increased in excess of 60 degrees, the frequency of shipping seas dramatically decreased. On
the other hand, when the angle of encounter of ship to the waves was increased to 60 degrees,
there was increased rolling motion (Photographs 75 and 76).

Photograph 75 Japan Captainsʼ Association, DVD

Photograph 76 Japan Captainsʼ Association, DVD②

When reducing speed

Next, results of trials to test for the probability of shipping seas were conducted using a shipmodel to simulate a wave length of 79 m, which would be equal to the ship’s length, with60

a reduction in speed from 11 to 3 knots, with a much greater ship to wave encounter angle
between the range of zero to 90 degrees. See Figure 77.

Probability of sea shipping
Frequency of sea shipping

9
11
119
0°

7

30°
Encounter angle ofthe ship to wave

Ship speed
60°

5(knots)Fig. 77 Japan Captainsʼ Association, DVD

Regarding the frequency of seas being shipped with an angle of encounter at zero degrees,
when the speed is reduced from 11 knots to 6 knots, shipping seas can be reduced signiﬁcantly. Further, no seas were shipped at a speed of 3 knots. Also, when the angle of encounter wasaltered to 60 degrees, the frequency of seas being shipped was decreased greatly.
In summing up the results of these trials, it is clear that the frequency of seas being shipped
increased in proportion to ship speed, and that until the angle of encounter was increased tomore than 60 degrees, changing the angle of encounter had limited aﬀect. Figure 78 indicatesship speed and angle of wave encounter and shows wave heights represented by wind forceson the Beaufort scale corresponding to the frequency of shipping seas (10 times/hour) which
are shown as blue lines. The relationship between wind forces on the Beaufort scale andwave height, as trial conditions, can been seen in the Table 79.

61

Head sea

Ship model

30°

Frequency of5

sea shipping

45°＝１０times／hour︵ Beaufort scale
︶

6
7
8

60°

3.0

6.0

9.0

12

15 （knots）

Fig. 78 Japan Captainsʼ Association, DVD

Beaufort scale

5

6

7

8

9

10

11

Wave Height（ｍ） 2.0

3.0

4.5

6.5

7.5

9.0

11.5

Fig. 79 Japan Captainsʼ Association, DVD

According to the results obtained from ship model trials, if the allowable frequency ofshipping seas is 10 times per hour in head seas under wind force 5, ship speed is 12 knots(Fig. 80). If the angle of encounter is altered to 45 degrees, a ship speed of up to 13 knots ispermissible (Fig. 81).
Head sea

Ship model

30°

Frequency of5

sea shipping

45°＝１０times／hour︵

6︶
Beaufort scale

7
8

60°

3.0

6.0

9.0

12

Fig. 80 Japan Captainsʼ Association, DVD62

15 （knots）

Head sea

Ship model

30°

Frequency of5

sea shipping

45°＝１０times／hour︵

6︶
Beaufort scale

7
8

60°

3.0

6.0

9.0

12

15 （knots）

Fig. 81 Japan Captainsʼ Association, DVD

If the allowable frequency of shipping seas is 5 times per hour in head seas, ship speed
should be 11 knots (Fig. 82). That is to say, when wind force is increased up to approximately 5.2, the frequency of shipping seas can be decreased from 10 times per hour to 5 times perhour if speed is reduced to 11 knots from 12 knots.
Head sea

Ship model

30°

Frequency of5

sea shipping45°＝ 5 times／hour︵

6︶
Beaufort scale

BF 5.2

7
8

60°

3.0

6.0

9.0

12

15 （knots）

Fig. 82 Japan Captainsʼ Association, DVD

Likewise, in the case of a fully laden container ship with a gross tonnage of 40,000 tons
sailing in head seas under wind force 10, the frequency of seas being shipped can be reducedby half, from 10 times per hour to 5 times per hour if ship speed is reduced from 19 knots to
17 knots. In the case of a fully laden ore carrier with a gross tonnage of 110,000 tons in headseas under wind force 5, the frequency of seas being shipped can be reduced by half, from 10times per hour to 5 times per hour if ship speed is reduced from 13 knots to 12 knots.
63To summarize these results, it is clear from Figure 83 that the frequency of seas being
shipped can be reduced by half by reducing speed only to around 1 〜 2 knots.

