541
1 INTRODUCTION
Wheel over point (WOP) is a term that refers to a
point on a course line that reminds the navigator to
initiate course alteration, which will ensure the ship
stays on the planned course [1], [2]. Keeping the ship
on its course helps to ensure the safety of ship
navigation [3], [4]. Inadequate awareness of a ship's
ability to turn and manoeuvre may result in a severe
accident.
Other than that, WOP can be used to observe pilot
behaviour since there have been several reports of
pilot-related mishaps throughout the years [5], [6]. For
instance, in one case, a vessel ran aground because the
pilot slept [7]. In a subsequent event, a pilot made a
late turning that the master subsequently overruled,
but the vessel ended up running aground as a result
of the late decision [8].
Then, in one instance, a vessel ran aground due to
a pilot's judgement error during the turn's execution
[9]. Another recorded incident occurred when
navigating with the pilot on board; the navigation
officer thought the pilot had everything under control
despite the fact that the vessel was slightly off course,
and the vessel ran aground due to inadequate course
alteration [10]. Additionally, owing to inadequate
turning, a cargo vessel ran aground during pilotage
[11]. Then there was an instance in which a pilot
repeatedly overshot a predetermined track before
finally aground [12], and a vessel ran aground owing
to the pilot's lack of expertise, and the navigation
officer was unable to establish the chain of the pilot's
error [13].
With WOP accurately indicated on the course line,
it is possible to monitor the evolution of human error
while turning. If the pilot initiates course alteration
prior to WOP, the ship is safe; however, the ship
A Comparison Study between Advance Transfer
Technique and Advance Transfer Mathematical Model
Using Bulk Carrier Ship: Cross-track Distance Validation
by Percentage Change and Mann Whitney U Test
A.S. Kamis
1,2
& A.F. Ahmad Fuad
2
1
Malaysian Maritime Academy, Kuala Sungai Baru, Melaka, Malaysia
2
University of Malaysia, Kuala Nerus, Terengganu, Malaysia
ABSTRACT: One of the methods of efficient course alteration is through the accurate identification of the WOP
by ATT. ATT is widely used by mariners worldwide, and recently, the technique has been restructured and
enhanced into ATMM. To prove the efficacy of ATMM over ATT, a few types of ships have been used to carry
out the manoeuvring analysis. This study extends the analysis by using a bulk carrier ship. A ship simulator
was used for a manoeuvring simulation study, which was carried out to verify the differences between these
two methods. Throughout the manoeuvring simulation study, XTD data for each simulation was monitored
and verified by XTL compliance, percentage variation, and the Wilcoxon-Mann Whitney U Test via IBM SPSS. It
was found that the ATMM can produce a significantly improved WOP compared to ATT and is suitable to be
used onboard a bulk carrier ship. This research's finding is expected to contribute as evidence to strengthen
ATMM's efficiency so that it can be accepted as an ECDIS algorithm for ship navigation.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 16
Number 3
September 2022
DOI: 10.12716/1001.16.03.17
542
would overshoot if the pilot altered the course after
WOP. As a result, if the pilot fails to act prior to WOP,
the bridge team, specifically the master, may override
the pilot's authority [14].
On January 27th 2016, a passenger ship, Azamara
Quest, was on its way to Picton in New Zealand,
carrying a total of 1046 passengers and the ship’s
crew. The pilot on board the ship made insufficient
steering by making small rudder angle changes.
When the pilot noticed the rudder was insufficient,
the rudder angle was gradually increased. However,
the ship still ends up damaging its bottom. According
to the investigation, even though the pilot did not
realise the turn was delayed, there was still sufficient
sea room for manoeuvre. Nonetheless, the bridge
team did not take the necessary action to override
pilot authority due to a lack of knowledge in
determining WOP [6], [15].
With references to the example given on the
grounding of Azamara Quest or a similar incident, the
ATT's benefit is that it is calculated using the hard
rudder angle, implying that the WOP produced is the
last point of action. If the WOP using hard rudder
angle had been correctly marked in the paper chart or
electronic chart display information system (ECDIS),
the Azmara Quest’s master could have taken over
control from the pilot when the ship was nearing the
WOP and instructed the helmsman to steer the rudder
hard over since he knows that the ship will overshoot
after that point.
