Performance Penalty of a Forward CG on a Short Runway
A Brunei CPL candidate is planning a departure from a 1200 m runway at high ambient temperature. The aircraft (MTOM 5600 kg) is loaded to 5400 kg with a CG of 2.90 m aft of datum, which is 0.30 m forward of the envelope midpoint of 3.20 m. The AFM take-off distance at MTOM and mid-CG is 1050 m; the AFM gives a penalty of 4% per 0.10 m of forward CG offset, and a mass penalty of 2% per 100 kg above 5000 kg. The runway has a 200 m stopway and the operator requires a 15% margin over the AFM distance.
1. Calculate the adjusted take-off distance and determine whether the departure is acceptable.
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Mass penalty
- Mass above 5000 kg = 5400 − 5000 = 400 kg
- Penalty = 4 × 2% = 8%
CG penalty
- Forward offset = 3.20 − 2.90 = 0.30 m
- Penalty = 3 × 4% = 12%
Combined
- Total penalty = 8% + 12% = 20%
- Adjusted distance = 1050 × 1.20 = 1260 m
Compare with available
- Runway 1200 m + stopway 200 m = 1400 m available, but the operator requires a 15% margin over the AFM distance.
- Required = 1260 × 1.15 = 1449 m
- Available 1400 m < 1449 m → not acceptable as loaded.
Interpretation: The forward CG is the dominant penalty (12% vs 8% for mass). The departure fails the operator's margin even though the aircraft is below MTOM.
2. The pilot moves 150 kg of cargo from a forward hold at arm 2.00 m to an aft hold at arm 4.40 m. Recompute the CG offset and the adjusted distance.
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CG shift
- Moment change = 150 × (4.40 − 2.00) = 150 × 2.40 = 360 kg·m
- New CG = old CG + (moment change / mass) = 2.90 + (360 / 5400) = 2.90 + 0.0667 = 2.967 m
- Forward offset = 3.20 − 2.967 = 0.233 m
CG penalty
- 0.233 / 0.10 = 2.33 increments × 4% = 9.3%
Combined penalty
- Mass penalty unchanged at 8%
- Total = 8% + 9.3% = 17.3%
- Adjusted distance = 1050 × 1.173 = 1232 m
- Required with 15% margin = 1232 × 1.15 = 1417 m
- Available 1400 m → still not acceptable (marginally short by 17 m).
Interpretation: Moving cargo aft reduced the penalty from 20% to 17.3%, but not enough. The candidate must recognise that partial fixes may still leave the departure illegal, and must check the final figure against the required margin.
3. State two further actions that would make the departure legal and explain the performance logic behind each.
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Action 1 - Reduce mass
- Offloading 200 kg of payload reduces mass to 5200 kg. Mass penalty = 2 × 2% = 4%.
- Assuming the offloaded mass is near the CG, the CG offset stays about 0.233 m, penalty 9.3%, total 13.3%.
- Adjusted distance = 1050 × 1.133 = 1189 m; required = 1189 × 1.15 = 1367 m < 1400 m available → acceptable.
- Logic: lower mass reduces both the mass penalty and the absolute distance, and the required margin falls with it.
Action 2 - Move more cargo aft
- Moving a further 200 kg from 2.00 m to 4.40 m adds 480 kg·m, shifting CG by 480 / 5400 = 0.089 m to 3.056 m.
- Offset = 0.144 m → penalty 5.8%; total with 8% mass = 13.8%.
- Adjusted distance = 1050 × 1.138 = 1195 m; required = 1195 × 1.15 = 1374 m < 1400 m → acceptable.
- Logic: a forward CG increases the elevator downforce required to rotate, adding drag and extending the ground roll; moving the CG aft reduces that penalty.
Best practice: Combine a modest mass reduction with an aft cargo shift to gain margin on both terms rather than relying on one fix, and always recompute the final figure against the required margin before signing the load sheet.