International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 4
Number 3
September 2010
273
1 INTRODUCTION AND OBJECTIVES
Deck officers simplify the problem of ship berthing,
whether made on her own or with tugs assistance, to
maintain proper local lateral velocities fore (at the
bow) and aft (at the stern). Both movements are able
to be measured by an onboard doppler log (with sen-
sors in the mentioned locations), an onboard docking
system (as the satellite-based one with two antennas,
or where the linear velocity vector, e.g. from a satel-
lite system, is integrated with the rate of turn from a
gyroscopic sensor, or in which inertial sensors are
finally applied), or a docking system ashore, if ap-
plicable. Some terminals report a maximum allowa-
ble lateral approach speed for various weather condi-
tions and ship sizes. By default, the essentially
parallel approach is therein assumed.
Of course, this practice really works when an at-
tempt is made to restrict these velocities as close as
possible to zero. However, some major or minor
problems can happen if the bow and stern velocities
are significantly non-zero, different from each other,
or occurring at the ship's non-zero direction angle to
a berth (thus making a 'single point' contact).
In the following a closer look into the ship-berth
(or ship-fender) interaction phenomenon is intended,
because the situation is more complex, as usual, in
the real-world. The local loads in fenders and ab-
sorbed energies will be studied in detail. The prob-
lem is tackled by the comprehensive ship manoeu-
vring simulation with a full control over the fender
effects. According to the author's opinion the exist-
ing full-mission ship-handling bridge simulators do
not allow any analysis of loads in fenders, except for
sending a 'broken fender' alert. Moreover, the im-
plemented fender dynamic effect on ship manoeu-
vring motions is often not well modelled
2 SIMULATION EXPERIMENTS
The designed simulation experiment consists of a
manoeuvring mathematical model of small chemi-
cal tanker 6000 DWT. The ship data as of direct in-
terest in berthing problems are briefed in Table 1.
Other hydrodynamic features of the model can be
found e.g. in (Artyszuk, 2005). The model runs
within the fast- and real-time interactive ship
manoeuvring simulation software SMART (all the
mechanical effects included) as developed by the
Author. As to properly evaluate the fender forces the
integration and recording time step 0.05s is adopted
on the basis of some preliminary convergence simu-
lation trials with the berthing manoeuvres in con-
cern.
Simulation of Load Distribution along a Quay
during Unparallel Berthing Manoeuvres
J. Artyszuk
Maritime University of Szczecin, Szczecin, Poland
ABSTRACT: The marine berths are normally secured for safety reasons with a system of fenders. Their role
is to absorb and dissipate the kinetic energy of a ship coming into a contact with a berth, so the structural in-
tegrity of both the berth and ship's hull is preserved. Normally the combination of a number and the single
fender strength indicate the ship's maximum allowable lateral speed in parallel berthing conditions (of course,
with a safety margin frequently taken into account). More or less directly and/or approximately, this is also a
general selection method for fender systems. The main objective of this conference contribution, as inspired
by some suggestions and needs within a domestic marine society since the author's developed and successful-
ly implemented fender effect in ship manoeuvring simulation, is to analyse the local loads in a particular
fender around the region of contact during an oblique berthing. Various conditions of ship's lateral and angu-
lar velocities are tested. The results are compared with some practical shiphandling tips, as to be found in the
literature, leading to a necessity of revision of the existing practice. The presented investigations are believed
to be very helpful also for fender system designers.
274
For reference purposes the deep water conditions
near the berth are selected, since there is a signifi-
cant scatter in the literature concerning the shallow
water correction factors for added masses and hull
hydrodynamic forces. The patterns of local loads in
the fendering system in such circumstances are how-
ever believed to be very similar to those of deep wa-
ter case, of course except for absolute values. Be-
cause the fender reaction forces really dominate
when a contact with fenders is already established
(even before or after that moment the hydrodynamic
damping forces are too small to change the ship very
slow motions in a rather short time period) the most
important for the shallow water berthing simulation
is the augmentation of added masses. Nevertheless,
some characteristic shallow water aspects will be
later raised in the study.
