As a simple check on the figure, it can be shown that the rolling period of a boat is a function of the metacentric height GM.
The evaluation of a number of inclining
and rolling tests according to various formulae showed that the following one gives the best results for GM estimation and that it has the advantage of being simple:
GMo ≈ kRP(BWL/TR)2
where BWL
GMo TR
kRP m = waterline breadth
= the initial metacentric height m = rolling period
= constant (the rolling coefficient) - The factor kRP is of the greatest importance and it should
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 vessel (i.e. for a hollow body) will be higher than that for a loaded vessel.
• the rolling coefficient for a vessel carrying a great amount of fuel and ballast which latter is usually located in the bottom (i.e. far away from the rolling axis) will be higher than that of the same vessel having an empty fuel tank.
Experiments have shown that the results of the rolling test method get increasingly less reliable the nearer they approach metacentric height values of 0.2 m and below.
For a normal narrowboat, the coefficient kRP
can be taken to
be about 0.45. The boat on the numerical example had a rolling period of 2.9 seconds so that, using the value for kRP
of 0.45,
the metacentric height should be approximately:
GM = 0.45 x (2.045/2.9)2 = 0.22 m hDF Which shows a very good agreement.
N.B.1 As a guide for the marine surveyor, if the rolling period in seconds is numerically greater than one and a half times the waterline breadth in metres, her stability should be considered very suspect.
38 | The Report • March 2019 • Issue 87 Cockpit DF W W Figure 5 Down Flooding Height and Angle at Cockpit DF L L Cockpit Side Shell Side Shell hDF
m s
(5)
N.B.2 The shape of the bottom of the boat is irrelevant,
The only realistic way of increasing the stability of the boat is to fit ballast as low as possible. A 10 mm thick bottom plate is very helpful in this respect.
The initial metacentric height, however, is only part of the stability problem. It applies up to a heel angle of about 5°. Above that angle of heel other factors have to be taken into account. As the heel increases, the righting lever GZ first increases up to a maximum at about a heel angle of 30° to 35° and the starts to decrease. At the angle at which the cockpit coaming touches the waterline, the GZ curve also called the Curve of Statical Stability takes a sudden plunger and rapidly becomes zero. At that point called the angle of vanishing stability or AVS the boat becomes totally unstable and will plunge sink rapidly. The angle at which the boat starts to flood called, unsurprisingly the minimum down flooding angle, is easily measured and should, in the author’s opinion, be noted in his survey report.
Figure 4 below shows a typical curve of statical stability for a standard narrowboat and Figure 5 the minimum down flooding angle at the after cockpit and how to measure it.
Maximum GZ Angle of Deck Edge Immersion GZ GZ metres metres | 10 | 10 | 20 | 20 Figure 4 A Typical Narrowboat’s Statical Stability Curve | Angle of Heel - Degrees Angle of Heel - Degrees 30
AVS AVS |
30 | 40 Angle of Deck Edge Immersion
Maximum GZ 57.3o 57.3o GMo GMo
| 40
| 50
| 50
C. L. C. L.
Coaming b
Coaming b
Deck Deck
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