161.23× +
2931.12× +
3568.32× =.
4620.64kg.m
passenger distibution fwd
152
C. BALANCE CHART DESIGN
b) Inaccuracy on the passengers’ weight
On the balance chart the passenger influence is taken into account as a delta index per passenger cabin section (CABIN OA, CABIN OB, …), this delta index is based on an average passenger weight for the corresponding cabin section. Now the real loading may have a total weight different from the one determined using average weight. This difference will generate an inaccuracy on the aircraft CG determination. This inaccuracy is named passenger weight inaccuracy.
. Passenger weight inaccuracy
The real passenger weight is Wpax real = Wpax average ±.Wpax Wpax average and .Wpax are determined in relation with the statistical survey used to determine the passenger weight.
Nb of pax
Pax average Pax weight
Weight
μ
Wpax average = μ and .Wpax= 3σ, the 3σ value is chosen to ensure that Wpax average covers 99,73 % of the population.
For each cabin section used on the balance chart we have
Wpax real OX = Wpax average OX ±.Wpax OX Wpax real OX = Wpax average x (number of pax in OX) ±.Wpax OX .Wpax OX is determined considering that each individual passenger weight inaccuracy is independent from the weight inaccuracy of the other passengers.
22 2
.W =
.W +
.W +
... +
.W
n pax pax1 pax2 paxn
The inaccuracy is the same for each individual passenger and equals 3σ.
.Wnpax =
n ×
(3σ
)2 =
3σ n
. Impact of pax weight inaccuracy on aircraft CG determination
Epassenger weight = ±.Wpassenger x (H-arm.Wpassenger - H-armlimit)
The passenger weight inaccuracy is determined for each cabin section that is represented on the
balance chart.
EcabinXX weight = ±.Wpassengers in cabin XX x (H-armcabin XX - H-armlimit)
The inaccuracy in weight is maximum when the cabin section is full of passengers so
Then the total inaccuracy is determined considering each cabin section inaccuracy independent from the other ones.
222
Epassenger weight fwd =.
E CabinOA fwd+E CabinOBfwd+E CabinOCfwd+... 222
Epassenger weight aft =+
E CabinOA aft+E CabinOBaft+E CabinOCaft+...
WEIGHT AND
BALANCE
WEIGHT AND
BALANCE
C. BALANCE CHART DESIGN
. Ex : A320 forward inaccuracy with the above example cabin layout Referring to 2.4 .Index for passenger boarding determine. HOA=10.44 m for 12 passengers HOB=16.39 m for 66 passengers HOC=25.53 m for 72 passengers Passenger average weight = 84 kg and corresponding standard deviation = 15 kg.
The forward limit CG of the A320 is between 15% (18.43 m) and 17% (18.51 m) for aircraft weight between minimum weight and 73 500 kg.
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