel saving? I understand that ECON mode is related to Cost Index & is acquired by an algorithm, but but how would one describe the factors that influence ECON mode?

[misd-agin]

767-300 at .80 fuel flow increases 5%-8% if you're 4000' too low(boxed data so it's not perfect, ergo the % range).

ISA deviation from STD is 3% for/less (hotter/colder) for every 10C.

So to get better fuel efficiency 4000' below OPT ALT you'd have to have a temperature deviation of approx. 20+ from the lower altitude - ie FL 310 ISA -10C, FL350 ISA +10 C.
That's a very rare occurance.

Jet engines fuel consumption is like a wind up toy, they're only going to last X long no matter what you do.

If you wanted to get max endurance you'd take off and climb at slow speed to the mid 20's at holding speed. Endurance would be increased about 10% over an efficient cruise speed.

Range will be significantly reduced to perhaps 50% of what you'd achieve at an efficient cruise speed.

[Escape Path]

Originally Posted by Ledhead27

As an additional question, would the application of using the ECON mode within the aircraft's FMC have any further effect time and/or fuel saving? I understand that ECON mode is related to Cost Index & is acquired by an algorithm, but but how would one describe the factors that influence ECON mode?

Normal line flights in fairly modern aircraft are conducted always with cost index as the primary performance factor. It's a matter of balancing the time costs (flight hours being put on the aircraft and its components, crew time=$$$) and fuel costs, for a particular pair of airports.

The higher the CI, the higher the speed, the lesser the flight time= more fuel being burnt. CI 0 is long range cruise, CI 99 or 999 (depends on FMS software) is max cruise speed.

N1EPR: On those flights with lower cruise altitudes the aircraft doesn't reach our usual "changeover" Mach number, which is about 0.76 with our regular cost index. So we actually fly a higher IAS than at 360(obviously), but Mach is usually around 0.61-0.67 or thereabouts. TAS is lower too, around 400

[jmmoric]

Maybe invent an engine with an optimum altitude at FL310-330.... Those levels are usually quite empty.