Four Adults, Full Bags, and a Hot Ramp
A four-place, normally aspirated single-engine airplane is being loaded for a 2.5-hour cross-country leg. Basic empty weight is 1,680 lb at an empty-weight arm of 39.5 in; maximum gross weight is 2,550 lb. Station arms are: front seats 37.0 in, rear seats 73.0 in, baggage area 1 at 95.0 in (120 lb limit); fuel arm 48.0 in at 6.0 lb/gal, 56 gal usable. The CG range is 35.0 to 47.3 in. Aboard are a 200 lb pilot, a 180 lb front-seat passenger, rear passengers of 170 lb and 160 lb, 60 lb of bags, and 40 gal of fuel. Ramp temperature is 92 °F, field elevation 1,200 ft, and the runway is 3,100 ft long. The pilot says the airplane "flew fine last month with three people aboard."
1. Compute total weight and CG position and evaluate them against the airplane's limits. Show your work.
Read the worked answer
Compute moments (weight × arm) and divide total moment by total weight.
| Item | Weight (lb) | Arm (in) | Moment (lb·in) |
|---|---|---|---|
| Empty | 1,680 | 39.5 | 66,360 |
| Front seats | 380 | 37.0 | 14,060 |
| Rear seats | 330 | 73.0 | 24,090 |
| Baggage area 1 | 60 | 95.0 | 5,700 |
| Fuel (40 gal × 6.0) | 240 | 48.0 | 11,520 |
| Total | 2,690 | 45.25 | 121,730 |
CG = 121,730 ÷ 2,690 = 45.25 in, which is inside the 35.0–47.3 in envelope but only about 2 in forward of the aft limit.
Weight, however, is 140 lb over maximum gross. The airplane is not airworthy for this loading regardless of where the CG falls - weight and CG are two separate limits and being inside one does not excuse the other.
2. The flight is still scheduled. Propose at least two legal loading changes and explain the operational trade-offs of each.
Read the worked answer
For every option, re-verify both weight and CG - removing weight aft of the CG moves the CG forward, and vice versa.
Option A - burn off fuel. Reducing from 40 gal to 16 gal removes 144 lb, giving 2,546 lb and a CG near 45.1 in. Legal, but 16 gal at a realistic 9–10 gph is roughly 1.6 hours - less than the 2.5-hour leg plus reserve. This option is legal on paper and useless in practice.
Option B - offload the 160 lb rear passenger. Weight becomes 2,530 lb; moment drops by 160 × 73.0 = 11,680, giving CG ≈ 43.7 in. Legal, keeps full fuel, and moves the CG toward the middle of the envelope.
Option C - split the difference: offload 60 lb of bags (5,700 lb·in) and 14 gal of fuel (84 lb, 4,032 lb·in). Weight 2,546 lb, CG ≈ 45.2 in. Legal but leaves both range and baggage short.
Best practice: offload the heaviest item farthest aft first, because removing it corrects weight and improves CG margin simultaneously. Also note that at 92 °F and 1,200 ft field elevation, even a legal 2,530 lb departure will not produce book performance - re-check the takeoff chart for the new density altitude before accepting the load.
3. Even after the load is made legal, the CG may sit near the aft limit. Explain why that matters on this particular departure.
Read the worked answer
An aft CG reduces the horizontal tail's downward load, so the airplane balances with less nose-down moment. Consequences:
- Static and dynamic longitudinal stability are reduced - lighter elevator forces, less resistance to pitch disturbance, more susceptibility to over-controlling in turbulence.
- Stall and spin behavior degrades. The wing stalls at the same angle of attack, but recovery authority is reduced and the aft CG can make spin recovery difficult or impossible in extreme cases. This is the reason manufacturers publish an aft limit at all.
- Climb performance is not improved. Pilots often assume aft CG means better climb; it mainly reduces trim drag slightly.
Combine aft CG with maximum gross weight, high density altitude, and a 3,100-ft runway, and the real hazard is an accelerated stall on climb-out after a marginal liftoff: the pilot raises the nose to clear obstacles, the wing exceeds critical angle of attack at low altitude, and the aft CG shortens the margin for recovery. The correct response is to load toward mid-envelope, not to fly a legal-but-aft load into a high-DA departure.