Aft CG exceeded by baggage loading
The aircraft has an empty weight of 1,650 lb and an empty-weight CG of 82.0 in aft of datum. You load a pilot of 170 lb at 85.0 in, a front passenger of 160 lb at 85.0 in, a rear passenger of 150 lb at 118.0 in, 60 lb of baggage at 140.0 in, and 40 US gal of usable fuel at 95.0 in (6 lb/gal). MTOW is 2,550 lb, maximum aft CG is 86.0 in, and maximum forward CG is 78.0 in. The loading envelope is rectangular between those limits. The rear passenger cannot be moved, but the baggage can be relocated to a forward compartment at 50.0 in. Evaluate the takeoff condition before fuel burn, decide whether the aircraft is within limits, and determine what must change if it is not.
1. Calculate the takeoff weight and takeoff CG.
Read the worked answer
Fuel weighs 40 × 6 = 240 lb.
Weights: 1,650 + 170 + 160 + 150 + 60 + 240 = 2,430 lb, which is below MTOW 2,550 lb.
Moments about the datum:
- Empty: 1,650 × 82.0 = 135,300 in·lb
- Pilot: 170 × 85.0 = 14,450
- Front passenger: 160 × 85.0 = 13,600
- Rear passenger: 150 × 118.0 = 17,700
- Baggage: 60 × 140.0 = 8,400
- Fuel: 240 × 95.0 = 22,800
Total moment = 135,300 + 14,450 + 13,600 + 17,700 + 8,400 + 22,800 = 212,250 in·lb.
CG = 212,250 ÷ 2,430 = 87.3 in aft of datum.
2. Is the aircraft within the weight and CG envelope? If not, how much baggage must move to the forward compartment?
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Weight is satisfactory at 2,430 lb, but the CG is 87.3 in against an aft limit of 86.0 in. The aircraft is 1.3 in aft of the limit and therefore outside the envelope.
The moment reduction needed is 1.3 in × 2,430 lb ≈ 3,160–3,280 in·lb (using the unrounded 1.35 in gives about 3,280 in·lb).
Moving 1 lb of baggage from 140 in to 50 in changes the moment by 90 in·lb. Required baggage movement = 3,280 ÷ 90 ≈ 36.5 lb. Moving at least 37 lb forward brings the CG to the aft limit; moving all 60 lb gives a useful margin:
New moment = 212,250 − (60 × 90) = 206,850 in·lb. New CG = 206,850 ÷ 2,430 = 85.1 in, which is within the 78.0–86.0 in range.
3. After moving all the baggage forward, check the landing CG after burning 20 US gal. Does the CG remain within limits?
Read the worked answer
Burning 20 US gal removes 20 × 6 = 120 lb of fuel from the 95.0 in station.
New weight = 2,430 − 120 = 2,310 lb.
Moment removed = 120 × 95.0 = 11,400 in·lb.
New moment = 206,850 − 11,400 = 195,450 in·lb.
New CG = 195,450 ÷ 2,310 = 84.6 in.
The CG has moved forward, as expected because the fuel station is behind the current CG, but it remains above the 78.0 in forward limit. The landing condition is therefore within both weight and CG limits. The check matters because a forward-moving CG can become a landing problem even when the takeoff CG was legal.