Locate CG inside the whole envelope

Why express CG as a percentage of a wing chord?

Percent MAC measures position behind the leading edge of the mean aerodynamic chord.

A relative wing coordinate

Use %MAC = 100 × (CG arm − LEMAC arm) / MAC length. LEMAC and CG must use the same datum and length units. Twenty-five percent MAC means one quarter of the MAC length aft of its leading edge; it does not mean one quarter of fuselage length.

The inverse is CG arm = LEMAC arm + (%MAC/100) × MAC. The MAC length is a length, whereas %MAC is a dimensionless percentage. Subtracting 25 m from a CG arm because the CG is 25% MAC is a unit error.

Why the envelope is a shape

A forward or aft CG limit may vary with aircraft mass and configuration. Plot the pair (CG, mass), not the CG alone. Use the applicable envelope for zero-fuel, take-off, landing or another specified condition.

A point on the boundary needs correct rounding and current data; display rounding must not turn an out-of-limit calculation into an accepted value.

Read percentage points correctly

A change from 20% to 25% MAC is five percentage points, equal to 0.05 times the MAC length. It is not a 5% relative increase of the original arm. On a 4 m MAC, those five points correspond to 0.20 m regardless of the datum position. This makes percent MAC useful for discussing a wing-relative balance range without carrying a long fuselage coordinate.

The mean aerodynamic chord is a defined aerodynamic reference, especially useful on tapered or swept wings. Its leading edge can lie well behind the chosen aircraft datum. If the CG is forward of LEMAC the formula can legitimately produce a negative percent MAC; arithmetic validity does not make the loading acceptable. The applicable envelope, not the sign alone, determines whether the aircraft may operate there.

Can the same CG be acceptable at one mass and unacceptable at another?

Read both coordinates and interpolate only where the supplied envelope allows it.

Connect adjacent limit points

A fictional envelope allows forward CG 18% at 40 t and 22% at 60 t, connected by a straight boundary. At 50 t, halfway between, the forward limit is 20%. A 19% CG is inside the lower-mass limit but outside the 50 t limit.

Interpolation preserves the chart’s local relationship. Extrapolating beyond its mass range invents an unapproved limit. A curved boundary or a table that prohibits interpolation must be treated as published.

Trace the flight through the envelope

Fuel burn and transfers move the mass/CG pair. Checking only take-off and landing can miss an intermediate excursion if tank sequence produces a nonlinear path. Use the prescribed fuel-use schedule and phase-specific limits.

An operational CG envelope may be deliberately narrower than a certified envelope to account for uncertainty and movement. Do not substitute the wider boundary for the operator’s required check.

A graphical answer still needs precision

A load-sheet plot contains uncertainty from line thickness, plotting resolution and reading the axes. A point that appears just inside a boundary may have inadequate resolution to support that conclusion. Use the prescribed numerical or graphical method and retain its required margins. Never use a broad sketch drawn for explanation as an approved envelope for dispatch.

If two adjacent points define a straight boundary, solve for the fraction of the mass interval first and apply the same fraction to the CG-limit interval. This method works whether the boundary slopes forward or aft, provided signs are preserved. Check the endpoints: using the lower mass must return the lower-mass limit, and using the upper mass must return the upper-mass limit. A reversed fraction fails this simple check.

Can you explain and apply the mechanism?

Four original questions. Work from the stated facts, then compare your reasoning with the explanation.