The Two-Percent Overload
You are the ground instructor for a private pilot applicant who has just finished the weight-and-balance lesson. The club's Cessna 172S has a maximum ramp weight of 2,558 lb, a maximum takeoff weight of 2,550 lb, and at maximum gross weight a forward CG limit of 41.0 in and an aft limit of 47.3 in. The planned load: basic empty weight 1,650 lb at 40.0 in; 56 gal of fuel at 48.0 in (6 lb/gal); pilot and front-seat passenger 340 lb total at 37.0 in; rear-seat passengers 200 lb at 73.0 in; baggage 80 lb at 95.0 in. The student totals the weight, looks up, and says, "We're just barely over - the airplane will carry it."
1. Complete the weight-and-balance computation and state the exact status of the load against both the weight limits and the CG limits. Show the moment table.
Read the worked answer
Moment table
| Item | Weight (lb) | Arm (in) | Moment (lb-in) |
|---|---|---|---|
| Empty | 1,650 | 40.0 | 66,000 |
| Fuel (56 gal) | 336 | 48.0 | 16,128 |
| Front seats | 340 | 37.0 | 12,580 |
| Rear seats | 200 | 73.0 | 14,600 |
| Baggage | 80 | 95.0 | 7,600 |
| Total | 2,606 | 116,908 |
CG = 116,908 ÷ 2,606 = 44.86 in.
Weight: the airplane is over max takeoff weight by 2,606 − 2,550 = 56 lb, and over max ramp weight by 48 lb.
CG: 44.86 in lies between 41.0 and 47.3 in, so the CG is legal but sits well aft of center.
The teaching point: the two checks are independent. A load can be inside the envelope and still be illegal, and a load can be under gross and still be illegal. Both must pass before the airplane moves. Note also that taxi fuel does not rescue this load - you cannot plan to be over the ramp limit and burn your way legal.
2. Determine the minimum offload that makes the flight legal, then evaluate three specific choices - baggage, rear-seat passengers, and fuel - and report the resulting CG for each.
Read the worked answer
The minimum offload is 56 lb; anything less leaves the airplane over 2,550 lb.
- 56 lb of baggage: moment drops by 56 × 95.0 = 5,320 → 111,588; CG = 111,588 ÷ 2,550 = 43.76 in.
- 56 lb from the rear seat: moment drops by 56 × 73.0 = 4,088 → 112,820; CG = 112,820 ÷ 2,550 = 44.24 in.
- 56 lb of fuel (9.3 gal): moment drops by 56 × 48.0 = 2,688 → 114,220; CG = 114,220 ÷ 2,550 = 44.79 in.
All three are legal because all three land inside 41.0–47.3 in. The choice is therefore operational, not regulatory: baggage moves the CG furthest forward (most margin on the aft side, 2.76 in of forward margin remaining), fuel moves it least and costs you 9.3 gal of endurance, and the rear-seat option depends on whether the passengers can be split up. The right answer to give the student is: compute all three, then pick using the mission, not by guessing.
3. The student argues that 2 percent over gross is "within tolerance" and that performance charts have a safety margin built in. How do you correct the misconception, and what do you have the student do next?
Read the worked answer
There is no tolerance. 2,550 lb is a design limit, not a target, and the published performance does not exist above it - the takeoff chart simply stops at 2,550 lb. Correct the misconception with consequences the student can picture:
- Takeoff and climb performance degrade non-linearly with weight and with density altitude simultaneously, so the margin you think you have is the margin you lose first.
- Stall speed rises with the square root of weight, so the approach and landing speeds published in the POH no longer apply.
- The 3.8 g limit load is certificated at maximum gross weight; above it, every gust and every firm landing loads the structure beyond its design case.
- It is a regulatory violation as well as an engineering one.
Then have the student rework a second load deliberately built to sit near the forward CG limit at a legal weight, so they experience that the weight check and the CG check are separate gates and passing one proves nothing about the other. Close by having them write, in their own words, why the POH chart ends where it ends.