Table 1. The ship basic data.
__________________________________________________
Symbol Value Name
__________________________________________________
m[t] 8948 displacement (mass)
L[m] 97.4 length between perpendiculars
B[m] 16.6 breadth
T[m] 7.1 draught
k11[-] 0.056 surge added mass coeff.
k22[-] 1.004 sway added mass coeff.
k66[-] 0.83 yaw added inertia coeff.
rz[-] 0.2465 ship's gyration radius (length units)
_________________________________________________
Furthermore, the model of discretely spaced line-
ar fenders, as described in (Artyszuk, 2003), is used
in the research - the fender reaction increases pro-
portionally to its compression while for decompres-
sion it practically disappears. Though the SMART
environment is capable of implementing any nonlin-
ear load-deflection chart of the fender (including the
so-called hysteresis), the adopted linear characteris-
tics enables a direct comparison of simulation results
with those obtained by the analytical dynamic meth-
od for a single fender. The latter analytical approach,
based on a set of linear ODEs, was introduced in
(Artyszuk, 2003). In view of the current concern
more results of this analytical method are contained
in Table 4. The analytical method is universal in
such a way that after some minor extensions it gives
ship movements after the impact for any initial con-
dition in terms of the direction angle, linear and an-
gular velocities. This certainly could help to solve a
dispute in the domestic literature (Magda, 2006)
with regard to the Vasco Costa formula (Vasco Cos-
ta, 1964) for the berthing energy absorption, as
based on the angular momentum conservation theory
for non-elastic collisions.
A berth secured with 20 fenders (each of the max-
imum force 100t at the deflection 20cm that contrib-
utes to the energy absorption E
F
=98.1kJ per single
fender) is set up from the practical viewpoint. As
opposed to (Artyszuk, 2003, 2005), in the present re-
search the linear reaction of a fender during the de-
compression phase is additionally assumed, though
set only at the level of 1% of the compression-
related reaction at the same deflection. These fend-
ers are spaced every 5m that corresponds to 1/20 of
the ship's length, since trials with 10 fenders, ar-
ranged every 0.1L, have failed in this sense that safe
berthing speed under such circumstances is relative-
ly low (even in deep water constituting the most fa-
vorable berthing conditions). It shall be here namely
emphasized that the usual curvature of the ship's wa-
terline contour (specifically the length of ship's par-
allel body), see Figure 1, leads in our case to the
compression of just 11 to 13 fenders (of the total
number 20) depending on the lateral speed. These
are 6(7) aft, 1 center, and 4(5) forward fenders for
the speed 0.3(0.6)kt.
ψ
active contour
(summer draft)
extreme contour
midship
accommodation
rear and front
fore mast
-8 -
7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8
fender label
V
xy
ω
z
Figure 1. Situational sketch of portside berthing manoeuvre.
All the fenders are labeled according to their rela-
tive location against the ship's midship section (Fig.
1). There are 15 runs considered in the experiment,
in which the ship after an initial excitation moves by
inertia towards the berth - see Table 2.
Table 2. Summary of simulation runs.
______________________________________________
Symbol Heading Mode of Motion
v
y
(sway) / ω
z
(yaw)
______________________________________________
R0. 090° neg. / -
R1. 090° neg. / -
A0. 088° neg. / -
B0. 085° neg. / -
C0. 080° neg. / -
D0. 075° neg. / -
E0. 070° neg. / -
F0. 060° neg. / -
B1. 085° - / neg.
B2. 085° pos. / neg.
B3. 085° neg. / pos.
G0. 095° neg. / -
G1. 095° - / pos.
G2. 095° pos. / pos.
G3. 095° neg. / neg.
