Fundamentals of CG calculation
Determining the Centre of Gravity (CG) is based on basic mechanics — specifically the equilibrium of moments.
What is a moment?
A moment is the product of force × arm:
Moment (kg·m or lb·in) = Mass (kg) × Arm (m)
Intuitively: a 10 kg weight on a 2 m lever produces a moment of 20 kg·m — that is the "turning effect" around the pivot.
Equilibrium conditions
An aircraft is in static equilibrium (at rest) when:
1. Sum of forces = 0:
- Lift = Weight (vertical),
- Thrust = Drag (horizontal).
2. Sum of moments about every point = 0:
- The turning effects of all masses cancel.
From the second condition follows the CG definition:
The centre of gravity is the point about which the sum of all moments is zero.
In other words: the CG is the mass centre — if the aircraft were suspended at this point, it would remain level.
The datum as reference point
Because CG is a position, a reference point is needed — the datum. The datum is defined in the AFM:
Examples:
- C172: Datum = forward tip of the fuselage (firewall).
- PA-28: Datum = ahead of the engine front plane.
- DA40: Datum = forward end bulkhead.
Arms are measured from the datum in one direction (typically positive aft).
CG calculation formula
CG (arm from datum) = Σ Moments / Σ Masses
Step by step:
- Build a table of all mass stations (BEM, crew, pax, baggage, fuel).
- Per station: Mass × Arm = Moment.
- Sum of masses → total mass.
- Sum of moments → total moment.
- CG = total moment / total mass.
Arms from the AFM
The AFM gives a typical arm for each station:
| Station (C172 example) | Arm |
|---|---|
| BEM | ~1.057 m (varies by aircraft) |
| Pilot/co-pilot (front seat) | 0.937 m |
| Pax 3/4 (rear seat) | 1.853 m |
| Baggage area 1 | 2.412 m |
| Baggage area 2 | 3.099 m |
| Fuel (tank) | 1.219 m |
Note: on some types the pilot seat is adjustable — the arm changes with seat position.
Worked example (excerpt)
| Station | Mass (kg) | Arm (m) | Moment (kg·m) |
|---|---|---|---|
| BEM | 767.5 | 1.057 | 811.20 |
| Pilot | 80.0 | 0.937 | 74.96 |
| Pax (rear) | 70.0 | 1.853 | 129.71 |
| Baggage 1 | 10.0 | 2.412 | 24.12 |
| Fuel 40 USG (109 kg) | 109.0 | 1.219 | 132.87 |
| TOTAL | 1036.5 | 1172.86 |
CG = 1172.86 / 1036.5 = 1.1316 m ≈ 1.13 m (from datum, aft).
Check the CG envelope
After calculation the point (total mass, CG) is plotted in the CG envelope diagram of the AFM:
- X-axis: CG position (arm in m or in).
- Y-axis: total mass (kg).
Inside the envelope → OK. Outside → redistribute or reduce load.
Mean Aerodynamic Chord (MAC) — percent
Some AFMs express CG in % MAC (Mean Aerodynamic Chord) instead of direct arm:
- MAC = mean aerodynamic wing chord (not a structural reference but an aerodynamic one).
- 0% MAC = MAC leading edge.
- 100% MAC = MAC trailing edge.
- Forward limit e.g. 14% MAC; aft limit e.g. 33% MAC.
Conversion: %MAC = (CG position − MAC leading edge position) / MAC length × 100.
Important notes
- Masses must be current — BEM from the latest weighing record.
- Convert fuel to mass (not direct litres → AVGAS 100LL density 0.72 kg/L at 15 °C, see Fuel density).
- For asymmetries (e.g. one tank full, other empty): check lateral CG — for many light aircraft uncritical by symmetry, but relevant on larger tanks.
- Trim sheet from EFB app, Excel or by hand is a valid record.