905
1 INTRODUCTION
Sea transportation has a much greater risk of
accidents than other means of transportation.
Dynamic and unpredictable shipping conditions have
implications for comfort [1]. The condition of the
maritime industry is the same. Always with different
challenges every time. One industry that is in line
with this is the mining industry. This industry
requires massive sea transportation to support the
supply chain from upstream to downstream.
One of the identical modes of maritime industry is
the tugboat. The construction of very massive
tugboats usually uses certain methods, depending on
the shipyard facilities [2][3]. Usually built in pairs
with a deck barge, Used to tow deck barges
containing mining products. Apart from that, it is also
used as a pilot boat and for mooring activities on large
ships in the port.
Much research has been done on tugboats [4][5] as
well as on barges [6][7][8][9]. Considering that
tugboats and barges are a mode of sea transportation
that is used massively, this research study aims to
optimize their operation to support maritime industry
activities, especially the shipping sector.
Tugboats are required to have high performance in
terms of maneuvering, stability, power, and
maneuverability because of their habitat and function
when operating. Ship maneuvering will be greatly
influenced by the characteristics of the water depth
[10]. The ship's maneuvering movements can be
controlled with a virtual automatic identification
Comparative Assestment of the Effect of Changing the
Breadth (B) of the Ship on the Stability of the Tugboat
A. Alamsyah
1
, M. Fikri
1
, S. Suardi
1
, M.U. Pawara
1
, R.J. Ikhwani
1
, W. Setiawan
1
& D. Paroka
2
1
Institut Teknologi Kalimantan, Balikpapan, Indonesia
2
Hasanuddin University, Gowa, South Sulawesi, Indonesia
ABSTRACT: This paper reviews the effect of changing the breadth of a tugboat before and after production on
ship stability. The numerical simulation method (maxurf stability) is applied. Likewise, another approach uses
the Benjamin Spence (integrator) method. The standard used is IMO. Several limits become parameters for
assessing the increase and decrease in ship stability. Several ship load cases are simulated to produce righting
arm curves. The construction of a tugboat with a length of 28 meters is the object of this research as a case study.
We compared the righting arm curve from the Maxurf stability analysis with Benjamin Spence's analysis to
confirm the accuracy of the calculation results. Both methods show a significant influence regarding changes in
the breadth of the tugboat. The produced righting arm curve consistently shows changes in the stability and
performance of the ship. There is a reduction in the area under the GZ curve. The IMO provides three of the five
standards and recommendations regarding the area under the GZ curve. The reduction of the area under the
GZ curve is 17~22% for the Benjamin Spence method and 12~18% for the Maxurf stability. This percentage
applies to all load-case simulations. This research contributes to providing an understanding of the effect of
changes in ship width on decreasing stability.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 18
Number 4
December 2024
DOI: 10.12716/1001.18.04.17
906
system and camera data [11]. Likewise, powering will
be greatly influenced by the ship's resistance when
operating [12]. On the other hand, ship stability shows
a significant influence from the even distribution of
cargo weight [13]. Placing cargo positions on different
decks will affect the stability of the ship [14].
Ship stability studies have been carried out using
various methods and approaches. The type of ship is
also a choice. Because it has its own characteristics
based on the size and shipping area. Hyeon Kim et al.
[15] studied the safety limits of submarine operations
with stability aspects. Woo et al. [16] evaluate ship
stability using a simple method based on cargo safety
with approximately 20 load cases. Negi et al. [17]
examine the steps for logically implementing second-
generation intact stability (SGISC) to detect failure
modes early [18]. Studies related to SGISC are very
interesting and are being massively encouraged
[19][20][21][22]. Guo et al. [23] studying the dynamic
rolling behavior of ships using algorithms. Paroka et
al. [24] Study the stability of traditional wooden ships
using alternative methods and evaluate them using
second-generation stability and weather criteria [25]
and weather criteria [26]. The study focuses on
comparing the breadth and draft of the ship's B/T
against the applicable criteria [27]. These studies used
an experimental test-method approach in
experimental tanks.
The shape of the ship's hull affects the quality of
the design, stability conditions, and other aspects of
production [15][28][29][30]. Apart from that, the main
size ratio also plays a role in determining the
performance of the ship [27]. In this research, we also
examine the main size ratios that have a significant
effect on ship stability performance. Construction and
design of a tugboat with a length of 28 meters as a
case study object. The design breadth of the ship is B =
9 m, but during production the breadth was reduced
to B = 8.6 meters with the design height and draft
remaining the same. In terms of material use, it is
relatively profitable because there is a reduction, but
from a technical perspective and the performance of
the ship, it will have a big impact, such as
maneuverability, stability, powering, and
maneuverability. The focus of this research is on how
the ship's stability performance occurs after breadth
reduction. Previous ship stability studies used
samples of container ships, submarines, passenger
ships, and traditional wooden ships. Likewise, the
method used is an experimental test. In contrast to our
research, which uses a tugboat case study with a
numerical simulation method approach using maxurf
stability [31][32][33] and the Benjamin Spence
(integrator) method [34][35].
