Loading decision at the aft centre-of-gravity limit
You are flying a Cessna 172 from Kaduna to Abuja with a colleague. At the aircraft you find that two other people also need the lift; both are about 180 lb and there is no room up front, so they climb into the rear seat. Baggage is 100 lb in the baggage area. You plan to take 20 US gal of fuel. Loading data: empty weight 1,400 lb at 39.6 in aft of datum; front seats arm 37.0 in; rear seats arm 73.0 in; baggage area arm 95.0 in; fuel arm 48.0 in. The envelope runs from 35.0 in to 47.3 in aft of datum, and MTOW is 2,300 lb. Your own weight is 180 lb and the flight is 1 h 20 min.
1. Compute the take-off weight and centre of gravity and state whether the loading is inside both limits.
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| Item | Weight (lb) | Arm (in) | Moment (lb-in) |
|---|---|---|---|
| Empty | 1,400 | 39.6 | 55,440 |
| Pilot | 180 | 37.0 | 6,660 |
| Rear passengers | 360 | 73.0 | 26,280 |
| Baggage | 100 | 95.0 | 9,500 |
| Fuel (20 US gal) | 120 | 48.0 | 5,760 |
| Total | 2,160 | 103,640 |
CG = 103,640 ÷ 2,160 = 47.98 in aft of datum.
- Weight: 2,160 lb, which is 140 lb below MTOW. Within limits.
- CG: 47.98 in against an aft limit of 47.3 in. Out of limits by 0.68 in.
The trap is that the aircraft is comfortably light while being out of balance. Weight and balance are two separate checks, and passing one says nothing about the other.
2. If the aircraft were flown as loaded, what would you notice at rotation and in the climb, and what is the aerodynamic reason?
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At rotation: the elevator would feel unusually light and the aircraft would tend to over-rotate and keep rotating unless checked. With the CG close to or behind the aft limit, the tail-down moment needed to hold a given pitch is small, and the pilot's stick force per unit of pitch change (stick-fixed and stick-free static margin) collapses.
In the climb and cruise: pitch would be sensitive and the aircraft would readily hold a nose-high attitude; the trim would sit further forward than expected for the speed. Longitudinal static stability is reduced because the CG has moved aft towards the neutral point, so a disturbance in pitch produces a weaker restoring moment. Dynamic stability in the short period also deteriorates.
Airspeed note: an aft CG slightly reduces the download the tail must produce, so the aircraft may be marginally faster or need less trim drag, which is exactly why the change is easy to miss.
Uncommanded pitch: in turbulence or on a go-around with power applied, the nose-up pitching moment from the thrust line and flaps has less stability to work against, and the aircraft can pitch up briskly.
3. What is the smallest practical change that brings the loading inside the envelope, and why does the aft CG matter so much if the aircraft stalls or spins?
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Finding the minimum change. Removing baggage from the 95 in arm reduces both weight and moment. Solve for x lb removed:
(103,640 − 95x) ÷ (2,160 − x) ≤ 47.3
103,640 − 95x ≤ 102,168 − 47.3x → 1,472 ≤ 47.7x → x ≥ 30.9 lb.
So removing about 35 lb of baggage gives 2,125 lb and a CG of ≈ 47.21 in - inside the envelope, but only 0.1 in from the aft limit. A practical answer moves more than the bare minimum, for example relocating 50–60 lb of baggage forward into the rear cabin, keeping the arm used for calculation honest.
Why the aft CG matters in a stall or spin. Aft CG reduces the nose-down pitching moment available to break the stall and lowers the stick forces needed to hold a high angle of attack. The result is a higher angle of attack at the stall, a greater tendency to drop a wing, and a flatter, faster-rotating spin in which the elevator may be unable to force the nose down for recovery. Aft CG is a stability and recovery problem, not merely a handling quirk.