International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 4

Number 3

September 2010

323

1 INTRODUCTION

Access channels to harbours are often subject to tide,

so that arrival and departure of ships may be limited

to a certain window. This window is mainly deter-

mined by the variations of the water level and is

therefore of particular importance for deep-drafted

vessels, but also other parameters such as lateral and

longitudinal current components, or penetration of

the keel into soft mud layers may be limiting factors.

In particular, tidal windows have to be imposed to

deep-drafted ships arriving at and departing from the

Belgian seaports of Zeebrugge and Antwerp. The

Scheur West channel links the deeper Wandelaar ar-

ea in the southern North Sea via the Pas van het

Zand to the port of Zeebrugge, and via the Scheur

East and Wielingen channels to the mouth of the riv-

er West Scheldt, which gives access to the port of

Antwerp, where deep-drafted ships can either berth

on one of the river terminals or the tidal Deurganck

Dock, or enter the Zandvliet or Berendrecht Locks.

For the sea channels giving access to the Belgian

harbours, a decision supporting software tool has

been developed. This tool results into an advisable

tidal window, based on a number of criteria that can

be both deterministic and probabilistic. In a deter-

ministic mode, the gross under keel clearance

(UKC), relative to both the nautical bottom and the

top of fluid mud layers, and the magnitude of current

components are taken into account. In case probabil-

istic considerations are accounted for, a positive ad-

vise will only be given if the probability of bottom

touch during the voyage – due to squat and response

to waves – does not exceed a selected maximum

value. The following input data are taken into con-

sideration: ship characteristics, waterway character-

istics, trajectory, nautical bottom level, top mud lev-

el, speed over ground and through the water, tidal

elevation, directional wave spectra, current, depar-

ture time.

The tool, called ProToel, can either be used for

supporting short term decisions for a particular ship,

or for long term estimations for the maximum al-

lowable draft. ProToel is presently in an evaluation

phase for supporting decisions taken by the Flemish

Pilotage and Shipping Assistance in a short term ap-

proach for ships arriving at and departing from the

harbour of Zeebrugge. For the harbour of Antwerp,

to be reached by sea channels and the river Scheldt,

the program can also be used as an approach policy

supporting tool for long term considerations; exten-

sions to support short term decisions are considered.

A description of the ProToel software will be

given, followed by practical examples of its use for

determining tidal windows for ships arriving at or

departing from Zeebrugge. Next, some applications

for the shipping traffic to Antwerp will be consid-

ered, and finally possible extensions will be covered.

Development of Decision Supporting Tools for

Determining Tidal Windows for Deep-drafted

Vessels

K. Eloot

Flanders Hydraulics Research, Antwerp, Belgium & Ghent University, Ghent, Belgium

M. Vantorre & J. Richter

Ghent University, Ghent, Belgium

J. Verwilligen

Flanders Hydraulics Research, Antwerp, Belgium

ABSTRACT: A decision supporting tool named ProToel for determining tidal windows for deep-drafted ves-

sels arriving at or departing from the Belgian harbours, based on both deterministic and probabilistic criteria,

has been developed. The program is presently being evaluated as a short-term decision tool by the pilots and

waterways authorities for optimising the shipping traffic to the coastal harbour of Zeebrugge. The software

can also be applied for long-term considerations, as is illustrated in the case of the port of Antwerp. Some re-

flections are made considering the extension of the tool to include other factors that may affect the safety of

shipping traffic, such as interaction with banks and with other shipping traffic.

324

2 DESCRIPTION OF THE PROTOEL

SOFTWARE

2.1 General principle

Based on a specified route and departure time, the

ProToel program calculates the UKCs and bottom

touch probabilities for a specific ship following the

route with a chosen speed along the trajectory. The

route is split into several intervals. In each interval,

the UKCs are calculated based on bottom depth, up-

to-date current and tide data and the speed depend-

ent squat. The bottom touch probability is calculated

from the directional wave spectrum for that time, lo-

cation and the motion characteristics of the ship. The

results for each interval are stored and can be dis-

played after computation.

