Weight and Balance After a Late Load Change
You are captain of a twin-engine turboprop with a maximum takeoff weight of 12,500 lb and a maximum landing weight of 12,000 lb. Basic empty weight is 8,200 lb at an empty-weight arm of 180 inches. Fuel is 2,000 lb at an arm of 175 inches. You have eight passengers at 170 lb each in rows 2 through 5 (arm 195 inches), plus 300 lb of baggage in the aft compartment at arm 240 inches. At the gate, two passengers are added in row 5, and 100 lb of cargo is shifted from the forward hold (arm 150 inches) to the aft hold (arm 240 inches). The center of gravity envelope is 185 to 205 inches.
1. Compute the new takeoff weight and CG, and determine whether the aircraft is within limits.
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Original passenger weight: 8 × 170 = 1,360 lb at 195 in. Added passengers: 2 × 170 = 340 lb at 195 in. Total passengers: 1,700 lb at 195 in.
Moments: basic empty 8,200 × 180 = 1,476,000. Fuel 2,000 × 175 = 350,000. Passengers 1,700 × 195 = 331,500. Baggage 300 × 240 = 72,000. Forward hold originally held some cargo; the shift moves 100 lb from 150 to 240, a moment change of 100 × (240 − 150) = 9,000 lb-in aft. Assuming the 300 lb baggage figure already accounts for the hold contents, add 9,000 to the total moment.
Total weight: 8,200 + 2,000 + 1,700 + 300 = 12,200 lb. Total moment: 1,476,000 + 350,000 + 331,500 + 72,000 + 9,000 = 2,238,500 lb-in. CG = 2,238,500 / 12,200 = 183.5 in. That is below the forward limit of 185 in, so the aircraft is out of the envelope forward.
2. What corrective action would you take, and how does it affect landing weight?
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The CG is 1.5 inches forward of the limit. To move it aft, shift weight rearward: move baggage from the forward hold to the aft hold, or move passengers aft. Moving 100 lb from arm 150 to arm 240 gives a moment change of 9,000 lb-in, which raises the CG by 9,000 / 12,200 = 0.74 in, to 184.2 in - still short. Moving another 100 lb aft gives another 0.74 in, reaching about 184.9 in, still marginal. Moving 200 lb from the forward hold to the aft hold would add about 1.48 in, bringing the CG to roughly 185.0 in, just at the limit.
A cleaner fix is to move a passenger or two aft, or to offload forward cargo. Each 170 lb passenger moved from row 2 to row 5 changes the moment by 170 × (arm difference), which can be several hundred lb-in per row. Recompute after any change. Landing weight is takeoff weight minus trip fuel; if trip fuel is 400 lb, landing weight is 11,800 lb, within the 12,000 lb limit.
3. What operational risks does a forward CG create on this flight?
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A forward CG increases the elevator force needed to rotate and flare, lengthens the takeoff roll, and can reduce the ability to hold the nose up on landing. In a turboprop with a forward CG near the limit, rotation may require near-full aft elevator, and a go-around may be sluggish. Stall recovery is also affected because the aircraft may resist pitch-up.
The practical response is to correct the CG before departure rather than accept a marginal condition. Verify the correction with a fresh weight and balance calculation, and confirm the landing weight and CG are also within limits, since fuel burn moves the CG during flight.