Angle of Loll

Naval Architecture

Ship Stability - Angle of Loll

Consider the following vessel in unstable equilibrium condition.


angle of loll 1

As the angle of heel increases, the CB moves out further until it is directly under G. The capsizing moment disappears now and this angle of heel at which this condition occurs is called the angle of loll.

The ship now moves around the angle of loll, but if the CB does not move out far enough to move directly under G, then the vessel will capsize.

angle of loll 2

If the heel increases beyond the angle of loll, the CB moves out further to the low side and the ship now moves around this angle.

angle of loll 3

The angle of loll can be on either side depending upon the external inclining force, such as the wind and the waves.

However, there is always the threat of the G rising above the M and this will create a situation of unstable equilibrium, thereby capsizing the ship.

List Caused By Negative Gm

When a ship’s center of gravity moves vertically upwards and slightly above the Metacenter, the ship will develop a list (or possibly capsize.) The vessel may also “flop” over, developing the same list to the other side.

angle of loll 4

Possible Causes

1.         Removal of low weight

2.         Addition of high weight (ice)

3.         Moving weight upward

4.         Free Surface Effect

5.         Free Flow Effect (if present)

How to Recognize

1.         Vessel will not remain upright and will assume a list to either port or starboard.

2.         Vessel “flops” to port or starboard.

3.         Vessel will have a very long, slow roll period about the angle of list.

4.         A small GM is known to exist plus any of the above.

Corrective Measures

1.         Eliminate Free Surface and Free Flow Effects (if present)

2.         Add low weight symmetrically about centerline.

3.         Remove high weight symmetrically.

4.         Shift weight down symmetrically.


List Caused By Off-Center Weight And Negative Gm

angle of loll 5

The vessel’s stability is reduced by both an increase in the height of the center of gravity and movement from centerline. A negative GM condition exists, represented by the “uncorrected” curve. An off-center weight, represented by the cosine curve, is added and a larger list develops.

Possible Causes

1.         A combination of the previous causes of list.

How to Recognize

1.         Vessel will assume a permanent list either port or starboard (vessel will not flop).

2.         Very slow roll period about this permanent list.

3.         The known off-center weight isn’t proportional to the ship’s list.

Corrective Measures

Correct Negative GM first.

a.         Eliminate Free Surface and Free Flow Effects (if present)

b.         Shift weight down, add weight low, or jettison weight high.

Correct for Gravity Off Centerline

a.         Add weight to higher side

b.         Remove weight from lower side

c.         Shift weight to higher side

*** ALWAYS correct Negative GM prior to shifting weights transversely ***

Written by Capt. Jayant Roy


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