_____________________________________________
275
The first two runs (R0, R1) deal with a parallel
approach at different lateral velocity (0.3m/s and
0.15m/s correspondingly). The other six in order
(A0÷E0) constitute an oblique, constant heading
bow-in (bow-first) berthing at a different ship-to-
berth direction (starting from 2° up to 30°), in which
the linear velocity v
xy
=0.15m/s (0.3kt) is kept normal
to the berth. Such a condition means the varying
forward and lateral (negative to portside) velocities,
v
x
and v
y
, according to the projections of total veloci-
ty vector in ship's body axes - see the first row of
Table 4a. The consecutive three runs (B1÷B3) take a
focus on a possible different combination of the lin-
ear and angular (positive to starboard) velocity as to
arrive at the same local lateral velocity (equal to
0.15m/s) for the ship's hull point of the first contact.
In the bow-in berthing the latter lies approximately
at the one quarter of the ship's length (~25m) from
the amidships position. The last four manoeuvres
(G0÷G3) comprise some cases of the stern-in berth-
ing at 5° to the berth. The varying combination of
lateral and yaw velocities also contributes to the lo-
cal contact velocity of order 0.15m/s, which is how-
ever now connected with the hull point placed 40m
astern from the ship's midship.
3 ANALYSIS OF RESULTS
As aforementioned, of a great assistance in physical
explaining and/or verifying the simulation results
appears an application of the analytical method - see
the following Table 3. If a ship moving nearly per-
pendicularly to the berth hits a single fender, the re-
sulting after the impact lateral v
y1
and yaw ω
z1
ve-
locities generally depend on the fender contact point
in relation to the ship's midship (index '1' denotes the
first impact, here the bow impact, '2' refers to the se-
cond impact i.e. by the stern). To be more precise
one should refer the fender position to the ship's ra-
dius of gyration r
z
- see also the early works of Vas-
co Costa (Vasco Costa, 1964, 1968). The instant
pivot point position x
PP
during the fender compres-
sion decreases from the infinity up to the conver-
gence with the fender position x
c
at the moment of
maximum deflection t
max
. For the chemical tanker in
concern with a berthing speed of 0.25m/s this is pre-
sented in Figure 2, where both magnitudes are ex-
pressed in units of the ship's length (the value +0.5
coincides with the ship's bow).
It is evident from Table 3 that the highest contri-
bution to the residual total kinetic energy after the
first impact, as actually coming from the ship's rota-
tion, is gained for a fender close to the midship sec-
tion - the parameter %E
1
(ω
z
) represents the ratio of
yaw-related energy to the total remaining energy E
1
.
The difference between E
1
and the initial energy E
0
(here arising from the pure lateral motion) is repre-
sented by dE
1
. Furthermore, the quantity %dE
1
means the ratio of just absorbed energy dE
1
to the
initial energy E
0
, while the expression dE
1
/E
F
indi-
cates the absorbed energy as compared to the fender
specific maximum energy E
F
that can be safely ab-
sorbed (here E
F
=98.1kJ). Values of dE
1
/E
F
in Table
3 higher than unity, specifically for fenders close to
the midship, are rather theoretical ones (although of
some practical implication), since the assumed linear
fender was allowed to be compressed outside the
limit of 20cm, which was necessary to completely
stop the ship and transfer her full kinetic energy to
the fender. It must be well understood that for the
mostly forward fenders the absorbed energy is es-
sentially lower, but the rest of initial energy still re-
mains on the ship and increases the risk of second
impact.
Table 3. Motions and energy absorption - analytical study
______________________________________________
fender abscissa (in ship's length from amidships)
0.0
+0.1
+0.2
+0.3
+0.4
+0.5
t
max
[s]
3.0
2.8
2.3
1.9
1.5
1.3
v
y1
[m/s]
0.0000
-0.0382
-0.1047
-0.1547
-0.1856
-0.2046
ω
z1
[°/min]
0.00
13.47
18.48
18.19
16.38
14.44
%E
1
(ω
z
)
0.00
0.85
0.58
0.38
0.26
0.18
E
1
[kJ]
0
86
235
347
416
459
dE
1
[kJ]
560
475
326
214
144
102
%dE
1
1.00
0.85
0.58
0.38
0.26
0.18
dE
1
/E
F
5.7
4.8
3.3
2.2
1.5
1.0
0
0.2
0.4
0.6
0.8
1
0 0.5 1 1.5 2 2.5 3
0
0.1
0.2
0.3
0.4
0.5
t[s]
x
PP
[-]
x
C
[-]
Figure 2. Ship's pivot point during the work of fender.
