International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 1
Number 4
December 2007
407
Depth Optimization of Designed New Ferry
Berth
S. Gucma & S. Jankowski
Maritime University of Szczecin, Szczecin, Poland
ABSTRACT: Increasing sea ferries traffic on Baltic Sea has in the recent years motivated the design of larger
ferries. Currently the lengths of the most ferries, which call at port of Świnoujście, do not exceed the limit of
170 meters. The new projected ferry berth will be adopted for ferries with LOA equal 220 and even 230
meters. It is obvious that propeller of that sea ferries will produce a propeller stream with greater velocity and
initial diameter as well, particularly that they will maneuver without any tugs. That water jet can much easier
cause bottom erosion especially at mooring berth. This article is a presentation of depth optimization process
at berth No 1 of Sea Ferries Terminal (SFT) in port of Świnoujście.
1 INTRODUCTION
The paper presents the simulation method of
determination the propeller jet stream’s velocity at
the bottom and depth optimization method for
berths, which take advantage of jet streams’ velocity
at the bottom for different value of depth. The
presented method was used to determine the depth of
berth no 1, at Świnoujście Sea Ferries Terminal
(SFT).
The ships model that was used in simulations was
worked out in Institute of Marine Traffic
Engineering at Maritime University of Szczecin.
The simulations of mooring maneuvers were
conducted for maximum allowed Ro-Pax ferry’s at
new building berth no 1 in Świnoujście SFT.
The safety of navigation is determined by vessel’s
size and her maneuvering characteristics. Those
parameters define a maximum vessel, which is the
biggest vessel which may safety maneuver at given
area, at given navigational conditions. Vessel may be
consider maximum if only one of her dimensions is
maximum (e.g.: draft, beam, length, speed).
After ferry market analysis and navigational
analysis of port of Świnoujście were done, the
maximum ferry was determined. It turned out, that
maximum Ro-Pax ferry for Świnoujście is 220 m
long and her main engines power is 14000 kW.
2 SIMULATION METHOD OF
DETERMINATION THE PROPELLER
WATER-JET VELOCITY AT THE BOTTOM
Presented method of determination the propeller
jetstream, takes advantage of simulation trials. The
series of trials are done for given vessel and given
conditions. During trials vessel movement’s
parameters are recorded as a text files. After trials
are done, the jest stream’s velocity is calculated for
every single vessel’s position recorded (fig. 1). Jet
stream’s velocities at the bottom are determined for
the whole area, due to adopted level of
discretisation. The jest stream’s velocity is a
function of following variables:
( )
RNKRyxhyx
ss
f
yx
V
,,,,,,,
,
=
(1)
408
where V
x,y
= stream velocity at (x, y) point of the
bottom, h = depth, (x
s
, y
s
) = vessel’s coordinates,
KR = vessel’s heading, N = current main engine
command, R = rudder deflection.
x
r
V [m/s]
x, r
Time of simulation [s]
Bottom of the area
Simulation 1 Simulation n
Fig. 1. Determination of maximum stream velocity, in the (x, y)
point of bottom area, for each simulation
The following vessel’s parameters, which are of
static nature, play also a vital role:
− length over all,
− vessel’s draught,
− power delivered on propeller,
− propeller coordinates’ shifting from recorded
vessel’s position (usually center of gravity’s
position is recorded),
− distance between the horizontal axis of propeller
and the bottom.
Existence of any harbor’s structure is also taking
into account. The velocity of water jet stream is
consider zero, if any part of hydrotechnical structure
is located in discrete area or obscure it (fig. 2).
Marine
engineering
structures
Fig. 2. Propeller stream obscured by harbor’s structures.
The algorithm to determine the jet stream
velocities at the bottom is as follows:
1 Calculate a speed of inducted water jet near
the propeller:
3
1
2
0
⋅
⋅
⋅=
ws
d
d
d
Pk
KV
ς
(2)
where V
0
= stream velocity nearby propeller,
K
d
= empirical coefficient equal 1.48 for free
propeller, k = power utilization coefficient, P
d
= a
power delivered on propeller, d
s
= propeller
diameter, ς
w
= water density.
2 Choose centre point of the discrete area (xd, yd)
according to discretisation level;
3 Check following items:
− is centre point of discrete area located on water
area?
− is it not covered by other quay structures?
4 Calculate the distance s, between the propeller
plane and projection of the point (x, y) onto a
propeller’s horizontal axis;
5 Calculate the speed Vx max, in calculated
distance s rom the propeller (rudder angle is 0);
a
s
d
h
max s
d
s
eVV
s
p
−
⋅⋅⋅=
161.0
0
88.1
(3)
where V
x, max
= the distance from the propeller
plane, h
p
= distance between bottom and propeller
horizontal axis, s = the distance from the propeller’s
plane and projection of point (x, y).
