Datum, Arm and Moment - ATPL 031 — Mass & Balance

Balance is about where mass sits, and 'where' needs a zero to be measured from. This lesson sets up the three ideas every later calculation is built from: the datum that provides the zero, the arm that measures distance from it, and the moment that weights that distance by the mass sitting there. It then turns to the centre of gravity itself: what it really is, where its position and its limits are published, and the different ways a document may quote it.

Datum, arm, moment

Datum — the reference point: a point on the aircraft's longitudinal axis, or on its extension, from which the positions of all masses are measured. The manufacturer chooses it, and nothing physical needs to exist there: it may sit at the firewall, at the nose, or metres ahead of the aircraft in empty air, which manufacturers often prefer precisely so that every arm comes out positive.
Moment arm (balance arm) — the distance from the datum to the centre of gravity of a mass, measured along the longitudinal axis. The sign convention is standard: positions aft of the datum carry positive arms, positions forward of it negative ones.
Moment — the product of a mass and its arm, in kilogram-metres or the document's equivalent units. The moment is what a mass contributes to the balance: it carries the arm's sign, so a mass ahead of the datum contributes a negative moment and a mass behind it a positive one.

Why moments and not just masses? Because two loadings with identical total mass can balance completely differently, and the moment is the number that knows the difference. Adding up masses answers the first question of the subject, is the aircraft light enough; adding up moments answers the second, is the weight in the right place. The next module turns exactly this into the working method: total moment divided by total mass gives the position where the whole loading acts.

Where the numbers are published

Every one of these numbers has a specific published home, and the exam expects you to know the map:

Aircraft data — the datum's position and the arms of every station, seat row, hold and tank: laid down in the manufacturer's documentation, the aircraft flight manual and the loading or mass-and-balance manual.
Weighing report (also called the mass-and-balance report) — the document produced when the aircraft was last weighed, and the source of the CG position of the aircraft at its basic empty mass; the weighing procedure itself is this module's closing lesson.
CG limits — the certified forward and aft boundaries the loaded aircraft must stay inside: published in the aircraft flight manual, with the loading manual repeating them in working form.

The centre of gravity

The centre of gravity is the point through which the force of gravity acts on the aircraft: the single point at which the whole mass can be considered concentrated without changing any balance calculation. Hang the aircraft from its CG and it would balance in any attitude; in flight, it is the point about which the aircraft rotates. The CG is not fixed by design: it moves with every bag loaded, every seat filled and every kilogram of fuel burned, and the whole purpose of this subject is to know where it is at every stage of the flight and to keep it inside the certified limits.

Documents quote the CG position in several forms, and the exam expects you to recognise each as the same information in different clothes:

As a distance from the datum — the direct form: 'CG at +42.6 in' means 42.6 inches aft of the datum, immediately comparable with limits quoted the same way.
As a distance from another reference — some documents measure from a physical landmark, such as the firewall, a spar or a numbered fuselage station; the information is identical once the reference's own position relative to the datum is known.
As a percentage of the mean aerodynamic chord (MAC) — large aeroplanes usually quote the CG as per cent MAC, locating it as a fraction of the wing's reference chord; the next lesson is devoted to this form.
As an index — a scaled, shifted stand-in for the moment used to make load-sheet arithmetic manageable; the index method has its own lesson in the next module.

Define datum, moment arm and moment, apply the aft-positive sign convention, and state where datum and arm data are found

Extract arms, limits and reference information from a given data sheet

Explain what the centre of gravity is, state where the empty-mass CG and the CG limits are published, and recognise the forms in which a CG position may be quoted

Datum, arm, moment

Check you understood

Where the numbers are published

The centre of gravity