International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 4
Number 4
December 2010
405
1 SAFETY OF NAVIGATION IN STOLPE
GUTTER
1.1 Introduction
This paper considers analysis of maximum draught
of a merchant vessel, which can maintain safety of
navigation in average and extreme exterior (weather)
conditions in Stolpe gutter and keep required under
keel clearance, i.e. navigational reserve of depth.
Analysis of navigational reserve of depth (under
keel clearance) is made in different exterior condi-
tion (average and extreme) for merchant vessels
such as:
− VLCC vessel or bulk carrier whose particulars
are: LOA (length over all) L=350,0 m, beam
B=60,0m, draught in the Baltic Sea
1
T
D
=T
R
=15,00 m, block coefficient C
B
=0,85.
− Container ship whose particulars are: LOA
(length over all) L=250,0 m, beam B=32,0m,
draught T
D
=T
R
=12,00 m, block coefficient
C
B
=0,70.
1
Limitation of draught T=15,0 m was accepted in Baltic Sea
such as maximum for the vessel wanted to sail safe across
Danish straits (Great Belt with Hn=17,0m). Since November
2007 according to the Notice to Marines limitation of ship’s
draught has been reduced to 14,50m due to shallow water in
Great Belt with depth Hn=16,50m.
− Passenger ferry whose particulars are: LOA
(length over all) L=140,0 m, beam B=16,0m,
draught T
D
=T
R
=7,50 m, block coefficient
C
B
=0,65.
− Fishing boat whose particulars are: LOA
(length over all) LOA= 40,0 m, beam B=8,5m,
draught T
D
=T
R
=4,00 m, block coefficient
C
B
=0,63.
Results are compared with guidelines published
by Decree of Minister of Transport and Maritime
Economy from 01.06.1998 about technical condi-
tions, which should be met by hydro mechanical sea
structure, which operate vessels with the given par-
ticulars.
2 GUIDELINES OF POLISH MINISTER OF
TRANSPORT AND MARITIME ECONOMY
CONCERNING UNDER KEEL CLEARANCE
Let us consider the theoretical establishing of Sepa-
ration Zone in the area of Stolpe gutter in accord-
ance with guidelines published in the Decree of
Polish Minister of Transport and Maritime Economy
from 01.06.1998 (Dz.U.98.101.645) about technical
conditions, which should be met by hydro mechani-
cal sea structure and the location – Section II, Chap-
ter 3, § 25 to § 35.
Simplified Method for Estimating Maximum
Ship’s Draught when Navigating in Shallow
Water on the South of Stolpe Bank in the
Aspect of the Vessels with Maximum
Dimensions and Draught
G. Rutkowski & A. Królikowski
Gdynia Maritime University, Gdynia, Poland
ABSTRACT: This paper considers analysis of maximum draught of a merchant vessel, which can maintain
safety of navigation in different exterior condition (average and extreme) on shallow water in Stolpe gutter
and keep required under keel clearance, i.e. navigational reserve of depth. To depict maximum draught of a
vessel we use practical method which incorporates risk of navigational and model of ship’s domain. Results
are compared with guidelines published by Decree of Minister of Transport and Maritime Economy from
01.06.1998 about technical conditions, which should be met by hydro mechanical sea structure, which operate
vessels with the given particulars.
406
Every sea structure situated within Polish area de-
scription three depths of water:
− Designed depth H
p
,
− Acceptable depth H
dop.
− Technical depth H
t
,
Designed depth H
p
is specified by formula:
H
p
= H
t
+ t
b
(1)
where: H
p
- designed depth, [m]; H
t
– technical
depth, [m]; t
b
- dredge reserve tolerance, [m].
A value of tolerance for dredge reserve, accepted
to estimate sea structures and design drawing works,
with respect to the location of drawing works, is:
− t
b
= 0,25 m – for drawing works made in port
and harbours,
− t
b
= 0,35 m – for drawing works carried out
outside limits of harbours, especially on the
roads, in the approaching channels, for placing
cables and pipelines in territorial sea and interi-
or sea waters as well as profiling sea bed for
sea’s structures.
Every designed project includes specific width of
sea bed lane along sea structure, in which one should
keep acceptable depth (H
dop.
). If the technical docu-
mentation, such as navigational chart, describes on-
ly one depth of the area, we assume that this depth
constitutes acceptable depth (H
dop.