Frequency reduction of shipping sea by speed reduction
CoasterContainer

BulkerGT

699 G/T

40,000 G/T

110,000 G/T

Lpp

78.5 ｍ

250m

280m

Frequency of shipping sea

Beaufort 5

Beaufort 10

Beaufort 5

10 times/hour

12 Kts19 Kts13 Kts5 times/hour

11 Kts17 Kts

12 KtsSpeed diﬀerence

1 Kts

2 Kts

1 Kts

Table 83 Japan Captainsʼ Association, DVD

７−１−４

Slamming Phenomenon

When a ship sails at a relatively high speed in head seas, slamming may occur. Slamming canbe broken down into the following categories.

①

Bottom slamming

Bottom slamming is caused by the interaction of a ship's bottom and the sea
surface when a raised hull plunges into the sea (Fig. 84).

Fig. 84 Japan Captainsʼ Association, DVD64

②

Bow ﬂare slamming

This phenomenon is caused by collision impact with the sea surface at a relatively
high speed. This phenomenon often occurs on a ship with a large bow ﬂare such asa relatively ﬁne container ship, PCC and ﬁshing boats (Fig. 85).

Fig. 85 Japan Captainsʼ Association, DVD③ Bow breaking wave impact
When a vessel sails on a calm sea surface, she propulsers pushing the seawater
forward. At that point, seawater is lifted at the bows（built-up waves）. Thisphenomenon often occurs when full-hull type ships such as tankers and bulkers
are fully loaded, by breaking wave impact which is caused by breaking waves
superimposed on built-up waves (Fig. 86).

Fig. 86 Japan Captainsʼ Association, DVD

65

These forms of slamming phenomena often not only cause structural damage to the bow,bottom or bow flare, but also lead to major cargo damage. Occasionally, such impact andconsequent hull damage may result in the ship sinking (Photographs 87 and 88).

Photograph 87 Japan Captainsʼ Association, DVD

Photograph 88 Japan Captainsʼ Association, DVD

Particularly relevant for large-sized container ships, springing and whipping will occur
simultaneously: the former can be defined as stationary oscillations of the hull due to acontinuous vibration between the hull construction and cyclic wave external force which
can occur in relatively calm oceanographic conditions, and the latter can be defined as
momentary oscillations of the hull induced by external impacts such as shock load associatedwith slamming in rough weather.
66

The author also has been aboard six large-sized container ships in total as a Master. As theauthor later learned, as a result of such phenomena known as springing or whipping, bowflare slamming occurred due to wind and waves and undulations (swells) diagonally infront, which caused the containers on the foremast and No.1 hold deck to slide from side toside. Although I knew that tankers and bulker hulls can be curved longitudinally, I was very
concerned as to whether or not the shell plating would crack, on account of the fact that I had
never seen containers slide from side to side in such a way before. At the dock inspection, I
remember that there were small, but not severe, cracks on the ﬂoor of the under deck passage
and handrails in the hold. I believe that new guidelines on the effects of vibrations while
operating a ship in rough seas will be necessary.
Just as with the trials that were conducted to analyse the frequency of seas being shippedusing a ship model above, trial results of the bottom slamming phenomenon are as follows:
The following conditions were applied: Ratio of wave length to ship length (Lpp): 1.0.

Gross
Lengthtonnage699
G/T

BreadthDepth

Design
draft

4.52m
78.5m
12.8 ｍ 7.8m
（Lpp）
Even Keel

Beaufort Wave
scale
hight
６

３m

Mean wave Wave Ship
periodlength speed
7.13 secs 79m 11knots

Whenever bottom slamming occurs, great pressure is instantaneously exerted on the bottomof the bow by the sea surface. The maximum force created during this impact acts to bend theship’s bow structure upward (Fig. 89).