ProToel requires the availability of a number of

databases:

− a ship database with dynamic response character-

istics and squat data for a large range of ship di-

mensions and types, valid for a realistic range of

forward speeds, drafts and water depths;

− a database of trajectories and trajectory points,

containing recent soundings (or design depths);

− forecasts or measurements of hydro-

meteorological data for a number of locations as a

function of time: tidal elevation, current speed

and direction, directional wave spectra, water

density.

The software is developed in an object oriented

programming environment, making use of Java.

2.2 Operational use

The graphical user interface (GUI), see Figure 1, al-

lows an easy selection of the desired ship, represent-

ed by her beam and length. The user specifies the

loading condition, namely the draft at the fore and

aft perpendicular and optionally the metacentric

height. Furthermore, the time of departure, the route

to follow and the speed of the ship along this route –

either through water or over ground – are inserted.

Additionally, a number of travels can be specified

before and after the desired time of departure to cre-

ate a tidal window, based on a number of determin-

istic and/or probabilistic criteria. The menu allows

specifying the data source (locally stored data, re-

mote data) of each environment condition (tidal ele-

vations, current, waves, bottom) separately. Recent

predictions and measurements of tide, waves and

current are stored in a remote database on a server

that can be connected by the user, while a local da-

tabase may contain long-term predictions, e.g. astro-

nomic tide data.

The output of the computations is stored in xml

format and contains the UKCs and cross currents at

significant locations along the route. If a probabilis-

tic approach is chosen, the bottom touch probability

for the entire route is also given. The results can be

viewed directly in ProToel and exported as a report

in pdf format. An example is shown in Figure 2.

Figure 1. ProToel’s graphical user interface.

325

Figure 2. ProToel output file, showing waypoints and criteria

as a function of departure time.

2.3 Background information

The ship data bank consists of squat and dynamic re-

sponse data on a large number of slender and full

hull forms, see Figure 3. The content of this data-

bank is based on seakeeping tests carried out with

five ship models in the Towing tank for manoeuvres

in shallow water (co-operation Flanders Hydraulics

Research – Ghent University) in Antwerp and addi-

tional numerical calculations with the 2D strip

method Seaway and the 3D BEM Aqua+. The data-

base covers a large number of draft – water depth

combinations, and also contains data for a variation

of metacentric heights.

Squat data can be directly obtained from the da-

tabase by interpolation; for container vessels, the

sinkage fore and aft can also be calculated by means

of model test based empiric formulae that also take

account of the lateral channel dimensions (Eloot et

al, 2008).

180.0 -

199.9

200.0 -

219.9

220.0 -

239.9

240.0 -

259.9

260.0 -

279.9

290.0 -

299.9

300.0 -

319.9

320.0 -

339.9

340.0 -

359.9

360.0 -

379.9

380.0 -

399.9

400.0 -

419.9

30.0 - 32.9 G100 F100 D080

33.0 - 35.9 G105 F105 F110 D085

36.0 - 38.9 G110 G115 F115 F120 D090 D095

39.0 - 41.9 G120 G125 F130 W072 D100

42.0 - 44.9 E080 F140 W078 D105 D110

45.0 - 47.9 E085 E090 W080 W085 D115 D118

48.0 - 50.9 E095 W090 D120 D125

51.0 - 53.9 E100 W095

54.0 - 56.9 W100

Source Containership Containership

Source Bulkcarrier Bulkcarrier

Length over all [m]

Beam [m]

Figure 3. Combinations of ship length and beam covered by the

database. The code refers to ship model (container carriers D,

F, W; bulk carriers/tankers E, G) and scale factor (%).

Figure 4. Access channels: 1: Scheur West, 2: Pas van het

Zand, 3: Scheur East, 4: West Scheldt. Harbours: A: Ant-

werp/Antwerpen (B), G: Ghent/Gent (B), O: Ostend /Oostende

(B), T: Terneuzen (NL), V: Flushing/Vlissingen (NL), Z: Zee-

brugge (www.maritiemetoegang.be).

The probability of bottom touch is calculated in a

way that is customary for seakeeping problems, and

which is based on a Rayleigh distribution of peak-to-

peak values of responses of a ship to irregular

waves. However, the probability calculation also ac-

counts for a number of additional uncertainties. Due

to the uncertainty of the bottom level, the still water

draft, the tidal level, the squat estimation, the net

UKC is not exactly known; for this reason, a stand-

ard deviation on this value is taken into account.

