Outer fuel CG position is obtained
Corresponding to 2865 kg at
fuel density = 0.785 kg/l

Back to the previous example, the outer fuel quantity (one side) was 2865 kg, i.e. 3650 l at 0.785
kg/l. The corresponding H-arm is therefore 38.579 m for both outer tanks (same quantity in both
tanks).
Using corresponding tables for inner and trim tanks, we can deduce:
Inner: 25935 kg centered at 31.287 m
Trim: 2400 kg centered at 59.096 m.

Thanks to these individual fuel tank tables, we can now determine the total fuel CG position
equal to the weighted average of the individual tank CG positions.
Total fuel = 60000 kg
Outer (one side) = 2865 kg centered at 38.579 m
Inner (one side) = 25935 kg centered at 31.287 m
Trim = 2400 kg centered at 59.096 m

The total fuel CG position is: 2 ×
2865 ×
38.579 +
2 ×
25935 ×
31.287 +
2400 ×
59.096
TotalFuelCG ==
33.096 m
60000

C. BALANCE CHART DESIGN

c) Determination of the fuel vector after the refueling process
The above process needs to be repeated for total fuel quantities from zero to full.
In the Weight and Balance Manual the result is displayed in a graph with fuel quantity in liter on
vertical axis and H-ARM in meter on horizontal axis : the fuel vector.

It is important to note that this fuel vector depends on the fuel density. In fact, weight break
points of the automatic refueling sequence lead to different volumes according to the fuel density
and so, the shape of the fuel vector is impacted.

33.093 meters
(corresponding to 60000 kg fuel CG position)
Thanks to the fuel vector and for a given fuel density (here, 0.785 kg/l), for any fuel quantity, the corresponding fuel CG position can be easily found. As per previous example, for 60000 kg FOB (equivalent to 76433 liter at fuel density 0.785 kg/l) the corresponding fuel CG position is 33.093m (as computed above).
WEIGHT AND
BALANCE
WEIGHT AND
BALANCE
C. BALANCE CHART DESIGN

d) Determination of the fuel vector expressed in .
Index after the refueling process
Now, for Balance Chart production purpose, we need to have this fuel vector expressed in .Index as a function of the fuel weight. This is realized converting the volume values into weight values and converting H-arm values into .Index.
W ×
(H .
arm .
H)
Fuel fuel Ref
.Index =
,
fuel Weight
C A new fuel vector is obtained giving for any fuel weight the impact in term of .Index. As for the WBM fuel vector (expressed in H-arm as a function of the fuel volume), this new fuel vector depends also on the fuel density.
The below graph presents two fuel vectors for two different fuel densities: the standard one 0.785kg/l and a higher one 0.83 kg/l.
　
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