Fig. 89 Japan Captainsʼ Association, DVD

67

Bow

Bow
Bow ﬂare slamming occurs

Bow

Impact force moves to the astern

Impact force disappears
Fig. 90 Japan Captains' Association, DVD

Figure 90 is a scene which was photographed using a ship model with a transparent bottom
so as to observe the process by which the phenomena associated with slamming occur
and the influences of such phenomena. The photograph shows that water pressure due toslamming runs toward the bow from the stern. Here, in a ship model trial, researchers studied
what conditions cause slamming to be generated.
Trial results of the frequency of bottom slamming are indicated in Figure 91 (three dimensional).

68Frequency of slamming

Loaded condition

11
9

Ship speed

75(knots)0°45°60°Encounter angle ofthe ship to wave

Fig. 91 Japan Captains' Association, DVD

Bow ﬂare slamming becomes more frequent when wave length is equal to ship length in headand countering seas, but the frequency of it considerably decreased when ship speed was
decreased to 6 knots. On the other hand, when ship speed was maintained at 11 knots and theencounter angle to the waves was changed (altered angle), the frequency of bow ﬂare slamming did not decrease so signiﬁcantly when the heading was changed to a course of less than
45 degrees. When the angle of encounter of ship to waves was increased to 60 degrees, there
was increased rolling motion, but the frequency of bow ﬂare slamming decreased somewhat.
In the same way as we studied the frequencies of shipping seas, trials were conducted using
model ships of a container ship and a bulker. A summary of the trials are shown in Table 92.
Decreasing the speed may reduce the frequency of slamming dramatically.
Frequency reduction of slamming by speed reduction
CoasterContainer

BulkerGT

699 G/T

40,000 G/T

110,000 G/T

Lpp

78.5 ｍ

250m

280m

Frequency of slamming

Beaufort 6

Beaufort 10

Beaufort 11

5 times/hour

5 Kts

17 Kts

8 Kts

2 times/hour

4 Kts

13 Kts

5 Kts

Speed diﬀerence

1 Kts

4 Kts

3 Kts

Table 92 Japan Captainsʼ Association, DVD69

７−１−５

Rough Weather Head and Countering Sea
Countermeasures

The most eﬀective countermeasure in head and countering seas of rough weather is to reduce
speed. Namely, as the above model ship trials have proved, if the angle of encounter is notaltered to more than 60 degrees, signiﬁcant results cannot be expected. Although changing
heading course can increase the four diﬀerent phenomena for head and countering seas, inthis case, a new problem will occur: increased rolling motion. Particularly, please pay extra
attention to parametric roll resonance.
The two diﬀerent situations are shown in Figure 93: The ﬁrst (with no deviation course froma to b) in the event of directly heading for the destination following the original course withslow steaming and the second (with deviation course a ⇒ c ⇒ b) in the event of navigating
to the destination with deviation by keeping the speed before deceleration. Each relationshipis as follows:
Initial Speed(Kts):Ｓ

Deceleration(Kts):Ｒ

Change-over Angle(degree):αbTime required for decelerating and proceeding directly（a ⇒ b）

２×x

α

hour

（S−R)

y

x

Time required, keeping Initial Speed, for detouring（a⇒c⇒b)

２×y

c

hour

S

Change-over angle, in case of same number ofrequired times, between deceleration and detouring

２×x
（S−R)

=

Cos α° =

２×y

α

S
x
y

=

x

y

（S−R)
= 1 ー
S

R
S

a
Fig. 9370

Table 94 shows the angle needed for a direct heading and detour heading of vessels under thesame time constraints that set sail at an initial speed of 20 knots or 15 knots.
Change-over angle when the required time in the case of direct deceleration anddetour is the same
Deceleration

Initial Speed 20 Kts

Initial Speed 15 Kts

Speed after

Change-overSpeed after

Change-overReducing(Kts)

Angle(degree)

Reducing(Kts)

Angle(degree)

