bachelor of engineering thesis - samuel davey · bachelor of engineering thesis ... the scope of...

Bachelor of Engineering Thesis

Use of Initial Trim to Minimise Dynamic Under Keel

Clearance for Full Form Vessels.

Samuel Davey

27 March 2013

Supervisor: Jonathan Duffy

Thesis submitted in partial fulfilment of the requirements for the degree

of

Bachelor of Engineering (Naval Architecture)

National Centre for Maritime Engineering and Hydrodynamics

ii

DECLARATION

This project report contains no material which has been accepted for a degree or diploma by

AMC, University of Tasmania or any other institution, except by way of background

information and duly acknowledged in the report, and to the best of my knowledge and belief,

no material previously published or written by another person except where due

acknowledgement is made in the text of the report.

Signed:

Date:

STATEMENT 1

This project report is the result of my own investigation, except where otherwise stated. Other

sources are acknowledged in the text giving explicit references. A list of references is

appended.

Signed:

Dated:

STATEMENT 2

I hereby give consent for my project report to be available for photocopying, inter-library

loan, electronic access to AMC and UTAS staff and students via the UTAS Library, and for

the title and summary to be made available to outside organisations.

Signed:

Dated:

1

Table of Contents

Declaration ............................................................................................................................................. ii

List of Figures ......................................................................................................................................... 2

List of Tables .......................................................................................................................................... 2

1. Project Title ......................................................................................................................................... 3

2. Aim ..................................................................................................................................................... 3

3. Supervisors.......................................................................................................................................... 3

4. Scope ................................................................................................................................................... 3

5. Preliminary Literature Survey and References ................................................................................... 4

5.1 Reasoning behind survey .............................................................................................................. 4

5.2 Literature Review .......................................................................................................................... 4

5.3 Papers Still to be Read .................................................................................................................. 5

6. Schedule and Milestones..................................................................................................................... 6

6.1 Key Milestones ............................................................................................................................. 6

6.2 Meetings ........................................................................................................................................ 6

6.3 Test Program ................................................................................................................................. 7

7. Resources Required .......................................................................................................................... 11

7.1 Experimental Facility .................................................................................................................. 11

7.2 Model Particulars ........................................................................................................................ 11

7.3 Apparatus .................................................................................................................................... 13

References ............................................................................................................................................. 14

Appendix B – Gantt chart ..................................................................................................................... 15

2

List of Figures

Figure 1 - Model Vessel ........................................................................................................................ 12

Figure 2 - Model Vessel with Largest Beam Attachments on .............................................................. 12

Figure 3 - Setup Apparatus ................................................................................................................... 13

List of Tables

Table 1 - Key Milestones ........................................................................................................................ 6

Table 2 - Test Program Day 1 ................................................................................................................. 7






Table 8 - Test Program Day 7 ............................................................................................................... 10

Table 9 - Test Program Day 8 ............................................................................................................... 10

Table 10 - Test Program Day 9 ............................................................................................................. 10

Table 11 - Test Program Day 10 ........................................................................................................... 11

Table 12 - Model Vessel Particulars ..................................................................................................... 11

Table 13 - Testing Equipment ............................................................................................................... 13

3

1. Project Title

Use of Initial Trim to Minimise Dynamic Under Keel Clearance for Full Form Vessels.

2. Aim

With the current demand for cargo vessels to be larger and travel faster the effects of shallow water

have become more significant to the shipping industry. When travelling in shallow water full form

vessels will undergo sinkage and trim due to pressure effects on the hull. Therefore the aim of this

research is to determine whether an initial trim on a full form vessel will reduce the amount of vessel

squat and trim when underway.

3. Supervisors

The primary supervisor is Jonathan Duffy from the Australian Maritime College (AMC). Chris Hens

and Giles Lesser from O'Brien Maritime Consultants International (OMCI) are industry participants

and will co-supervise the project.

4. Scope

The scope of this project is to investigate the effect initial trim has on a full form generic bulk carrier

with regards to ship squat in shallow waterways. This will be achieved through physical scale model

tests in calm water in the Model Test Basin (MTB) at the AMC. A 2.385 metre long ship model will

be tested at a number of different speeds and depth to draft ratios for a range of initial bow down

trims. The heave and pitch will be measured using the motion capturing system Qualisys. A detailed

test program can be seen in 6.3.

