PHAK Ch. 10 · Ch. 5 CG link · study note

Weight and balance

Loading is not just “don’t exceed gross weight.” You must keep total weight and the center of gravity (CG) inside the approved envelope. Math is simple; judgment is not. Practice: Weight & Balance Lab (toy airplane, not your AFM).

Why it matters

Controllability / stability: CG position drives longitudinal stability (see stability). Outside limits, elevator authority or recovery can fail.
Structure: overweight raises loads in turbulence and on landing gear.
Performance: higher weight → higher stall speed, longer takeoff/landing, worse climb (stacks with density altitude).

Core math

Pick a fixed reference (the datum). Each loaded item has a weight and an arm (distance from the datum). Their product is a moment. The airplane’s balance point is the total moment divided by total weight.

Side view: yellow datum line at the reference plane, blue dimension labeled arm to a weight block W, with formulas Moment equals Weight times Arm and CG equals sum of moments over sum of weights — **Figure 1.** Arms are measured from the manufacturer’s **datum** (usually near the nose or firewall). `Moment = Weight × Arm` · `CG = Σ Moments ÷ Σ Weights`

Units: weight in lb (or kg), arm in inches (or mm) from datum, moment in lb·in (or equivalent). Aft of the datum is usually positive.

Term	Meaning
Datum	Imaginary reference plane; all arms measured from it
Arm / station	Distance from datum to an item’s CG
Moment	Weight × arm (rotational “leverage” about the reference)
Basic empty weight	Common starting point (empty + optional equipment; check aircraft records)
Useful load	Max weight − empty (people, bags, usable fuel…)
Payload	Occupants + cargo (fuel separate in many definitions)
Usable fuel	Fuel that can be used in flight (~6 lb/gal avgas rule of thumb)

The two checks

Weight versus CG envelope with approved region — **Figure 2.** You need both: under max weight *and* CG inside forward/aft limits (limits can change with weight on real envelopes).

Start with empty weight and empty moment from the aircraft’s W&B data.
Add each item: fuel, seats, baggage—with the correct arm from the AFM/POH.
Sum weights and moments → compute CG.
Compare to max weight and CG envelope (graph or table method in the AFM).

Forward vs aft CG

Forward CG versus aft CG effects on stability and handling — **Figure 3.** Same physics as longitudinal stability in Ch. 5—loading is how you move the CG day to day.

Fuel burn and shifts

Burning fuel changes weight and often CG (depends where the tanks are).
Moving bags between compartments changes moment without changing total weight much if only shifting.
When in doubt, recompute for takeoff and for landing (fuel remaining).

Pilot habits

Use this airplane’s current empty weight/moment (equipment changes matter).
Don’t trust passenger “guess weights”—pad for safety.
Heavy + high DA + aft/forward extreme CG is a common accident recipe.

Practice

Open Weight & Balance Lab →

Sources

FAA PHAK Ch. 10 — Weight and Balance
PHAK Ch. 5 — longitudinal stability / CG
MIT 16.687 Lecture 18 — terms, moment, forward/aft effects

Figures are educational schematics. Real limits come only from the AFM/POH.

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