2 Kts

18 Kts26 degree

13 Kts30 degree

3 Kts

17 Kts32 degree

12 Kts37 degree

4 Kts

16 Kts37 degree

11 Kts42 degree

5 Kts

15 Kts41 degree

10 Kts48 degree

6 Kts

14 Kts45 degree

9 Kts

53 degree

7 Kts

13 Kts49 degree

8 Kts

57 degree

8 Kts

12 Kts53 degree

7 Kts

62 degree

9 Kts

11 Kts56 degree

6 Kts

66 degree

10 Kts

10 Kts60 degree

5 Kts

70 degree（Kts）

Table 94

As can be seen in Tables 83(P.64) and 92(P.69), if speed is reduced by 2 to 3 knots, thefrequency of seas being shipped and bottom slamming due to head and countering seas will
be reduced by half.
On the other hand, when calculating the altered angle of the heading needed for a course,
requiring the same amount of time to reach the destination, in the event of slow steamingwith deviation and without reducing speed by 3 knots, when ship speed is at 20 knots, thealtered angle necessary will be 32 degrees. For a ship sailing at 15 knots, the angle will beless than 37 degrees. Namely, if course heading angle is increased to 60 degrees in order71

avoid shipping seas or bottom slamming, even if the initial speed can be maintained, the timeof arrival will still be delayed because of the deviated course taken.
On the contrary, in order to not be aﬀected by such phenomenon on an altered course headingof 60 degrees, if a vessel sailing at 20 knots is reduced to 10 knots, and a vessel sailing at 15
knots is reduced to 7 knots (a speed reduction of approximately one-half), the time of arrival
will be the same.
Compared with taking a detour, if speed is reduced by adjusting engine output, the amountof fuel consumption will be reduced. In addition, as described above, because there are wind
and waves and huge undulations (swells) coming from several different directions, a shipcannot maintain her initial speed even if she can alter her heading course.
From the above, regarding rough weather head and countering sea countermeasures, if a
speciﬁc ETA is to be realised, having the nerve to reduce speed so as not to expose the engine
to the torque rich effect until out of the rough weather, only then is it recommendable toincrease speed in order to make up for the delay, resulting in a safe voyage.

７−２

Ship Handling in Following Seas of Rough
Weather

Commonly, it may have been thought that ship handling in head and countering seas,
whereby the vessel heads towards the waves and wind, was considerably more challenging
than handling a ship in following seas. However, from a ship operational point of view, theMaster and Navigation Oﬃcers, for example, consider it to be easier because a ship in headand countering rough weather seas is easier to control as the ship’s bow can be positioned
towards wind and waves, paying extra attention to the ensuing influences (see previous
chapter) the hull may undergo. On the contrary, when being exposed to following seas,
more prudent ship operation will be necessary in rough weather, because there is a situation
whereby the ship will be unmaneuverable.
When operating in following seas, attention must be paid to the four phenomena below:

72

“Encounter Wave Grouping Phenomena”

1

occur when a ship is sailing in rough seas that involve irregular waves
with sudden serial high waves attacking the ship regularly from the aft“Parametric Rolling Phenomena”

2

occurs when the amplitude of the ship’s roll is gradually magnified“Reduction of Stability”

3

is a phenomena that occurs when a ship rides on a crest equal in length
to the ship’s length at midships, thus making the vessel unstable“Broaching-to Phenomena”

4

often resulting from surf-riding in which a ship loses steerage

７−２−１

Encounter Wave Grouping Phenomena

Ocean waves are an integration of irregular waves comprising those of diverse lengths,
heights and directions. Speciﬁcally, when a ship is sailing at the same speed as a high wave
group or navigating whereby the speed of the waves are faster than the speed of the ship
speed at the aft, the ship is continuously being hit repeatedly and severely by a series ofhigh waves that cause its manoeuvrability to be uncontrollable. Also, similar to head andcountering seas, damage to the hull and steering can be caused by seas being shipped fromthe astern (poop down). This is a dangerous encounter group wave phenomenon. According
to a number of experiment results, the most probable conditions under which a ship might becaught in a dangerous encounter wave grouping phenomena can be seen in Figure 95. Shownare the combination of encounter angles of the ship to the wave coming from aft, the ship’s
speed and the wave period.