The ship's kinematic behaviour during berthing as
experienced within the scope of the simulation ex-
periment (see Section 2) is summarised in Table 4a
and 4b, except for the run R0 that is similar to R1 in
output. The subscripts '0' and '1' relate to the condi-
tion before and after the first impact, the indices '2'
and '3' deal with the second impact accordingly (if
applicable). Time t
2
is the moment of beginning the
second impact as counted from the start of the first
impact. The parameter dE
3
stores the released (ab-
sorbed) energy during the second impact. Though
the first impact in the bow-in berthing can affect up
to maximum three particular forward fenders, see
276
the last row in Tables 4a and 4b, the second impact
is somehow a continuous pressing of all fenders in
sequence (strictly related to the hull parallel body),
as installed on the berth, commencing from the
fenders of the first impact. In this context t
2
indicates
the point of time when the ship activates the first aft
(negative) fender, see Figure 1. The meaning of
other symbols in both Tables is identical to that of
Table 3.
Table 4a. Motions and energy absorption - simulation.
______________________________________________
Run no.
R1
A0
B0
C0
D0
E0
F0
v
y0
[m/s]
- 0.1475
-0.1460
-0.1433
-0.1409
-0.1386
-0.1313
-0.1232
ω
z0
[°/min]
0.00
0.03
0.13
0.33
0.44
0.84
0.83
%E
0
(ω
z
)
0.00
0.00
0.00
0.00
0.00
0.00
0.00
E
0
[kJ]
195
191
185
181
179
167
162
v
y1
[m/s]
0.0167
-0.0631
-0.0693
-0.0802
-0.0871
-0.0883
-0.0938
ω
z1
[°/min]
-2.43
11.86
11.66
11.11
10.74
10.37
9.54
%E
1
(ω
z
)
0.49
0.61
0.56
0.46
0.40
0.38
0.29
E
1
[kJ]
5
92
97
107
114
113
124
dE
1
[kJ]
190
99
88
74
65
54
39
%dE
1
0.98
0.52
0.47
0.41
0.36
0.32
0.24
dE
1
/E
F
1.94
1.01
0.89
0.76
0.67
0.55
0.39
t
2
[s]
-
11
28
62
100
146
255
v
y2
[m/s]
- -
0.0505
-
0.0597
-0.0406
-
0.0366
-
0.0303
-
0.0268
ω
z2
[°/min]
-
11.99
10.06
9.78
8.72
7.61
5.93
%E
2
(ω
z
)
-
0.72
0.56
0.72
0.72
0.74
0.69
E
2
[kJ]
-
80
72
53
42
31
20
v
y3
[m/s]
-
0.0287
0.0252
0.0273
0.0241
0.0213
0.0159
ω
z3
[°/min]
-
2.71
1.69
2.65
2.43
2.08
1.70
%E
3
(ω
z
)
-
0.28
0.17
0.30
0.31
0.30
0.34
E
3
[kJ]
-
10
7
9
8
6
3
dE
3
[kJ]
-
70
66
43
35
26
17
% dE
3
-
0.87
0.91
0.82
0.82
0.82
0.83
dE
3
/E
F
-
0.71
0.67
0.44
0.35
0.26
0.17
fenders of
1st impact
from -6
to +4
+3, +4,
+5
+4, +5
+5, +6
+6
+ 6, +7
+8
The second impact, though very important in cer-
tain circumstances, has received in the literature ra-
ther less interest so far. (Vasco Costa, 1964, 1968,
1987) gives only some general shiphandling conclu-
sions, probably due to the lack of appropriate simu-
lations tools to perform such a research.