Other types of uncertainty that are taken into consid-

eration concern the quality of wave climate predic-

tions, errors on response amplitude operators, effects

of unknown parameters such as weight distributions

and initial stability; the effect of such deviations is

accounted for by introducing a standard deviation on

the significant wave height.

326

3 APPLICATIONS

3.1 Use of ProToel as a short term planning tool

for shipping traffic to Zeebrugge

3.1.1 Criteria

Presently deep-drafted ships arriving at or depart-

ing from Zeebrugge need to take account of follow-

ing tidal restrictions (see Figure 4):

− in the Scheur West and Pas van het Zand chan-

nels, a gross UKC of at least 15% and 12.5% of

draft, respectively, is required;

− in the outer harbour of Zeebrugge, i.e. within the

breakwaters, the minimum gross UKC is reduced

to 10%;

− in areas subject to sedimentation where the bot-

tom of the navigation areas is covered with fluid

mud, a penetration of 7% of draft in the mud lay-

er is considered as acceptable in case sufficient

tug assistance is available;

− passage of the breakwaters is subject to a current

window limited by a value for the cross current of

2 knots.

For LNG-carriers, however, stricter criteria are

maintained. The required UKC in the sea channels

Scheur West and Pas van het Zand is increased to

20% of draft, and to 15% in the harbour area, while

the acceptable cross current at the breakwaters is re-

duced to 1.5 knots.

According to a probabilistic approach, a tidal

window should be determined in such a way that the

probability of undesired phenomena – such as bot-

tom touch – does not exceed a selected value. More

important than the probability, however, is the risk,

defined as the probability of occurrence multiplied

by the financial and impact consequences. The latter

depend on the channel bed (rock, sand, mud, …), the

type of vessel (tanker, general cargo, container, …)

and environmental sensitivity of the area. Considera-

tions on acceptable risk and probability have been

formulated by Savenije (1996), PIANC (1997) and

others, and is usually related to an acceptable num-

ber of groundings during the lifetime of a channel.

The acceptable overall probability of bottom touch is

of the order of magnitude of 10

-4

, while 10

-2

may be

considered as a maximum value for any ship transit.

Examples.As a (fictitious, but realistic) example,

the results of ProToel are given for a container carri-

er (W100) with a length of 397.7 m, a beam of 56.4

m and a draft of 15.5 m departing from and arriving

at the harbour of Zeebrugge in favourable wave

conditions (significant wave height 0.9 m). The

speed over ground is assumed to be 12 knots in the

Scheur West channel, 10 knots in the Pas van het

Zand, and 4 knots in the harbour area. Following a

deterministic approach based on gross UKC, the tid-

al window for the departing ship (Figure 5) opens at

11:30 and closes at 17:30; however, between 13:30

and 15:45 no traffic is possible due to the tidal cur-

rents. From a probabilistic point of view, the proba-

bility of bottom touch is acceptable between 9:15

and 19:30, but the limiting criterion will be the pene-

tration in the mud layer, which only takes acceptable

values between 11:15 and 19:15. While the effect on

the opening time of the tidal window is only margin-

al, the departure time can be postponed by 1.75

hours if a reduced gross UKC were accepted and a

probabilistic approach were followed in this particu-

lar case. For the arriving ship (Figure 6), no ad-

vantage is obtained by introducing a probabilistic

criterion in this particular case: the opening time of

the window remains unchanged, while the closing

time is determined by the acceptable penetration into

the fluid mud layer. Also here, the tidal window is

interrupted due to exceedance of the allowable cross

current.

3.1.2 Present status

Actually (January 2009) ProToel can be used

within the intranet of the Department of Mobility

and Public Works of the Flemish Government. Fore-

casts for waves, tidal elevations and tidal currents

are updated continuously by the Flemish Hydrogra-

phy on the server of Flanders Hydraulics Research.

In a next phase, the program will be validated and

the probabilistic approach will be evaluated.