If time permits the effect of changing the vessel beam will also be investigated. The model will be

tested at 3 different beams. Only two initial trims will be tested for the different beams, as well as zero

trim due to the limited testing time available. After the completion of the first beam test, if insufficient

time remains this part of the research may be removed from the scope.

As part of another first semester subject a CFD analysis may also be conducted. If this project is

completed it will also be used in this thesis. Results will be compared to experimental data and an

empirical formula and the correlation between the three methods will be analysed.

The data obtained will be compared to zero trim tests to determine if there are any benefits of loading

vessels with set trim by the bow.

4

5. Preliminary Literature Survey and References

5.1 Reasoning Behind Survey

The literature survey will be conducted to achieve the following:

To see if any other research has been undertaken in this field.

To gain a wide range of knowledge about the subject.

To determine what methods should be used.

To decide upon what parameters to investigate.

To determine what results are to be expected.

5.2 Literature Review

Dietze et al (1997) investigated the problem of squat and compared current methods to predict vessel

squat. Work they compared and discussed included Huuska (1976), Icorels (1980), Millward (1990)

and Barrass (1971). Three common hull forms were chosen to compare these techniques to predict

vessel squat in shallow waters. The tests were conducted in straight channels with no ship interaction

and no sudden changes in channel configuration. From the tests they concluded that it was not

possible to recommend one single squat estimation method as each method had different answers,

with the largest variation came at a Froude Depth Number of 2. However, from the tests they were

able to develop guidelines and graphs to recommend the most accurate method depending on different

situations.

Millward (1990) conducted experiments to investigate the influence of hull-form on vessel squat. His

results showed that the largest instances of squat were usually located at a Froude Depth Number of

0.9, while at supercritical speeds the squat would usually become negative, hence the vessel would

rise in the water rather than squat. He concluded that the squat curve will follow the same shape

regardless of the hullform with the only difference being in the values of squat. He took an empirical

approach to find a family of curves for the prediction of ship squat. Millward used Gibbing’s curve

fitting technique to find formulas to fit the curves. He found 4 constants, 3 of which were similar for

any hull form and one which was based on hull parameters. For the constant based on hull parameters

he used the extreme points from his results so his squat predictions would be larger to err on the side

of caution. From his results he deduced that the squat of the vessel was always greater at the bow

compared to amidships, especially for fuller formed vessels. He also concluded that the way the vessel

will trim is to do with where the centre of buoyancy (COB) is compared to amidships. For example if

the COB was forward of midships the vessel was more likely to trim towards the bow. In conclusion

Millward’s formulae showed good agreement to current squat formulae, in almost every case gave a

better agreement than the simple formulae previously used.

Eryuzlu (1994) conducted experiments into the under keel requirements for large vessels in shallow

waterways for the Canadian Coast Guard. They tested 5 models at a scale of 1/100, with varying

depth to draft ratios and speeds while keeping level trim in an unrestricted waterway. Over 1000 tests

were conducted and through multiple regression analyses two dimensionless equations were derived.

He stated that these equations can be applied with confidence to certain vessels (19000-227000DWT

with depth to draft ratios of 1.1 – 2.5). Extra tests were also conducted to determine the effect of

channel width. From these tests a channel width factor was derived and included in the equations. The

new equations were then compared to field data and other squat formulae, including Tuner, Barrass

and Simard’s equations. These equations were more accurate in both unrestricted and restricted

5

waterways than previous formulae, nothing that accuracy in restricted waterways was only high when

the width factor was used. The results from the tests concluded that for vessels with no trim, bow

squat was predominant. He made special mention as to the limits of applicability of their equations

and not to use them outside these bounds.

Dand (1971) investigated the effect of bulbous bows on ship squat. Again he did this as most of the

methods in use did not take into account any hull shape when predicting squat. He conducted model

tests in shallow water with two different hulls, one with a hemispherical bulb and the other having an

S-type protruding ram bow. The models were self-propelled and without rudders. The expected results

were that both sinkage and trim would increase at the same rate with a decreasing depth to draft,

however the results showed that only the mean sinkage increased. Dand was unsure of the reasons but

speculated that it would likely be to do with how close the bulb is to the free surface and the suction

effects a bulb would experience at different speeds. He concluded that certain ships with bulbous

bows and high block coefficients will have an increased value of mean sinkage, but they will not trim

by the head when h/T ratio is decreased, as many normal full form vessels would.