73

Probable conditions under which
dangerous encounter wave
grouping phenomena may occur

V (Ship's speed Kts）
T（Meanwave period：sec）＝1.5

Definition of Encounters Wave Angle

WAVE
DIRECTION

SHIP COURSE

ENCOUNTER
ANGLE

Fig. 95 Japan Captainsʼ Association, DVD

According to 4.2.2. for successive high-wave attack of the IMO’s Ship Handling Guidlines(MSC.1/Circ.1228: 11 January 2007), in the event of a ship being exposed to following seas
directly from the aft, the dangerous zone is deﬁned to be within a range of 1.3 to 2.0, as canbe seen in Figure 96.

V/T Diagram
V （Kts）
Tw（sec）

0.8

0.8

1.0

1.0

1.2

1.2

1.4

1.4

1.6

1.6

1.8

1.8

2.0

2.0

2.2
2.4
2.6
2.8

2.2

Dang er ous Zone

2.6
2.8

3.0

3.0

230°

130°
140°

220°
150°

210°
200°

160°
190°

Fig. 96

74

2.4

180°

170°

IMO MSC.1/Circ.1228

Also, in 4.2.2.1 the guidelines deﬁne how to evaluate whether a ship is being successively
attacked by high waves:①

The average wave length is larger than 0.8 L（Lpp：Length between
Perpendicular）(MSC/Circ.1228) (See Note 4)②

The significant wave height is larger than 0.04 L (Lpp: Length between
Perpendicular）

Note4: According to the“Safety measure for ferries and RORO vessels” in Ministry of Land,
Infrastructure, Transport and Tourism.” (28 April 2011), the average wave length isrecommended to be larger than 0.6 L

Method of evaluation to assess whether a ship is being
successively attacked by high waves
For instance, if a ship’s Lpp is 120m, wave length is 126m and the signiﬁcant wave heightis 5m, it is possible to ascertain that the ship is being successively attacked by high waves(Calculating formula 97).

① ⇒ 120 ｍ × 0.8＝ 96 ｍ≦ 126 ｍ② ⇒ 120 ｍ × 0.04 ＝ 4.8 ｍ ≦ ５ｍ
Calculating formula 97

When evaluating, the actual values of wave length and wave height shall be applied.
However, because a ship obtains speed ahead while navigating, the actual wave period andlength will be diﬀerent from that experienced by the sway motion of a ship. A graph (Fig.
98) for determining the actual wave period from the wave period as experienced onboard
is introduced both in the MSC.1/Circ.1228 and in “Safety measure for ferries and RORO
vessels” by the Ministry of Land, Infrastructure, Transport and Tourism.

75How to determine the actual wave period and wave length
when experiencing a wave period on board a ship
α= 0°
360°

10°
350°

20°
340°

Wave Direction
30°
330°
40°
320°
50°
310°
60°
300°
70°
290°
80°
280°

Actual Wave Period
Wave period TW [s] 14 13 12 11 10 9 8 7 6 5

2

4

6

Obtain the actual periodof the wave from theperceived cycle.
In this case = 9 sec..

8 10 12 14 16 18 20 22 24 90°
270°
knots
100°
260°
110°
250°
120°
240°

5
6

130°
230°

7
8

5s

9
10
11

140°
220°

…

6s

14

32

30

28

26

24

25

22

20

18

16

14

10

Period of encounter TE

Perceived Period = 25 sec..

862

4 180°

170°
190°

160°
200°

150°
210°

MSC 1/Circ./1228 : Japan Ministry of Land, Infrastructure and Transport

Locate the point where angle of encounter of ship to waves
at 150 degrees intersects with a ship speed of 20 knots
Fig. 98 IMO MSC.1/Circ.1228 and “Safety measure for ferries and RORO vessels” in Ministryof Land, Infrastructure, Transport and Tourism.”

For instance, if a ship is sailing with its angle of encounter to waves at 30°, its speed at 20
knots and feeling as though the period of waves are around 25 seconds, the actual wave
period can be calculated using the following formula (The red lines in Fig. 98).

