To explain in different words, the FMS evaluates fuel burn and flight time as a function of speed, and outputs a speed schedule that minimizes Cost = a * fuel burn + b * flight time, where a and b are constants and the ratio between them is defined by the cost index.

Boeing publishes a manual which you can download here:

Jet Transport Performance Methods

This gives the principles for performance calculations and also the reference wing area for Boeing types, from which you can calculate coeficient of lift. However in order to replicate the FMC I think you would also need the airframe specific drag polars and engine fuel flow data which are not given in detail.

If you look at page 32-20 figure 32-21 there is an example of how to determine best endurance (holding) speed for a B757 at FL350. We previously discussed the theory about speeds for range and endurance of "jet" aircraft which is usually taught to ATPL students. According to this theory, best endurance occurs at the speed for minimum drag. The theory implies constant TSFC, i.e the blue fuel flow lines in figure 32-21 would be horizontal . However in this Boeing example the fuel flow lines slope downwards (TSFC decreases with speed) such that the speed for best endurance is about 23 knots TAS (13 knots EAS) slower than minimum drag speed.

I think this is a significant difference. In this example best endurance speed may perhaps be closer to Vmp than Vmd. Should we be teaching student pilots theories about range and endurance of "jet" aircraft which are quite innacurate for modern turbofan transport types?

TSFC also increases with lower throttle settings.
TSFC is actually quite complex. And we have to keep in mind: TSFC is no physical value, it is simply fuel flow divided by thrust. Sometimes it can be misleading. For example: TurboProps have low TSFC, but the lower cruise speed might result over higher fuel burn for a given distance (depends heavily on some other variables, too).

But Flight Performance is always fun.
But Flight Performance requires good data, for aircraft drag and engine performance. Both are hard to obtain (but are available to some extent). With an Excel-Spreadsheet however you will probably run into problems.

I agree with what you wrote, but don't understand the last sentence. Please explain. (I'm just fond of Excel, as you may have noticed).

regards,
HN39

That Boeing document is solid gold. Thanks.

Flight performance means different weights, altitudes and some other parameters. Excel is limited to 2D-matrices.
For example: I want to calculate Rate of Climb for a given weight over the entire Mach/Speed-Altitude region.
First I need local speed of sound and air density for each altitude-Mach pair.
Then the lift coefficient.
Then using an analytical drag model the drag (if I have a look-up table or a hybrid with analytical polar but look-up zero lift drag it gets tricky).
Thrust is usually a look-up table, so again a big pain when using Excel.
The resulting calculations from this point on are rather simple.

One can use Excel with some Visual Basic scripts, but then a real programming language might quickly become more handy. I am using Matlab, a similar but free software is Scilab. Easy to program, easier than Excel VB.

Thanks CabinMaster, that explains it.

regards,
HN39