2 LITERATURE REVIEW
2.1 Route monitoring through Advance Transfer
Technique (ATT)
Figure 1. Example of ship’s manoeuvring characteristic [16]
ATT is one of many methods that can be used to
determine WOP [17]. As opposed to other technique,
ATT use maximum angle while executing course
alteration [1]. The name Advance Transfer Technique
is used because this technique requires advance and
transfer information from a ship manoeuvring
characteristic, as seen in Figure 1. It is frequently used
for navigating harbours and confined water (HCW)
while under pilotage [18]. The WOP is calculated
through ATT, explained as follows.
With reference to Figures 2, 3, and 4, the following
symbols and abbreviations are used to describe the
formula:
dadv = Advance as per ship turning circle
dtrs = Transfer as per ship turning circle
dCG-WPT = Distance measured from CG to WPT
θ = The alteration angle
ATT is constructed with references to the model, as
seen in Figure 2. The formula to calculate the position
of WOP was able to be created. According to Anwar
(2015), WOP is measured from the WPT to the ship’s
CG. Hence, for this study, it is termed as dCG-WPT. To
acquire dCG-WPT, da is substracted from the advance
distance, dadv, for this reason:
CG WPT adv a
d d d
−
=−
(1)
da can be obtained as follows by applying the tangent
rule:
tan
tan
trs
a
trs
a
d
d
d
d
=
=
Therefore, the formula of ATT [1] is acquired as
below:
trs
CG WPT adv
d
dd
tan
−
=−
(2)
Figure 2. Marking WOP [1]
2.2 The problems that lead to the need to improve ATT
Mariners are using ATT to identify the WOP.
However, few problems are associated with the
technique [2], [19]. The following are the primary
concerns that were discovered:
543
2.2.1 Negative WOP value for 20° change of course or
less
As shown in equation (2), the formula for ATT has
a disadvantage for course alteration that is less than
20°. The following is a sample of WOP calculated for
20° and 50° alteration angles (The ship’s advance
distance is 0.455nm, and the transfer distance is
0.231nm).
Table 1. Calculated WOP using ATT formula
_______________________________________________
Scenario Change of dadv (nm) dtrs (nm) WOP
course (θ)
_______________________________________________
1 20° 0.455 0.231 -0.180
2 50° 0.455 0.231 0.261
_______________________________________________
As seen in Table 1, the computed WOP is negative
in scenario one but becomes positive in scenario 2.
The value indicates that in scenario 1, the ship's
course must be altered 0.18nm after WPT, implying
that the vessel had deviated from the charted course
before the course alteration was initiated. However,
the course alteration for 50° will occur 0.261nm prior
to WPT.
2.2.2 Charted course and final heading not aligned
The method operates on the concept depicted in
Figure 3, where the final heading and the charted
course are not aligned. The primary reason for this
problem is that advance and transfer provided in ship
manoeuvring characteristics are measured referring to
90° course change [20]. As a result, the identical
advance and transfer values are utilised in the
calculation, even though the change of course is less
than 90°.
Figure 3. Advance transfer technique principle [19]
2.3 Development of an Improved Mathematical Model
The turning circle is utilised to ensure the final
heading and charted course are aligned, as seen in
Figure 4. Thus, the new concept has moved WOP to
WOP’ as shown in Figure 4. For this reason, another
term will be added and used as follows:
dWOP = Distance of WOP’ from WPT
Figure 4. ATMM development concept [2]
A mathematical model can be created using the
related previous analysis equation as a starting point
[21]. For this reason, the ATT equation was used as
the foundation of the advance transfer mathematical
model (ATMM). Figure 5 was constructed by
following the generic turning circle to interpret the
ATMM's development.
Figure 5. Distribution details [2]
As seen in Figure 5, the distance from the bridge's
global navigation satellite system (GNSS) antenna to
the CG will be included in the ATMM design. As a
result, in equation (1), the distance between WOP' and
WPT, otherwise abbreviated as, dWOP, is added, made
up of 1) dCG-WPT and 2) dc. Hence:
WOP CG WPT c
d d d
−
=+
Based on the existing ATT formula in (1),
CG WPT adv a
d d d
−
=−
, the above equation can be re-
written as:
WOP adv a c
d d d d= − +
(3)
The following step is finding the value of da and dc.