As shown in Table 4a, the higher angles of ap-
proaching the berth, while maintaining the same
normal velocity, lead to significant drops in the en-
ergy dE
1
absorbed by fenders and rotation-related
contribution %E
1
(ω
z
) to the remaining energy. Also
proportionally lower energy is absorbed within the
second impact, see dE
3
. The latter is always weaker
than the first impact - the hydrodynamic damping of
hull motions during a period till the ship is finally
reaching the alongside position seems to be respon-
sible for that.
Table 4b. Motions and energy absorption - simulation.
______________________________________________
Run no.
B1
B2
B3
G0
G1
G2
G3
v
y0
[m/s]
0.0000
0.1464
-
0.2471
-0.1475
0.0000
0.1485
-
0.2486
ω
z0
[°/min]
-20.13
-39.25
13.53
-0.04
12.77
25.30
-8.54
%E
0
(ω
z
)
1.00
0.76
0.12
0.00
1.00
0.56
0.05
E
0
[kJ]
162
807
621
195
65
453
583
v
y1
[m/s]
0.0671
0.2089
-0.1546
-0.1077
0.0357
0.1828
-0.2010
ω
z1
[°/min]
-8.71
-24.76
26.28
-10.31
3.31
15.21
-19.53
%E
1
(ω
z
)
0.43
0.38
0.56
0.29
0.28
0.24
0.30
E
1
[kJ]
71
636
490
146
16
392
515
dE
1
[kJ]
91
171
130
49
49
61
69
%dE
1
0.56
0.21
0.21
0.25
0.76
0.14
0.12
dE
1
/E
F
0.93
1.75
1.33
0.50
0.50
0.63
0.70
t
2
[s]
-
-
11
31
-
-
16
v
y2
[m/s]
-
-
-0.1095
-0.0787
-
-
-0.1546
ω
z2
[°/min]
-
-
25.41
-11.25
-
-
-20.60
%E
2
(ω
z
)
-
-
0.71
0.48
-
-
0.44
E
2
[kJ]
-
-
365
106
-
-
384
v
y3
[m/s]
-
-
0.0663
0.0311
-
-
0.0584
ω
z3
[°/min]
-
-
5.57
-5.02
-
-
-7.75
%E
3
(ω
z
)
- -
0.24
0.54
- -
0.44
E
3
[kJ]
-
-
52
19
-
-
55
dE
3
[kJ]
-
-
314
87
-
-
329
% dE
3
-
-
0.86
0.82
-
-
0.86
dE
3
/E
F
-
-
3.20
0.89
-
-
3.36
fenders of
1st impact
+5
+5,+6
+4,+5
-8
-8
-8
-7,-8
However, when it comes to fender loads the situa-
tion is somehow indefinite - dependent on the num-
ber of fenders in contact with the ship's hull, the
maximum loads (kN) experienced in fenders are ap-
proximately as follows: 790(420), 940(400),
680(350), 800(300), 530(280), 620(210) for runs
A0÷E0 correspondingly. The first value regards
forward fenders during the first impact, while a val-
ue in parenthesis refers to aft fenders in the second
impact. Some of the these results will be supported
later with figures. With reference to the less danger-
ous second impact similar but only qualitative issues
have been known in the literature.
It is worthwhile to report that in all the runs the
ship, though keeping its almost parallel position very
close to the berth, is unnoticeably and slowly losing
the contact with fenders that can be called a slight
rebound. It also happens in the parallel approach R1.
This effect, basically recognizable by the positive
lateral velocity v
y3
after the second impact (or v
y1
if
only the first impact exists), is surprisingly mostly
produced by the implementation of the decompres-
sion reaction, though very small as mentioned be-
fore. The ship's parallel body over its full length
namely collects reactions from a number of fenders
that give pretty high force in the aggregate. The in-
duced yaw motion in the berthing R1 is due to the
asymmetry of fenders around the midship as simul-
taneously acting on the ship's parallel body.
