Learning hub · Mass and Balance · Lesson 1
Loading an aeroplane: mass, balance and the centre of gravity
An aeroplane has two loading limits, not one. Its mass must not be too high, and the mass must be in the right place. This lesson shows how to check both with simple multiplication.
About 14 minutes, plus the quiz. Part of Mass and Balance.
1. Two limits
The mass limit (the maximum take-off mass) protects the structure and keeps the performance in the manual true. The balance limit keeps the centre of gravity (CG), the point where the whole mass acts, inside a range chosen by the manufacturer. If the CG is outside that range the aeroplane can be unstable or too heavy on the controls to fly safely, even if the total mass is fine.
2. The words and the one formula
- Datum: a reference point from which every distance is measured, given in the manual.
- Arm: the distance from the datum to where an item is (seat, baggage area, fuel tank).
- Moment: the turning effect of an item about the datum.
Moment = mass × arm
CG position = total moment ÷ total mass
You add up every item, including the empty aeroplane, the people, the bags and the fuel. The total mass must be below the limit, and the CG position must be inside the permitted range for that mass.
3. Fuel is mass too
Fuel is measured in litres or gallons, but the table needs kilograms or pounds. Avgas has a mass of about 0.72 kg per litre and Jet A-1 about 0.8 kg per litre (the flight manual gives the density to use). So 100 litres of avgas is 72 kg. Always check which units the manual uses, since a mix-up between kilograms and pounds, or litres and US gallons, is a classic error.
4. A worked example
The aeroplane in this example is invented. Its maximum take-off mass is 1,100 kg and, at this mass, the CG must be between 0.95 m and 1.15 m behind the datum.
| Item | Mass (kg) | Arm (m) | Moment (kg·m) |
|---|---|---|---|
| Empty aeroplane | 700 | 1.00 | 700.0 |
| Pilot and front passenger | 160 | 0.90 | 144.0 |
| Rear passenger | 70 | 1.80 | 126.0 |
| Baggage | 20 | 2.40 | 48.0 |
| Fuel, 100 L of avgas | 72 | 1.10 | 79.2 |
| Total | 1,022 | 1,097.2 |
CG = 1,097.2 ÷ 1,022 = 1.07 m
The mass, 1,022 kg, is under the 1,100 kg limit, and the CG, 1.07 m, is between 0.95 m and 1.15 m. The loading is acceptable. Now try a change: the rear passenger has a mass of 90 kg instead of 70. The mass becomes 1,042 kg, the moment becomes 1,097.2 + 20 × 1.80 = 1,133.2, and the CG moves back to 1.09 m. It is still inside the limits, but closer to the aft one. Mass at the back moves the CG back.
In European (EASA) texts the empty aeroplane in the table is the basic empty mass. Adding the crew and operating items gives the dry operating mass, adding the payload gives the zero fuel mass, adding the fuel gives the take-off mass, and the landing mass is the take-off mass minus the fuel burnt.
5. Why the CG position matters
- CG too far forward. The nose is heavy. You need more elevator to lift the nose, so the rotation and the flare get harder, and the stall speed goes up. The aeroplane is very stable.
- CG too far back. The aeroplane becomes less stable and pitches more easily. Recovery from a stall or a spin may be harder or impossible. This is generally the more dangerous direction.
Remember that the CG moves in flight as fuel burns, so check the loading for take-off and for landing. If the numbers are outside the limits, change the loading (for example move baggage forward if the CG is too far aft, remove mass, or take less fuel) and then do the sum again.
Use the loading data and limits for your own aeroplane, from its approved flight manual, for every flight. The numbers here are invented.
6. Try it yourself
Work each one out on paper first, then open the answer to compare. The numbers are invented.
- Use the invented aeroplane from the worked example (limit 1,100 kg, CG between 0.95 m and 1.15 m, other items unchanged: empty 700 kg at 1.00 m, front seats 160 kg at 0.90 m, rear passenger 70 kg at 1.80 m, baggage 20 kg at 2.40 m). You carry only 60 L of avgas instead of 100 L, at arm 1.10 m. What are the new mass and CG? Is it acceptable?
Show the answer
Fuel mass = 60 × 0.72 = 43.2 kg. Moment of the fuel = 43.2 × 1.10 = 47.5 kg·m.
The old fuel was 72 kg with a moment of 79.2. New total mass = 1,022 − 72 + 43.2 = 993.2 kg. New total moment = 1,097.2 − 79.2 + 47.5 = 1,065.5 kg·m.
CG = 1,065.5 ÷ 993.2 ≈ 1.07 m. The mass is under 1,100 kg and the CG is between 0.95 m and 1.15 m, so it is acceptable. Here the CG hardly moved, because the fuel arm (1.10 m) is close to the CG.
- Same aeroplane, loaded as in the worked example (1,022 kg, moment 1,097.2), but the baggage is 90 kg instead of 20 kg. Check the mass and the CG. If a limit is broken, remove baggage to fix it and check again.
Show the answer
The extra 70 kg at 2.40 m adds 168 kg·m. Mass = 1,022 + 70 = 1,092 kg, which is under 1,100 kg. Moment = 1,097.2 + 168 = 1,265.2.
CG = 1,265.2 ÷ 1,092 ≈ 1.16 m. That is behind the aft limit of 1.15 m, so the loading is not acceptable, even though the mass is fine. This is the more dangerous direction.
Remove 30 kg of baggage (60 kg left). Mass = 1,062 kg, moment = 1,265.2 − 72 = 1,193.2, CG = 1,193.2 ÷ 1,062 ≈ 1.12 m. Now both limits are met. Moving some baggage forward would also work, if the manual allows it.
- Starting from the worked example (1,022 kg including 100 L of avgas), how many extra litres of avgas can you add before you reach the 1,100 kg limit? Ignore the tank size and the CG. How many litres of Jet A-1 (about 0.8 kg per litre) would the same extra mass be?
Show the answer
Mass available = 1,100 − 1,022 = 78 kg.
Avgas at 0.72 kg per litre: 78 ÷ 0.72 ≈ 108 L. Round down to 108 L, because rounding up would take you over the limit.
Jet A-1 at 0.8 kg per litre: 78 ÷ 0.8 ≈ 97 L. The same mass is fewer litres of the denser fuel, which is why you convert litres to kilograms before you add up the loading. In a real case you would also recheck the CG, and the tank capacity.
7. Watch
Another explanation of the datum, arm, moment and the CG, with an example. This video is American, so wording (for example “weight” for mass) and some rules differ from European (ICAO/EASA) practice.
Open on YouTube if the player does not load. Not made by VectorEFB; check what you learn against your flying school’s material and your instructor.
More to watch
A short video on what a forward or an aft CG does to the aeroplane, which goes with section 5 of this lesson.
Open on YouTube if the player does not load. Not made by VectorEFB.
8. Check yourself
Five original practice questions. Answer them, press Check answers and read each explanation.
Next: density altitude and take-off performance. Back to the learning hub.