The following trigonometric function can be used to
determine da:
544
tan
tan
a
a
QR
d
QR
d
=
=
(4)
From QS, subtract RS to obtain QR. QS = dtrs. As
seen in Figure 5, RS is represented as db. Hence, QR
=dtrs-db. Subsequently, (4) can be re-written as follows:
tan
trs b
a
dd
d
−
=
(5)
Because ΔROS is a right-angled triangle, db can be
acquired by using the trigonometry tangent rules:
tan
tan
b
trs
b trs
d
ROS
d
d d ROS
=
=
(6)
To determine ∠ROS, first, due to TU ⊥ OP, in
other words, ∟UPO = 90°. With regards to triangle
rules, the total interior angle is 180°. Thus, PUO =
180°, which is the sum value of ∠UOP, ∟UPO, and
∠PUO. Therefore:
90 UOP
= −
Consistent with the rule for a line tangent to a
circle, RS and RP have the same value, |RP|=|RS|,
which makes ∠ROS=∠POR. For this reason, ∠ROS
is half of ∠POS. Hence, ∠ROS can be expressed as:
2
90
2
POS
ROS
ROS
=
−
=
(7)
The following is derived with reference to (6) and the
input from (7):
tan
90
2
b trs
b trs
d d ROS
d d tan
=
−
=
(8)
Inserting (8) into (5), da can be obtained as:
90
2
tan
trs trs
a
d d tan
d
−
−
=
(9)
The location of the ship is monitored via the GNSS
receiver during navigation is typically located at the
bridge. Due to the reason that the turning circle is
drawn referring to the ship’s CG, the specific WOP
shall contain the distance between CG and the bridge,
hence dCG=dc, and this is applied as follows.
To identify the location of dCG, firstly, the position
of CG needs to be confirmed. In an actual ship, LCG
can be accessed directly from the ship's loadicator
[22]. On the other hand, when a ship floats, the ship's
longitudinal centre of buoyancy (LCB) will be vertically
aligned with LCG. For this reason, LCG can also be
equated to the LCB [23]. The small differences between
LCB and LCG is not significant, therefore it can be
neglected [23].
Figure 6. dCG is measured from the vessel’s longitudinal CG
(LCG) and the ship’s bridge (LSB) [2]
With reference to Figure 6, the dCG can be located as
follows:
2
c CG CG SB
LBP
d d L L= = + −
(10)
In conclusion, with reference to (3), dWOP can be
simplified as follows [2]:
90
tan
2
t
n
a2
trs trs
WOP adv S
WOP ad
GB
c
C
va
d
d
d d d
dd
LBP
d L L
−
−
= − + + −
=−
+
(11)
2.4 Problem statement and the research AIMS
For a long time, ATT has been used in maritime
navigation to determine the most favourable WOP,
particularly during navigation in HCW. A recent
study was able to improve the ATT into a
mathematical model, namely ATMM. Two research
was conducted using tanker ship [17] and LNG ship
[2] to prove the effectiveness of the ATMM.
Therefore, this study aims to assess the
effectiveness of ATMM using a bulk carrier ship while
in ballast condition and fully loaded condition. This
study has considered the International Maritime
Organisation (IMO) requirements towards ensuring
the developed mathematical model is accepted to be
used onboard a merchant's vessel. According to IMO
ISM (2018) [24], when developing a new safety
system, the following should be considered:
1. A new system should comply with the regulations.
2. A new system should enhance the safety
management system (SMS).
For this reason, the following are the objective of
the study:
− Objective 1 : To verify that ATMM complies with
XTL as required by IMO
− Objective 2 : To verify that ATMM can enhance the
safety of navigation as outlined in SMS
545
3 METHODOLOGY
The research begins with an explanation of how the
ATMM was developed, taking into account the
shortcomings of the previous ATT model through a
literature review. Then, both methods were used to
calculate WOP where a bulk carrier was manoeuvred
using a ship simulator to obtain the XTD data.
Following that, a comparison study on the XTD data
was carried out to corroborate the ATMM’s
improvement over the ATT [25]. The comparison
study between ATT and ATMM was verified in three
stages to accomplish the research's objectives.
The first objective is to verify that ATMM
conforms to all the applicable rules and regulations.
For this reason, the XTD results shall comply with the
cross-track limit (XTL) as required by the IMO [26].
An XTL is defined as a limit where a ship is allowed
to diverge from the planned track [27].
The second objective is to verify that ATMM can
enhance SMS. The intended improvement in this
research was obtained by maintaining the ship on the
targeted course while reducing XTD. The reduction
was justified by adopting the methodology for
calculating percentage variation [28]. The magnitude
of XTD reduction and its trend can be observed
numerically through percentage change. However,
the significant reduction can only be verified through
a statistical test. Therefore, in the third analysis, to
establish the statistical dominance of one of two
random variables over the other, the Wilcoxon Mann
Whitney U test was used [29], [30]. The test is well-
known in clinical studies, where it is often used to
assess the efficacy by comparing two treatments [31].