At given rudder angle:
( )
1
8.2
102.51
1
25.3
6
0max
b
s
s
d
s
VV
−
−
⋅
⋅⋅+
=
δ
(4)
where δ= rudder angle.
6 Calculate the distance r between propeller’s
horizontal axis and the centre of the discrete
area (x, y),
7 Calculate the velocity of the propeller jet stream
at the bottom, in a middle of discrete area;
−
⋅=
2
max s,
V
s
r
m
rs
eV
(5)
where V
s,r
= the stream velocity in distance s from
the propeller plane and distance r from the propeller
axis, r = the distance from the propeller axis (a
radius).
8 Record, as a text file, the maximum value of
screw jet stream velocity at the bottom for given
coordinate (x, y).
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3 PROPELLER JET STREAM
DETERMINATION FOR FERRY BERTH
DESIGN
The design vessel’s parameters, for berth no 1 at
Świnoujście SFT, is as follow:
LOA 220 [m],
Beam 32 [m],
Draft 7.0 [m],
Nominal power of ME 2 x 14000 [kW],
Diameter of propeller 4.0 [m],
Two pitch adjustable, left handed propellers.
Several conditions were chosen for simulations’
trials. Number of single trials within given
conditions was at least 15.
The following conditions were considered
the hardest:
− unmooring and swinging by port side, wind
W 15 m/s, inbound current 1.5 kn,
− mooring with port side, wind E 15m/s, inbound
current 1.5 kn,
− unmooring and swinging by starboard side, wind
W 15 m/s, outbound current 1.3 kn,
Two series were done, for zero-state conditions –
no wind, no current:
− mooring with port side,
− unmooring and swinging by any side.
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Fig. 3. Berth no 1 layout with a ferry moored at
Maximum propeller jet stream’s velocity was
calculated for the depth shown in table 1.
Table 1. Depths and distances to a bottom [m]
Available
depth
Depth for
calculation
Under keel
clearance
Distance
from
propeller’s
axis to
bottom
9
12
8
11
1
4
3.4
6.4
Mean sea level in port of Świnoujście, which has
been recorded for many years, is 4.90m. Minimal
mean sea level, calculated for the last 10 years is 1
meter less than mean sea level. Therefore, an
appropriate depth allowance was considered.
Bottom at berth no 1 was loaded with jet streams
the most during maneuvers with the inbound current.
The mooring maneuvers were done with the pushing
away eastern wind, whilst unmooring maneuvers
were conducted with pushing western wind. In both
cases, vessel was to stand up the great wind force,
which produced significant lateral pressure. That
pressure forced captain to use top command on main
engine telegraph.
The distribution of maximum jet streams’
velocity is shown on fig. 4. The depth of considered
area is 8 meters. The distributions differ in that areas
heavily loaded with jet streams are shifted. For
mooring operations that area is moved to the middle
of investigated area, whilst for unmooring
manoeuvres the area is smaller and is close to berth’s
wall. It is worth to emphasize, that jet stream’s
velocities were higher for unmooring manoeuvres.
The maximum velocity of jet streams whilst
mooring was 8.9 m/s, and whilst unmooring it
exceeded 9.5 m/s. However the area affected by
streams with velocity more than 8.5 m/s was not
extensive. Taking that into consideration, as well as
1 meter depth allowance for area depth 9 m, it was
assumed that bottom affecting velocity of jet streams
is 7.5 m/s.
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0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
A) B)
Fig. 4. Distribution of maximum water jet velocity at a bottom,
depth 8m. A) mooring port side, wind E 15 m/s, current
inbound average max (1.5 kn); B) unmooring and swing by port
side, wind W 15 m/s, inbound current average max (1.5 kn)
Distributions of maximum velocities at berth no
1, for mooring and unmooring maneuvers are shown
on fig.5. The available depth is 12 meters. The
N
410
maximum velocity for mooring is 5.7 m/s and for
unmooring is 6.1 m/s. Taking that into consideration,
as well as 1 meter depth allowance, it was assumed
that bottom affecting velocity of jet streams is
4.5 m/s.
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0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
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A) B)
Fig.5. Distribution of maximum water jet velocity at a bottom,
depth 11m. A) mooring port side, wind E 15 m/s, current
inbound average max (1.5 kn); B) unmooring and turn by port
side, wind W 15 m/s, inbound current average max (1.5 kn)
The picture below presents decreasing of jet
streams’ velocity at the bottom as a result of depth
increase up to 12 meters.
