The CG as Per Cent MAC - ATPL 031 — Mass & Balance

A CG quoted as '652.5 inches aft of the datum' is precise and almost meaningless: it says nothing about where the CG sits relative to the wing that has to carry it. Large-aeroplane documents therefore quote the CG in a second currency, per cent MAC, which measures it as a fraction of the wing's reference chord. This lesson explains the principle, teaches the conversion in both directions, and shows where the MAC data and the longitudinal CG limits are found in the documents.

The wing's reference chord

The mean aerodynamic chord (MAC) is the wing's representative chord: a single chord length that stands in for the whole tapered, swept wing in aerodynamic bookkeeping. Its formal definition and construction belong to Principles of Flight (081); mass and balance only borrows the result. What matters here is that the MAC has a definite length and a definite position, and both are printed in the aircraft's documents. For the sample medium-range jet used in the exam's loading manual, the MAC is 134.5 inches long and its leading edge, the LEMAC (leading edge of the mean aerodynamic chord), lies 625.6 inches aft of the datum. Those two numbers are the whole toolkit: everything per cent MAC ever does is measure the CG's position along that 134.5-inch ruler.

Why per cent MAC

The datum is an arbitrary bookkeeping zero, and a distance from it carries no aerodynamic meaning by itself. What decides stability and trim is where the CG sits relative to the wing's lift, and the wing's aerodynamic geography is measured in chords. Expressing the CG as a percentage of the MAC, zero at the leading edge, one hundred at the trailing edge, produces a number that speaks aerodynamics directly: the certified range of a transport aeroplane might run from around 8 to around 27 per cent MAC, a stabiliser-trim scale can be graduated against it, and a given percentage means broadly the same thing about where the CG sits relative to the wing on any aircraft, whatever its datum. That is the principle: per cent MAC converts a bookkeeping position into an aerodynamic one.

Longitudinal CG limits in the documents

The certified forward and aft CG limits of a large aeroplane are published in the flight manual and the loading manual, usually in per cent MAC, and usually not as two bare numbers but as an envelope: a diagram or table of the permitted CG range against mass. The range is widest in the middle of the mass scale and narrows toward the heavy end, where structural and control margins tighten. Reading it is an extraction skill the exam tests directly: enter with a mass, come out with the forward and aft limits that apply at that mass, in the same units the question's CG is quoted in. The envelope diagram itself, and checking a computed CG against it, is the working material of the next module's load-sheet lessons; what this lesson adds is knowing where the limits live and in which currency they are quoted.

The wing's reference chord

Why per cent MAC

Check you understood

Longitudinal CG limits in the documents