As a result, this research will contribute to the
deciding factor of whether ATMM is preferable
compared to ATT in assessing the WOP.
3.1 Data collection through ship simulator test
The information about the bulk carrier selected for
this study is shown in Table 2 and Figure 7 below.
Table 2. Ship general characteristic
_______________________________________________
Description Ballast Fully Loaded
_______________________________________________
Vessel Type Bulk carrier
Displacement 23565 tonnes 33089 tonnes
Speed 15 kts 14 kts
Engine Type Slow speed diesel (1 x 8827 kW)
Propeller Type FPP
Bow Thruster None
Length 182.9 m
Breadth 22.6 m
Bow draft 7.5 m 10.1 m
Stern draft 7.6 m 10.7 m
Height of eye 22 m 19 m
_______________________________________________
Figure 7. Turning circle extracted from the simulator
The data regarding the chosen ship were obtained
from the simulator. The data from Figure 7,
specifically the advance and transfer, were used to
calculate WOP for nine courses for every 10° and
drawn in the simulator. A helmsman was assigned to
follow the courses and carry out the course alteration
at calculated WOP by the application of hard rudder
angle. Then, the XTD of the vessel was monitored and
recorded.
It is worth emphasising once more that the
purpose of this study was to assess which WOP
mathematical model capable of providing a more
accurate track-keeping function by lowering XTD. As
a result, manoeuvring simulations were conducted
using both ATT and ATMM, and the XTDs for both
approaches were compared to see if ATMM achieved
a significant improvement. Three steps of analysis
were performed on the data collected from the
manoeuvring simulation. For the first study, the
results were compared to the International Maritime
Organization's XTL standards for XTD deriving from
ATT and ATMM [32]–[34] following guidelines
published by Kristić et al. (2020) [27], as shown in
Table 3 below.
Table 3. XTL value
_______________________________________________
HCW
_______________________________________________
Zone of confidence 6.5
Half Ship’s breadth 11.3
Position accuracy 15
Safety Allowance 50
20
2
LOAxSin
31
XTL (m) 113.8
_______________________________________________
546
Table 4. Analysis of deep-water manoeuvring under ballast conditions
Location
Side
d
adv
(nm)
d
trs
(nm)
d
CG
(nm)
d
WOP
XTD < XTL(113.8m) ?
XTD graph
ATT
ATMM
( )
ATT m
( )
ATMM m
Kemaman
Malaysia
ENC
number:
3JS P9200
0410.78’
N
10335.4’E
23.8-
29.3m
(deep
water)
Starboard
10
0.24
0.108
0.0329
-0.372
0.174
58
YES
20
YES
20
0.24
0.108
0.0329
-0.057
0.184
115
NO
25
YES
30
0.24
0.108
0.0329
0.053
0.194
119
NO
8
YES
40
0.24
0.108
0.0329
0.111
0.204
125
NO
30
YES
50
0.24
0.108
0.0329
0.149
0.215
105
YES
2
YES
60
0.24
0.108
0.0329
0.178
0.227
83
YES
12
YES
70
0.24
0.108
0.0329
0.201
0.241
50
YES
2
YES
80
0.24
0.108
0.0329
0.221
0.256
48
YES
19
YES
90
0.24
0.108
0.0329
0.240
0.273
45
YES
22
YES
Port
10
0.23
0.102
0.0329
-0.348
0.17
84
YES
6
YES
20
0.23
0.102
0.0329
-0.050
0.179
127
NO
16
YES
30
0.23
0.102
0.0329
0.053
0.188
131
NO
5
YES
40
0.23
0.102
0.0329
0.108
0.198
156
NO
17
YES
50
0.23
0.102
0.0329
0.144
0.208
102
YES
10
YES
60
0.23
0.102
0.0329
0.171
0.22
91
YES
17
YES
70
0.23
0.102
0.0329
0.193
0.232
74
YES
3
YES
80
0.23
0.102
0.0329
0.212
0.246
65
YES
21
YES
90
0.23
0.102
0.0329
0.230
0.263
55
YES
39
YES
Compliance to XTL by %
83%
100%
Table 5. Analysis of shallow water manoeuvring under ballast conditions
Location
Side
d
adv
(nm)
d
trs
(nm)
d
CG
(nm)
d
WOP
XTD < XTL(113.8m) ?
