Aft CG and Marginal Grass-Runway Takeoff
An aeroplane has MTOW 1,150 kg, empty mass 700 kg, empty CG 0.78 m aft of datum, CG limits 0.75–1.05 m aft of datum. Arms: pilot and front passenger 0.85 m, rear passengers 1.75 m, baggage 2.20 m, fuel 1.00 m. Fuel density 0.72 kg/L. Load: pilot 85 kg, front passenger 80 kg, two rear passengers 75 kg each, baggage 20 kg, fuel 140 L. The planned departure runway is 620 m dry grass, elevation 1,400 ft, OAT 22°C, wind calm. POH sea-level ISA ground roll is 285 m; add 10% per 1,000 ft of density altitude and 15% for dry grass; takeoff over 50 ft is 1.6 times ground roll. The aircraft has no performance-enhancing modifications. The pilot plans a no-flap takeoff.
1. Calculate the total mass and CG. Is the loading within limits?
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Mass: empty 700 + pilot 85 + front 80 + rear 150 + baggage 20 + fuel (140 × 0.72 = 100.8) = 1,135.8 kg. Moment: 700×0.78 = 546.0; 165×0.85 = 140.25; 150×1.75 = 262.5; 20×2.20 = 44.0; 100.8×1.00 = 100.8; total = 1,093.55 kg·m. CG = 1,093.55/1,135.8 = 0.963 m aft of datum. The CG limit is 0.75–1.05 m, so it is within limits but only 0.087 m forward of the aft limit. Mass is 14.2 kg below MTOW. The loading is legal but has little aft-CG margin, which reduces static stability and can increase rotation tendency.
2. Calculate density altitude and the takeoff distance over 50 ft. Does the runway provide an acceptable margin?
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Pressure altitude 1,400 ft. ISA temperature = 15 − 2×1.4 = 12.2°C; OAT 22°C is ISA+9.8°C. Density altitude ≈ 1,400 + 120×9.8 = 2,576 ft. Ground-roll factor: 1 + 0.10×(2.576) = 1.258 for altitude, and 1.15 for dry grass, so 285×1.258×1.15 = 412 m. Takeoff over 50 ft = 1.6×412 = 659 m. The runway is 620 m, so the calculated 50-ft distance exceeds the available runway by about 39 m. With no wind and a near-aft CG, this is not an acceptable margin.
3. What operational changes would you make, and why does moving the CG forward matter?
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Reduce mass and move the CG forward: offload baggage or a rear passenger, reduce fuel to the planned trip plus reserve, and use a longer or sealed runway. Waiting for a cooler time of day lowers density altitude; a headwind helps but cannot be assumed. A near-aft CG reduces pitch stability and can make the aircraft rotate more easily, but it does not fix the runway margin. Recompute after changes; the takeoff should have a clear margin over the 50-ft distance, not just equal it. If no combination gives that margin, delay or change departure airport.