MAC Lab — Understanding the Centre of Gravity
%MAC is the most memorised yet least understood topic in load control. Here you see the physics behind the index tables step by step: what MAC is, why CG is expressed as a percentage rather than metres, how moment arithmetic produces %MAC, and why the envelope narrows as weight increases.
A wing is wide at the root and narrow at the tip — there is no single "chord length". The MAC (Mean Aerodynamic Chord) is one equivalent chord representing the wing's aerodynamic behaviour. Balance work needs just two numbers: its length and the distance of its leading edge from the nose (LEMAC).
These are typical training values for the A320 family. Every type has its own MAC length and LEMAC, which is why %MAC values cannot be compared across types.
Saying the CG is "18.85 m from the nose" only means something for that one type. Saying it as a percentage of MAC tells you where it sits relative to the wing — and therefore the centre of lift — which means the same thing on every aircraft. Move the slider and watch the two languages convert:
LEMAC100% MAC
TEMAC
BA (balance arm) is the arm measured from the datum. So 25% MAC means "the CG sits a quarter of the way back along the representative chord of the wing".
Every load item has a weight and an arm. Weight × arm = moment. Sum every moment, divide by the total weight and you have the arm of the centre of gravity — which the formula above turns into %MAC. Move the sliders and watch the table and the point on the envelope move:
| Item | Weight | Arm (m) | Moment | |
|---|---|---|---|---|
| DOW | Dry operating weight | 42,500 | 18.85 | 801,125 |
| PAX-F | Passengers — fwd zone | 5,880 | 14.00 | 82,320 |
| PAX-A | Passengers — aft zone | 6,384 | 24.00 | 153,216 |
| CPT-F | Forward hold | 800 | 11.70 | 9,360 |
| CPT-A | Aft hold | 1,200 | 26.50 | 31,800 |
| BULK | Bulk hold | 300 | 31.00 | 9,300 |
| ZFW | 57,064 | → 19.051 | 1,087,121 | |
| MACZFW = (arm − 17.8) ÷ 4.19 × 100 | 29.9% | |||
| TOW (+ fuel) | 64,864 | → 19.069 | — | |
| MACTOW | 30.3% | |||
Notice: raising or lowering fuel barely moves %MAC — the tanks sit at an arm very close to the CG. But shifting hold load forward or aft moves it quickly. Trim is far more about where the weight is than how much it is.
The green area is the certified CG envelope. The horizontal axis is %MAC, the vertical is weight. The area narrows as weight rises: a heavy aircraft leaves less margin for the tail surface and the gear, so the range the CG may roam shrinks.
The forward limit (left edge) preserves elevator authority — a nose-heavy aircraft is hard to rotate. The aft limit (right edge) preserves stability — too far aft and the aircraft tends nose-up with a growing tailstrike risk.
A single number on the loadsheet — MACTOW — converts directly into the cockpit stabiliser setting. A forward CG makes the aircraft nose-heavy and needs more trim to rotate; an aft CG needs less. It is one of the first items the captain cross-checks.
| MACTOW | Meaning | Consequence |
|---|---|---|
| < fwd limit | Outside envelope — far too nose-heavy | No departure; shift load aft |
| ~18–22% | Toward the forward side | More nose-up trim, slightly more fuel burn |
| ~25–32% | Ideal working band | Margin to the limits, low trim drag |
| ~33–37% | Toward the aft side | Fuel-efficient but the LMC margin shrinks |
| > aft limit | Outside envelope — instability risk | No departure; shift load forward |
1) The MAC is a single chord representing the wing; LEMAC is its distance from the nose.
2) We state the CG as a percentage of that chord so it means the same on every type and shows its position relative to the centre of lift.
3) What produces %MAC is moment arithmetic: (Σ weight×arm) ÷ Σ weight = CG arm → convert to a percentage. The index is simply that arithmetic made doable by hand.