Dand (1972) also conducted research into the effect of squat in shallow water. The main difference in

his work to previous papers was that his research was based on predicting squat in waters with

unrestricted width while most previous papers predicted squat in restricted waterways. Dand

investigated three methods, a simple one-dimensional method, the Sogreah Method which is an

empirical method and a theoretical method by Tuck (1970). According to Dand these methods have

merit but they all disregard the effect of viscosity, propeller and squat due to the hull wave system,

therefore under predicting squat. From this investigation and model tests, Dand developed a

prediction method using the one dimensional theory with some modifications. Through his model

tests he calculated an effective channel width factor using the fluid disturbance around the hull as an

effective channel width. He then provided correction factors for the viscosity and the effect of the

propeller directly from model tests.

5.3 Papers Still to be Read

The first list of papers is directly relevant to this thesis. These papers will all be read for the

completion of this thesis as well as others that are found to be relevant. The second lists papers that

have some relevance to this thesis and therefore will only be read if time permits.

List 1:

Tuck (1966)

Hooft (1974)

ICORELS (1980)

Millward (1992)

Barrass I (1979)

Barrass II (1979, 81)

Eryuzlu and Hausser (1978)

List 1 Cont:

Romisch (1989)

Harting et al (2009)

Briggs et al (2009)

Gourlay (2007, 08)

Stocks et al (2004)

Harting et al (1999, 2002)

Lataire et al (2012)

Briggs (2010)

List 2:

Huuska (1976)

Ankudinov et al. (2006)

Barras (2004)

Beaulieu et al (2009)

Dunker (2002)

Delefortrie et al (2010)

Eloot et al (2008

6

6. Schedule and Milestones

6.1 Key Milestones

The final year thesis subject for 2013 has 6 submissions. Table 1 shows the dates each submission is

due. A Gantt chart with every milestone has been included in Appendix B – Gantt

Table 1 - Key Milestones

Date Milestone

19/04/2013 Project Plan

21/06/2013 Interim Report

21/06/2013 JEE418 Completed

TBD Testing

03/10/2013 Journal Article Submission

03/10/2013 Executive Summary Submission

03/10/2013 Supporting Documents

25/10/2013 Oral Presentation

29/11/2013 JEE419 Completed

6.2 Meetings

Meetings will be held every Wednesday at 11am in the Towing Tank conference room with

Jonathon Duffy, Shaun Denehy, Tim Vaughan, Rohan Langford and Mitchell Todd.

Additional meetings will be held with Jonathon Duffy when deemed appropriate.

Minutes will be taken at every meeting and will be discussed at the following meeting to keep

track of progress.

Additional meetings between the four students will take place when deemed appropriate.

7

6.3 Test Program

The testing will be conducted in a group basis with Timothy Vaughan, Rohan Langford and Mitchell

Todd. The testing program is shown in Table 2 to Table 11. Each table represents one days’ worth of

testing. The test runs that will be of interest for my research are highlighted in grey. The testing has

been estimated to take 10 full days. This includes re runs, change over times, time needed for the tank

to settle and time needed to alter the model for different conditions. Set up time has not been included.

A length of time for setup will need to be decided upon discussing with technicians.

Preliminary testing has already taken place. This testing was done to confirm whether the Qualisys

system would be accurate enough to determine the small changes in heave and pitch needed for this

investigation. Another reason for the preliminary testing was to see whether the capture area for the

Qualisys program was large enough to record both the initial condition and a steady state in a single

run. Results from the initial testing indicate that Qualisys will have sufficient capture period to record

an initial value and a steady state period.

Table 2 - Test Program Day 1

Run

No.

h/T Water

Depth (m)

Draft

(m)

Beam

(m)

Trim

(deg)

Speed

(m/s)

