Mass and Balance Effect on Climb and Navigation Performance
A light twin is planned for a 420 NM sector. The basic empty mass is 1,680 kg with a moment of 2,520 kg·m. Pilot and passenger together are 160 kg at a station 1.2 m forward of the datum. Baggage is 40 kg at 2.8 m aft of the datum. Fuel is 320 kg in tanks whose centroid is 0.6 m aft of the datum. The maximum take-off mass is 2,300 kg and the forward CG limit is 0.30 m aft of the datum. Forecast conditions give a climb gradient of 4.5% at the planned mass, but the aircraft's single-engine climb gradient at maximum take-off mass in the same conditions is 1.9%. The sector has a 2,400 ft minimum obstacle clearance altitude near the departure end and the terrain rises to 3,100 ft within 6 NM.
1. Compute the take-off mass and CG position and check them against the limits.
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Sum the masses: 1,680 + 160 + 40 + 320 = 2,200 kg. This is below the 2,300 kg maximum, with 100 kg margin.
Sum the moments about the datum. Basic empty: 2,520 kg·m. Pilot and passenger: 160 kg at −1.2 m gives −192 kg·m. Baggage: 40 kg at +2.8 m gives +112 kg·m. Fuel: 320 kg at +0.6 m gives +192 kg·m. Total moment = 2,520 − 192 + 112 + 192 = 2,632 kg·m.
CG = 2,632 ÷ 2,200 = 1.196 m aft of the datum.
That is well aft of the forward limit of 0.30 m. The forward limit is not the problem; the pilot must check the aft limit, which is not given here. A CG of about 1.2 m aft of datum is far aft for a light twin and is likely to be beyond the aft limit. The loading as described is probably invalid and must be redistributed, for example by moving baggage forward or reducing aft baggage.
2. Assess the climb performance against the terrain and explain how mass affects it.
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The all-engine climb gradient of 4.5% at 2,200 kg is the normal climb case. Over 6 NM, which is 36,480 ft, a 4.5% gradient gives a height gain of about 1,641 ft. If the aircraft lifts off at the departure airfield elevation and the terrain rises to 3,100 ft within 6 NM, the aircraft must gain enough height to clear it. The margin depends on the airfield elevation, which is not stated, so the pilot must verify it.
The single-engine case is the critical one. At maximum take-off mass the gradient is 1.9%, giving about 693 ft over 6 NM. That is unlikely to clear terrain rising to 3,100 ft unless the airfield is high enough. The aircraft is 100 kg below maximum mass, so the single-engine gradient will be slightly better than 1.9%, perhaps 2.0%, but the improvement is small.
Mass affects climb gradient roughly in proportion to the excess thrust divided by weight, so a 10% mass increase reduces the gradient by more than 10%. The pilot should compute the single-engine net gradient at the actual mass, apply the net take-off flight path requirements, and consider a reduced mass or a different departure procedure.
3. Explain how the aft CG would affect the navigation of the sector.
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An aft CG reduces longitudinal static stability and can reduce elevator effectiveness. In cruise the aircraft may require less nose-up trim, which slightly reduces trim drag, but the handling qualities deteriorate and the stall recovery characteristics worsen.
For navigation, the main effects are on fuel and endurance. A more aft CG may give a small reduction in cruise drag and therefore a slightly better specific range, but the difference is small and not a reason to accept an out-of-limit loading. The greater risk is that the pilot must fly with continuous attention to pitch trim, which increases workload and makes precise heading and altitude keeping harder.
If the CG is beyond the aft limit, the aircraft is not airworthy for the flight. The pilot should redistribute the load, recompute mass and CG, and only then compute fuel, ETA and climb performance for the sector. The navigation plan is secondary to restoring a legal CG.