3.2 Use of ProToel for long-term accessibility

predictions

In order to perform a long term accessibility analysis

with ProToel, the program was extended to allow

the execution of batch computations. In this way, the

length of tidal windows can be calculated for all tid-

al cycles within a longer period, e.g. a year. For such

a long term prediction, only astronomical tide data

can be used, so that only deterministic criteria based

on gross UKC can be applied for determining the

tidal windows. For the statistical post-processing of

the resulting tidal windows, additional tools have

been developed.

This type of application was performed for a con-

tainer carrier arriving at and departing from the har-

bour of Antwerp. An example of the output is given

in Figure 7, and can be interpreted as follows: for

both the arriving and departing ships with the con-

sidered draft values, a tidal window of at least 60

minutes is expected in more than 92% of the cases.

It should be mentioned that in the example the arriv-

ing ship has a larger draft than the departing ship.

The computations appeared to be in good agree-

ment with an existing analysis, but also revealed that

the results may be very sensitive to the detailed

depth profile and the assumptions used for interpola-

tion of the tidal curves along the trajectory.

327

Figure 5. ProToel results for a container vessel departing from Zeebrugge (fictitious example)

Figure 6. ProToel results for a container vessel arriving at Zeebrugge (fictitious example)

location limit 9:00 9:15 9:30 9:45 10:00 10:15 10:30 10:45 11:00 11:15 11:30 11:45 12:00

Zeebrugge_Kaai min gross UKC to nautical bottom [%]

10 4.85 4.82 5.29 5.8 7.23 8.04 9.51 10.06 10.89 11.29 12.29 12.83 13.93

min gross UKC to top mud [%]

-7 -13.21 -13.24 -12.78 -12.27 -10.84 -10.03 -8.56 -8 -7.17 -6.77 -5.78 -5.23 -4.14

Zeebrugge min gross UKC to nautical bottom [%]

10 4.82 4.82 5.29 5.8 7.23 8.04 9.51 10.06 10.89 11.29 12.29 12.83 13.93

min gross UKC to top mud [%]

-7 -13.24 -13.24 -12.78 -12.27 -10.84 -10.03 -8.56 -8 -7.17 -6.77 -5.78 -5.23 -4.14

Zeebrugge_Ingang min gross UKC to nautical bottom [%]

12.5 4.82 5.29 5.8 7.23 8.04 9.51 10.06 10.89 11.29 12.29 12.83 13.93 14.51

min gross UKC to top mud [%]

-7 -6.79 -6.33 -5.82 -4.38 -3.57 -2.11 -1.55 -0.72 -0.32 0.67 1.22 2.31 2.9

max current speed [knts]

2 1.88 1.82 1.79 1.71 1.67 1.55 1.49 1.37 1.3 1.13 1.01 0.77 0.66

Pas_van_het_Zand min gross UKC to nautical bottom [%]

12.5 9.36 9.8 10.61 11.75 12.96 14.02 14.83 15.41 16.02 16.8 17.62 18.44 19.33

min gross UKC to top mud [%]

-7 9.36 9.8 10.61 11.75 12.96 14.02 14.83 15.41 16.02 16.8 17.62 18.44 19.33

Scheur_West min gross UKC to nautical bottom [%]

15 10.37 11.27 12.34 13.4 14.34 15.09 15.77 16.47 17.23 18.05 18.88 19.81 20.86

Kwintebank-Scheur min gross UKC to nautical bottom [%]

15 11.27 11.97 13.4 14.04 15.09 15.55 16.47 16.97 18.05 18.6 19.81 20.5 22.15

probability of bottom touch

1.0E-02 1.4E-01 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

12:00 12:15 12:30 12:45 13:00 13:15 13:30 13:45 14:00 14:15 14:30 14:45 15:00 15:15 15:30 15:45 16:00 16:15 16:30

13.93 14.51 15.81 16.58 18.45 19.57 22.32 23.93 27.38 28.97 31.35 32.04 32.44 32.29 31.64 31.24 30.26 29.65 28.25

-4.14 -3.55 -2.25 -1.49 0.38 1.51 4.25 5.87 9.32 10.91 13.29 13.98 14.38 14.22 13.58 13.17 12.2 11.59 10.18

13.93 14.51 15.81 16.58 18.45 19.57 22.32 23.93 27.38 28.97 31.35 32.04 32.29 32 31.24 30.78 29.65 28.97 27.49

