3.4 Weight and Balance Equations and Records

Why Weight and Balance Matters

Weight and balance (W&B) controls two safety-of-flight properties: total weight must stay within structural limits, and the center of gravity (CG) must stay within the forward and aft limits set by the manufacturer. An overweight aircraft needs more runway, climbs poorly, and overstresses structure. A CG too far forward makes the aircraft nose-heavy and hard to flare or rotate; a CG too far aft reduces stability and can make recovery from a stall difficult. Mechanics own W&B because installing, removing, or relocating equipment changes both numbers, and 14 CFR Part 43 requires that those changes be computed and recorded.

The datum is an imaginary reference plane (often the nose, firewall, or leading edge) from which all horizontal distances are measured. The arm (moment arm) is the horizontal distance in inches from the datum to an item; arms aft of the datum are positive, arms forward are negative. This sign convention is essential when an item sits ahead of the datum.

The Core Equations and Terms

Three relationships answer almost every W&B test item:

The moment is the turning effect of a weight about the datum, and because moment = weight x arm, a small weight on a long arm can equal a large weight on a short arm. To find CG you add every item's weight, add every item's moment, then divide total moment by total weight. The moment index simply scales moments down (dividing by 100 or 1,000) so the arithmetic is manageable - remember to keep the divisor consistent.

A Fully Worked CG Calculation

Compute the loaded CG of a light aircraft (datum at the firewall):

Step 1 - Moments: multiply each weight by its arm (1,495 x 101.4 = 151,593, and so on). Step 2 - Totals: total weight = 2,055.0 lb; total moment = 193,193.0 lb-in. Step 3 - CG: CG = total moment / total weight = 193,193 / 2,055 = 94.0 in aft of datum.

Now compare to limits: if the approved CG range is 92.0 to 99.0 in, the 94.0-in result is within limits and the 2,055-lb total is below a 2,300-lb max gross - the loading is legal. The most common test mistake is forgetting an item's moment or dividing weight by moment instead of moment by weight. Always check that the CG falls between the forward and aft limits and that gross weight is not exceeded.

Empty-Weight CG, Adverse Loading, and Records

Empty-weight CG (EWCG) is found by weighing the aircraft per FAA-H-8083-1: level the aircraft, place calibrated scales under each wheel, subtract tare (chocks, blocks), sum the net scale weights and their moments, and divide total moment by total weight. Drain or account for fuel and oil per the procedure. The EWCG is the starting point for every later loading computation and is recorded in the aircraft W&B record.

Adverse-loading (extreme-condition) checks verify that the worst realistic loadings still stay in limits: a forward check loads everything ahead of the CG and minimizes aft items to test the forward limit, and an aft check does the reverse to test the aft limit. If an extreme but realistic load drives the CG out of range, the aircraft must be re-loaded or limited.

When a mechanic installs, removes, or relocates equipment that changes weight or balance, the regulations require computing the new empty weight and EWCG, revising the equipment list, and making the maintenance/weight-and-balance record entry. Ballast (temporary or permanent) may be added to bring CG within limits, and its weight and arm enter the calculation. A current, accurate W&B record is the legal basis for every load sheet the operator builds.

Mean Aerodynamic Chord and Common Traps

CG limits may be published in inches from the datum or as a percentage of mean aerodynamic chord (% MAC) for larger aircraft. To convert, you need the leading-edge of MAC (LEMAC) location and the MAC length: % MAC = ((CG - LEMAC) / MAC) x 100. For example, a CG 39 in aft of a LEMAC at an arm of 100 in, with a 156-in MAC, is at (39 / 156) x 100 = 25% MAC. The moment index (moment divided by 100 or 1,000) keeps loading-graph numbers small, but you must apply the same divisor everywhere.

The biggest exam traps are: dividing weight by moment instead of moment by weight; forgetting an item's moment; mishandling a forward (negative) arm; failing to subtract tare when weighing; and reporting a CG without checking it against the forward and aft limits. A loading can be within the weight limit yet outside CG limits, or vice versa - both must pass.