76

1

In the protractor to the right in the chart above, locate the point where the 30 degree
angle represents waves coming from the aft (angle of encounter of ship to waves at
150 degrees) intersects with a ship speed of 20 knots.

▼

2

Trace along the dotted line to the left side of the graph to find the point at which thewave period is experienced onboard the ship (25 seconds in this case).

▼

3

The actual wave period will be the curve that is closest to the intersection at 25
seconds (9 seconds in this case).

The approximate values of wave length can be calculated using the formula below (seeCalculating formula 99).

Wave length（m）＝ 1.56 × the square of wave period
Calculating formula 99

In the above formula, 1.56 × 9 × 9 ＝ 126m (wave length). Also, the wave height can beobserved by the naked eye.
Then, the Master will determine if the ship is within the dangerous zone using Figure 95.
Namely, if the actual wave period and calculated wave length can be determined from thewave period experienced onboard, it will be possible to conﬁrm whether the ship is within
the dangerous zone using the actual wave period and ship speed (Fig. 100).
In this example, when sailing at 20 knots, the wave period and ship speed ratio show 2.22,
thus it is possible to judge whether the ship is within the dangerous zone. By keeping theencounter angle to the waves unchanged and by reducing speed down to 10 knots, the ratio
becomes 1.11, which means that it is possible to escape from the dangerous zone (Fig. 100).

77

V/T Diagram
Ship's speed 10 Kts
Wave Direction 150°
Tw= 9 sec

V （Kts）
Tw（sec）
0.8

0.8

1.0

1.0

1.2
1.4
1.6

▶ V/T = 1.11
Outside of the
1.2
Dangerous Zone
1.4
1.6

1.8

1.8

2.0

2.0

2.2
2.4
2.6
2.8

2.2

Da ng er ous Zone

2.4
2.6
2.8

3.0

3.0

230°

130°

Ship's speed 20 Kts
140°

220° Wave Direction 150°

Tw= 9 sec

150°

210°

▶ V/T = 2.22
200°
190°
With in the Dangerous
Zone
Fig. 100

160°
180°

170°

IMO MSC.1/Circ.1228 and “Safety measure for ferries and RORO vessels” in
Ministry of Land, Infrastructure, Transport and Tourism.”

In reality, if your ship does end up within the dangerous zone as a result of the Encounter
Wave Grouping Phenomenon, it is required that you navigate using a combination of speed
reduction and alter course in order to escape from the zone.

７−２−２Parametric Rolling Phenomena

When a ship proceeds through regular longitudinal waves, the ship rolls repeatedly, forinstance, to the starboard side on the ﬁrst crest and to the port side on the following trough(Fig. 101).

78

Fig. 101 Japan Captainsʼ Association, DVD

However, when parametric rolling occurs, a ship rolls to the starboard side on the ﬁrst crestand to port side on the following crest, which means that one rolling cycle is completed forevery two wave cycles. Consequently, the amplitude of the ship’s roll is gradually magniﬁed.
The ship rolls only once for every two cycles of passing waves, while the ship pitches
once synchronous to the cycle of passing waves. This type of rolling is magniﬁed when theencounter wave period reaches half of the ship’s natural rolling period (Fig. 102).

Fig. 102 Japan Captainsʼ Association, DVD

79

Regarding this parametric rolling phenomena, the above conditions can occur not only inrough weather, but also in calm oceanographic conditions, when a ship may be approached
by a huge swell from a quarter stern.
When the author operated a pure car carrier in the Indian Ocean, the carrier was exposed towind from 30 degrees on the starboard under wind force 2 and a huge swell from a quarter
stern also on the starboard side. The author experienced only a small tolling to begin with,however this gradually developed into a rolling motion and, suddenly, the carrier was on a 15
to 20 degree inclination to the port side.
Even if your ship is exposed to a weak wind during her voyage, it is essential to keep sailing,
while paying extra attention to the swells. Also, please remember that this is more likely tooccur on ships with smaller GM. Countermeasures to avoid parametric rolling are as below:

Countermeasures for parametric rolling
The encounter wave period shall not coincide with one half of the natural rolling
period of ship.
When the ship rolls once while pitching twice, and you believe that the ship isparametrically rolling, you should reduce the ship’s speed as much as possible inorder to maintain course. Or, in the case that there are several huge swells, you
should observe which swells are causing parametric rolling and alter course by awide margin if necessary.
In addition, care must be taken regarding the synchronous rolling motion whichmight occur when the encounter wave period is equal to the natural rolling periodof the ship.

