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Calculate the centre of gravity location for the take-off mass, given:

BEM: 2 635 lb
BEM moment: 204 793.5 in.lb
Mass on front seat: 90 lb
Arm on front seat: 78 in
Mass on aft seat: 186 lb
Arm on aft seat: 117 in
Block fuel: 850 lb
Taxi fuel: 85 lb
Fuel arm: 86 in

  • A
    80.66 inches aft of datum.
  • B
    81.25 inches aft of datum.
  • C
    81.44 inches aft of datum.
  • D
    81.54 inches aft of datum.
Formulas needed:
Center of gravity = Total moment / total mass
Moment = Mass x Arm

(1) Calculate total mass:
Total Mass = BEM + Front Seat + Aft Seat + Take-off Fuel
Total Mass = 2 635 lb + 90 lb + 186 lb + 765 lb = 3 676 lb
(2) Calculate the Moments:
  • BEM = 204 793.5 in.lb
  • Front Seat = 90 lb x 78 in = 7 020 in.lb
  • AFT Seat = 186 lb x 117 in = 21 762 in.lb
  • Take-off Fuel = 765 lb x 86 in = 65 790 in.lb

(3) Calculate Total Moment:
Total Moment = 204 793.5 + 7 020 + 21 762 + 65 790 = 299 365.5 lb.in

(4) Calculate CG position:
Centre of gravity = Total moment / total mass
Centre of gravity = 299 365.5 / 3676 = 81.44 in aft of datum

Note: Question asks for Centre of gravity at take-off - Taxi fuel will be consumed before take-off, therefore is must be subtracted from our calculations.

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