How the problems work
Pick topics, an aeroplane and a number of problems. The two trainers are made up, each with a loading table, a CG limits table and a drawn envelope, and every mass is in kilograms and every volume in litres. Choose metres, centimetres or millimetres for the arms; the same problems are then shown and marked in that unit.
Answers are worked at full precision and rounded once, at the end: the CG to the nearest millimetre, masses to the kilogram. Wrong answers that come from a known slip get a hint: litres used as kilograms, a removal added instead of subtracted, fuel burn left out, a CG in centimetres where metres were asked, or kilograms and pounds swapped.
Landing CG after fuel burn, worked
The four-seat trainer takes off at 1,048 kg with its CG at 2.152 m and burns 60 litres of AVGAS from tanks at 2.100 m. The fuel weighs 60 × 0.72 = 43.2 kg, with a moment of 43.2 × 2.100 = 90.720 kg·m.
| Item | Mass (kg) | Arm (m) | Moment (kg·m) |
|---|---|---|---|
| Take-off | 1,048.0 | 2.152 | 2,255.296 |
| Fuel burnt (60 l) | −43.2 | 2.100 | −90.720 |
| Landing | 1,004.8 | 2,164.576 |
Landing CG = 2,164.576 ÷ 1,004.8 ≈ 2.154 m to the nearest millimetre, so the CG moves 2 mm aft as the fuel burns. Try five fuel problems.
The figures used and where they come from
| What | Figure | Source |
|---|---|---|
| AVGAS | 0.72 kg/l | CAP 696 Section 3, para 2.2.1: 6 lb per US gallon (6 × 0.454 ÷ 3.785 = 0.72 kg/l) |
| Jet A-1 | 0.80 kg/l | FAA Weight and Balance Handbook, Fig. 3-4 (6.68 lb/US gal at 15 °C) |
| kg and lb | kg × 2.205 = lb, lb × 0.454 = kg | CAP 696 Section 1, para 5 (ICAO Annex 5) |
| Gallons | US gal × 3.785 = l, imp gal × 4.546 = l | CAP 696 Section 1, para 5 |
| Mass terms | ZFM, ramp mass, TOM, landing mass | CAP 696 Section 1, para 4 |
| Loading manifest | zero fuel, + fuel, − start and taxi fuel, − trip fuel | CAP 696 Section 2, para 2 (layout only; our own numbers) |
| CG and moments | CG = total moment ÷ total mass | FAA Weight and Balance Handbook, ch. 2 and 5 |
Sources checked 24 October 2026.
Questions
What density should I use for AVGAS?
Use 0.72 kg per litre for AVGAS 100LL unless your course says otherwise. CAP 696 uses 6 lb per US gallon, and 6 × 0.454 ÷ 3.785 is 0.72 kg per litre. Diesel trainers burn Jet A-1, about 0.80 kg per litre; pick it under Conventions.
How do I convert kilograms to pounds?
Multiply kilograms by 2.205 to get pounds, and pounds by 0.454 to get kilograms. Those are the CAP 696 factors, taken from ICAO Annex 5. A pound is less than half a kilogram, so the number in pounds is always the bigger one.
What are ZFM, ramp mass, TOM and landing mass?
Zero fuel mass is everything except usable fuel. Add the fuel loaded for the ramp (taxi) mass, take off the start, taxi and run-up fuel for the take-off mass, and take off the trip fuel for the landing mass. Each one must be inside the CG envelope.
How do I find the CG after fuel burn?
Take the burnt fuel's mass and moment off the take-off figures, then divide the new moment by the new mass. Convert litres to kilograms first: 60 litres of AVGAS is 43.2 kg, not 60 kg.
Should the arm be in metres, centimetres or millimetres?
Any of them, as long as every arm uses the same unit. The moment unit follows: kg·m, kg·cm or kg·mm. Pick the one your aircraft's flight manual uses under Conventions; the CG is always worked to the nearest millimetre.
Are these real aeroplanes?
No. Both trainers are made up, with numbers close to real two- and four-seat trainers but matching none of them. For a flight, use your aircraft's flight manual and its own mass and balance report.
How do I give my whole class the same problems?
Pick the topics, aeroplane, number of problems and conventions, then tap Share with class and send the link. It always opens the same set, even if the defaults here change later. Print the answer key for yourself.
Practice only. Not for flight planning. Use your aircraft's flight manual (AFM/POH) and its own mass and balance report. The two trainers, their loading tables and their envelopes are made up so the numbers work.
Sources: UK CAA CAP 696, Mass and Balance Manual (Aeroplanes), 3rd edition, July 2006 (PDF); Austro Control, ECQB-PPL question catalogue (Fragenkatalog PPL(A), in German); FAA-H-8083-1B Aircraft Weight and Balance Handbook, 2016 (PDF). US student? Weight and balance practice in pounds and inches.