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1 INTRODUCTION

Figure 1. Various connected charted course in a voyage plan

on a nautical chart

A ship is navigated by following one-course line to

another to complete a voyage [7]. A charted course, as

shown in Figure 1, is the course line drawn on the

nautical chart and connected by waypoints (WPT) [7].

WPT is the point at which two different course lines

are linked [7]. A navigator or watchkeeping officer

must alter a course at an exact distance, or the ship

will overshoot from the track. Unable to do this

correctly may result in a cross track distance (XTD)

(Figure 1), which can lead to an accident [5, 8].

Therefore, a wheel over point (WOP) must be marked

on the charted course to indicate the point of change

[7].

A Concept Explanation on the Development of Wheel

Over Point Mathematical Model for Efficient Course

Alteration

A.S. Kamis

& A.F. Ahmad Fuad

Malaysian Maritime Academy, Kuala Sungai Baru, Melaka, Malaysia

University of Malaysia, Kuala Nerus, Terengganu, Malaysia

ABSTRACT: This concept paper described the process of bridging the gaps in one of the methods for

determining wheel over point (WOP). WOP is a marking made on charted courses to indicate a point at which a

ship should change course. Identifying WOP is vital to avoid the vessel overshooting the planned track. One

method for determining WOP is the advanced transfer technique. However, two issues were identified while

reviewing this technique. Therefore, an improved mathematical model could be developed to overcome these

problems. A manoeuvring analysis using a ship simulator will be performed to test the developed mathematical

model's efficacy. The data obtained from the simulation study can be validated further by its adherence to the

cross track limit, reduction in percentage change, and using IBM SPSS for the Mann-Whitney U test. The

developed mathematical model is expectantly capable of producing a better track-keeping function and suitable

for use onboard a cargo ship. The mathematical model also could be implemented as an algorithm in the

Electronic Chart Display and Information System to help navigators make more efficient course changes.

http://www.transnav.eu

the International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 15

Number 4

December 2021

DOI: 10.12716/1001.15.04.11

796

2 REVIEW ON ADVANCED TRANSFER

TECHNIQUE IN DETERMINING WOP

The advanced transfer technique (ATT) is a method to

identify the WOP [1]. The advance transfer technique

by Anwar (2015) requires two variables from the

maneuvring characteristics as shown in Figure 2

namely 1) advance and 2) transfer, hence the names.

Advance and transfer distances are measured by

referring to the positioning of the ship’s centre of

gravity (CG) [3].

Figure 2. Typical manoeuvring characteristic of a ship [3]

Advance and transfer can be measured from the

moment vessel initiates the turn by hard over the

rudder until the ship’s heading changes by 90° from

the initial heading, where the distance of advance is

on the X0 axis, and transfer Y0 axis as shown in Figure

2 [3]. The advance and the transfer distances are

usually given in nautical miles that need to be

extracted from the manoeuvring characteristic. Anwar

[1] has found a way to use the given information to

determine the WOP as explained below;

Figure 3. WOP identification using the advance transfer

technique [4]

With references to Figure 5, the steps of

determining WOP are as follows:

1. At point B, extend the present course line 270°T

2. At any point, ‘X’ is on this line, draw a

perpendicular line ‘XY’ towards the alteration so

that ‘XY’ = Transfer

3. At ‘Y’, draw a line parallel to ‘BX’ so that it cuts the

course line 310°T. The point at which the parallel

line cuts the next course line is ‘D’. Now, if the line

is drawn at ‘D’, which is parallel to ‘XY’, point ‘C’

would be obtained on the extension of the present

course line.

4. From ‘C’, measure the advance backwards i.e. in

the direction 090°T (reciprocal of 270°T) to obtain

point ‘A’. ‘A’ is the WOP, where ‘CA’ equals

advance distance.

This study conducted a practical exercise on a

nautical chart to better understand the use of the ATT.

During this practice, two problems were identified.

2.1 Issue 1 – Negative value for alteration is less than 20°

The formula of WOP for ATT is as follows;

Trs

WOP Adv

Tan



=−

Table 1 shows an example of WOP calculated for

20° and 50° course alteration for a ship with advance

(Adv) of 0.24nm, and transfer (Trs) of 0.108nm.

Table 1. WOP distance from WPT

_______________________________________________

Situation Change of Adv Trs WOP

a course

_______________________________________________

1 20° 0.24 0.108 - 0.057

2 50° 0.24 0.108 0.149

_______________________________________________

Based on Table 1, a negative value of WOP in

Situation 1 indicates that the ship has deviated from

the planned track, requiring a course alteration of

0.057nm after WPT.