7.5
4.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8 9 10 11 12 13
Depth [m[
Stream velocity [m/s]
Fig. 6. Distribution of maximum water jet velocity at a bottom,
depth 11 m
Increase of available depth considerably reduced
jet streams’ velocities at the bottom. But there is one
question, concerning economical aspect of new-
building berth. Either more profitable is to dredge
the considered area or apply proper bed protection?
4 BERTH NO 1 OF ŚWINOUJŚCIE SFT AS
AN EXAMPLE OF BED PROTECTION
PARAMETERS’ OPTIMIZATION
Evaluating the optimizing function of berth depths’
optimize as a cost of berth building and bed
reinforce, following assumptions were adopted:
− investigated vessel maneuvers on restricted area,
her position is defined on Cartesian axes,
− investigated area is a set of elements x ∈ X,
y ∈ Y,
− coordinates that define the set are Cartesian’s
product,
− on investigated area, only vessels that are
included within set i ∈ I, are allowed to
maneuver. It concerns either vessel’s size (LOA,
beam, draft) or engine power and type,
− vessel maneuvering on the area, may perform one
of the maneuvers, that are within set j ∈ J. It is
the set of all available maneuvers on given area,
− investigated vessels may maneuver in conditions
that are within set k ∈ K. It concerns either hydro
meteorological (wind, current, sea, ice) conditions
or navigational and traffic conditions.
The safety of navigation and harbor’s structures,
evaluated by means of berth depths’ optimizing
model, is determined by following items:
− under keel clearance,
− jet streams velocity at the bottom.
Adopting above assumptions, optimizing function
may be presented as a following formula:
Z = a · l · b · h + q · l · b + c · l → min (6)
where l = f
1
(D), b = f
2
(D), q = f
3
(V
x,y
), c = f
4
(h),
with following constraints:
1. d
ijk
⊂ D
where
i ∈ I, j ∈ J, k ∈ K
2. h
xy
≥ T
i
+ ∆
ijk
3. V
xyijk
> V
xydna
4. V
xyijk
≤ V
dxy
where:
Z – costs of building new berth, dredging
maneuvering area, bed protection;
a – cost of dredging of 1m3;
l – berth length;
b – bed protection width;
p(x,y) ∈ D
p(x,y) ∈ D
p(x,y) ∈ D
411
h
– depth of area at designer berth;
q – cost of protection of 1m3 of bed;
c – cost of 1m of berth;
d
ijk
– maneuvering area, for ith vessel, jt type
of maneuvers, kt navigational conditions,
where Vxy > Vxydna;
D – maneuvering area, that meet requirement
Vxy > Vxydna, for investigated set of
vessel I, maneuvers J, and navigational
conditions K.
T
i
– maximum draft of ith vessel,
∆
ijk
– under keel clearance, for ith vessel, jt type
of maneuvers, kt navigational conditions,
V
xyijk
– maximum jet streams velocity at the bottom
in certain position (x, y) for ith vessel,
jt type of maneuvers, kt navigational
conditions,
V
xydna
– available velocity of water at the bottom,
for position (x, y) for existing bed type,
V
xyd
– available velocity of water at the bottom,
for position (x, y) for bed after protection.
Based on simulations’ results, existing
bathymetrical and hydro meteorological conditions
and above detailed costs of designed berth No 1 at
Świnoujście SFT, the safety depth at berth was set to
12,5 m. During the whole optimization project, the
depth of waterways near berth and southern
swinging area depth were considered as well.
5 CONCLUSION
The paper presents depth optimizing models at ferry
terminals, which take advantage of propeller jet
velocities at the bottom, determined by means of
original simulation method.
The method was used to determine the depth at
the new building berth no 1 at Świnoujście Sea
Ferries Terminal.
The method is all purpose. After adaptation, it
may be used to optimize the depths at any berth, for
any type of vessels.
REFERENCES
Blaauw H.G., Van De Kaa E.J., Erosion of bottom and sloping
banks caused by the screw of manouvring ships, 7th
International Harbour Congress, Antwerp 1978.
Fuehrer M, Pohl H, Römisch K.— „Effects of modern ship
traffic on inland and ocean waterways and their structures”,
24th International Navigation Congress, Leningrad 1977.
Verhey H.J., “The stability of bottom and banks subject to the
velocities in the propeller jet behind ships” – Delft
Publication no 303, Delft Hydraulics Laboratory 1983.
Römisch, K.: Propellerstrahlinduzierte Erosionserscheinungen
in Häfen. HANSA, Nr. 8, 1993.
