Tools › Aerodynamics › Stability and Control › Weight and Balance › Example

Four-seat single-engine airplane: loaded weight 3,027 lb and c.g. +43.54 in against the c.g. envelope (FAA-H-8083-1B sample loading problem)

ToolWeight and Balance
SourceFederal Aviation Administration (2016). Aircraft Weight and Balance Handbook. FAA-H-8083-1B, U.S. Department of Transportation, Oklahoma City. Chapter 5, Figures 5-1 to 5-8, pp. 5-2 to 5-6 (the loading problem); Figure 7-6, p. 7-6 (LEMAC and MAC of the similar airplane).
LevelUndergraduate

Problem

A four-seat airplane has a basic empty weight of 1,874 lb at +36.1 in. It carries 300 lb in the front seats (+37.0), 175 lb in the rear seats (+74.0), 88 gal of usable gasoline at 6 lb/gal (+46.6), 100 lb in baggage area A (+97.0) and 50 lb in area B (+116.0). The c.g. range is +40.9 to +46.0 in at 3,100 lb and +33.0 to +46.0 in at 2,250 lb or less with straight-line variation between; the maximum weight is 3,100 lb for take-off and 2,950 lb for landing. Find the loaded weight, moment and c.g., and whether the airplane is within limits for take-off and for landing.

Inputs to Enter

  • Stations (weight lb, arm in): airplane 1,874 at 36.1; front seats 300 at 37.0; rear seats 175 at 74.0; baggage A 100 at 97.0; baggage B 50 at 116.0
  • Fuel 88 gal at 6.0 lb/gal, arm 46.6 in; taxi fuel 0; trip fuel 180 lb (30 gal, the page's own illustrative figure)
  • Envelope corners (weight lb, c.g. in): 1,800 at 33.0; 2,250 at 33.0; 3,100 at 40.9; 3,100 at 46.0; 1,800 at 46.0; maximum take-off 3,100 lb, landing 2,950 lb
  • LEMAC 25.98 in, MAC 58.00 in (Figure 7-6); station ranges for the adverse-loading check: front seats 120 to 340 lb, rear seats 0 to 340 lb, baggage A 0 to 100 lb, B 0 to 60 lb, fuel 115 to 528 lb (the page's own illustrative figures)
Open the Weight and Balance tool (loaded with this example)

Answers

  • Moments: 67,651.4 + 11,100.0 + 12,950.0 + 24,604.8 + 9,700.0 + 5,800.0 = 131,806.2 lb-in (book 131,806.2); moment / 1,000 = 131.8 (book 131.8)
  • Loaded weight 3,027 lb (book 3,027); c.g. = 131,806.2 / 3,027 = +43.54 in (book +43.54); 30.3 % MAC
  • Take-off: 73 lb under the 3,100 lb maximum; limits at 3,027 lb are 40.22 to 46.00 in, so the c.g. is inside by 3.32 in forward and 2.46 in aft (book: the lines cross inside the envelope)
  • The take-off weight is 77 lb over the 2,950 lb landing weight (book: 77 lb, slightly less than 13 gal, to burn before landing)
  • With 180 lb burned: landing 2,847 lb at +43.35 in, inside the envelope; zero fuel 2,499 lb at +42.90 in; the c.g. stays inside throughout the burn
  • Adverse loadings: most forward 2,109 lb at +36.72 in, most aft 3,022 lb at +45.84 in, both inside; moving the 50 lb of baggage B to area A shifts the c.g. 50 ⋅ 19 / 3,027 = 0.314 in forward

Notes

The tool's default inputs are this airplane; press Submit. The loading, the envelope and the maximum weights are the handbook's; the trip fuel, the station weight ranges and the baggage shift are the page's own illustrative additions, and LEMAC and MAC are those of the similar airplane of the handbook's chapter 7. Checked by test_weight_and_balance.php (3,316 checks): the worked examples of FAA-H-8083-1B chapters 2, 3 and 5 to 10, of FAA-H-8083-25B chapter 10 and of AC 43.13-1B chapter 10 to the printed digits, 20 seeded loadings and 1,500 random points in three envelopes against an independent numpy script, and the page in both unit systems. Use the limits of the aircraft's own type certificate data sheet and flight manual for a real loading.