2 METHODOLOGY
2.1 Benjamin Spence Method
This method is often used. To determine the buoyancy
value and metacentre point (Mo), Benjamin created
several water lines (WL) parallel to the cross section of
the ship [36][37].
Figure 1. Parallel water lines of a ship's cross section
Figure 1 provides the coordinates for creating the
cross-sectional area of the water line (AWL) and the
pressure point (Tcf), as well as the static moment. In
the process, we use Simpson's First Rules. This
condition is carried out repeatedly at every angle of
inclination to produce pantocarena. The Panto Carena
curve (cross curve) connects the arm value (NK sin φ)
and the ship displacement value (Δ).
= c
(1)
1
3
=
draft WL
h A Fs
(2)
( )
1
A
3
= +
WL station
L ym yk Fs
(3)
( ) ( )
( )
1
T
2
− +
=
+
cf
ym yk ym yk Fs
ym yk Fs
(4)
sin
=
WL cf
WL
A Fs T
NK
A Fs
(5)
where ∆ is displacement [tons]; γ is the density of sea
water [1.025 tons/m
3
]; c is the skin factor = 1.00675 –
1.0075 for steel ships; ∇ is volume [m
3
]; hdraft is the
distance between waterlines [meters]; AWL is the cross-
sectional area of the water line [m
2
]; Fs is the Simpsons
factor; Lstation is the distance between stations [meters];
ym is the horizontal distance of the KK axis (centre
line) to the point where the water line intersects with
the right hull section line [meters]; yk is the horizontal
distance of the KK axis (centre line) to the point where
the water line intersects with the left hull section line
[meters]; -yk is a condition where the horizontal
distance of the KK axis (center line) to the point where
the waterline intersects with the left hull section line is
not detected and follows the ym direction of the right
hull [meters]; and Tcf is the pressure point of the water
line measured from the KK (centerline) [meters].
907
The next step is to calculate the weight
components and center of gravity of the ship.
LWT DWT = +
weight
(6)
M
=
KG
w
(7)
where ∆weight is the displacement weight [tons];
LWT is light weight tons [tons]; DWT is dead weight
tons [tons]; KG is the total vertical gravity of the ship
[meters]; for steel ships, ∇ is volume [m3]; Ʃw is total
weight [tons]; and ƩM is the total force moment
[tons.meters].
Next, calculate and draw the curve of the righting
arm at each tilt angle. The righting arm (h) will be the
parameter as required by IMO [18].
sin sin
=−h NK KG
(8)
where h is the righting arm [meters]; NK sin φ is the
buoyancy arm [meters]; and KG sin φ is the arm of
gravity [meters].
2.2 Numerical Simulation
Construction and design of a tugboat with a length of
28 meters as a case study object. This ship was
assembled at one of the yards in the IKN supporting
area. The ship was modeled in 3D at a 1:1 scale using
the Maxurf modeler and analyzed using Maxurf
stability [31][32][33]. The hull form and main
dimensions of the Tugboat are listed in Table 1,
Table 2, and, for further visualization, Figure 1.
Table 1. Tugboat ship parameters B = 9.00
________________________________________________
Descriptions Unit Value
________________________________________________
Ship length L [m] 28.000
Ship breadth B [m] 9.000
Design ship draft T [m] 3.300
Ship depth H [m] 4.300
Frame spacing a0 [m] 0.500
Volume ∇ [m
3
] 335.480
Vertical Centre of Grafity KG [m] 3.370
________________________________________________
Table 2. Tugboat ship parameters B = 8.60
________________________________________________
Descriptions Unit Value
________________________________________________
Ship length L [m] 28.000
Ship breadth B [m] 9.000
Design ship draft T [m] 3.300
Ship depth H [m] 4.300
Frame spacing a0 [m] 0.500
Volume ∇ [m
3
] 320.740
Vertical Centre of Grafity KG [m] 3.568
________________________________________________
Figure 2 shows the main dimensions of the ship
according to the initial design, with breadth (b) = 9.00
m, height (h) = 3.60 m, and length (lwl) = 25.8 m. The
second stage is to design it in 2D, then develop it in
3D for ship breadth of 9.00 m and 8.60 m. The ship
design is shown in Figure 3.
Figure 2. General Arragement
Figure 3. 3D ship with B=9.00 and B=8.60
The next stage is tank design. The tank dimensions
seen in Figure 2 are developed in 3D form, as shown
in Figure 4.
