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Refer to figure.
Calculate the CG position and moment for the BASIC EMPTY MASS by using the data given from the attached table:
  • A
    113.6 in aft of datum and the moment is 430 998 in.lb
  • B
    95.3 in aft of datum and the moment is 380 373 in.lb
  • C
    115.7 in aft of datum and the moment is 365 074 in.lb
  • D
    111.4 in aft of datum and the moment is 489 666 in.lb

Refer to figure.
The Moment can be calculated by the formula: Moment = Arm x Mass and the CG position can be found from the formula: CG = Moment / Mass.

By convention all the arms aft of datum are positive, so the corresponding momets are positive too. All the arms of the figure are positive, therefore the moments will be all positive and the BEM CG will be positive too, thus aft of datum.

The Zero Fuel Mass (ZFM) is the total mass of the aircraft not considering the usable fuel, i.e. is the DOM plus the Traffic Load. Thus, the ZFM moment is the total moment of the aircraft not considering the moment of usable fuel, i.e. is the DOM moment plus the Traffic Load moment. DOM is the BEM plus the Variable Load.

For this question, to calculate the CG position for the BASIC EMPTY MASS (BEM), you have to calculate firstly the Moment for the BEM.

The Moment for the BEM is: ZFM Moment - Pilot and Front Passenger Moment - Passengers (centre) Moment - Baggage Zone 1 Moment = (113.6 in x 3 794 lbs) - (85.6 in x 180 lbs) - (118.2 in x 420 lbs) - (21.8 in x 40 lbs) = 430 998in.lbs - 15 408 in.lbs - 49 664 in.lbs - 872 in.lbs = 365 074 in.lbs.

The CG position for the BASIC EMPTY MASS is: CG BEM = Moment for the BEM / BEM = 365 074 in.lbs / 3 154 lbs = 115.7 in aft of datum.

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