CI - some info you may find useful
Just to say this might help as to background. And try Airbus Flight Operations Support & Line Assistance - download Getting to Grips with CI, Issue 2 - May1998. It is written a bit in franglais so you have to read it once or twice. But this summary might help kick off a better start than Airbus's intro.
The cost index (CI) approach to flight optimisation is to balance time-related (CT) operating costs ($/hr; $/min) against fuel-related (CF) operating costs ($/100lb; $/kg).
In other words CI = CT /CF .
Rearrange the expressions: [($/hr) / ($/100lb)] = 100lb/hr
[($/min) / ($/kg)] = kg/min
These expressions in 100lb/hr or kg/min represent alternative views of the cost index. Note that 100lb/hr = 0.756kg/min and 1kg/min = 132.3lb/hr.
To remove time dependence from these foregoing expressions it is only necessary to divide cost index by speed:
[(100lb/hr)x(hr/nm)] = 100lb/nm
The right hand side of this last expression can be recognised as the inverse of the specific range (SR), that is the distance travelled in nautical miles per 100lb of fuel. Alternative units also widely used are nm/1000lb, nm/100kg and nm/1000kg.
It is therefore possible to write a specific cost function per nautical mile, T, as follows:
T = (1/SR) + (CI/V)
Generally speaking V is expressed in terms of Mach Number modified by windspeed component
V = (aM + VC) where a is the local speed of sound, M is Mach Number of course and VC is the usual wind component speed normally written with c as a subscript, negative for headwind, positive for tailwind.
Thus the specific cost function T can be written in coherent units as
T = (1/SR) + (CI/(aM + VC))
Two important conclusions can be drawn from this. That for a given sector distance the minimum cost is achieved by combining fuel related costs (1/SR) and time related costs (CI/(aM + VC)) in the correct proportion. And for a given cost index Mach Number variations can compensate for actual fluctuations in windspeed.
With time related costs the faster the aircraft can be flown, the better but the faster it flies the more the fuel burn increases. There must be a point at which each counterbalances the other and this is known as ECON speed. This is calculated within the Flight Management System Computer and generally speaking is given the range 0-999 or 0-99 depending on the style (vendor) chosen.
Remember that CI = CT /CF . If CI is small and tends to zero then relatively speaking time-related costs ($/hr; $/min) are small and fuel-related costs ($/100lb; $/kg) are large. Think of it as time being long with little fuel burnt. This equates to minimum fuel consumption and maximum range. Conversely if CI is large and tends to 999 (99) it is the time-related costs that loom relatively large and fuel-related costs that are relatively small. Think of it as time being short and a lot of fuel burnt which equates to minimum time at maximum speed. There is a restriction applied however by the Maximum Mach Operating Number inasmuch as MMAX = (MMO – 0.02) but the CI value is the tool through which trip fuel is traded against trip time.