XTD graph
ATT
ATMM
( )
ATT m
( )
ATMM m
Balti-
more,
USA
ENC
number:
4414n12
0
3855.21’
N
07624.7
8’W
10.7-
14m
(shallow
water)
Starboard
10
0.29
0.139
0.0329
-0.498
0.196
71
YES
12
YES
20
0.29
0.139
0.0329
-0.092
0.208
112
YES
4
YES
30
0.29
0.139
0.0329
0.049
0.221
185
NO
3
YES
40
0.29
0.139
0.0329
0.124
0.234
146
NO
4
YES
50
0.29
0.139
0.0329
0.173
0.249
98
YES
6
YES
60
0.29
0.139
0.0329
0.210
0.264
88
YES
19
YES
70
0.29
0.139
0.0329
0.239
0.281
90
YES
24
YES
80
0.29
0.139
0.0329
0.265
0.301
104
YES
40
YES
90
0.29
0.139
0.0329
0.290
0.323
126
NO
59
YES
Port
10
0.28
0.132
0.0329
-0.472
0.189
64
YES
5
YES
20
0.28
0.132
0.0329
-0.092
0.201
127
NO
2
YES
30
0.28
0.132
0.0329
0.048
0.213
203
NO
1
YES
40
0.28
0.132
0.0329
0.120
0.226
178
NO
3
YES
50
0.28
0.132
0.0329
0.166
0.239
137
NO
9
YES
60
0.28
0.132
0.0329
0.201
0.254
103
YES
15
YES
70
0.28
0.132
0.0329
0.229
0.27
120
NO
27
YES
80
0.28
0.132
0.0329
0.254
0.289
143
NO
40
YES
90
0.28
0.132
0.0329
0.277
0.31
158
NO
52
YES
Compliance to XTL by %
50%
100%
Table 6. Analysis of deep-water manoeuvring under fully loaded conditions
Location
Side
d
adv
(nm)
d
trs
(nm)
d
CG
(nm)
d
WOP
XTD < XTL(113.8m) ?
XTD graph
ATT
ATMM
( )
ATT m
( )
ATMM m
Auck-
land,Ne
w Zea-
land
ENC
number:
4vjqzr11
3637.55’
S
17505.6
4’E
42-43m
(deep
water)
Starboard
10
0.296
0.144
0.0329
-0.521
0.197
63
YES
9
YES
20
0.296
0.144
0.0329
-0.100
0.210
112
YES
6
YES
30
0.296
0.144
0.0329
0.047
0.223
181
NO
16
YES
40
0.296
0.144
0.0329
0.124
0.237
121
NO
19
YES
50
0.296
0.144
0.0329
0.175
0.252
110
YES
4
YES
60
0.296
0.144
0.0329
0.213
0.268
94
YES
12
YES
70
0.296
0.144
0.0329
0.244
0.286
102
YES
1
YES
80
0.296
0.144
0.0329
0.271
0.306
118
NO
11
YES
90
0.296
0.144
0.0329
0.296
0.329
119
NO
22
YES
Port
10
0.283
0.137
0.0329
-0.494
0.191
69
YES
4
YES
20
0.283
0.137
0.0329
-0.093
0.203
120
NO
11
YES
30
0.283
0.137
0.0329
0.046
0.216
170
NO
12
YES
40
0.283
0.137
0.0329
0.120
0.229
112
YES
12
YES
50
0.283
0.137
0.0329
0.168
0.243
93
YES
0
YES
60
0.283
0.137
0.0329
0.204
0.258
71
YES
14
YES
70
0.283
0.137
0.0329
0.233
0.275
65
YES
1
YES
80
0.283
0.137
0.0329
0.259
0.294
91
YES
10
YES
90
0.283
0.137
0.0329
0.283
0.316
99
YES
28
YES
Compliance to XTL by %
78%
100%
547
Table 7. Analysis of shallow water manoeuvring under fully loaded conditions
Location
Side
d
adv
(nm)
d
trs
(nm)
d
CG
(nm)
d
WOP
XTD < XTL(113.8m) ?