-4.14 -3.55 -2.25 -1.49 0.38 1.51 4.25 5.87 9.32 10.91 13.29 13.98 14.22 13.94 13.17 12.72 11.59 10.91 9.43

14.51 15.81 16.58 18.45 19.57 22.32 23.93 27.38 28.97 31.35 32.04 32.44 32.29 31.64 31.24 30.26 29.65 28.25 27.49

2.9 4.2 4.96 6.84 7.96 10.71 12.32 15.77 17.36 19.74 20.43 20.83 20.67 20.03 19.63 18.65 18.04 16.63 15.88

0.66 0.49 0.48 0.72 0.97 1.68 2.1 2.89 3.18 3.45 3.44 3.17 2.98 2.58 2.4 2.1 1.98 1.76 1.65

19.33 20.33 21.5 22.96 24.69 26.84 29.29 31.9 34.23 35.87 36.61 36.44 36.12 35.31 34.8 33.55 32.84 31.37 30.63

20.86 22.15 23.67 25.58 27.77 30.18 32.51 34.37 35.67 36.21 36.06 35.6 35.02 34.28 33.4 32.35 31.25 30.08 28.88

22.15 23.14 25.58 27.02 30.18 31.75 34.37 34.63 34.15 33.01 32.36 30.91 30.1 28.37 27.47 25.63 24.69 22.82 21.86

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

16:30 16:45 17:00 17:15 17:30 17:45 18:00 18:15 18:30 18:45 19:00 19:15 19:30 19:45 20:00 20:15 20:30 20:45 21:00

28.25 27.49 25.95 25.16 23.48 22.62 20.85 19.86 17.59 16.34 13.91 12.79 10.77 9.82 8.08 7.3 5.94 5.35 4.33

10.18 9.43 7.89 7.09 5.42 4.56 2.78 1.8 -0.47 -1.72 -4.16 -5.27 -7.3 -8.24 -9.99 -10.76 -12.13 -12.72 -13.73

27.49 26.73 25.16 24.34 22.62 21.75 19.86 18.78 16.34 15.1 12.79 11.75 9.82 8.92 7.3 6.59 5.35 4.81 3.91

9.43 8.66 7.09 6.27 4.56 3.69 1.8 0.71 -1.72 -2.97 -5.27 -6.31 -8.24 -9.14 -10.76 -11.48 -12.72 -13.25 -14.16

27.49 25.95 25.16 23.48 22.62 20.85 19.86 17.59 16.34 13.91 12.79 10.77 9.82 8.08 7.3 5.94 5.35 4.33 3.91

15.88 14.34 13.55 11.87 11.01 9.23 8.25 5.98 4.73 2.29 1.18 -0.85 -1.79 -3.54 -4.31 -5.68 -6.27 -7.28 -7.71

1.65 1.41 1.27 0.94 0.76 0.57 0.61 0.8 0.9 1.09 1.2 1.41 1.49 1.62 1.66 1.71 1.72 1.75 1.75

30.63 29.08 28.28 26.62 25.72 23.63 22.45 20.01 18.84 16.69 15.69 13.85 13 11.5 10.85 9.72 9.24 8.46 8.07

28.88 27.64 26.36 25.02 23.56 21.88 20.09 18.34 16.71 15.23 13.85 12.61 11.49 10.51 9.65 8.94 8.35 8.01 7.92

21.86 19.93 18.93 16.91 15.95 14.21 13.43 12.03 11.4 10.31 9.87 9.25 9.1 8.94 8.22 8.01 8.01 7.93 8.01

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 7.0E-11 1.6E-14 1.0E+00 1.0E+00 1.0E+00 1.0E+00 1.0E+00 1.0E+00

location limit 8:15 8:30 8:45 9:00 9:15 9:30 9:45 10:00 10:15 10:30 10:45 11:00 11:15

Kwintebank-Scheur min gross UKC to nautical bottom [%]

15 11.77 12.07 12.71 13.16 14.23 14.81 15.98 16.59 17.79 18.37 19.49 20.07 21.35

Scheur_West min gross UKC to nautical bottom [%]

