Cessna 172 loading with an unrevised W&B schedule
You are loading a Cessna 172N for a Saturday trip from Ardmore to Taupo with three friends. Basic empty weight is 1,400 lb at 39.5 in; MTOW is 2,300 lb; the normal-category CG envelope is 35.0 to 47.3 in. Arms: front seats 37.0 in, rear seats 73.0 in, baggage area 95.0 in, fuel 48.0 in. Usable fuel is 40 US gal at 6.0 lb/gal. Load: pilot 200 lb, front passenger 200 lb, two rear passengers 190 lb and 180 lb, baggage 100 lb, and you plan to fill the tanks. The aircraft has recently had a new avionics stack fitted, but the W&B schedule has not been revised; the engineer says the change is 'about 15 lb at 60 in'. The density altitude at Taupo is forecast to be 5,500 ft and the runway is 1,200 m. One passenger asks whether you can also take a 40 lb cooler in the baggage compartment.
1. Compute total weight and CG with full fuel and determine whether the loading is legal.
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Moments (lb·in):
- BEW: 1,400 × 39.5 = 55,300
- Front seats: 400 × 37.0 = 14,800
- Rear seats: 370 × 73.0 = 27,010
- Baggage: 100 × 95.0 = 9,500
- Fuel: 240 × 48.0 = 11,520
Total weight = 2,510 lb; total moment = 118,130 lb·in. CG = 118,130 / 2,510 = 47.06 in.
MTOW is 2,300 lb, so the aircraft is 210 lb over. The CG at 47.06 in is inside the 47.3 in aft limit, but only by 0.24 in. The loading is illegal on weight and operationally unacceptable on CG: there is no margin for a different passenger or for fuel burn, which moves the CG further aft.
2. Propose a realistic offload that brings the aircraft within both weight and CG limits, and check the 40 lb cooler.
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Offload the 180 lb rear passenger and 30 lb of baggage: 210 lb removed.
Weight removed = 180 + 30 = 210 lb, so weight = 2,510 − 210 = 2,300 lb (at MTOW). Moment removed = 180 × 73 + 30 × 95 = 13,140 + 2,850 = 15,990 lb·in. New moment = 118,130 − 15,990 = 102,140 lb·in. New CG = 102,140 / 2,300 = 44.41 in - inside 35.0–47.3 in with about 2.9 in of aft margin.
Cooler: adding 40 lb at 95 in adds 3,800 lb·in. Weight becomes 2,340 lb and CG becomes 105,940 / 2,340 = 45.27 in. The CG is still legal, but the aircraft is 40 lb over MTOW, so the cooler cannot go.
3. Explain the effect of the unrevised avionics change and of the aft CG on handling and performance.
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Avionics change: 15 lb at 60 in adds 900 lb·in. On the offloaded load: weight = 2,300 + 15 = 2,315 lb; moment = 102,140 + 900 = 103,040 lb·in; CG = 44.51 in. The CG shift is negligible, but the aircraft is now 15 lb over MTOW even after the offload. The W&B schedule must be amended and the loading rechecked; 'about 15 lb' is not a signed revision.
Aft CG handling: at 47.06 in the static margin is small. Expect lighter pitch forces, a greater tendency to over-rotate, a more abrupt stall with a higher risk of wing drop, and slower spin recovery. Cruise speed may be slightly higher because tail downforce is reduced, but takeoff and climb performance still suffer from the 210 lb overload: V_S rises by √(2,510/2,300) = 1.044, about 4.5%, and climb gradient falls roughly in proportion to the excess weight.