Safety First The Airbus Safety Magazine Edition February 2010(5)

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2. TOCG calculation methods
2.1. Complete calculation
To determine the TOCG (expressed in percent of the Mean Aerody-namic Chord, %MAC) it is nec-essary to determine the Takeoff Weight (TOW) and the Takeoff In-dex (TOI) (fig. 1).
The TOW and TOI are calculated with the following formulae:

Figure 1

For TOW, airlines use a standard value for taxi fuel weight. This is an acceptable simplification. How-ever for TOI, the determination of the Taxi Fuel Index is complex because it depends both on the amount and the location of the fuel consumed during taxi. There-fore airlines often prefer to use the simplified calculation method de-scribed here below.
2.2. Simplified TOCG calculation
(As used during the 2008 A330 event.) The TOI is calculated with the following formula:

Determination of the TOCG Aircraft CG (%MAC) TOCG
Weight
TOW

 

8 Issue 9 | FEBRUARY 2010  Safety
TheTakeoff Fuel index is taken from the ramp fuel index table, which gives for each fuel weight the cor-responding total fuel index. The ta-ble assumes a pre-determined tank refueling sequence, (fig. 2).
Fuel Weight  Index 
…  … 
37500  - 6 
38000  0 
38500  + 5 
39000  + 10 
…  … 

The utilization of the ramp fuel index table to calculate the takeoff weight index is possible as long as the taxi fuel burn sequence is the reverse of the tank refueling se-quence, i.e. if the taxi fuel is con-sumed from the last refueled tank.
If the taxi fuel is not consumed from the last refueled tank, the distance between the CG after refueling and the aircraft’s CG at takeoff is:
.Negligible if the taxi fuel quantity
is low or if the tank used for taxi is near the last refueled tank.
.Large if the fuel used for taxi is
high and if the tank used for taxi is far from the last refueled tank.
On the A330 example mentioned in the introduction, the Ramp Fuel was 39 tons and the Taxi Fuel was
2.6 tons. In this configuration, the last refueled tank is the trim tank, and the taxi fuel is burnt from the inner tanks, as shown in fig.3.
The simplified TOCG calculation gives a TOCG at 22.2%MAC, that corresponds to a pitch trim set-ting of 6.4 degrees NOSE UP. The complete calculation taking into account the taxi fuel burn gives a TOCG at 26.7%MAC, that corre-sponds to 4.1 degree NOSE UP.
The aircraft CG moves backward during the taxi-out, whereas the simplified method considers that the CG moves forward.
The respective TOCG positions are shown in fig.4.
The cause of the rapid rate of rota-tion of the aircraft was the differ-ence in pitch trim settings.
3. Improved simplified TOCG calculation
To avoid any large CG discrepancy, Airbus recommends an improved
Figure 2
simplified method where the TOI
　
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