Learning hub · Mass and Balance · Lesson 2

Fuel mass, unit conversions and a loading sheet

The first mass and balance lesson showed the idea. Here you do the whole job: turn fuel in litres into kilograms, avoid unit mistakes, fill in a complete loading sheet and decide what to do if it fails.

About 14 minutes, plus the quiz. Part of Mass and Balance. It builds on Loading an aeroplane: mass, balance and the centre of gravity.

1. Fuel is measured in volume but loaded as mass

You fill a tank in litres (or US gallons), but the loading sheet needs kilograms (or pounds). The link is the density of the fuel:

mass (kg) = volume (L) × density (kg/L)

Avgas has a density of about 0.72 kg/L at 15°C. This is a typical value, not an exact one: density varies with temperature and from batch to batch. Jet A-1, used by turbine aeroplanes and by many diesel-engined ones, is roughly 0.8 kg/L. Fuel gets lighter per litre as it warms (roughly 0.1 per cent per °C), so the same litres weigh a little less on a hot day. Use the density that your flight manual or school gives.

Example: 110 L of avgas × 0.72 = 79.2 kg.

2. Litres, gallons, kilograms, pounds

A mix-up of units is a classic loading mistake. Keep these in mind:

To convert	Use
US gallons to litres	× 3.785
Litres to US gallons	÷ 3.785
Kilograms to pounds	× 2.205
Pounds to kilograms	÷ 2.205
Avgas, US gallon to pounds	about 6.0 lb per US gallon

Check: 0.72 kg/L × 3.785 L/gal = 2.73 kg per US gallon, and × 2.205 = 6.0 lb per gallon. The figures agree. European aeroplanes are mostly in litres and kilograms, but an American-built type may have a manual in gallons and pounds, with its arms in inches. Always write the unit next to every figure. Note: a US gallon is not the same as an imperial gallon (4.546 L).

3. A full loading sheet, step by step

The aeroplane here is invented. Its maximum take-off mass is 1,150 kg. The arms are in metres behind the datum. In this invented envelope the CG must be between 0.95 m and 1.18 m for any mass up to the maximum. (A real envelope is often a polygon whose limits change with mass, so read yours carefully.)

1. Write each item with its mass and arm, taken from the manual and the weighing report.
2. Convert the fuel: 110 L × 0.72 = 79.2 kg.
3. Multiply mass × arm for each item to get its moment.
4. Add the masses, then add the moments.
5. CG = total moment ÷ total mass. Compare the mass and CG with the limits.

Item	Mass (kg)	Arm (m)	Moment (kg·m)
Basic empty mass	720.0	1.02	734.40
Pilot and front passenger	150.0	0.95	142.50
Rear passenger	85.0	1.85	157.25
Baggage	15.0	2.45	36.75
Fuel, 110 L	79.2	1.15	91.08
Take-off total	1,049.2		1,161.98

CG = 1,161.98 ÷ 1,049.2 = 1.11 m. The mass is below 1,150 kg and the CG is between 0.95 and 1.18 m, so the take-off loading is acceptable.

Now check the landing. Suppose 60 L (43.2 kg) is burned. The landing mass is 1,049.2 − 43.2 = 1,006.0 kg. The moment falls by 43.2 × 1.15 = 49.68, to 1,112.30. The CG is 1,112.30 ÷ 1,006.0 = 1.11 m, still within limits. Fuel is close to the CG here, so burning it changes the CG very little. In some aeroplanes the tank is far from the CG and the effect is large, so check it.

4. When the numbers are out of limits

If the mass is over the maximum, or the CG is outside the envelope, you must change the load before flying. Never fly hoping it will be fine. Your options, in the order that often works:

• Too heavy: take less fuel (keeping legal and safe reserves), carry fewer people or less baggage, or split the trip.
• CG too far aft: move heavy items forward, for example baggage to a forward position if the manual allows, or remove baggage or a rear passenger.
• CG too far forward: the opposite, with heavy items moved aft.

Changing the wrong item may make things worse. Removing fuel that sits ahead of the CG moves the CG aft. Always do the sum again after the change. Do not forget that the baggage compartment has its own maximum.

Training only. The aeroplane and the numbers in this lesson are invented. For a real flight use the approved flight manual, the current weighing report and the limits for your aeroplane.

5. Try it yourself

Work each one out on paper first, then open the answer to compare. The numbers are invented.

1. (a) How many kilograms of avgas is 85 L, at 0.72 kg/L? (b) A pilot of an American-built aeroplane adds 20 US gallons. How many litres and how many kilograms is that? (c) What error results if the pilot enters 20 as litres?
   Show the answer

   1. (a) 85 × 0.72 = 61.2 kg.
   2. (b) 20 × 3.785 = 75.7 L. 75.7 × 0.72 = 54.5 kg.
   3. (c) 20 L × 0.72 = 14.4 kg. The sheet would be low by 54.5 − 14.4 = about 40 kg, so the aeroplane would be heavier than the sheet says.
2. Use the lesson’s invented aeroplane (limits 1,150 kg, CG 0.95 to 1.18 m). Today there are two rear passengers of 90 kg each (180 kg at 1.85 m), 30 kg of baggage (2.45 m), the same front seats (150 kg at 0.95 m) and 110 L of fuel (79.2 kg at 1.15 m). Basic empty mass is 720 kg at 1.02 m. Find the mass and the CG. If it fails, what is a good fix?
   Show the answer

   1. Mass: 720 + 150 + 180 + 30 + 79.2 = 1,159.2 kg. That is 9.2 kg over the 1,150 kg limit.
   2. Moments: 734.40 + 142.50 + 333.00 + 73.50 + 91.08 = 1,374.48.
   3. CG = 1,374.48 ÷ 1,159.2 = 1.186 m, which is aft of the 1.18 m limit. Both limits fail.
   4. Removing 13 L of fuel (arm 1.15, ahead of the CG) fixes the mass but moves the CG further aft. Instead take out the 30 kg of baggage: mass 1,129.2 kg, moment 1,300.98, CG = 1.15 m. Both are within limits.
3. With the lesson’s invented aeroplane, a pilot flies alone (80 kg, arm 0.95 m) with no rear passenger, no baggage and 60 L of avgas (arm 1.15 m, 0.72 kg/L). Find the take-off mass and the CG, and say whether the loading is acceptable.
   Show the answer

   1. Fuel: 60 × 0.72 = 43.2 kg. Its moment = 43.2 × 1.15 = 49.68.
   2. Pilot moment = 80 × 0.95 = 76.00. Empty aeroplane: 720 kg and 734.40.
   3. Mass = 720 + 80 + 43.2 = 843.2 kg. Moment = 734.40 + 76.00 + 49.68 = 860.08.
   4. CG = 860.08 ÷ 843.2 = 1.02 m, between 0.95 and 1.18 m. The loading is acceptable, but note that it is nearer the forward limit than the earlier loading.

6. Watch

A worked explanation of how to calculate the centre of gravity from a loading table. The word weight is used where European texts say mass.

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 second worked example from a flight training channel. This video is American, so wording (for example weight for mass, pounds and inches) and some rules differ from European (ICAO/EASA) practice.

Open on YouTube if the player does not load. Not made by VectorEFB.

7. Check yourself

Five original practice questions. Answer them, press Check answers and read each explanation.

Next: Fuel, the navigation log and in-flight monitoring. Back to the learning hub.