Some doubts from "Ace the Technical Pilot Interview".

[FE Hoppy]

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.



p.s. Jimmygill is wrong to say de-rate is done by maintenance staff. It can be done by the pilots through the FMC/MCDU before each flight on most modern FADEC engines.