Commuter loading: weight, CG, and runway limit
You are preparing a twin-turboprop commuter for departure. Basic empty weight is 10,200 lb at arm 295.0 in. Two crew members weigh 190 lb each at arm 150 in. Nineteen passengers average 190 lb each at arm 330 in. Cargo is 1,000 lb at arm 420 in. Fuel is 3,000 lb at arm 300 in. Maximum takeoff weight is 16,950 lb; maximum zero-fuel weight is 15,200 lb; the CG envelope is 293.0 to 315.0 in aft of datum. The runway is 5,600 ft, dry, OAT 25 °C, pressure altitude 2,000 ft; the AFM chart for these conditions and 16,950 lb gives a takeoff distance of 5,450 ft. No wind. The next available fuel stop is 35 minutes away; the passengers are already boarded.
1. Compute zero-fuel weight, takeoff weight, and CG. Is the airplane legal as loaded?
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Zero-fuel weight is 10,200 + 380 + 3,610 + 1,000 = 15,190 lb, which is 10 lb under the 15,200-lb maximum zero-fuel weight. Takeoff weight is 15,190 + 3,000 = 18,190 lb, which is 1,240 lb over the 16,950-lb maximum takeoff weight. The moment is (10,200 × 295) + (380 × 150) + (3,610 × 330) + (1,000 × 420) + (3,000 × 300) = 3,009,000 + 57,000 + 1,191,300 + 420,000 + 900,000 = 5,577,300 lb-in. CG is 5,577,300 ÷ 18,190 = 306.6 in, which is inside 293.0–315.0 in. So the CG is acceptable but the weight is not. The airplane is illegal as loaded. The runway is not the immediate problem at 16,950 lb because 5,450 ft is less than 5,600 ft, but the weight must come down first.
2. Find a legal loading, and state the effect on CG.
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Offload 1,240 lb of fuel, leaving 1,760 lb. Takeoff weight becomes 16,950 lb. The new moment is 5,577,300 − (1,240 × 300) = 5,205,300 lb-in, so CG is 5,205,300 ÷ 16,950 = 307.1 in, still inside the envelope. Zero-fuel weight remains 15,190 lb, and its CG is 4,677,300 ÷ 15,190 = 307.9 in, also inside. Offloading fuel at arm 300, which is slightly aft of the original CG, shifts the CG forward? No-removing weight aft of the CG moves the CG forward only if the removed arm is aft of the CG; here 300 in is forward of 306.6 in, so removing it moves the CG aft, which is why CG increases slightly. The loading is legal on both weight and CG, and the takeoff chart at 16,950 lb still gives 5,450 ft, within the 5,600-ft runway. If fuel offload is undesirable, cargo at arm 420 could be removed, but 1,000 lb of cargo would still leave 240 lb over weight and would shift the CG forward significantly.
3. What would you check before accepting the new loading?
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I would verify that the reduced fuel still meets the flight plus reserve requirement, because 1,760 lb may not be enough for the planned trip and alternate. I would recheck the takeoff distance at the actual weight and temperature, and confirm the landing weight at destination is within limits. I would also check the zero-fuel CG and the takeoff CG separately, since fuel burn changes the CG. Finally, I would confirm with the captain and dispatcher that the fuel stop is acceptable and that no passenger baggage must be relocated. The arithmetic is only the first step; the operational question is whether the reduced fuel is sufficient and whether the new CG remains in range throughout the flight.