15 12.96 13.95 14.85 15.63 16.28 16.93 17.64 18.41 19.26 20.16 21.23 22.5 24.08

Pas_van_het_Zand min gross UKC to nautical bottom [%]

12.5 14.12 15.07 15.83 16.42 16.99 17.67 18.43 19.25 20.13 21.15 22.34 23.84 25.61

min gross UKC to top mud [%]

-7 14.12 15.07 15.83 16.42 16.99 17.67 18.43 19.25 20.13 21.15 22.34 23.84 25.61

Zeebrugge_Ingang min gross UKC to nautical bottom [%]

12.5 14.84 15.61 16.18 16.75 17.49 18.29 19.13 20.03 21.08 22.34 23.92 25.8 28.04

min gross UKC to top mud [%]

-7 14.84 15.61 16.18 16.75 17.49 18.29 19.13 20.03 21.08 22.34 23.92 25.8 28.04

max current speed [knts]

2 1.41 1.31 1.22 1.12 0.98 0.82 0.64 0.49 0.45 0.58 0.92 1.4 1.99

Zeebrugge min gross UKC to nautical bottom [%]

10 10.86 11.29 12.04 12.47 13.5 14.05 15.2 15.85 17.38 18.33 20.63 22.01 25.12

min gross UKC to top mud [%]

-7 -7.21 -6.4 -6.02 -5.09 -4.56 -3.45 -2.86 -1.5 -0.68 1.34 2.57 5.46 7.06

Zeebrugge_Kaai min gross UKC to nautical bottom [%]

10 11.29 11.67 12.47 12.97 14.05 14.61 15.85 16.56 18.33 19.41 22.01 23.52 26.73

min gross UKC to top mud [%]

-7 -6.77 -6.4 -5.59 -5.09 -4.02 -3.45 -2.22 -1.5 0.26 1.34 3.95 5.46 8.66

probability of bottom touch

1.0E-02 1.0E+00 1.0E+00 1.0E+00 1.0E+00 1.0E+00 1.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

11:15 11:30 11:45 12:00 12:15 12:30 12:45 13:00 13:15 13:30 13:45 14:00 14:15 14:30 14:45 15:00 15:15 15:30 15:45

21.35 22.08 23.78 24.79 27.12 28.43 31.09 32.31 34.22 34.85 35 34.62 33.63 33.02 31.63 30.89 29.35 28.55 26.9

24.08 25.96 28.13 30.39 32.48 34.19 35.23 35.72 35.56 35 34.62 33.63 33.02 31.63 30.89 29.35 28.55 26.9 26.04

25.61 27.74 30.05 32.31 34.24 35.49 36.15 36.06 35.54 35.13 34.12 33.48 32.04 31.28 29.74 28.94 27.26 26.4 24.55

28.04 30.45 32.76 34.68 35.85 36.41 36.36 36.03 35.54 34.93 34.12 33.14 32.04 30.9 29.74 28.53 27.26 25.96 24.55

1.99 2.58 3.04 3.33 3.35 3.21 2.96 2.69 2.43 2.21 2.03 1.86 1.7 1.52 1.31 1.07 0.82 0.6 0.58

25.12 26.73 29.56 30.61 31.75 31.85 31.36 31.02 30.16 29.6 28.26 27.52 26 25.22 23.59 22.75 20.99 20.03 17.86

7.06 10.18 11.5 13.27 13.68 13.78 13.29 12.95 12.09 11.54 10.2 9.45 7.93 7.15 5.53 4.68 2.92 1.97 -0.2

26.73 28.25 30.61 31.33 31.91 31.85 31.36 31.02 30.16 29.6 28.26 27.52 26 25.22 23.59 22.75 20.99 20.03 17.86

8.66 10.18 12.55 13.27 13.84 13.78 13.29 12.95 12.09 11.54 10.2 9.45 7.93 7.15 5.53 4.68 2.92 1.97 -0.2

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00

15:45 16:00 16:15 16:30 16:45 17:00 17:15 17:30 17:45 18:00 18:15 18:30 18:45 19:00 19:15 19:30 19:45 20:00 20:15