Figure 4. Ship tank modeling
The difference in ship breadth B = 9.00 m and B =
8.60 m results in changes in the ship's displacement,
908
which is in line with changes in the ship's DWT and
LWT, which can be seen below:
Table 3. Displacement of different
________________________________________________
B of type Δ [tons] DWT [tons] LWT [tons] KG [m]
________________________________________________
9.00 343.90 196.381 147.519 3.370
8.60 328.80 187.351 141.351 3.568
________________________________________________
The next stage is a loadcase simulation by varying
the ship's DWT by 100% DWT, 75% DWT, 50% DWT,
and 25% DWT. Meanwhile, the LWT value adjusts to
changes in the breadth of the ship.
Table 4. Laodcase tugboat B=9.00
________________________________________________
Component 100% 75% 50% 25%
DWT DWT DWT DWT
[tons] [tons] [tons] [tons]
________________________________________________
Lightship 147.51 147.51 147.51 147.51
Ballast tank 18.27 18.27 18.27 18.27
Dry fuel oil tank 4.019 4.019 4.019 4.019
Fuel oil tank 100.42 75.31 50.21 25.10
Fresh water tank 72.86 54.64 36.43 18.21
________________________________________________
Table 5. Laodcase tugboat B=8.60
________________________________________________
Component 100%
________________________________________________
Component 100% 75% 50% 25%
DWT DWT DWT DWT
[tons] [tons] [tons] [tons]
________________________________________________
Lightship 141.35 141.35 141.35 141.35
Ballast tank 16.50 16.50 16.50 16.50
Dry fuel oil tank 4.019 4.019 4.019 4.019
Fuel oil tank 95.69 71.76 47.84 23.92
Fresh water tank 70.34 52.75 35.17 17.58
________________________________________________
The loadcase set-up is applied to vessels B = 9.00
and B = 8.60. The goal is to find the righting arm
curve. Next, it is evaluated based on IMO standards
[18]. This work is to find out the recommended
loadcase and vice versa when the ship is operating.
3 RESULT AND DISCUSSION
After the loadcase set-up is carried out, the righting
arm curves for ships B=9.00 and B=8.60 are produced,
which are shown in the following figure.
Figure 5. GZ curve B=9.00 of Loadcase 100%DWT
Figure 6. GZ curve B=9.00 of Loadcase 75%DWT
Figure 7. GZ curve B=9.00 of Loadcase 50%DWT
Figure 8. GZ curve B=9.00 of Loadcase 25%DWT
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Figure 9. GZ curve B=8.60 of Loadcase 100%DWT
Figure 10. GZ curve B=8.60 of Loadcase 75%DWT
Figure 11. GZ curve B=8.60 of Loadcase 50%DWT
Figure 12. GZ curve B=8.60 of Loadcase 25%DWT
Figures 5 to 12 show the righting arm curves of
ships with different breadths. More than one method
is used to verify and validate calculation results. Also
as a control for the results of the data analysis. The GZ
curve is then summarized and evaluated based on
IMO standards [18].
Figure 13. GZ curve B=9.00 of Loadcase all with Benyamin
Spence
Figure 14. GZ curve B=8.60 of Loadcase all with Benyamin
Spence.
910
Figure 15. GZ curve B=9.00 of Loadcase all with Maxurf
Stability.
Figure 16. GZ curve B=9.00 of Loadcase all with Maxurf
Stability.
Table 6. Evaluation of GZ curve B=9.00 from Maxurf
Stability
________________________________________________
Evaluation of 100% 75% 50% 25%
Component DWT DWT DWT DWT
________________________________________________
MG ≥0.15 m 2.79 2.60 2.68 2.67
A0 – A30 ≥3.151 m.deg 20.60 18.47 18.85 18.40
A0 – A40 ≥5.156m.deg 34.13 29.99 31.01 28.20
A30 - A40 ≥1.718m.deg 13.52 11.52 11.15 9.80
Max GZ at 30 or 1.41 1.17 1.13 0.98
greater≥0.2 m
Angle of maximum 42.70
o
40
o
38.2
o
32.7
o
GZ≥25 deg
Range of Stability > 60
o
103
o
90
o
87
o
75
o
________________________________________________
Table 7. Evaluation of GZ curve B=8.60 from Maxurf
Stability
________________________________________________
Evaluation of 100% 75% 50% 25%
Component DWT DWT DWT DWT
________________________________________________
MG ≥0.15 m 2.39 2.20 2.26 2.23
A0 – A30 ≥3.151 m.deg 17.83 18.47 15.81 15.11
A0 – A40 ≥5.156m.deg 29.71 25.54 25.21 23.02
A30 - A40 ≥1.718m.deg 11.88 9.88 9.40 7.90
Max GZ at 30 or 1.25 1.01 0.95 0.80
greater≥0.2 m
Angle of maximum 43.60
o
40
o
37.3
o
31.8
o
GZ≥25 deg
Range of Stability > 60
o
102
o
87
o
82
o
75
o
________________________________________________
Table 8. Evaluation of GZ curve B=9.00 from Benyamin
