Question regarding fuel consumption at higher altitude

[LikeABoss]

Firstly, I understand that fuel consumption becomes less at higher altitudes as air is thinner, which results in less interference allowing to fly a longer range.
But isn't thinner air also bringing down the engine performance?

Also, I get that below the optimum altitude, you would burn more fuel as a penalty, but above that, where air is even thinner, why exactly would you burn more fuel.

I think I am missing the main concept.
Explanation please?

[rudderrudderrat]

Hi LikeABoss,
but above that, where air is even thinner, why exactly would you burn more fuel.
Because you'll probably exceed Mach Crit.

See Bookworm's explanation: http://www.pprune.org/tech-log/453278-maximum-range-speed-jet.html of best IAS.

[Intruder]

There is less air drag for a given True Air Speed, so less thrust is required. Note that thrust (or fuel flow) to maintain a given INDICATED airspeed is relatively constant at any altitude.

[Old Smokey]

Consider this -

For a given speed profile such as Maximum Range Cruise (MRC), and for a given weight (mass), then for every level flown, there is an optimum speed. This will be a constant Equivalent Airspeed (EAS) up to the level where Mcrit becomes a factor (which it inevitably will). After Mcrit becomes a factor, the optimum speed will be a Mach number. This takes care of the optimum speed for each level, the next consideration is to find the Optimum Level. This Optimum Level will be that at which the engine/s are operating at an engine speed for Optimum Thrust Specific Fuel Consumption (TSFC).

Optimum Thrust Specific Fuel Consumption (TSFC) is typically in the vicinity of 90% N, at higher and lower engine speeds the engine is 'off optimum' and fuel expended per unit of thrust produced is greater. Typically, TSFC at engine speeds above optimum N is worse than for the same N variation below optimum speed.

Now, at low altitudes where the air is dense, to fly at the optimum aerodynamic speed, much lower engine speed is required (because of greater air density), thus, although we are doing the best possible FOR THAT ALTITUDE, we are doing less than the best possible.

The best possible occurs as the air becomes less dense (increasing altitude), and the engine speed must be increased to the optimum (about 90% N) to achieve the required thrust. This level, then, is the Optimum Level, any higher or lower will incur a greater fuel penalty.

If we fly higher into less dense air, the engine speed must be increased to above optimum TSFC speed to provide the requisite thrust. For each % N increase above optimum, the penalty is approximately double that for the same % N decrease if flying lower. Thus, if the Optimum Level is not available, it is better to take 1 level lower than 1 level higher.

There are other factors such as, colder air (which is associated with increasing level below the tropopause) requires less work to compress, thus enabling more efficient engine operation. A good bonus, but the effect is much less than the fact that the thinner air requires increasing engine speed than at a lower level, up to the point where the engine is at optimum TSFC speed to attain the required speed.:ok:

Somebody said - "Because you'll probably exceed Mach Crit." - I hope that you DO exceed Mcrit at higher levels, that's where Normal operation for Jet aircraft occur (Especially Maximum Range Cruise).

[Dariuszw]

Somebody said - "Because you'll probably exceed Mach Crit." - I hope that you DO exceed Mcrit at higher levels, that's where Normal operation for Jet aircraft occur (Especially Maximum Range Cruise).


Can you tell me one airline or commercial aircraft which flies above Mcrit as normal operation ?

As soon as you hit Mcrit shock wave will develop which will significantly increase drag. Are you telling me that max range will increase ?????:}

[rudderrudderrat]

Seasons Greetings Old Smokey,

My reference to Mcrit was that Mach No will have to be considered.
If flying higher at LRC Mach Number results in an IAS further away from best IAS (as Bookworm showed) - then there will be a penalty.

I didn't know that max engine efficiency is "typically in the vicinity of 90% N". I thought engine efficiency improved with higher temperature and pressure, so up to MAX Cruise power was more efficient.

I will do some homework.

Regards, RRR

[Old Smokey]

[B]Dariuszw,

You asked - Can you tell me one airline or commercial aircraft which flies above Mcrit as normal operation ?

All of them, as long as we're talking about Jet high altitude operations. At lower than normal levels, EAS will be the controlling speed.

rudderrudderrat,

Seasons Greetings to you too rudderrudderrat.

I hope that a thousand words is better than a picture, as I cannot post the requisite diagrams from this computer. There was considerable discussion on this topic 2 to 3 years ago, and you may find diagrams with a little digging. The word version goes like this -

As an example, if we are talking about Maximum Range Cruise (MRC), it is developed (for still air) by taking the point of tangency from the 0/0 origin to the Total Drag curve. At lower altitudes where only the Low Speed Drag Polars come into play (typically not used by jets excepting short sectors), for a given weight, this results in a constant EAS for all levels. This means a slowly increasing CAS with increasing Altitude. With increasing Level (typically about 30,000 feet for aircraft such as the A320/B737) the High Speed Drag Polars resulting from Wave Drag formed above Mcrit are added to the Low Speed Polars to ascertain the total drag. If the typical drag curve is envisaged, it appears first at the high speed end of the curve, above Vmo and of no concern. As altitude increases further, the higher end of the normal drag curve is 'lopped off' as the High Speed polar slides down the curve, and replaced by a more steeply rising curve.

The nature of the now-modified curve is that for approximately the first M0.04 or so after Mcrit, we have only gently increasing drag, with a steeper increase after that. When the tangent is taken for MRC, the point of tangency is still somewhat ABOVE Mcrit. MRC is about the lowest of the commonly used en-route speeds, and higher speeds (such as LRC or Cost Index above 0) will be further above Mcrit. Earlier crude fatter and unswept wings did not enjoy such an increase above Mcrit, but still had a point of tangency .02 to .03 above Mcrit.

LRC is out of fashion now, and there is indeed a penalty in flying at this speed, in fact the LRC speed is derived from an arbitary penalty of 1.0%, i.e. a penalty of 1% fuel burn increase for flying above MRC. An unusual figure - derived from a penalty.

With respect to your comment - "I thought engine efficiency improved with higher temperature and pressure, so up to MAX Cruise power was more efficient"., I think that we agree, Max Cruise Thrust is typically ABOUT 91 to 92% N, which is within the Optimum TSFC band. We have to be careful, as individual engine characteristics vary.

Best Regards,

Old Smokey

[latetonite]

V=A x (T exhaust-T inlet), i.e the more temp. difference you can create, (with a lower OAT and same TIT or EGT) the more thrust you can make. So optimum engine operating altitude should be in theory at the tropopause.
Then there are of course other factors, as described before.

[Stuck_in_an_ATR]

By the way - what will be the Mcrit value for a modern airliner? I know it depends on many things like airfoil shape, wing sweep, AoA, etc. I am looking for ballpark figure...

Thx

Stuck

[Old Smokey]

Hi ATR,

If you want a 'ballpark' figure for Mcrit (ballpark but a pretty good one), Mcrit is typically at or slightly below the Climbing Mach Number. For example, if the aircraft climbs at M0.74 and typically cruises at M0.78, you can put your money on Mcrit being very close to M0.74

Cruise performance depends upon the point of tangency from the 0/0 origin to the drag curve, thus most economical cruise speed is typically a little above Mcrit (about 0.04 to 0.05). Climb performance looks at Power (not thrust) Available Vs Power Required, and therefore looks at the delta between the two, thus, best climb is typically very close to Mcrit (or slightly above it).

Best Regards,

Old Smokey