26.9 26.04 24.22 23.22 21.01 19.85 17.63 16.59 14.69 13.81 12.21 11.5 10.23 9.68 8.75 8.37 7.9 7.85 7.85

26.04 24.22 23.22 21.01 19.85 17.63 16.59 14.69 13.81 12.21 11.5 10.23 9.68 8.75 8.37 7.9 7.84 7.86 8.23

24.55 23.51 21.19 19.98 17.71 16.67 14.74 13.83 12.19 11.46 10.18 9.62 8.65 8.25 7.7 7.59 7.72 8.28 8.95

24.55 22.96 21.19 19.39 17.71 16.17 14.74 13.39 12.19 11.11 10.18 9.35 8.65 8.07 7.7 7.58 7.89 8.59 9.69

0.58 0.7 0.83 0.97 1.12 1.28 1.42 1.53 1.61 1.66 1.69 1.71 1.72 1.72 1.7 1.69 1.66 1.64 1.6

17.86 16.67 14.3 13.19 11.17 10.22 8.47 7.68 6.27 5.66 4.6 4.14 3.41 3.18 3.06 3.14 3.81 4.43 6.01

-0.2 -1.39 -3.76 -4.87 -6.9 -7.85 -9.6 -10.39 -11.79 -12.4 -13.47 -13.93 -14.65 -14.88 -15 -14.69 -14.25 -12.89 -12.05

17.86 16.67 14.3 13.19 11.17 10.22 8.47 7.68 6.27 5.66 4.6 4.14 3.41 3.18 3.14 3.38 4.43 5.18 6.85

-0.2 -1.39 -3.76 -4.87 -6.9 -7.85 -9.6 -10.39 -11.79 -12.4 -13.47 -13.93 -14.65 -14.88 -14.93 -14.69 -13.64 -12.89 -11.21

0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 0.0E+00 1.0E+00 1.0E+00 1.0E+00 1.0E+00 1.0E+00 1.0E+00 1.0E+00 1.0E+00 1.0E+00

328

Figure 7. Distribution of length of tidal windows for container

vessels arriving at / departing from Antwerp with given drafts

(different for arrival and departure, values not communicated),

based on a one-year period. The cumulative distribution shows

the fraction of the tides offering a window with a length of at

least the abscissa value. Note that a percentage of tides (espe-

cially for arriving vessels) does not result into a tidal window

for the given draft, yielding a nonzero distribution value for a

window length equal to zero.

4 TOWARDS A GENERALISED

PROBABILISTIC METHODOLOGY

4.1 Introduction

Although the present tool can be applied to a wide

range of access channels, the development of a gen-

eral methodology for a probabilistic approach re-

quires a number of extensions.

In the first place, squat not only depends on the

ship characteristics and speed through water, but is

also affected by the channel characteristics (water

depth, lateral limitations), the proximity of banks

and interaction with meeting and overtaking or over-

taken ships.

Furthermore, the probability of bottom touch

does not only depend on squat and the response to

the local wave climate, but other effects may be of

importance as well (e.g. wind, heel in bends). In

some cases, even the basic principle for determining

the probability of undesired events might have to be

reconsidered. This is especially the case if the re-

sponse to waves is not the main cause of bottom

touch.

Finally, it should always be born in mind that not

only contact with the bottom due to vertical motions

should be taken into account, but that all undesired

events (groundings, collisions with fixed structures

or with other ships) are of importance in order to as-

sess the total safety of shipping traffic.

4.2 Practical case: access to Antwerp for large

container vessels

The importance of additional effects on squat can be

illustrated by the results of real-time simulations that

have been executed on the ship manoeuvring simula-

tors of Flanders Hydraulics Research (SIM225 and

SIM360+) to evaluate the accessibility of the West

Scheldt for large containerships with a length over

all of 366 – 380 – 400 m. Both simulators were cou-

pled so that with two operating bridges the encoun-

ters are as realistic as possible.

During the simulations the sinkage fore and aft

was calculated taking into account ship dependent

parameters (draft, displacement, block coefficient,

midship section area); environmental parameters

(water depth, distance to banks); operational pa-

rameters (forward and lateral velocities and accel-

erations, yaw rate and acceleration, propeller rate)

and other shipping traffic (draft of target ship, dis-

placement of target ship, block coefficient of target

ship, lateral distance between ships, longitudinal ve-

locity of target ship) (Eloot et al. 2008).