＝ Synchronous rolling motions ＝These phenomena might occur when the encounter wave period is equal to the natural rolling
period of the ship. This synchronous rolling motion means that there is greater probabilityof ship rolling motion intensifying dramatically to cause a large angle inclination, and that
control of the ship may be lost (Fig. 103).

80

Synchronized Rolling

Rolling

Strength of Stability

Wave TroughWave Crest
Fig. 103

７−２−３Reduction of Stability

Firstly, stability will be reviewed.

＝ Stability ＝
When a ship ﬂoats under stableconditions, both the downward
gravitational force, acting on
the centre of gravity G, and the
upward buoyant force, acting
on the centre of buoyancy B,
act on the same vertical line inequilibrium (Fig. 104).

Fig. 104 Japan Captainsʼ Association, DVD81

If a ship heels due to an external force, the centre of buoyancy shifts from the initial verticalline due to the relocation of the immersed section, although the centre of gravity remains
at the initial position. This creates an imbalance between the gravitational force and thebuoyant force, which had previously been in line (Fig. 105).

Fig. 105 Japan Captainsʼ Association, DVD

The intersection point M of the vertical line passing the centre of buoyancy and the verticalcentreline of the ship is called the metacentre, and the span between G centre of gravity andM metacentre is called GM. This GM governs a ship’s stability and its dynamic characteristics.
The scope of a ship's stability is defined primarily by the length of the lever between thecentre of buoyancy and the centre of gravity GZ, which is obtained by the formula whereby
GM is multiplied by sinθ (Fig. 106).
Stability can be calculated with the following calculation formula:82

Fig. 106 Japan Captainsʼ Association, DVD

Stability ＝
Displacement tonnage（Ｗ）
× righting arm (righting lever)（GZ）
In addition, there is the following relationship between the natural rolling period of a ship (T)and GM which is closely related to stability (Calculating formula 107).

GM =4π² × Ｋ²

≒ 0.64 ×Ｔ ≒Ｔ：Rolling period（sec)ｇ × Ｔ²Ｂ²
Ｔ²

0.8 × Ｂ

Ｋ：Radius of gyration(Large vessel 0.4×B）m
Ｂ：Breadth（ｍ）
ｇ：Gravitational acceleration（9.8ｍ／sec2）

GM

Calculating formula 107

In the case of loaded dry bulk cargo or a ship loaded with liquid cargo such as a tanker, there
is not a significant difference between the actual GM and the GM that was calculated bycargo stowage calculation software.
However, in the case of actual cargo weight being diﬀerent from the declared weight, i.e. a
83

container ship, there is a large diﬀerence between the actual GM and the calculated GM thatuses cargo information provided from the terminal.
The author has also been aboard an 8,000 TEU type container carrier. The author experienced
several occasions whereby the calculated draft on departure was less than the actual draft by more than 30cm. At the time of loading 1,000 containers, as the Ton per Centimeter (TPC)
was 100 tons (this is the amount of weight necessary to submerge the ship’s hull at 1 cm), itmeans that containers which were heavier than the declared weight (by 3,000 tons at grossweight) were loaded (each container was on average 3 tons heavy). Thus, calculated GM andactual GM are diﬀerent (on occasion there may be a signiﬁcant diﬀerence, for example, theactual measured GM may be around 30cm smaller than that of the calculated GM).
Regarding container ships with a large number of ports of call, stability is calculated (including each calculation of estimated departure draft, strength and GM) by reading the declared
weights and diﬀerences compared to the actual weight from the drafts of each port, based on
accumulated data and past records. In order to take the diﬀerences into consideration, ﬁrstly
a calculation is carried out using the cargo information provided by the terminal. Then, thevalue, which multiplies the diﬀerence per one container which is calculated using the empirical value multiplied by the quantity of containers, is to be purposefully input into the 1st tierof the cargo on deck most closely located to the centre of hull gravity G - we calculated theestimated departure draft and GM using a wide margin to be on the safe side.
After having departed port, each duty oﬃcer gauges the natural rolling period of the ship, theMaster checks actual GoM (values added that account for the reduction of GM due to liquidwith free surface in the tank) against a reference list of GM and natural rolling period, theﬁnal drawing of which is provided by the shipyard.