). In this way
technical depth (H
t
) can be presented in meters on
the basis of the following formula:
H
t
= H
dop.
- t
b
(2)
where: H
t
- technical depth, [m]; H
dop
- acceptable
depth, [m]; t
b
- full tolerance for dredge reserve, [m].
When we use navigational depth (H
n
) we think
about difference between horizontal planes, meas-
ured from average sea level SW to horizontal plane,
which is adjoined with the highest bed situated in the
given area, which is designed for vessel traffic.
Actual navigational depth (H
na
) is navigational
depth (H
n
), which refers to actual water level.
Acceptable depth (draught) of the ship (T
a
) in
traffic areas describes difference between actual
navigational depth (H
na a
) and total under keel clear-
ance (R
t
) required in sailing condition:
T
a
= H
na
– R
t
(3)
where: T
a
- acceptable ship’s depth (draught), [m];
H
na
- actual navigational depth, [m]; R
t
- total under
keel clearance depth, which enables the vessel to
float in the place where sea structure is located,
even for the unfavourable hydro meteorological
conditions, [m].
The next link (4) shows relationship between the
highest acceptable ship’s depth (draught) (T
c
) and
technical depth (H
t
):
H
t
= T
c
+ R
t
(4)
where: T
C
- is the highest ship’s depth (draught) on
even keel, [m]; R
t
- total under keel clearance depth,
which enables the vessel to float in the place where
sea structure is located, even for the unfavourable
hydro meteorological conditions [m].
Total under keel clearance, which is included in
formulae (3) and (4), cannot be smaller than mini-
mum of total reserve of water depth (R
t
min
), de-
scribed in meters by the following formula:
R
t
min
≥ η
ּ
◌ T
c
(5)
where: T
C
- is maximum acceptable ship’s depth
(draught) on even keel, [m]; η - not dimensional co-
efficient, dependent on the type of area or fairway,
described in Table 1.
Table 1. Values of not dimensional coefficient, with respect to
type of area or fairway. Dz.U.98.101.645.
___________________________________________________
No Type of area or fairway
η
___________________________________________________
1 Harbour areas covered from waves 0,05
2 Interior fairways, ship’s rotary area, basin and
port channel in which floating units use tugs 0,05
3 Exterior approaching lane from sea to port and
marina 0,10
4 Open sea areas 0,15
___________________________________________________
In this case the minimum value of total reserve of
water depth R
t
min
established for different type of
ships (unit) is described in Table 2.
Table 2. Minimum value of total reserve of water depth R
t
min
established for different type of ships (units) in shallow water
in Stolpe gutter.
___________________________________________________
No Type of units (L,B,T, CB) Tc R
t
min
[m] [m]
___________________________________________________
1. VLCC (350m; 60m; 15m; 0,85) 15,0 2,25
2. Container ship (250m; 32m; 12m; 0,70) 12,0 1,80
3. Passenger’s ferry (140m; 16m; 7,5m; 0,65) 7,50 1,13
4. Fishing boat (40m; 8,5m; 4m; 0,63) 4,00 0,60
___________________________________________________
Assuming actual navigational depth area in aver-
age navigational conditions H
na
=17,00m and ship’s
particulars of the biggest units which could enter to
the Baltic Sea through the Danish Strait (Great Belt,
H
na
=17,00m, T=15,0m) minimum of under keel
clearance should be not less than 2,25 m. In this case
criterion of safety navigational depth cannot be used,
because: H
t
= 17,0m-2,25m= 14,75m and is smaller
than maximum unit’s draught T
a
=15,0m.
In extreme conditions, such as huge wave, situa-
tion can be worse, as one should reduce navigational
depth of the area to H
n1
=16,50m and increase the
maximum of ship’s draught T
a
due to wave effect:
yawing, pitching, rolling etc. For example mere list
of about ±5º of the rolling vessel whose beam
407
B=60m and departure draught T
a0
=15,0 m, can in-
crease maximum of ship’s draught for 2,56m to
T
a1
=17,56m.
The increase of the ship’s draught, which is
caused by the list, can be depicted by means of the
following formula:
( )
[ ]
( )
θθ
sinB
2
1
1cosTT
M
II
7
⋅⋅+−=∆
(6)
where: ∆T
II
7
- change of draught in case of ship’s
list [m]; T
M
- average ship’s draught [m]; θ - angle
of ship’s list [ °]; B - ship’s beam [m].