Time

1 2 0.18 0.09 0.473 0 0.23 900

2 2 0.18 0.09 0.473 0 0.23 930

3 2 0.18 0.09 0.473 0 0.46 1000

4 2 0.18 0.09 0.473 0 0.69 1030

5 2 0.18 0.09 0.473 0 0.92 1030

6 2 0.18 0.09 0.473 0.5 0.23 1100

7 2 0.18 0.09 0.473 0.5 0.46 1130

8 2 0.18 0.09 0.473 0.5 0.69 1200

9 2 0.18 0.09 0.473 1 0.23 1230

10 2 0.18 0.09 0.473 1 0.23 1300

11 2 0.18 0.09 0.473 1 0.46 1330

12 2 0.18 0.09 0.473 1 0.69 1400

13 2 0.18 0.09 0.473 2 0.23 1430

14 2 0.18 0.09 0.473 2 0.46 1500

15 2 0.18 0.09 0.473 2 0.69 1530

16 1.4 0.18 0.129 0.473 0 0.23 1600

17 1.4 0.18 0.129 0.473 0 0.23 1630

18 1.4 0.18 0.129 0.473 0 0.46 1700


19 1.4 0.18 0.129 0.473 0 0.69 900

20 1.4 0.18 0.129 0.473 0 0.92 930

21 1.4 0.18 0.129 0.473 0.5 0.23 1000

22 1.4 0.18 0.129 0.473 0.5 0.46 1030

23 1.4 0.18 0.129 0.473 0.5 0.69 1030

24 1.4 0.18 0.129 0.473 1 0.23 1100

25 1.4 0.18 0.129 0.473 1 0.23 1130

8

26 1.4 0.18 0.129 0.473 1 0.46 1200

27 1.4 0.18 0.129 0.473 1 0.69 1230

28 1.4 0.18 0.129 0.473 2 0.23 1300

29 1.4 0.18 0.129 0.473 2 0.46 1330

30 1.4 0.18 0.129 0.473 2 0.69 1400

31 1.2 0.18 0.15 0.473 0 0.23 1430

32 1.2 0.18 0.15 0.473 0 0.23 1500

33 1.2 0.18 0.15 0.473 0 0.46 1530

34 1.2 0.18 0.15 0.473 0 0.69 1600

35 1.2 0.18 0.15 0.473 0 0.92 1630

36 1.2 0.18 0.15 0.473 0.5 0.23 1700


37 1.2 0.18 0.15 0.473 0.5 0.46 900

38 1.2 0.18 0.15 0.473 0.5 0.69 930

39 1.2 0.18 0.15 0.473 1 0.23 1000

40 1.2 0.18 0.15 0.473 1 0.23 1030

41 1.2 0.18 0.15 0.473 1 0.46 1030

42 1.2 0.18 0.15 0.473 1 0.69 1100

43 1.2 0.18 0.15 0.473 2 0.23 1130

44 1.2 0.18 0.15 0.473 2 0.46 1200

45 1.2 0.18 0.15 0.473 2 0.69 1230

46 1.1 0.18 0.164 0.473 0 0.23 1300

47 1.1 0.18 0.164 0.473 0 0.23 1330

48 1.1 0.18 0.164 0.473 0 0.46 1400

49 1.1 0.18 0.164 0.473 0 0.69 1430

50 1.1 0.18 0.164 0.473 0 0.92 1500

51 1.1 0.18 0.164 0.473 0.5 0.23 1530

52 1.1 0.18 0.164 0.473 0.5 0.46 1600

53 1.1 0.18 0.164 0.473 0.5 0.69 1630

54 1.1 0.18 0.164 0.473 1 0.23 1700


55 1.1 0.18 0.164 0.473 1 0.23 900

56 1.1 0.18 0.164 0.473 1 0.46 930

57 1.1 0.18 0.164 0.473 1 0.69 930

58 1.1 0.18 0.164 0.473 2 0.23 1000

59 1.1 0.18 0.164 0.473 2 0.46 1030

60 1.1 0.18 0.164 0.473 2 0.69 1100

61 1.05 0.18 0.171 0.473 0 0.69 1130

62 1.05 0.18 0.171 0.473 0 0.23 1200

63 1.05 0.18 0.171 0.473 0 0.46 1230

64 1.05 0.18 0.171 0.473 0 0.69 1300

9

The afternoon of day 4 will be spent changing the beam ready for the beginning of day 5.


