# What is Free Surface Moments?

The moment of inertia (I), often termed the second moment of area, of the free liquid surface of a rectangular tank may be determined by:

If the value of I is multiplied by the liquid density then a value of ‘Free Surface Moments’ (FSM’s) (t-m) is obtained.

Consider the previous Free Surface Effect formula:

Therefore:

Since:

It is evident from the above that the greater the value of the free surface moments, the greater the value of the effective KG and the greater the loss of GM (GGV).

In calculating the effective GM it is usual to make allowances for free surfaces by incorporating the FSM’s in the KG table where they must always be ADDED.