Weight and Balance and Loading
Mass and moment
Weight and balance is arithmetic with consequences. You need the empty mass and empty moment from the aircraft documents, then add crew, passengers, baggage, fuel and cargo, each with its own arm or moment. Total mass must lie within the maximum take-off and landing masses and the zero-fuel mass limit. The centre of gravity must lie within the forward and aft limits for the mass at that moment, and the limits may vary with mass.
Reading the envelope
Be able to plot a point on a load sheet or envelope and to say what happens when fuel burns off or when a heavy item moves. Forward limits are usually set by elevator authority and landing performance; aft limits by stability and control. Know that fuel burn shifts the centre of gravity, and in which direction for a given tank layout.
Traps
Questions often give masses and arms and ask for a new centre of gravity after a change, or ask how much ballast is needed to bring an out-of-limit aircraft back inside. Watch for units: inches, metres, pounds, kilograms, and moment units that differ between types. Another trap is the zero-fuel mass limit, which is easy to forget when fuel is loaded after the load sheet is prepared.
Worked example
If an item of mass m is moved a distance d, the moment changes by m × d and the centre of gravity shifts by m × d divided by total mass. Moving 50 kg aft by 2 m in a 2000 kg aircraft shifts the centre of gravity by 100 divided by 2000, which is 0.05 m, or 5 cm aft.