XTD graph
ATT
ATMM
( )
ATT m
( )
ATMM m
Great
Belt,
Den-
mark
ENC
number:
b0hsdx0
0
5515.52’
N
01052.0
8’E
13.6-
15.3m
(shallow
water)
Starboard
10
0.359
0.175
0.0329
-0.633
0.232
68
YES
4
YES
20
0.359
0.175
0.0329
-0.122
0.248
138
NO
2
YES
30
0.359
0.175
0.0329
0.056
0.264
203
NO
13
YES
40
0.359
0.175
0.0329
0.150
0.281
155
NO
27
YES
50
0.359
0.175
0.0329
0.212
0.299
166
NO
43
YES
60
0.359
0.175
0.0329
0.258
0.318
142
NO
61
YES
70
0.359
0.175
0.0329
0.295
0.339
124
NO
76
YES
80
0.359
0.175
0.0329
0.328
0.364
148
NO
94
YES
90
0.359
0.175
0.0329
0.359
0.392
181
NO
101
YES
Port
10
0.341
0.166
0.0329
-0.600
0.222
63
YES
4
YES
20
0.341
0.166
0.0329
-0.115
0.237
131
NO
6
YES
30
0.341
0.166
0.0329
0.053
0.252
185
NO
5
YES
40
0.341
0.166
0.0329
0.143
0.268
138
NO
7
YES
50
0.341
0.166
0.0329
0.202
0.285
148
NO
22
YES
60
0.341
0.166
0.0329
0.245
0.304
115
NO
29
YES
70
0.341
0.166
0.0329
0.281
0.324
128
NO
44
YES
80
0.341
0.166
0.0329
0.312
0.347
114
NO
66
YES
90
0.341
0.166
0.0329
0.341
0.374
147
NO
70
YES
Compliance to XTL by %
22%
100%
4 RESULT AND DISCUSSION
Tables 4 and 5 summarise the analysis of deep-water
and shallow-water manoeuvring under ballast
conditions, respectively, whilst Tables 6 and 7
summarise the analysis of deep-water and shallow-
water manoeuvring under fully loaded situations. The
tables show whether or not the XTD complies with
XTL as indicated by a simple ‘YES’ or ‘NO’.
4.1 XTL compliance analysis
Figure 8. Compliance to XTL according to simulation
From Figure 8, it can be seen that, for the first
simulation study, a bulk carrier at ballast condition
was used in the deep-water area. Only 67% of the
turns conformed to XTL when ATT was used and
100% when ATMM was used.
The subsequent analysis used the identical bulk
carrier in ballast condition but with a shallow water
area. Only 44% of the turns conformed to XTL when
ATT was used and 100% when ATMM was used.
During the third simulation study, the bulk carrier
was changed to a fully loaded condition, and the
manoeuvring was conducted in deep water. Using
ATT, the compliance was only 67%. This contrasted to
the manoeuvring using the ATMM, where compliance
to XTL continued at 100%.
During the final simulation study in shallow water
using a fully loaded bulk carrier, the ATT model only
achieved 11% XTL compliance, whereas when
manoeuvring using ATMM, 100% compliance was
recorded. It can be concluded that ATMM provides
better XTD in terms of its compliance with XTL. ATT
has slight disadvantages, particularly when the
simulation is carried out in shallow water.
4.2 XTD percentage change
Table 8. Percentage change by course change
__________________________________________________________________________________________________
Course change Condition Water depth Direction XTD (m) % Change of XTD
ATT ATMM Individual turn Average
__________________________________________________________________________________________________
10° Ballast Deep Starboard 58 20 -65.5% -87.7%
Port 84 6 -92.9%
Shallow Starboard 71 12 -83.1%
Port 64 5 -92.2%
Fully Deep Starboard 63 9 -85.7%
Loaded Port 69 4 -94.2%
Shallow Starboard 68 4 -94.1%
Port 63 4 -93.7%
20° Ballast Deep Starboard 115 25 -78.3% -92.5%
Port 127 16 -87.4%
