WEIGHT AND
BALANCE
ENGINEERING
Getting to Grips with Aircraft Weight and Balance
119

C. BALANCE CHART DESIGN

C. BALANCE CHART DESIGN
1. MOMENT AND INDEX DEFINITIONS
The purpose of the balance chart is to give an —easy way“ to determine the influence on aircraft
CG position of the loading of any item (passenger, cargo load, fuel, …).
This —easy way“ consists in introducing the notions of aircraft moment and item moment and
consequently in defining the index.

1.1. Moment
a) 1 Item moment :
Moment =
Weight ×
Distance from item CG position to Reference axis
W = item weight

Moment = Weight ×(H . armItem .H. armReference axis )
Note : in the whole process the moment notion has been simplified, normally a moment is determined by a Force multiplied by a distance. In this case the Force is simplified to the Mass of aircraft. Note : As common vocabulary uses Weight term instead of Mass, the wording is kept throughout the document.
b) (Item1 +Item2) moment
Moment = Moment + Moment
(Item +Item ) Item Item
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WEIGHT AND
BALANCE
WEIGHT AND
BALANCE
C. BALANCE CHART DESIGN

c) HOW TO DETERMINE THE CG position of the set (Item+Additional item) ?

MomentItem+Additional Item = MomentItem + MomentAdditional Item
(W + w’) x (H-armItem+Additional item -H-armReference axis) = W x (H-armItem -H-armReference axis) + w’ x (h-armAdditional item -H-armReference axis)
W × H -arm + w'×H . arm
Item Additional Item
H -arm =
Item + Additional item
W + w'
d) ZFCG and TOCG determination
So to determine the aircraft Zero Fuel and TakeOff CG positions we can use the following : Moment + Moment + Moment
emptyaircraft onboardpassenger loadedcargo
ZFCG =
WEIGHT
Zero Fuel
Moment +
Moment +
Moment +
Moment
emptyaircraft onboardpassenger loadedcargo fuelonboard
TOCG =

WEIGHT
Takeoff
To calculate each moment individually, a common reference axis has to be fixed. For all Airbus current aircraft the reference has been set for standard balance chart design at 25% of Mean Aerodynamic Chord as it is approximately in the middle of the certified envelopes of Airbus aircraft.

C. BALANCE CHART DESIGN

H-arm = H25
Moment =
W ×
(H .
arm .
H)
item item 25
Note : If an item is loaded forward to the reference the resulting moment will be a negative value
(<0).
If an item is loaded forward to the reference the resulting moment will be a positive value (>0).

Note 2 : For the A380 as the certified limits will be more aft than for the other Airbus fleet aircraft
the reference will be set at 35% of Mean Aerodynamic Chord.
　
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