Spence
________________________________________________
Evaluation of 100% 75% 50% 25%
Component DWT DWT DWT DWT
________________________________________________
MG ≥0.15 m 2.80 3.00 3.35 3.40
A0 – A30 ≥3.151 m.deg 17.51 14.77 13.74 20.24
A0 – A40 ≥5.156m.deg 20.47 16.49 21.08 29.61
A30 - A40 ≥1.718m.deg 9.83 5.9 7.69 8.82
Max GZ at 30 or 1.05 0.87 0.85 1.15
greater≥0.2 m
Angle of maximum 40
o
31
o
32
o
30
o
GZ≥25 deg
Range of Stability > 60
o
100.5
o
84
o
81.5
o
66.5
o
________________________________________________
Table 9. Evaluation of GZ curve B=8.60 from Benyamin
Spence
________________________________________________
Evaluation of 100% 75% 50% 25%
Component DWT DWT DWT DWT
________________________________________________
MG ≥0.15 m 2.73 2.90 3.20 3.31
A0 – A30 ≥3.151 m.deg 17.80 14.77 13.43 16.61
A0 – A40 ≥5.156m.deg 28.22 22.70 22.68 24.17
A30 - A40 ≥1.718m.deg 6.53 6.91 6.48 8.29
Max GZ at 30 or 0.85 0.76 0.75 1.00
greater≥0.2 m
Angle of maximum 34
o
30
o
31
o
30.5
o
GZ≥25 deg
Range of Stability > 60
o
98
o
74.5
o
71.9
o
62
o
________________________________________________
Tables 6 to 9 show the evaluation of the GZ curve
based on IMO standards. A ship with B = 9.00 shows
superior stability compared to a ship with B = 8.60,
even though both still meet the standard. There was a
significant reduction in the area under the GZ curve,
as shown in Figures 17 to 24. This can be seen in the
GZ curve produced using the Benjamin Spence
method and also in Maxurf stability.
Figure 17. GZ curve B=9.00 vs B=8.60 of Loadcase 100%DWT
with Maxurf Stability.
911
Figure 18. GZ curve B=9.00 vs B=8.60 of Loadcase 75%DWT
with Maxurf Stability.
Figure 19. GZ curve B=9.00 vs B=8.60 of Loadcase 50%DWT
with Maxurf Stability.
Figure 20. GZ curve B=9.00 vs B=8.60 of Loadcase 25%DWT
with Maxurf Stability.
Figure 21. GZ curve B=9.00 vs B=8.60 of Loadcase 100%DWT
with Benyamin Spence.
Figure 22. GZ curve B=9.00 vs B=8.60 of Loadcase 75%DWT
with Benyamin Spence.
Figure 23. GZ curve B=9.00 vs B=8.60 of Loadcase 50%DWT
with Benyamin Spence.
912
Figure 24. GZ curve B=9.00 vs B=8.60 of Loadcase 25%DWT
with Benyamin Spence.
Figures 17 to 24 show a comparison of the GZ
curve using the Benjamin Spence and Maxurf stability
methods. The curve shows all loadcases before and
after changing the breadth of the ship. Observations
were made on the percentage reduction in area under
the GZ curve. Benjamin Spence's method shows a
reduction in the area under the GZ curve of 17 ~ 22%.
Meanwhile, maxurf stability shows a reduction in the
range of 12 to 18%.
Figure 25. Percentage of reduce area under GZ curve
maxurf stability vs benyamin spence.
Reducing the area under the GZ curve will have
implications for stability and performance. After
being evaluated based on IMO, the change in the
breadth of the ship shows that it still meets the
standards. However, changing the planning breadth
and breadth during production is not recommended
considering that tugboats have complex and dynamic
habits, so they must have high stability like fishing
boats, which require higher stability.
[38][39][40][41][42][43][44][45][46].
4 CONCLUSIONS
This research, with data analysis, proves the
significant influence related to changes in the breadth
of tugboats. The Benjamin Spence and Maxurf
stability methods consistently show changes in ship
stability performance after changes in breadth. There
is a reduction in the area under the GZ curve. The
IMO provides three of five standards and
recommendations regarding the area under the GZ
curve. The reduction in area under the GZ curve is
17~22% for the Benjamin Spence method and 12~18%
for Maxurf stability. This percentage applies to all
load-case simulations. The next investigation will
focus on stability analysis using other methods such
as CFD, the ship shape coefficient approach, and, if
necessary, experimental methods in experimental
pools. Considering that tugboats have complex and
dynamic habits, maneuvers, obstacles, and capsize
opportunities will be investigated.
ACKNOWLEDGMENT
I acknowledge the support of time and facilities form Center
of maritime infrastructure Engineering Kalimantan Institute
of Technology University.
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