The increase in the ship’s draught, which is
caused by yawing, can be calculated by means of the
formula:
( ) ( )
Ψ⋅⋅≈Ψ⋅⋅=∆ tgLtgLT
ppw
I
2
1
2
1
7
(7)
where: ∆T
I
7
- change of draught in case of yawing
[m]; L
W
- ship’s length on sea surface [m]; L
pp
-
ship’s length between perpendiculars [m]; Ψ - angle
of trim due to yawing [ °].
In bad weather conditions one can observe heav-
ing, yawing, pitching, rolling, swaying and surging
due to huge influence of sea wave to ship’s hull. In
practice in order to define maximum ship’s draught
one uses only bigger value of corrections ∆T
I
7
or
∆T
II
7
defined by the formulas (6) and (7).
For this reason, on the basis of formulas (4) and
(5) one can define simplified formula for maximum
acceptable ship’s draught Tc, which could indicate
safe navigation in area with technical depth H
t
:
η
+
≤
1
t
c
H
T
(8)
where: T
C
- is maximum acceptable ship’s draught,
on the even keel, [m]; η - not dimensional coeffi-
cient, dependent on type of area or fairway, de-
scribed in table 1; H
t.
- technical depth, [m].
According to formula (8) in order to navigate
safely near the Stolpe gutter (open area) the highest
acceptable ship’s draught T
c
, should not be higher
than T
c1
=14,78m for H
t
=17,0m (average conditions)
and T
c1
=14,35m for H
t
=16,5m (rough sea).
When planning separation zone area on the south
of the Stolpe Bank, minimum of water depth read
from navigational chart (chart 252, INT1219) is 18
m estimated with reference to chart datum with re-
spect to MSL (Mean Sea Level). According to the
formula (2) this depth should be treated as accepta-
ble depth of area (H
dop
) with error for so-called ac-
ceptable unevenness of sea bottom. For open sea ar-
eas, such as Stolpe gutter, in which sea bed isn’t
durably strengthened, acceptable sea depth H
dop
could be described by formula:
H
dop.
= H
t
+ R
p
(9)
where: H
dop
- acceptable draught of sea structures,
[m]; H
t
- technical depth of sea structures, described
with accordance to the rules mentioned above; R
p
-
reserve for acceptable unevenness of sea bottom in
the area, where sea bed isn’t durably strengthen,
during the whole period when the sea structure is
used.
According to the Decree of Minister of Transport
and Maritime Economy value of reserve for ac-
ceptable unevenness of sea bottom shouldn’t be less
than R
p
=1,0 m. For the sea structures without dura-
ble strengthening and for sea structures located in
the following areas:
− on bend and outlet of river and strait to the sea,
− on narrowing river bed,
− with huge wave or significant stream of water
near the sea bed, the value of reserve R
p
cannot
be less than 1,5 m.
Hence, with respect to the formulae (3), (4) and
(6) we assume the value of navigational depth of ar-
ea as H
n1
=17,0m in normal navigational conditions
(18,0m–1,0m=17,0m), and H
n2
=16,5m (18,0m–
1,5m=17,0m) for extreme conditions, i.e. huge wave
or strong stream of water near sea bottom.
The research about the real value of navigational
depth of the given area is confirmed by the opinion
from employers of Maritime Office in Gdynia. The
depth of the discussed area depth was controlled by
employers of Maritime Office in Gdynia in 2007.
They confirmed the localization of the navigational
dangers such as rock, sand, wrecks within shallow
water on the depth from 17,00 m with respect to ac-
tual sea level, the possible inaccuracy being ±0,50m.
Polish sea areas are treated as sea without tides.
Water depth is measured on these areas from chart
datum, which is defined from average sea level SW
(±0,50m). According to long term observation made
by Institute of Meteorology and Water Management
in Gdynia in the area which we discuss one can ex-
pect significant changes of sea level in the aspect of
mean sea level (MSL=500). Those changes cross the
value ΔHn=Rp=±1m. They are especially visible in
autumn–winter term. For example in 2001 difference
between extreme values of high sea water level
(HHW) and low water (LLW) on the Polish coast
varied from 146 cm in Ustka, 150cm in Łeba to 206
cm in Świnoujście (Institute of Meteorology and
Water Management, 2004).