Run

No.

h/T Water

Depth (m)

Draft

(m)

Beam

(m)

Trim

(deg)

Speed

(m/s)

Time

65 2 0.18 0.09 0.433 0 0.23 900

66 2 0.18 0.09 0.433 0 0.23 930

67 2 0.18 0.09 0.433 0 0.46 1000

68 2 0.18 0.09 0.433 0 0.69 1030

69 2 0.18 0.09 0.433 0 0.92 1030

70 2 0.18 0.09 0.433 0.5 0.23 1100

71 2 0.18 0.09 0.433 0.5 0.23 1130

72 2 0.18 0.09 0.433 0.5 0.46 1200

73 2 0.18 0.09 0.433 1 0.23 1230

74 2 0.18 0.09 0.433 1 0.46 1300

75 1.4 0.18 0.129 0.433 0 0.23 1330

76 1.4 0.18 0.129 0.433 0 0.23 1400

77 1.4 0.18 0.129 0.433 0 0.46 1430

78 1.4 0.18 0.129 0.433 0 0.69 1500

79 1.4 0.18 0.129 0.433 0 0.92 1530

80 1.4 0.18 0.129 0.433 0.5 0.23 1600

81 1.4 0.18 0.129 0.433 0.5 0.23 1630

82 1.4 0.18 0.129 0.433 0.5 0.46 1700


83 1.4 0.18 0.129 0.433 1 0.23 900

84 1.4 0.18 0.129 0.433 1 0.46 930

85 1.2 0.18 0.15 0.433 0 0.23 1000

86 1.2 0.18 0.15 0.433 0 0.23 1030

87 1.2 0.18 0.15 0.433 0 0.46 1030

88 1.2 0.18 0.15 0.433 0 0.69 1100

89 1.2 0.18 0.15 0.433 0 0.92 1130

90 1.2 0.18 0.15 0.433 0.5 0.23 1200

91 1.2 0.18 0.15 0.433 0.5 0.23 1230

92 1.2 0.18 0.15 0.433 0.5 0.46 1300

93 1.2 0.18 0.15 0.433 1 0.23 1330

94 1.2 0.18 0.15 0.433 1 0.46 1400

95 1.1 0.18 0.64 0.433 0 0.23 1430

96 1.1 0.18 0.64 0.433 0 0.23 1500

97 1.1 0.18 0.64 0.433 0 0.46 1530

98 1.1 0.18 0.64 0.433 0 0.69 1600

99 1.1 0.18 0.64 0.433 0 0.92 1630

100 1.1 0.18 0.64 0.433 0.5 0.23 1700

10


101 1.1 0.18 0.64 0.433 0.5 0.23 900

102 1.1 0.18 0.64 0.433 0.5 0.46 930

103 1.1 0.18 0.64 0.433 1 0.23 1000

104 1.1 0.18 0.64 0.433 1 0.46 1030

105 1.05 0.18 0.171 0.433 0 0.23 1030

106 1.05 0.18 0.171 0.433 0 0.23 1100

107 1.05 0.18 0.171 0.433 0 0.46 1130

108 1.05 0.18 0.171 0.433 0 0.69 1200

The afternoon of day 7 will be spent changing the beam ready for testing at the start of Day 8.


Run

No.

h/T Water

Depth

(m)

Draft

(m)

Beam

(m)

Trim

(deg)

Speed

(m/s)

