Given:
Datum: at the nose
Front seats: 65 in
Rear seats: 105 in
Compartment: 145 in
Aft limit: 149 in aft
Actual CG: 160 in aft
You are flying a bridal pair, both seated in the rear seats. However, as indicated by the provided data, the actual center of gravity (CG) is outside the limits. With the right front seat being empty, you'd like to add some ballast to shift the actual CG to the aft limit. The total weight of your aircraft is 2570 lbs, so the required ballast amounts to…
Current Situation:
The AFT CG limit is 149 inches aft of the datum.
However, due to the current arrangement of passengers, the CG exceeds the AFT CG limits by 11 inches (making the current CG at 160 inches aft of the datum).
How may we bring the CG Forward by 11 inches to meet the CG aft limit without re-arranging the passengers? We will use an extra ballast (mass) forward of the aircraft (front seats) to bring the CG to the aft limit.
How much Extra Ballast?
CG is 11 in behind the aft limit. Therefore, the CG is 160 in aft of datum.
- Old Total moment = 2570 x 160 lb.in
To bring the CG forward to within limits, a ballast ("m") must be added to the front seat. The front seat is located at 65 in aft of datum.
- Ballast moment = m x 65 lb.in
The New Total Mass will be:
- New total mass = 2570 + Mass
This will result in a New Total Moment:
- New Total Moment = (2750 +Mass) x 149 lb.in
Now apply the formula:
- Old Total Moment + Moment of the ballast = New Total Moment
- 2570 x 160 + Mass x 65 = (2570 + Mass) x 149
- 411 200 + Mass x 65 = 382 930 + Mass x 149
- 411 200 – 382 930 = Mass x (149 – 65)
- 28 270 = Mass x 84
- Mass = 28 270 / 84 = 336.5 lbs
Alternatively, simply apply the following formula:
- New mass x New CG = (Old mass x Old CG) ± (Mass x arm)
- (2570 + Mass) x 149 = (2570 x 160) + (65 x Mass)
- 411 200 + 149 Mass = 382 930 + 65 Mass
- 84 Mass = 28 270
- Mass = 336.5 lbs
Your Notes (not visible to others)
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