277
0E+0
1E+5
2E+5
3E+5
4E+5
5E+5
6E+5
7E+5
8E+5
9E+5
1E+6
0 1 2 3 4 5
27.5 28 28.5 29 29.5
0E+0
1E+5
2E+5
3E+5
4E+5
5E+5
6E+5
7E+5
8E+5
9E+5
1E+6
0 1 2 3 4
10 10.5 11 11.5 12
0E+0
1E+5
2E+5
3E+5
4E+5
5E+5
6E+5
7E+5
8E+5
9E+5
1E+6
0 0.2 0.4 0.6 0.8 1 1.2
FDR '- 08'
FDR '- 07'
FDR '- 06'
FDR '- 05'
FDR '- 04'
FDR '- 03'
FDR '- 02'
FDR '- 01'
FDR '00'
FDR '+01'
FDR '+02'
FDR '+03'
FDR '+04'
FDR '+05'
FDR '+06'
FDR '+07'
FDR '+08'
`
t[s]
0E+0
1E+5
2E+5
3E+5
4E+5
5E+5
6E+5
7E+5
8E+5
9E+5
1E+6
0 0.5 1 1.5 2
50 55 60 65
t[s]
t[s]
t[s]
F
FND
[N]
F
FND
[N]
F
FND
[N]
F
FND
[N]
R1
A0
B0
C0
Figure 6. Fender local loads for constant heading parallel and
bow-in berthing.
It is very interesting that for runs B1 and B2, see
Table 4b, dealing with the negative yaw velocity
(i.e. turning the bow towards the berth), there is no
second impact and the ship leaves the berth with
45% and 80% of the initial energy accordingly. An-
yhow in the case of B3 simulation (positive angular
movement i.e. the bow tends out of berth) the stern
impact in terms of the energy is almost 2.5 times
stronger than the bow impact. This is an essential
quantitative improvement over the Vasco Costa
guidance.
0E+0
1E+5
2E+5
3E+5
4E+5
5E+5
6E+5
7E+5
8E+5
9E+5
1E+6
0 0.5 1 1.5 2 2.5 3 3.5 4
0E+0
1E+5
2E+5
3E+5
4E+5
5E+5
6E+5
7E+5
8E+5
9E+5
1E+6
0 0.5 1 1.5 2
t[s]
0E+0
1E+5
2E+5
3E+5
4E+5
5E+5
6E+5
7E+5
8E+5
9E+5
1E+6
0 1 2 3
9 10 11 12 13
0E+0
1E+5
2E+5
3E+5
4E+5
5E+5
6E+5
7E+5
8E+5
9E+5
1E+6
0 1 2
27 30 33
F
FND
[N]
t[s]
F
FND
[N]
t[s]
F
FND
[N]
t[s]
F
FND
[N]
B1
B2
B3
G0
Figure 7. Fender local loads for bow-in berthing with turning
and the constant heading stern-in berthing (G0).
The stronger second impact, as compared with
the first one, also arises for the stern-in berthing in
variants G0 (a constant heading, oblique approach)
and G3 if we are of course considering the energy.
It shall be underlined that the second impact
measurement in terms of the absorbed energy is not
a reliable and comprehensive indication of the ship-
berth interaction, since the number of activated
fenders is often unknown if they are continuously
(close to each other) distributed along the berth. This
is partially shown in subsequent Figures 6-8 where
278
the maximum value 1x10
6
N at the scale of vertical
axis F
FND
, representing the fender reaction, is nearly
the breaking strength of the fender. The general pat-
tern of fender loads in the time domain as presented
agrees with the investigations of (Fontijn, 1988).
0E+0
1E+5
2E+5
3E+5
4E+5
5E+5
6E+5
7E+5
8E+5
9E+5
1E+6
0 0.4 0.8 1.2 1.6
0E+0
1E+5
2E+5
3E+5
4E+5
5E+5
6E+5
7E+5
8E+5
9E+5
1E+6
0 0.4 0.8 1.2 1.6
0E+0
1E+5
2E+5
3E+5
4E+5
5E+5
6E+5
7E+5
8E+5
9E+5
1E+6
0 1 2 3
12 14 16 18
t[s]
F
FND
[N]
t[s]
F
FND
[N]
G1
G2
G3
Figure 6. Fender local loads for stern-in berthing with turning.
