1 Recognizing the desirability of supplying to masters of small ships instructions for a simplified
determination of initial stability, attention was given to the rolling period tests. Studies on this
matter have now been completed with the result that the rolling period test may be recommended
as a useful means of approximately determining the initial stability of small ships when it is not
practicable to give approved loading conditions or other stability information, or as a supplement to
2 Investigations comprising the evaluation of a number of inclining and rolling tests according to
various formulae showed that the following formula gave the best results and it has the advantage
of being the simplest:
3 The factor f is of the greatest importance and the data from the above tests were used for
assessing the influence of the distribution of the various masses in the whole body of the loaded
4 For coasters of normal size (excluding tankers), the following average values were observed:
.1 Empty ship or ship carrying ballast f ~ 0.88
.2 Ship fully loaded and with liquids in tanks comprising the following percentage of the
total load on board (i.e. cargo, liquids, stores, etc.)
20% of total load f ~ 0.78
10% of total load f ~ 0.75
5% of total load f ~ 0.73
The stated values are mean values. Generally, observed f-values were within +0.05 of
those given above.
5 These f-values were based upon a series of limited tests and, therefore, Administrations should
re-examine these in the light of any different circumstances applying to their own ships.
6 It must be noted that the greater the distance of masses from the rolling axis, the greater the
rolling coefficient will be.
Therefore it can be expected that:
- the rolling coefficient for an unloaded ship, i.e. for a hollow body, will be higher than that
for a loaded ship.
- the rolling coefficient for a ship carrying a great amount of bunkers and ballast - both
groups are usually located in the double bottom, i.e. far away from the rolling axis - will
be higher than that of the same ship having an empty double bottom.
7 The above recommended rolling coefficients were determined by tests with vessels in port and
with their consumable liquids at normal working levels; thus the influences exerted by the vicinity
of the quay, the limited depth of water and the free surfaces of liquids in service tanks are covered.
8 Experiments have shown that the results of the rolling test method get increasingly less reliable
the nearer they approach GM-values of 0.20 m and below.
9 For the following reasons, it is not generally recommended that results be obtained from rolling
oscillations taken in a seaway:
.1 Exact coefficients for tests in open waters are not available.
.2 The rolling periods observed may not be free oscillations but forced oscillations due to
.3 Frequently, oscillations are either irregular or only regular for too short an interval of
time to allow accurate measurements to be observed.
.4 Specialized recording equipment is necessary.
10 However, sometimes it may be desirable to use the vessel's period of roll as a means of
approximately judging the stability at sea. If this is done, care should be taken to discard readings
which depart appreciably from the majority of other observations. Forced oscillations
corresponding to the sea period and differing from the natural period at which the vessel seems to
move should be disregarded. In order to obtain satisfactory results, it may be necessary to select
intervals when the sea action is least violent, and it may be necessary to discard a considerable
number of observations.
11 In view of the foregoing circumstances, it needs to be recognized that the determination of the
stability by means of the rolling test in disturbed waters should only be regarded as a very
12 The formula given in 2 above can be reduced to:
and the Administration should determine the F-value(s) for each vessel.
13 The determination of the stability can be simplified by giving the master permissible rolling
periods, in relation to the draughts, for the appropriate value(s) of F considered necessary.
14 The initial stability may also be more easily determined graphically by using the attached
sample nomogram, as described below:
.1 The values for B and f are marked in the relevant scales and connected by a straight line
(1). This straight line intersects the vertical line (mm) in the point (M).
.2 A second straight line (2) which connects this point (M) and the point on the Tr scale
corresponding with the determined rolling period, intersects the GM scale at the
15 The annex to appendix 3 shows an example of a recommended form in which these instructions
might be presented by each Administration to the masters. It is considered that each Administration
should recommend the F-value or values to be used.
ANNEX TO APPENDIX 3
SUGGESTED FORM OF GUIDANCE TO THEMASTER ON
AN APPROXIMATE DETERMINATION OF SHIP'S STABILITY
BY MEANS OF THE ROLLING PERIOD TEST
1 If the following instructions are properly carried out, this method allows a reasonably quick and
accurate estimation of the metacentric height, which is a measure of the ship's stability.
2 The method depends upon the relationship between the metacentric height and the rolling
period in terms of the extreme breadth of the vessel.
3 The rolling period required is the time for one complete oscillation of the vessel and to ensure
the most accurate results in obtaining this value the following precautions should be observed:
.1 The test should be conducted with the vessel in harbour, in smooth water with the
minimum interference from wind and tide.
.2 Starting with the vessel at the extreme end of a roll to one side (say port) and the vessel
about to move towards the upright, one complete oscillation will have been made when
the vessel has moved right across to the other extreme side (i.e. starboard) and returned to
the original starting point and is about to commence the next roll.
.3 By means of a stop-watch, the time should be taken for not less than about 5 of these
complete oscillations; the counting of these oscillations should begin when the vessel
is at the extreme end of a roll. After allowing the roll to completely fade away, this
operation should be repeated at least twice more. If possible, in every case the same
number of complete oscillations should be timed to establish that the readings are
consistent, i.e. repeating themselves within reasonable limits. Knowing the total time for
the total number of oscillations made, the mean time for one complete oscillation can
.4 The vessel can be made to roll by rhythmically lifting up and putting down a weight as
far off the centreline as possible; by pulling on the mast with a rope; by people running
athwartships in unison; or by any other means. However, and this is most important, as
soon as this forced rolling has commenced the means bywhich it has been induced
must be stopped and the vessel allowed to roll freely and naturally. If rolling has been
induced by lowering or raising a weight it is preferable that the weight is moved by a
dockside crane. If the ship's own derrick is used, the weight should be placed on the
deck, at the centreline, as soon as the rolling is established.
.5 The timing and counting of the oscillations should only begin when it is judged that the
vessel is rolling freely and naturally, and only as much as is necessary to accurately count
.6 The mooring should be slack and the vessel "breasted off" to avoid making any contact
during its rolling. To check this, and also to get some idea of the number of complete
oscillations that can be reasonably counted and timed, a preliminary rolling test should be
made before starting to record actual times.
.7 Care should be taken to ensure that there is a reasonable clearance of water under the keel
and at the sides of the vessel.
.8 Weights of reasonable size which are liable to swing, (e.g. a lifeboat), or liable to move
(e.g. a drum), should be secured against such movement. The free surface effects of slack
tanks should be kept as small as is practicable during the test and the voyage.
Determination of the initial stability
4 Having calculated the period for one complete oscillation, say T seconds, the metacentric height
GM0 can be calculated from the following formula:
where f is ... (to be determined for each particular vessel by the Administration).
5 The calculated value of GMo should be equal to or greater than the critical value which is ... (to
be determined for each particular vessel by the Administration).
Limitations to the use of this method
6 A long period of roll corresponding to a GMo of 0.20 m or below, indicates a condition of low
stability. However, under such circumstances, accuracy in determination of the actual value of
GMo is reduced.
7 If, for some reason, these rolling tests are carried out in open, deep but smooth waters, inducing
the roll, for example, by putting over the helm, then the GMo calculated by using the method and
coefficient of paragraph 3 above should be reduced by... (figure to be estimated by the
Administration) to obtain the final answer.
8 The determination of stability by means of the rolling test in disturbed waters should only be
regarded as a very approximate estimation. If such test is performed, care should be taken to
discard readings which depart appreciably from the majority of other observations. Forced
oscillations corresponding to the sea period and differing from the natural period at which the
vessel seems to move should be disregarded. In order to obtain satisfactory results, it may be
necessary to select intervals when the sea action is least violent, and it may be necessary to discard
a considerable number of observations.