Weight & balance / CG
Centre of gravity (CG): balance point of loaded aircraft: weight-weighted average of load positions.
CG = Σ(weightᵢ · armᵢ) / Σ weightᵢ
Terms:
- Datum: reference point for all measurements. Usually placed so all useful loads sit aft, arms positive.
- Arm: distance from datum. Item ahead of datum (e.g. oil reservoir): negative arm and moment (TP 1102).
- Moment = weight × arm: that load's turning effect about datum.
Inputs:
- Include every loaded station: empty aircraft, front and rear seats, baggage, fuel.
- Empty weight, empty CG, arms: from aircraft's own Weight and Balance Report, calculated at factory. Empty weight in pounds, empty CG in inches from datum.
- Per flight: add each passenger's and item's weight and location (TP 1102).
- Heavy item pulls CG toward its arm far more than light one. Plain average of arms is wrong.
Fuel and oil: filled by volume, moment needs weight. Convert first.
Avgas weight (colder fuel is denser, so weight per gallon rises as it cools; TC AIM RAC 3.4.8, Table 3.4):
| Avgas | -40°C | -20°C | 0°C | 15°C | 30°C |
|---|---|---|---|---|---|
| lb/US gal | 6.41 | 6.26 | 6.12 | 6.01 | 5.90 |
| lb/UK gal | 7.68 | 7.50 | 7.33 | 7.20 | 7.07 |
| lb/L | 1.69 | 1.65 | 1.62 | 1.59 | 1.56 |
- Example at 15°C: 40 US gal ≈ 240 lb.
| Fluid | Density | Example | Source |
|---|---|---|---|
| Avgas, metric | 0.72 kg/L | 250 L = 180 kg | TP 1102 metric example |
| Engine oil | 7.5 lb/US gal | n/a | TP 1102 worked example |
| Piston oil at 0°C | 7.46 lb/US gal | n/a | TC AIM RAC 3.4.8 Table 3.5 |
- Metric: mass = litres × density.
In flight:
- CG shifts as fuel burns off. Know how it shifts in own aircraft (PHAK ch.5).
- Trim tabs and adjustable stabilizers partly counter moment shift from fuel burnoff and from loading or off-loading passengers and cargo (PHAK ch.5).
After computing CG: check against forward and aft limits (aircraft-specific, in POH/AFM; TC AIM RAC 3.4.3). Outside limits: reposition load, recompute (see the weight-balance-limits lesson).
Trap: transposing weight and moment, wrong datum, or leaving a station (fuel, baggage) out.
References
- Aircraft POH/AFM (weight & balance section)
- TP 1102 (Flight Training Manual)
- TC AIM RAC 3.4.8 (fuel and oil weights)
- PHAK ch.5 (moment and moment arm)