Twin-Piston Loading: Aft CG Exceedance
An operator is loading a twin-piston aircraft for a 2 h 30 min sector. The aircraft has a basic empty mass of 2,100 lb at an arm of 81.5 in, maximum takeoff mass 3,400 lb, and a CG envelope of 80.0 in to 86.0 in at all weights. The load sheet shows pilot 170 lb at 85 in, front passenger 160 lb at 85 in, two rear passengers 170 lb each at 118 in, baggage 60 lb at 155 in, and 80 US gal of fuel at 6 lb/US gal and an arm of 90 in. The crew has already calculated that the takeoff mass is below the maximum. The baggage compartment is full, but 60 lb of baggage can be left behind. Forward ballast can be added at an arm of 40 in. The dispatcher wants to know whether the aircraft is inside the CG envelope and, if not, the smallest practical change that restores compliance without exceeding maximum takeoff mass.
1. Calculate the total mass, total moment, and CG position for the proposed load.
Read the worked answer
Fuel mass = 80 × 6 = 480 lb.
| Item | Mass (lb) | Arm (in) | Moment (lb-in) |
|---|---|---|---|
| Basic empty | 2,100 | 81.5 | 171,150 |
| Pilot | 170 | 85 | 14,450 |
| Front passenger | 160 | 85 | 13,600 |
| Rear passengers | 340 | 118 | 40,120 |
| Baggage | 60 | 155 | 9,300 |
| Fuel | 480 | 90 | 43,200 |
| Total | 3,310 | - | 291,820 |
CG = 291,820 ÷ 3,310 = 88.16 in. The takeoff mass is 3,310 lb, below the 3,400 lb limit, but the CG is not yet compared with the envelope.
2. Is the aircraft within the CG envelope? If not, quantify the exceedance and identify the load that should be changed first.
Read the worked answer
The aft limit is 86.0 in, so the CG is 88.16 − 86.0 = 2.16 in aft of the limit. The excess moment is about 2.16 × 3,310 = 7,150 lb-in.
The aft load is dominated by the rear passengers at 118 in and baggage at 155 in. Removing the 60 lb baggage alone gives mass 3,250 lb and moment 282,520 lb-in, so CG = 86.93 in, still aft. Removing one 170 lb rear passenger alone gives mass 3,140 lb and moment 271,760 lb-in, so CG = 86.55 in, still aft. Removing both the baggage and one rear passenger gives mass 3,080 lb and moment 262,460 lb-in, so CG = 85.21 in, which is inside the envelope. That is the first effective no-ballast change.
3. Recommend a practical loading change using forward ballast rather than offloading a passenger, and show that maximum takeoff mass is respected.
Read the worked answer
First offload the 60 lb baggage, giving mass 3,250 lb and moment 282,520 lb-in, CG 86.93 in. Add W lb of ballast at 40 in and solve for CG = 86.0 in:
(282,520 + 40W) ÷ (3,250 + W) = 86.0 282,520 + 40W = 279,500 + 86W 3,020 = 46W W = 65.7 lb
Use 70 lb of secured forward ballast. New mass = 3,320 lb; new moment = 282,520 + 2,800 = 285,320 lb-in; CG = 285,320 ÷ 3,320 = 85.94 in. This is inside the envelope, and 3,320 lb is below the 3,400 lb maximum takeoff mass. The load sheet and CG must be recomputed after ballast is secured.