Free Surface Correction (FSC)

Free-surface correction for a slack tank - reduction in effective GM caused by liquid shifting in a partially-filled compartment.

StabilityFree surface

Tank geometry

Tank length lmTank breadth bmLiquid density ρ_liquidt/m³Ship displacement Δt

Moment of inertia i = l·b³/12: 512.0m⁴

FSC: 0.0105m

Reduces effective GM by 1.0 cm.

Changing the inputs requires JavaScript. The calculator above shows its default inputs and result. The formula, symbols, and regulatory sources are shown in the Formula section below.

Formula, assumptions, and limits

i = \tfrac{l \cdot b^3}{12}, \quad \text{FSC} = \frac{i \cdot \rho_\text{liquid}}{\Delta}

Symbol	Meaning	Unit
$l, b$	Tank length and breadth at free surface	m
$\rho_\text{liquid}$	Liquid density	t/m³
$\Delta$	Ship displacement	t
$i$	Second moment of tank free surface	m⁴
$FSC$	Effective GM loss	m

Source: IMO IS Code Part B Ch.3; Derrett & Barrass Ch.13

In short

Compute the loss of effective GM from a slack tank's free surface moment.

Learn the theory Intact stability