As an example, Figure 8 shows a particular en-

counter of a departing containership (366 m x 48.8

m x 13.1 m) with a larger ship (400 m x 56.4 m x

14.5 m) in the bend of Bath on the river Scheldt

(maximum flood current, wind SW 5Bf). The en-

counter occurred with a lateral distance equal to 56m

and a relative speed through the water for both ships

of approximate3ly 12 knots. The velocity parameters

and sinkages of the downstream ship can be studied

based on the graphs in Figure 8. The lowest obtained

static UKC along the whole trajectory is approxi-

mately 50% while the maximum sinkage occurs at

the stern with a maximum UKC reduction of ap-

proximately 10% of the ship’s draft.

4.3 Requirements

At least the following investigations are required to

develop a generalised probabilistic admittance poli-

cy for deep-drafted ships:

− Redefinition of the probability of bottom touch in

navigation channels that are not exposed to wave

action. The present method for calculating this

probability is based on a Rayleigh distribution of

the peak-to-peak values for the vertical motion of

a number of critical points. Hence, the overall

probability during a transit requires the availabil-

ity of a value for the average encounter period,

which cannot be defined in absence of waves.

Therefore, there is a need for an alternative meth-

odology resulting into a probability of bottom

contact that is not merely dependent on the char-

acteristics of the wave spectrum.

− Integration of the influence of wind on net UKC.

This effect may be caused in several ways: the

lateral force and yawing moment caused by non-

longitudinal relative wind directions result into

the occurrence of both heel, which directly reduc-

0.1

0.2

0 60 120 180 240 300

Window Length [min]

Distribution [-]

0.2

0.4

0.6

0.8

Cumulative Distribution [-]

arrival

departure

arrival (cum)

departure (cum)

329

es the UKC, and drift, which may lead to in-

creased squat, but also to reduced speed.

− Integration of the effect of cross currents and

waves on drift and, eventually, on squat;

− Integration of the effect of bends in the fairway,

which may cause speed reduction, but also heel

and increased squat due to yawing and drift.

− Integration of the effect of interaction with other

shipping traffic, particularly on squat;

− Integration of the effect of interaction with banks,

particularly on squat;

− Link with occurrence of other undesired effects.

5 CONCLUSIONS

A software tool for supporting operational and stra-

tegic decisions concerning accessibility of harbours

for (deep-drafted) vessels subject to tidal windows

has been presented. For short-term planning the tool

has been implemented for the approach to the har-

bour of Zeebrugge, where multiple criteria (gross

UKC, probability of bottom touch, keel penetration

into fluid mud layers, cross currents) are of im-

portance. An example is also given of a long-term

statistical analysis of the length of tidal windows.

Finally, requirements are formulated that have to be

fulfilled to develop a generalised probabilistic ad-

mittance policy for deep-drafted ships.

Figure 8. Real-time simulation of an encounter at the bend of Bath during flood tide: trajectories of both ships during the total ma-

noeuvre and parameters of the ship sailing downstream with the encounter position indicated with a dashed vertical line.

330

REFERENCES

Eloot, K.; Verwilligen, J.; Vantorre, M. 2008. An overview of

squat measurements for container vessels in restricted wa-

ter. International conference on safety and operations in ca-

nals and waterways SOCW 2008, Glasgow, 19-20 Septem-

ber 2008.

PIANC. 1997. Approach Channels: A Guide for Design, Final

Report of the Joint PIANC-IAPH Working Group II-30 in

cooperation with IMPA and IALA, Supplement to PIANC

Bulletin, No. 95.

Savenije, P. 1996. Probabilistic admittance policy deep draught

vessels. PIANC Bulletin, No. 91, June 1996.

Vantorre, M.; Laforce, E.; Eloot, K.; Richter, J.; Verwilligen,

J.; Lataire, E. 2008. Ship motions in shallow water as the

base for a probabilistic approach policy. Proceedings of the

ASME 27th International Conference on Offshore Mechan-

ics and Arctic Engineering OMAE2008, Estoril, 15-20 June

2008