The load sheet proved the masses; the trim sheet proves the balance and hands the crew a number they will physically dial into the aircraft. Its purpose is threefold: determine the CG of the loading, in index form and as per cent MAC; prove it inside the limits at zero fuel mass and at take-off mass; and convert the result into the stabiliser-trim setting for take-off. This lesson works the whole chain, explains why the operational limits on the sheet are tighter than the certified ones, and ends with the reason any of it matters: what the CG does to the pitch control the pilot holds.
From DOI to the zero-fuel index
The trim sheet starts where the operator's data stops: the dry operating index published for the flight's configuration. Every entry of the loading then contributes its own small index correction, pre-computed per cabin zone and cargo compartment so the user adds instead of multiplying: passengers in a forward zone drag the index down (their arm lies ahead of the reference arm), an aft hold pushes it up, and the running total after the last entry is the zero fuel mass index. Plotted against the zero fuel mass on the sheet's grid, that index must fall inside the zero-fuel portion of the envelope: the first of the sheet's two mandatory checks, and the one that also proves the aircraft could fly its whole fuel load away and still be in balance.
The fuel index correction
Fuel cannot be added zone by zone: as the tanks fill, the fuel's collective CG wanders with the tank geometry, so its index effect is not proportional to its quantity. The sheet solves this with the fuel index correction table: enter with the take-off fuel quantity, read the single correction it applies, and add it, sign included, to the zero-fuel index:
The take-off index