Aft CG After Last-Minute Cargo Loading
A twin-jet is being loaded for a 2-hour flight. Basic empty weight is 11,000 kg at arm 17.5 m. Crew 200 kg at 5.0 m; front passengers 500 kg at 8.0 m; rear passengers 800 kg at 23.0 m; forward cargo 300 kg at 10.0 m; aft cargo 900 kg at 25.0 m; fuel 2,500 kg at 19.0 m. Maximum zero-fuel weight is 14,000 kg; MTOW is 16,500 kg; the CG limits are 16.50 m to 17.60 m from the datum. The load sheet shows the aircraft within weight limits, and the dispatcher has signed it off. The crew notices that the aft cargo compartment is nearly full and that the takeoff CG is close to the aft limit. No ballast is available. The runway is limiting for takeoff weight.
1. Calculate the zero-fuel CG and the takeoff CG. State whether the aircraft is within weight and balance limits and identify the limiting condition.
Read the worked answer
ZFW = 11,000 + 200 + 500 + 800 + 300 + 900 = 13,700 kg; below 14,000 kg. ZFW moment = 11,000×17.5 + 200×5 + 500×8 + 800×23 + 300×10 + 900×25 = 192,500 + 1,000 + 4,000 + 18,400 + 3,000 + 22,500 = 241,400 kg·m. ZFW CG = 241,400/13,700 = 17.62 m, which is 0.02 m aft of the 17.60 m limit. Takeoff weight = 13,700 + 2,500 = 16,200 kg; below 16,500 kg. Takeoff moment = 241,400 + 2,500×19.0 = 288,900 kg·m. Takeoff CG = 288,900/16,200 = 17.83 m, which is 0.23 m aft of the limit. The aircraft is within weight but out of balance; the takeoff CG is the more limiting condition.
2. How much cargo must be moved from the aft compartment to the forward compartment to bring the takeoff CG to 17.55 m? Verify the resulting ZFW CG and the landing CG after burning 1,700 kg of fuel.
Read the worked answer
Moving x kg from arm 25.0 m to arm 10.0 m changes the moment by x(10.0 − 25.0) = −15x kg·m. The current takeoff moment is 288,900 kg·m and weight is 16,200 kg. Target moment = 17.55 × 16,200 = 284,310 kg·m. Required change = 288,900 − 284,310 = 4,590 kg·m, so x = 4,590/15 = 306 kg. Move about 310 kg. New ZFW moment = 241,400 − 15×310 = 236,750 kg·m; ZFW CG = 236,750/13,700 = 17.28 m, within limits. New takeoff moment = 288,900 − 4,650 = 284,250 kg·m; takeoff CG = 284,250/16,200 = 17.55 m. After burning 1,700 kg at 19.0 m, landing weight = 14,500 kg and moment = 284,250 − 1,700×19.0 = 251,950 kg·m; landing CG = 17.38 m, within limits. Fuel burn moves the CG forward because the fuel arm is aft of the CG.