Nevertheless, the figures obtained when calculating each moment individually are very large and consequently not easy to manipulate. In order to reduce the figures of moments to a more workable magnitude, we use the Index.
1.2. Index
a) Definition
The index is a means to both reduce figures manipulated by the user, and represent the weight and the location of each item.
Moment W ×
(H .
arm .
H )
item item
Index =
I =+
K =+
K
item item
CC It is a value with no unit. In the following chapter it may appear as IU : Index Unit. Two constants appear in this formula:
C: constant that allows having more workable figures. It has the same units as the moment (kg.m or lb.in).
K: constant that is set so that the final ZF and TO index value is never negative.
The value of these constants depends on the aircraft type and on the airline policy. But usually, Airbus applies the following constants to its aircraft:
A300B2 /A300B4  A300-600 /A310  A318  A319 /A320 /A321  A330 /A340  A340-500 /A340-600 
C  (kg.m)  2 000  1 000  500  1 000  2 500  5000 
(lb.in)  200 000  100 000  40 000  100 000  200 000  500 000 
K  50  40  50  50  100  100 

WEIGHT AND
BALANCE
WEIGHT AND
BALANCE
C. BALANCE CHART DESIGN

Note : two different index formulae can be used depending on the unit of item H-arm : length (m or in) or %MAC.
Weight × (H . arm . H)
Item 25
Index =+ K = Weight × (%MACitem . 25 ) ×C′+ K
C
Length of RC

with : C′=
100 ×C
b) .
Index : Index variation for any additional item loaded
For any item loaded on board the aircraft, the index variation due to this specific loading can be determine
MomentAdditional Item
=
.
IndexAdditional Item
C
c) ZF Index and TO Index determination
So to determine the aircraft Zero Fuel and TakeOff index we can use the following :
ZF Index = Index +.Index +.Index
emptyaircraft onboardpassenger loadedcargo
TO Index = Index +.Index +.Index +.Index
emptyaircraft onboardpassenger loadedcargo fuelonboard
Then it is possible to determine the moment corresponding to the resulting index and then the corresponding CG position.
In the following paragraph, the method to determine the .Index for any item loaded on the aircraft is detailed (passengers, cargo, fuel, additional catering…).

C. BALANCE CHART DESIGN

2. INDEX VARIATION CALCULATION (.
INDEX)

The index variation calculation is used to fill in the AHM560 document and to design the Balance Chart.
2.1. .
Index for one item
Moment Weight ×
　
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