＝ Reduction of stability in following seas ＝
The degree of stability is determined generally by the area of the water plane as previously
shown in the chart. For instance, if a ship rides on a crest equal in length to the ship’s length
at midships, stability is reduced as the water planes at her bow and stern decrease due to thelower water lines at both ends (Fig. 108).
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Wave crest at midships

water planes ▶ small ▶ reduction of stability

Fig. 108 Japan Captainsʼ Association, DVD

On the other hand, when a trough of the same wave passes the midships, stability is increased
as the water planes at her bow and stern increase due to higher water lines (Fig. 109).

Wave trough at midships water planes ▶ large ▶ increase of stability
Fig. 109 Japan Captainsʼ Association, DVD85

Even if a ship is in a situation with reduced stability, the time span the ship might endure thiswill be shorter when sailing in counter seas. Conversely, the possibility of risk is increased infollowing and quartering seas, as the time span is greatly increased (Fig. 110).

ｈCounter Seas :encounter period will become shorterｔｈFollowing Seas :encounter period will become longerｔFig. 110 Japan Captainsʼ Association, DVD

Figure 111 shows the increase or decrease of a container ship’s stability. The curves showthat stability drastically decreases at the crest of the wave.

Stability Curves of Container Ship
GZ[m](Righting Level of Length)
1.2

Trough

0.8

Still

0.4

Crest

0.0
‑0.2
0

10

30

50

angle

Fig. 111 Japan Captainsʼ Association, DVD

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The reduction of stability tends to be more signiﬁcant in ﬁne ships with a large ﬂare, suchas: container ships, ﬁshing vessels and pleasure boats; and least signiﬁcant in full-hull ships,
such as: tankers and bulkers (Fig. 112).

Fig. 112 Japan Captainsʼ Association, DVD

Reduction of stability like this occurs when the ship speed is the same as the speed of the
waves. When the crest of a wave stays under the metacentre, the risk can be increased. Figure
113 shows a diagram of tank experiments of a model container ship, and at which angle theship capsizes. It is possible to observe that capsizing occurred at around 1.5, when dangerous
encounter wave grouping phenomena are more frequent.
(Dimensions of the model ship)
LengthBreadth

Depth

Draft

150.0m

27.2m

13.5m

8.5m

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Diagram of tank experiments of a model container ship
Dangrous degree

0.8

1.5 2.0

3.0 V/T

V
1.5

T

= 1.5

WAVE
DIRECTION
capsizing
SHIP COURSE
Fig. 113 Japan Captainsʼ Association, DVD

Using the same model ship sailing at 22 knots, Figure 114 indicates the frequency of capsizes
due to a reduction of stability by changing the angles of encounter in following seas. One
can see that the frequency of capsizes increases when sailing in following seas that approach
the aft from 10 to 50 degrees. In particular, 20 to 40 degrees aft is conspicuously the mostdangerous area.

Fig. 114 Japan Captainsʼ Association, DVD

From data obtained by past experiments, we can see how the frequency of capsizes due to a
reduction of stability changes depending on the ship’s speed. The data indicate that the fasterthe ship sails in those sea states, the greater the risk of capsizing is due to the reduction of88stability, and in contrast, the risk decreases at reduced speeds (Fig. 115).

Fig. 115 Japan Captainsʼ Association, DVD＝ Countermeasures for the reduction of stability in following seas ＝
If the angle of encounter is not altered to 20-40 degrees, the frequency of capsizes will
decrease. However, the most eﬀective countermeasure is to reduce speed so that the crest of awave does not stay under the metacentre as described above.

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