Shallow Starboard 112 4 -96.4%
Port 127 2 -98.4%
Fully Deep Starboard 112 6 -94.6%
Loaded Port 120 11 -90.8%
548
Shallow Starboard 138 2 -98.6%
Port 131 6 -95.4%
30° Ballast Deep Starboard 119 8 -93.3% -95.3%
Port 131 5 -96.2%
Shallow Starboard 185 3 -98.4%
Port 203 1 -99.5%
Fully Deep Starboard 181 16 -91.2%
Loaded Port 170 12 -92.9%
Shallow Starboard 203 13 -93.6%
Port 185 5 -97.3%
40° Ballast Deep Starboard 125 30 -76.0% -89.0%
Port 156 17 -89.1%
Shallow Starboard 146 4 -97.3%
Port 178 3 -98.3%
Fully Deep Starboard 121 19 -84.3%
Loaded Port 112 12 -89.3%
Shallow Starboard 155 27 -82.6%
Port 138 7 -94.9%
50° Ballast Deep Starboard 105 2 -98.1% -91.4%
Port 102 10 -90.2%
Shallow Starboard 98 6 -93.9%
Port 137 9 -93.4%
Fully Deep Starboard 110 4 -96.4%
Loaded Port 93 0 -100.0%
Shallow Starboard 166 43 -74.1%
Port 148 22 -85.1%
60° Ballast Deep Starboard 83 12 -85.5% -78.8%
Port 91 17 -81.3%
Shallow Starboard 88 19 -78.4%
Port 103 15 -85.4%
Fully Deep Starboard 94 12 -87.2%
Loaded Port 71 14 -80.3%
Shallow Starboard 142 61 -57.0%
Port 115 29 -74.8%
70° Ballast Deep Starboard 50 2 -96.0% -80.6%
Port 74 3 -95.9%
Shallow Starboard 90 24 -73.3%
Port 120 27 -77.5%
Fully Deep Starboard 102 1 -99.0%
Loaded Port 65 1 -98.5%
Shallow Starboard 124 76 -38.7%
Port 128 44 -65.6%
80° Ballast Deep Starboard 48 19 -60.4% -65.0%
Port 65 21 -67.7%
Shallow Starboard 104 40 -61.5%
Port 143 40 -72.0%
Fully Deep Starboard 118 11 -90.7%
Loaded Port 91 10 -89.0%
Shallow Starboard 148 94 -36.5%
Port 114 66 -42.1%
90° Ballast Deep Starboard 45 22 -51.1% -56.3%
Port 55 39 -29.1%
Shallow Starboard 126 59 -53.2%
Port 158 52 -67.1%
Fully Deep Starboard 119 22 -81.5%
Loaded Port 99 28 -71.7%
Shallow Starboard 181 101 -44.2%
Port 147 70 -52.4%
__________________________________________________________________________________________________
As seen in Table 8, the negative value of the
percentage change implies a reduction of XTD. As a
result, a considerable reduction in XTD was observed
during the manoeuvring analysis. It can be seen that
during ballast conditions while manoeuvring in deep
water, the XTD was reduced by 51.1%–98.1% for the
manoeuvring analysis with starboard alteration, while
for manoeuvring analysis with port alteration, the
XTD was successfully reduced by 29.1%–95.9%.
Meanwhile, in shallow water, the XTD for starboard
manoeuvring analysis was reduced by 53.2% to 98.4%,
and by 67.1% to 99.5% for port manoeuvring analysis.
For manoeuvring analysis with a fully loaded
condition, the bulk carrier recorded 81.5%–99.0% of
XTD reduction during the manoeuvring analysis to
starboard and 71.7%–100% of XTD reduction for port
alteration. In shallow water, the fully loaded bulk
carrier reduced the XTD by 36.5%–98.6% for starboard
alteration and 42.1%–97.3% for port alteration.
The succession of reductions for every ten degrees
of course deviation suggested that the bulk carrier
was approaching the intended course. Even though it
is apparent that the ATMM was able to reduce the
XTD, it is necessary to determine whether the two
independent datasets originated from the same
distribution using the Mann-Whitney U test. To
accomplish this, IBM SPSS was used to analyse the
data.