Time

109 2 0.18 0.09 0.393 0 0.23 900

110 2 0.18 0.09 0.393 0 0.23 930

111 2 0.18 0.09 0.393 0 0.46 1000

112 2 0.18 0.09 0.393 0 0.69 1030

113 2 0.18 0.09 0.393 0 0.92 1030

114 2 0.18 0.09 0.393 0.5 0.23 1100

115 2 0.18 0.09 0.393 0.5 0.23 1130

116 2 0.18 0.09 0.393 0.5 0.46 1200

117 2 0.18 0.09 0.393 1 0.23 1230

118 2 0.18 0.09 0.393 1 0.46 1300

119 1.4 0.18 0.129 0.393 0 0.23 1330

120 1.4 0.18 0.129 0.393 0 0.23 1400

121 1.4 0.18 0.129 0.393 0 0.46 1430

122 1.4 0.18 0.129 0.393 0 0.69 1500

123 1.4 0.18 0.129 0.393 0 0.92 1530

124 1.4 0.18 0.129 0.393 0.5 0.23 1600

125 1.4 0.18 0.129 0.393 0.5 0.23 1630

126 1.4 0.18 0.129 0.393 0.5 0.46 1700


127 1.4 0.18 0.129 0.393 1 0.23 900

128 1.4 0.18 0.129 0.393 1 0.46 930

129 1.2 0.18 0.15 0.393 0 0.23 1000

130 1.2 0.18 0.15 0.393 0 0.23 1030

131 1.2 0.18 0.15 0.393 0 0.46 1030

132 1.2 0.18 0.15 0.393 0 0.69 1100

133 1.2 0.18 0.15 0.393 0 0.92 1130

134 1.2 0.18 0.15 0.393 0.5 0.23 1200

135 1.2 0.18 0.15 0.393 0.5 0.23 1230

11

136 1.2 0.18 0.15 0.393 0.5 0.46 1300

137 1.2 0.18 0.15 0.393 1 0.23 1330

138 1.2 0.18 0.15 0.393 1 0.46 1400

139 1.1 0.18 0.64 0.393 0 0.23 1430

140 1.1 0.18 0.64 0.393 0 0.23 1500

141 1.1 0.18 0.64 0.393 0 0.46 1530

142 1.1 0.18 0.64 0.393 0 0.69 1600

143 1.1 0.18 0.64 0.393 0 0.92 1630

144 1.1 0.18 0.64 0.393 0.5 0.23 1700


145 1.1 0.18 0.64 0.393 0.5 0.23 900

146 1.1 0.18 0.64 0.393 0.5 0.46 930

147 1.1 0.18 0.64 0.393 1 0.23 1000

148 1.1 0.18 0.64 0.393 1 0.46 1030

149 1.05 0.18 0.171 0.393 0 0.23 1030

150 1.05 0.18 0.171 0.393 0 0.23 1100

151 1.05 0.18 0.171 0.393 0 0.46 1130

152 1.05 0.18 0.171 0.393 0 0.69 1200

7. Resources Required

7.1 Experimental Facility

Testing will be conducted in the MTB at the AMC.

7.2 Model Particulars

The model to be used in the study can be seen in Figure 1and Figure 2. Particulars of the model ship

are shown in Table 12. The plasticine seen at the bow of the vessel in Figure 1 shows how the vessel

is faired at the bow when the beam extensions are attached. In Figure 2 the widths of the extension

pieces can be seen, taking the beam from 393mm at its skinniest to 473mm as depicted

Table 12 - Model Vessel Particulars

Length (m) 2.385

Beam A (m) 0.393

Beam B (m) 0.433

Beam C (m) 0.473

Draft (m) 0.09 – 0.171

12

Figure 1 - Model Vessel

Figure 2 - Model Vessel with Largest Beam Segments Attached

Beam Segments

13

7.3 Apparatus

The model test has a fairly simple set up. Figure 3 depicts how the model will be set up when testing

is conducted. The equipment needed for the setup is shown in Table 13.

Table 13 - Testing Equipment

Equipment Use

Qualisys - Motion Capture System

To record all the motions of the vessel including heave, pitch and to verify the speed of the model.

4 x Qualisys Capture Markers and Stands

To act as markers on the model for the Qualisys program.

Qualisys Battery Pack and Radio System

To provide power to the Qualisys marker system and to transmit signals back to the computer.

Ball Joint An attachment at the forward end of the model which has 3 DOF in each rotation.

Slide/Ball Joint An attachment at the aft end of the model which has 5 DOF (not sway).

Winch Cart Setup To attach the model to the propulsion system.

Winch Cables and Motor

To provide a means of propulsion for the model.

Mass Ballast for the model.

Poles To extend the capture width of the model for higher accuracy.

Winch Speed Capture System

To record the vessel speed.

Posts & Post Bearings Attaches mode to cart & allows vertical displacement.

Figure 3 - Setup Apparatus

14

References

Dand, I. W. (1971). Squat Measurements: Bulbous Bow Ships in Shallow Water. London, National

Physical Laboratory.

Dand, I. W. (1972). Full Form Ships In Shallow Water: Some Methods for Prediction of Squat in

Subcritical Flows. London, National Physical Laboratory.

Eryuzlu, N. E., Y. L. Cao, et al. (1994). Under Keel Requirements for Large Crafts in Shallow

Waterways. 28th International Navigation Congress. PIANC, PIANC: 17-25.

Dietze, W., Rekonen, T., van Toorenburg, J.C.K., Vantorre, M., Wijinstra, R. (1995)

Joint PIANC-IAPH Working Group II-30., International Maritime Pilots Association., et al.

Approach channels, preliminary guidelines. Brussels, Belgium

Millward, A. (1990). "A Preliminary Design Method for the Prediction of Squat in Shallow-Water."

27: 10-19.

15

Appendix B – Gantt chart