getting to grips with the cost index(14)

For high TOW (above 230t) it is not worth climbing direct to max flight levels (e.g. FL 350 or 370), especially in hot conditions due to or because of :
-increased time of climb (above OPT FL)
-higher fuel consumption (above OPT FL)
-lower TAS.

If we consider still air or constant wind conditions, whatever the level, fuel consumption increases approximately as shown in Table 10.
Table 10. A340-311/CFM56-5C2

FLIGHT LEVEL  FUEL INCREMENT 
OPT + 2000ft  + 1.5 % 
OPT FL  -
OPT - 2000ft  + 1.5 % 
OPT - 4000ft  + 3 % 

(b) Cost factor in the choice of optimum altitude
Moreover, at the beginning of the flight it is also more interesting to stay at lower flight levels to take profit of better true airspeeds as indicated in Figure 18.

This can amount to some 10 to 15kt (or approximately 2 minutes per hour) depending on Climb Mach Number and Climb CAS. This assumes that there is no FL competition or no subsequent risk of being restricted to the first assigned flight level.
Practically, the following can be said to summarize :
.  
There is no gain in climbing above OPT FL +2000 ft, either in terms of fuel consumption or time, except in case of subsequent ATC flight level constraints.

.  
As already shown in Table 9, one should avoid staying below OPT FL -3000 ft but rather choose OPT FL +1000 ft, especially in case of heavy traffic.

.  
The best strategy is to perform :

(a)
a 4000 ft step climb when reaching OPT FL -4000 ft at low FL (290, 310, 330), which will help make TAS and mileage, taking about 4 hours to save about 8 to 10 minutes flight time in the process.

(b)
a 4000 ft step climb when reaching OPT FL -3000 ft as graphically shown in Figure 18, to rejoin OPT FL +1000 ft for a higher FL at the end of the flight.

To give a practical example of the impact of step climbing, we compare below the two flight profiles depicted in Figure 20 with time/fuel calculations shown in Tables 11 and 12.

Table 11. Close to optimal FL profile
TOW (t)  Time at FL 310  Time gain at FL 310 (min)  Fuel increment at FL 310 (kg) 
230  1 h 30  - 4  + 300 
240  2 h 45  - 7  + 500 
250  4 h 00  - 10  + 700 

Table 12. Maximum FL profile

TOW (t)  Time at FL 310  Time gain at FL 310 (min)  Fuel increment at FL 310 (kg) 
230  3 h 00  - 6  + 800 
240  5 h 30  - 11  + 1400 
250  8 h 00  - 18  + 2000 

.  
Saving 7 minutes but spending 500kg to stay 2 h 45 at FL 310 after taking off at 240t results in :

–  
saving 7 x 20 $/min (average CT) = 140$

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