For the aforementioned run B3 (Fig. 7) the very
high reactions in the aft fenders are really very simi-
lar in magnitude to those of the first (bow) impact -
both take about 90% of the breaking strength, how-
ever the stern impact involves quite a large number
of fenders that allows to essentially 'resist' the se-
cond impact. Moreover, the nearly twice higher ab-
sorbed energy in the second impact is even accom-
panied by 50% reduction of fender loads.
Additionally, the five times higher energy of the se-
cond impact in run G3 (here made by the bow), Fig.
8, is just connected with 50% increase of the fender
load, though in our particular case the latter assumes
nearly breaking value.
The maximum lateral speed for parallel berthing
in deep water is the speed of run R0, see also Table
4a, that is equal to 0.3m/s(0.6kt). For the assumed
fender arrangement this ensures fender loads nearly
at the level of their breaking strength. When some-
one wants to introduce shallow water conditions, the
mentioned limit speed is being reduced to 0.52kt,
0.48kt, or 0.42kt if multipliers of order 1.5, 2.0, 3.0
are accordingly applied to the sway added mass. The
selected 'reference' velocity for all the peformed
simulation runs, see Section 2, at the level of
0.15m/s just ensures the safe berthing under any
tested circumstance i.e. without damage to fenders.
4 FINAL REMARKS
The performed research has proved a great potential
of simulating the fender local loads, even in real-
time, and demonstrated a ready-for-use software en-
vironment serving this purpose.
This study has among others revealed that some
meaningful discrepancy between the impact (ab-
sorbed) energy and local loads in fenders appears.
This shall be taken into account when attempts or ef-
forts are made to establish the best shiphandling
guidance with reference to the most favorable com-
bination of lateral (linear) and angular velocity for a
given ship, fendering system, depth and weather
conditions. Such recommendations, if properly ap-
plied, should ease both the first and second impact in
terms of local loads. Though the latter is often miti-
gated by the wheel order.
To quantify the observed rebound phenomenon,
that is also of practical importance, further investiga-
tions have to be planned, where the fully nonlinear
real-world fenders are programmed.
REFERENCES
Artyszuk, J. 2003. Fender Impact Effect upon Ship Manoeu-
vring Motion - a Dynamic Approach. In Proc. of X Interna-
tional Conference 'Marine Traffic Engineering', Maritime
University of Szczecin, Scientific Bulletin no. 70: 25-36.
Artyszuk, J. 2005. Simulation of a Spring Line Application to
Enhance Berthing/Unberthing Manoeuvres. In C. Guedes
Soares et al. (eds), Maritime Transportation and Exploita-
tion of Ocean and Coastal Resources, vol. 1: 17-25; IMAM
2005. London: Balkema/Taylor&Francis.
Fontijn, H.L. 1988. Fender Forces in Ship Berthing. Part 1 and
2. Ph.D. Thesis, Delft: University of Technology.
Magda, W. 2006. Absorbtion of Ship Kinetic Energy by Berth
Fenders. Inżynieria Morska i Geotechnika 27(5): 306-311
(in Polish).
Vasco Costa, F. 1964. The Berthing Ship. The Effect of Impact
on the Design of Fenders and Berthing Structures. London:
Foxlow Publications Ltd..
Vasco Costa, F. 1968. Berthing Manoeuvres of Large Ships.
The Dock and Harbour Authority XLVIII(569-March):
351-358.
Vasco Costa, F. 1987. The Probabilistic Approach in the Selec-
tion of Ropes and Fenders. In E. Bratteland (ed.), Advances
in Berthing and Mooring of Ships and Offshore Structures:
323-327; Proc. of the NATO Advanced Study Institute on
Advances in Berthing and Mooring of Ships and Offshore
Structures, Trondheim, 7-17 Sep 1987. Dordrecht: Kluwer
Academic Publishers.