getting to grips with the cost index(18)

Important : All these values are available whatever the model or engine type, but pilots should bear in mind that cost indices will not correspond to LRC speed if the aircraft is far from its optimum FL (as may be the case because of ATC constraints or if encountered winds are significant (see following section).

7.5 Wind effect on ECON speeds
(a) Cost index  purpose being a compromise between trip fuel and trip time, the resulting ECON Mach Number accounts for the actual wind component encountered in order to integrate ground speed.
This was already reviewed in Section 2 and is the result of the cost index definition itself and not of any particular FMS mechanization whatsoever.
The following figure (example for the A340) explains this point best :
A340-311 /CFM56(200 tonnes)

We notice that :
- headwinds command higher ECON speeds (less exposure time to higher winds)
- tailwinds command lower ECON speeds (let winds work).

Indeed, in the case of headwind, the fuel increment (due to higher speeds) is compensated for by the reduced trip time in terms of cost and vice versa (see next section).
Moreover, the following rule results from the preceding graph :
The ECON Mach wind correction being referred to herebelow is (for all Airbusmodels) of the order of :
+1/2 point of Mach per 50kt headwind-1/2 point of Mach per 50kt tailwind.
Important : in case of "managed" cruise, pilots should pay particular attention to the Mach Number in case of strong headwinds, especially with high inserted cost indices, since this could lead to significant cruise speeds.
Whatever the aircraft model and external conditions, the ECON Mach is always limited by MMO-0.02.
(b) To illustrate this point, let us compare the difference between a flight managed (with ECON Mach wind correction) and a flight selected (without Mach wind correction) in case of headwind :
A340-311 (6000nm)
Headwind : 50kt

TYPE OF CRUISE  TRIP TIME  TRIP FUEL 
Cost index -150 Mach 0.82  14 h 20 14 h 30  90 500 kg 89 500 kg 

Indeed, considering a time cost of 25US$/min and a fuel cost of 0.25US$/kg, the fuel cost increment (1000 x 0.167=167$) is compensated for by the time cost gain (10 x 25=250$).
Moreover, this Mach wind correction allows the airline to maintain its schedule in case of unexpected winds.

7.6 Summary
The following figure (specific example for the A310-304) summarizes the influence of all the preceding parameters on the ECON Mach computation as performed by the FMS.
Final climb, cruise and initial descent Mach for strategic mode

8. DESCENT PERFORMANCE VERSUS COST INDEX
8.1 Cost index - descent profile relationships
Let us now look at the influence of the cost index on the descent profiles depicted in the following figure. We can readily appreciate how the FMS computes the Top of Descent (TOD) as a function of the cost index.
　
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