Every balance calculation starts from two numbers no formula can produce: what the empty aircraft weighs and where its CG sits. Those numbers come from putting the aircraft on scales, and this lesson covers the whole trail: when and by whom an aircraft must be weighed, how the scales' readings become a mass and a CG, what the resulting mass report records, and how the basic empty mass, its CG and the corrections for non-standard configuration are then extracted from the documents for daily use.
When an aircraft is weighed
The rules attach weighing to three kinds of moment in an aircraft's life:
Entry into service — mass and CG are established by actual weighing before an aircraft first enters service. A new aircraft weighed at the factory need not be weighed again on delivery, provided the records have been adjusted for any alterations since; an aircraft transferred between EU operators likewise keeps its weighing, unless more than four years have passed since it was last on the scales.
Fixed intervals — thereafter the aircraft is reweighed every four years if the operator uses individual aircraft masses, or every nine years if it uses fleet masses (the fleet system is explained below).
Modification and drift — the accumulated effects of modifications and repairs must be tracked and documented, and the aircraft must be reweighed whenever their effect on mass and balance is not accurately known. The working thresholds: mass and CG are revised, by weighing or by calculation, when the cumulative change in dry operating mass exceeds half a per cent of the maximum landing mass, or the cumulative CG change exceeds half a per cent of the mean aerodynamic chord.
The weighing itself is a controlled procedure, carried out by the aircraft's manufacturer or by an approved maintenance organisation, with the classic precautions: the aircraft complete and clean, fluids properly accounted for, the weighing done in an enclosed building so wind cannot lean on the result, and the scales calibrated, zeroed and used according to their manufacturer's instructions.
From scale readings to mass and CG
On the scales, the aircraft rests on its weighing points, one under each landing gear or jacking point, and each scale reports the reaction force it carries. Two sums turn the readings into the answer: the total mass is simply the sum of the reactions, and the CG position follows from the moments, each reaction times the arm of its weighing point from the datum, added and divided by the total. This is the formula this module's first lesson promised and the whole of the next module runs on: CG position equals total moment divided by total mass.
Check you understood
Three questions from this lesson — one straightforward, one that applies it, one that pushes a little further. Nothing is recorded, and you can draw a new set as often as you like.
1. Warm-up
After its initial weighing, an aircraft must be reweighed at intervals of:
2. Applying it
At a weighing, the scales read: nose point 1,200 kg at arm 2.0 m; each of two main points 5,400 kg at arm 6.0 m. The aircraft's mass and CG position are:
3. Pushing it
Why is an equipment list appended to the mass report?
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What you are looking at: an aeroplane on its weighing points, in side view. The nose scale reads 1,000 kg at an arm of 1.0 m from the datum; the main-gear scales together read 9,000 kg at an arm of 5.0 m. Total mass is the sum of the reactions, 10,000 kg. The moments are 1,000 kg·m from the nose and 45,000 kg·m from the mains, 46,000 kg·m together, and dividing by the total mass places the CG at 4.6 m aft of the datum, marked on the fuselage. The CG lands close to the main gear, which is where it must be: the mains carry nine tenths of the reaction, so the balance point sits nine tenths of the way toward them.
The mass report
The weighing's paperwork is the mass (weight) report, also called the weighing or mass-and-balance report, and interpreting its entries is an exam skill. The report records the as-weighed readings and the weighing conditions, then applies the corrections that bridge from what stood on the scales to the basic empty mass: items that were on board but do not belong in the BEM are subtracted, missing standard items are added, and unusable fuel and fluids are accounted for. The result lines give the BEM, its CG position or its moment, and the date and signature that make them the aircraft's official starting point until the next weighing or the next documented change. Appended to it lives the equipment list: what removable equipment the figures include, so that any later equipment change can be traced through mass and moment without a fresh weighing.
Fleet masses
An operator with many aeroplanes of the same model and configuration may use fleet values: one average dry operating mass and CG applied to the whole group. The scheme is bounded by tolerances, and the exam asks for them: an individual aeroplane may use the fleet values only while its own dry operating mass differs from the fleet DOM by no more than half a per cent of the maximum structural landing mass, and its CG differs from the fleet CG by no more than half a per cent of the mean aerodynamic chord. The fleet values are maintained by a rolling programme of sample weighings, evaluated at intervals of no more than 48 months, with the aeroplanes unweighed the longest chosen first, and this is why the fleet route stretches the individual reweighing interval to nine years: the fleet's samples keep watch in between. An aeroplane that drifts outside the tolerances flies on its individual values, unless the operator establishes new fleet values instead; and in the halfway case, mass within tolerance but CG outside it, the aeroplane may keep the fleet DOM while using its own individual CG position.
Extracting BEM, DOM and the deviations
For daily work, the documents hand over three things:
Basic empty mass and its CG or moment — from the mass report, as above.
Dry operating mass — built from the BEM by adding the operating items for the intended operation: crew and crew baggage, catering and removable passenger-service equipment, tank (potable) water and lavatory chemicals. Operators publish it per configuration so it can be read rather than rebuilt.
Corrections for deviations — because real operations deviate from the standard configuration, the documents list each departure from it, an extra crew member, a different catering fit, a removed pantry, with its mass and its moment or arm, so the DOM and its CG can be adjusted by addition and subtraction.
Extraction questions are exactly that: find the right configuration line, apply the right correction, and keep mass and moment moving together.
State when an aircraft must be weighed or reweighed, by whom, and under what precautions, including the fleet-mass tolerances and intervals