549
Table 9. Test by manoeuvring conditions
__________________________________________________________________________________________________
Test Manoeuvring Models N Mean Sum Mann- Wilcoxon Z Asymp. Sig
No conditions rank of Rank Whitney U W (2-Tailed) P-Value
__________________________________________________________________________________________________
1 Ballast condition, ATT 18 27.5 495 .000 171 -5.127 .000
Deep water. ATMM 18 9.5 171
2 Ballast condition, ATT 18 27.5 495 .000 171 -5.126 .000
Shallow water ATMM 18 9.5 171
3 Fully Loaded Condition, ATT 18 27.5 495 .000 171 -5.128 .000
Deep water ATMM 18 9.5 171
4 Fully Loaded Condition ATT 18 27 486 9.000 180 -4.842 .000
Shallow water ATMM 18 10 180
__________________________________________________________________________________________________
Table 10. Test by the course change
__________________________________________________________________________________________________
Course Models N Mean Sum Mann- Wilcoxon Z Asymp. Sig
change rank of Rank Whitney U W (2-Tailed) P-Value
__________________________________________________________________________________________________
10° ATT 8 12.5 100 .000 36 -3.373 .001
ATMM 8 4.5 36
20° ATT 8 12.5 100 .000 36 -3.371 .001
ATMM 8 4.5 36
30° ATT 8 12.5 100 .000 36 -3.368 .001
ATMM 8 4.5 36
40° ATT 8 12.5 100 .000 36 -3.361 .001
ATMM 8 4.5 36
50° ATT 8 12.5 100 .000 36 -3.361 .001
ATMM 8 4.5 36
60° ATT 8 12.5 100 .000 36 -3.361 .001
ATMM 8 4.5 36
70° ATT 8 12.13 97 3.000 39 -3.048 .002
ATMM 8 4.88 39
80° ATT 8 11.88 95 5.000 41 -2.838 .005
ATMM 8 5.13 41
90° ATT 8 11.5 92 8.000 44 -2.522 .012
ATMM 8 5.5 44
__________________________________________________________________________________________________
4.3 Mann-Whitney U Test
The following are the null and two-sided research
hypotheses for the nonparametric test in this study:
− H0: The two models' mean XTD ranks are
identical.
− H1: The two models' mean XTD ranks are not
identical.
The null hypothesis H0 will be rejected if the P-
Value < 0.05.
The first test was carried out according to the
manoeuvring area, as shown in Table 9, in which the
difference was statistically significant with p = 0.000 <
0.05 for all tests. Therefore, H0 was rejected. The
Wilcoxon W value represented the sum of rank for all
tests that pointed to ATMM, implying that ATMM
had a lower rank XTD value, consistent with the
study's objectives.
The next test was carried out for nine-course
changes, as shown in Table 10. Evidently, there was a
statistically significant difference for all nine
alterations, where U varied from .000 to 8.000, z
varied between -2.522 to -3.373 and P-Value varied
from .001 to .012, which was less than 0.05. Therefore,
H0 was rejected for all nine-course changes. The
Wilcoxon W value represented the sum of rank for all
tests that pointed to ATMM, implying that ATMM
had a lower rank XTD value, consistent with the
study's objectives.
5 CONCLUSION
Ships sail from one destination to another by
navigating along the course line prepared by the
navigation officer. Navigating on the planned track is
vital for the ship’s safety and can reduce fuel
consumption. Nevertheless, more importantly, it will
keep the vessel safe as many accidents happen due to
ignorance of the XTD. XTD can be reduced by various
methods; one of them is through the correct
application of WOP through ATT.
It is essential to highlight that ATT has been used
in marine navigation for a long period of time to
calculate the most optimal WOP. Recently, a study
was able to convert the ATT into a mathematical
model termed ATMM. A small number of studies
were undertaken utilising tanker ships and LNG
tankers to demonstrate the ATMM's usefulness. As
such, this study aims to evaluate the efficiency of
ATMM by utilising a bulk carrier ship.
It may be concluded that this study accomplished
its objectives because the ATMM significantly
lowered the XTD and is suitable for use onboard bulk
carrier ships as one of the ways to determine WOP,
particularly during channel turns and pilotage. The
ATMM algorithm can be utilised in the ECDIS. An
ECDIS equipped with pre-installed vessel
manoeuvring data may automatically calculate the
WOP for each course change made during trip
planning, considering the vessel's ballast and fully
loaded states. As a result of this research, a
mathematical model embedded in the ECDIS might
be able to detect when the navigator makes an
incorrect WOP calculation. For instance, if the
550
navigator's value is less than the predicted WOP, the
ECDIS will display a warning to inform the user that
the input is incorrect. The present study found that
during the simulation analysis, when the course lines
were formed, the ECDIS simulator suggested the
WOP line; however, the WOP line suggested was
significantly less than the WOP estimated using the
mathematical model used in this study. This indicates
that the ECDIS simulator does not include a WOP
limit. As a result, this issue can be resolved using the
developed ATMM.
According to this research, efficient route
monitoring will reduce the distance covered and
assist in minimising fuel usage. Although the
mathematical model used in this study improves
course keeping abilities when changing courses,
additional research can be conducted on the effect of
fuel consumption when applying a large rudder angle
while turning. Perhaps further research can be
conducted to determine the effect of reducing XTD on
energy efficiency.
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