2.2 Issue 2 – The final heading of the ship does not match

the charted course

Figure 4. Advance transfer technique principle [4]

Meanwhile, Figure 4 illustrates the technique’s

principle. The ship’s final heading is 090°T, which

does not match the desired course of 045°T, resulting

in a second overshoot.

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3 PROBLEM STATEMENT AND NEED OF THE

STUDY

Hence, based on the observations and review, the

following situations were identified;

1. The ATT is not suitable for course alteration less

than 20° as it will result in a negative value. A ship

will start to make a course alteration after WPT.

2. The ship's final heading and the charted course are

contrary.

Since an Electronic Chart Display and Information

System (ECDIS) is currently preferred in maritime

navigation; hence mathematical modelling will be a

more appropriate approach in determining WOP.

However, the formula provided by Anwar [1] in the

advance and transfer technique cannot be applied in

the electronic chart due to the negative value

produced for alteration less than 20°. Therefore, this

research intends to restructure and develop an

advance transfer mathematical model (ATMM) that

may solve the problems.

4 OBJECTIVE

1. To develop and improve the advance transfer

mathematical model (ATMM);

2. To conduct a simulation study with a ship

simulator;

3. To validate the improved mathematical model.

5 METHODOLOGY

The research started with reviewing the ATT to

understand the WOP's concept. However, several

flaws in the technique were discovered. The

application of manoeuvring characteristics in

determining WOP has been restructured and

developed. Hence, the advance transfer mathematical

model (ATMM) was proposed. Following the

mathematical model's development, the ATT and

ATMM will be tested with various cargo ships in a

ship simulator for validation by determining their

impact on the cross track distance (XTD) [9].

Researchers may find these data useful for their

future use [9]. Therefore, the XTD result for both

methods will be compared and analysed by

examining their compliance to cross track limit (XTL),

percentage change, and the Mann-Whitney U test. The

test will allow a different conclusion between the

ATMM and ATT in determining WOP.

Figure 5. The research’s graphical methodology

5.1 Development of a mathematical model

This research also aims to improve and enhance the

ATT so that the final ship's course coincides with the

charted course in the passage plan in determining

WOP. Thus, to reach the last passage with the ship's

heading, this study intends to redesign the technique,

as depicted in Figure 5. The heading should match the

desired next course to avoid second overshooting. The

method's refinement will be translated into the form

of a mathematical model.

Figure 6. A study concept (ship heading and course are

parallel at the end of alteration)

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5.2 Simulation study

The ATT and ATMM will be tested using a ship

simulator. The selected ship simulator should have

core manoeuvring elements and deliver accurate

navigation simulation for various ship types.

The simulator is used to obtain the necessary data

and variables involving the preferred ship. It will

generate a set of charted courses consisting of nine

turning angles (each with a 10° change). Then, the

developed mathematical model will be used to

identify the WOP. The model's effectiveness is

determined by comparing the XTD generated by the

ATT and ATMM during the manoeuvring

simulations.

5.3 Data validation

In this study, a WOP mathematical model will be

developed for better track-keeping function when

minimising the XTD. The particular ship simulator

will test both the ATT and ATMM. Next, the data on

the XTD will be compared to see if there is an

improvement in the model. Finally, the ATT and

ATMM will be validated through three stages, as

follows:

1. Cross track limit (XTL). An XTL is a limit whereby

a ship could safely deviate from the track [4]. This

research will look into which method provides the

best XTL compliance.

2. The XTD reduction. The reduction could be

justified by modifying the formula to calculate

percentage change [2].

3. A Mann-Whitney U test. A comparison study will

be conducted using the Mann-Whitney U test to

determine whether the mean XTD of the ATT and

ATMM are significantly different [6].

5.4 Timeline

This research study is expected to be completed in

four semesters (24 months), with the following

activities listed in Table 2.

Table 2. Research Timeline

_______________________________________________

Research Section Duration (month(s))

_______________________________________________

Introduction 1

Literature review 4

Development of the mathematical model 3

Simulation study 5

Validation analysis 5

Data interpretation and discussion 4

Conclusion 2

_______________________________________________

REFERENCES

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Division of Witherbys Publishing Group Limited (2015).

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Literacy. Pythagoras. 38, 1, (2017).

https://doi.org/10.4102/pythagoras.v38i1.314.

3. ITTC: Full Scale Measurements Manoeuvrability Full

Scale Manoeuvring Trials Procedure. (2002).

4. Kristić, M., Žuškin, S., Brčić, D., Valčić, S.: Zone of

Confidence Impact on Cross Track Limit Determination

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