Worked example Mass and Balance (Cessna 172 style)
Important: these figures are generic and illustrate the procedure. For your actual flight always use the current AFM/POH and the current weighing record of your aircraft.
Scenario
Aircraft: Cessna 172S (generic example) Flight: EDFE (Egelsbach) → EDLE (Essen-Mülheim), VFR day Crew: pilot + 1 passenger front + 1 passenger rear + 1 child rear
Constants (from AFM/POH)
| Quantity | Value |
|---|---|
| MTOM | 1 157 kg (2 550 lb) |
| Maximum Landing Mass | 1 157 kg |
| Forward CG limit (at MTOM) | 0.889 m (35.0 in) |
| Aft CG limit (at MTOM) | 1.201 m (47.3 in) |
| Datum | firewall (forward tip) |
Station arms (generic, C172-style)
| Station | Arm (m) |
|---|---|
| BEM | 1.040 (from weighing record) |
| Front seats (pilot + co-pilot) | 0.937 |
| Rear seats | 1.853 |
| Baggage area 1 (behind rear seat) | 2.412 |
| Baggage area 2 (tail) | 3.099 |
| Fuel (53 USG / 200 L main tank) | 1.219 |
Step 1 — collect data
BEM (from fictional weighing record): 737 kg. BEM moment: 737 × 1.040 = 766.48 kg·m.
Crew:
- Pilot: 82 kg.
- Front passenger: 70 kg.
- Rear passenger: 75 kg.
- Child rear: 30 kg.
Baggage:
- Area 1: 8 kg (cabin baggage).
- Area 2: 0 kg.
Fuel:
- Pre-flight: full = 53 USG / 200.6 L.
- Arrival should be with 30 min reserve → flight time ~1 h + reserve, so ~25 USG remain.
- Depart with 40 USG (151.4 L) — see Fuel density for conversion.
AVGAS density 0.72 kg/L at ISA:
- Fuel mass: 151.4 L × 0.72 = 109 kg.
Step 2 — fill the table
| Station | Mass (kg) | Arm (m) | Moment (kg·m) |
|---|---|---|---|
| BEM | 737.0 | 1.040 | 766.48 |
| Pilot (front) | 82.0 | 0.937 | 76.83 |
| Pax front | 70.0 | 0.937 | 65.59 |
| Pax rear | 75.0 | 1.853 | 138.98 |
| Child rear | 30.0 | 1.853 | 55.59 |
| Baggage Area 1 | 8.0 | 2.412 | 19.30 |
| Fuel (40 USG) | 109.0 | 1.219 | 132.87 |
| TOTAL | 1 111.0 | 1 255.64 |
Step 3 — check total mass
- Total mass: 1 111 kg.
- MTOM: 1 157 kg.
- 1 111 < 1 157 → ✓ OK (46 kg margin).
Step 4 — compute CG
code
CG = total moment / total mass
CG = 1 255.64 / 1 111.0
CG = 1.1302 m (1.13 m, or 44.5 in)
Step 5 — check CG envelope
At total mass 1 111 kg:
- Forward limit ≈ 0.889 m.
- Aft limit ≈ 1.201 m.
CG 1.1302 m lies between 0.889 m and 1.201 m → ✓ OK (inside the envelope).
Step 6 — compute landing values
After 1 h flight: ~8 USG burnt (C172 burns about 8 USG/h cruise).
- Fuel at landing: 40 − 8 = 32 USG = 121 L = 87 kg.
- Fuel-mass change: 109 − 87 = −22 kg (less).
- Fuel-moment change: −22 × 1.219 = −26.82 kg·m.
At landing:
- Total mass: 1 111 − 22 = 1 089 kg.
- Total moment: 1 255.64 − 26.82 = 1 228.82 kg·m.
- CG at landing: 1 228.82 / 1 089 = 1.128 m (almost same CG, since fuel is near the CG).
Both MLM and CG limits ✓.
Notes on the flow
- Compute fuel first — it is the only entry that changes during the flight.
- Moving pax/baggage between seats can shift the CG substantially — recompute.
- Pax mass estimates: EASA standard values are 84 kg (summer) / 88 kg (winter) for adults and 35 kg for children 2–11 — see AMC1 NCO.POL.105. For non-commercial ops the actual weight may be used if reliably known.
- Asymmetry (e.g. one tank full only): plan tank changes in flight.