The Aft-Loaded 172 and the Club Legend
Your club's Cessna 172S has a basic empty mass of 745 kg at an arm of 1.00 m aft of datum, a maximum take-off mass of 1,157 kg and a CG range of 0.89 m to 1.20 m aft of datum. Station arms are: front seats 0.94 m, rear seats 1.85 m, baggage area 2.41 m, fuel tanks 1.22 m. For a two-hour local flight from Ilorin you plan to board pilot 90 kg, front passenger 100 kg, rear passenger 85 kg, and 54 kg of baggage - the maximum the baggage area is approved for. You intend to fill the tanks with 144 L of usable fuel (SG 0.72). A club member tells you the aircraft 'always flies fine a little aft' and that the aft limit is a paperwork figure. The OAT is 34°C and the runway is 1,400 m of asphalt at 800 ft elevation. You have not yet prepared a load sheet.
1. Prepare the load sheet: calculate take-off mass, total moment and CG position, and state whether the loading is acceptable.
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Build the moment table (moment = mass × arm):
| Item | Mass (kg) | Arm (m) | Moment (kg·m) |
|---|---|---|---|
| Basic empty | 745.0 | 1.00 | 745.0 |
| Pilot | 90.0 | 0.94 | 84.6 |
| Front pax | 100.0 | 0.94 | 94.0 |
| Rear pax | 85.0 | 1.85 | 157.3 |
| Baggage | 54.0 | 2.41 | 130.1 |
| Fuel 144 L × 0.72 | 103.7 | 1.22 | 126.5 |
| Total | 1,177.7 | - | 1,337.5 |
CG = 1,337.5 ÷ 1,177.7 = 1.136 m aft of datum.
CG is inside the 0.89–1.20 m envelope, but only 0.064 m forward of the aft limit. Mass, however, is 20.7 kg above MTOW, so the loading is illegal regardless of CG. Note that removing all 54 kg of baggage would leave 1,123.7 kg, so the baggage is what is tipping the aircraft over - but fuel and passengers together still leave very little margin.
2. Propose the minimum practical change that makes the flight legal, and show that the CG stays in limits for both take-off and landing.
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Any reduction of 20.7 kg restores legality; the choice is about which change keeps CG sensible and is operationally realistic.
Option A - reduce fuel to 115 L (82.8 kg): mass 1,156.8 kg; moment 1,337.5 − (20.9 × 1.22) = 1,312.0; CG = 1.134 m. Fuel is only 29 L below full, so range is barely affected.
Option B - offload 21 kg of baggage (leaving 33 kg): mass 1,156.7 kg; moment 1,337.5 − (20.7 × 2.41) = 1,287.6; CG = 1.113 m. This buys more static margin but takes baggage away from a passenger.
Both are legal. Check the landing case: burning roughly 68 L (49 kg) from the 1.22 m tank shifts the CG forward by only about (49 × (1.22 − 1.134)) ÷ 1,108 ≈ 0.004 m, because the fuel arm is close to the CG. There is no forward-limit risk, so Option A is the cleanest: cut fuel to 115 L, keep the baggage, and re-run the sheet before boarding.
3. Explain what an aft CG near the limit actually does to handling, and why 'it always flies fine' is not an airworthiness argument.
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Moving the CG aft reduces the static margin between the CG and the aerodynamic centre. The tailplane carries less download, so stick forces lighten, the aircraft is easier to over-rotate on take-off, and longitudinal stability - the tendency to return to the trimmed speed after a gust - is weakened. In the stall the aircraft pitches less sharply, giving poorer stall warning, a flatter stall and a greater tendency to drop a wing and enter a spin, with a slower recovery. Flare and trim become more sensitive, and the effect of a rear-seat passenger shifting position is amplified.
'It always flies fine' is a subjective impression from benign conditions; it says nothing about the gust, the mis-trimmed approach or the go-around that exposes the reduced margin. The envelope limits are certificated values, and the aircraft is unairworthy for the flight the moment it exceeds them - the load sheet is the evidence, not the pilot's opinion.