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APPENDIX III

MEMORANDUM TO ADMINISTRATIOS ON AN APPROXIMATE DETERMINATION
OF SHIP’S STABILITY BY MEANS OF THE ROLLING PERIOD TESTS
(for ships up to 70 m in length)

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 such information.

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:

Where:
f = factor for the rolling period/rolling coefficient (different for feet and metric system)
B = breadth of the ship in feet or metric units

T_r = time for a full rolling period in seconds (i.e. for one oscillation "to and fro" port - starboard - port, or vice versa).

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 ship.

4. For coasters of normal size (excluding tankers), the following average values were observed:

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 coefficents 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 test in open waters are not available.
2. The rolling periods observed may not be free oscillations but forced oscillations due to seaway.
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 oscillatins 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 appropriate estimation.

12. The formula given in paragraph 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 one of the attached sample nomograms for feet and/or metric units 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 T_r scale corresonding with the determined rolling period, intersects the GM scale at the requested value.

15. The Annex to Appendix III 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.

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