In long-term scale (between 1971-2000) one can
observe high water (HW) 130 higher than mean sea
level (MSL) in Ustka and 140cm in Łeba and low
water (LW) about 54 cm lower than mean sea level
(MSL) in Łeba and 60 cm in Ustka.
408
Total reserve of ship’s draught R
t
should be ana-
lyzed for every vessel navigating in this area. In eve-
ry case total reserve of ship’s draught R
t
should not
be less than minimum of total reserve of sea depth
R
t
min
defined earlier. Additionally, the reserve of
ship’s draught R
t
should enable navigation and
manoeuvring of a ship in the worst hydro-
meteorological conditions, possible in this area.
According to the Decree of Minister of Transport
and Maritime Economy from 1998 in order to estab-
lish the total reserve draught R
t
one must consider
the total of following components:
Reserve R
1
for inaccurate hydrographical measure-
ment of water depth.
The value of reserve R
1
depends on the area’s
depth. Depth in navigational charts is presented with
accordance to the defined standard of accuracy. In-
ternational Hydrographic Organization IHO (Joseph,
1991) accepted the following standard (P= 95,4 %)
in 1987:
0,52 m for H= (0 ÷30)m;
1,72 % h for H> 30m.
Since January 1991 in the British Admiralty
charts (BA) the accuracy of data has been defined
with measurement depth error (P= 95,4%) and has
the value:
( )
2
2
009,05,02 H
H
⋅+=⋅
δ
[m] (10)
Hence, the error equals about 0,53m for the area
of Stolpe gutter whose average depth is about 20m.
Charts published by local maritime administra-
tion (other than British) may have different standard
accuracy due to local legal regulations. According to
S.Gucma and I.Jagniszczak (1997) navigational re-
serve R
1
for area whose depth is 20m should be
about 0,20m in practice.
Table 3. Reserve R
1
for hydrographical measurement error of
water depth (sound error). Gucma, Jagniszczak, 1997.
___________________________________________________
Area’s Depth H [m] Water Reserve R1 [m]
___________________________________________________
1. do 4 0.10
2. 4-10 1015
3. 10-20 0.20
4. 20-100 0.01H
___________________________________________________
We do not make mistake if we accept for further
research 0.35m as average value of reserve R
1
for
hydrographical error of measurement of water depth.
Navigational reserve R
2
, is minimum of under keel
clearance units, which is sufficient to floating, and
depends on type of sea bed or method of sea bed for-
tification near sea structure
Navigation reserve R
2
results from the fact that
we do not know the exact sea depth, sea bed clear-
ance, interpolation error between sounding or result
of the hull contact with sea bed. In practice, the val-
ue of reserve R
2
ranges from 1,00m to 1,50m for not
coastal areas, which are exposed to huge wave and
currents near the sandy and rocky sea bed with low
density of sounding. In the area of Stolpe gutter sea
bed is tough and sandy with many rocks and stones.
Reserve R
3
for low level of sea waters, defined on
the basis of: a) curve of total time of stay water lev-
el, with respect to the measurements on sea water
level patch, which are based on long term research,
when the water level remained on the higher level
during about 99% of time during research period or
b) differences between sea level SW and sea level
SNW,
Navigational reserve R
3
is the result of observa-
tion of difference of sea level with reference to chart
datum which is caused by specific hydro-
meteorological conditions. Long lasting and strong
wind which blows in land direction as well as flood-
ing on the river increase the water level. Strong
winds blowing from the land and low water state on
the river decrease this level.
In practice, navigational reserve R
3
in such areas
as in the Stolpe gutter without tides on South Baltic
Sea, navigational reserve R
3
can reach 0,30m. Any-
way, we must remember that long term observations
of water state in this area carried out by measure-
ment stations in Ustka and Łeba confirm higher, that
is about 0,60m reduction of water state from mean
sea level (MSL). Those observations are also kept
the whole year (Institute of Meteorology and Water
Management, 2004). In extreme weather (hydro-
meteorological) conditions value of navigational re-
serve R
3
should be increased to 0,60m.
Reserve R
4
for shallow water in the area, which en-
ables full exploitation of area in period between
dredging and bottom cleaning operation
In the area which we discuss there is no dredging
or bottom cleaning operation. Sea Bed is formed
naturally, so we can omit the value of navigational
reserve R
4
for future considerations.
Reserve R
5
for wave and swell,
In order to estimate value of parameter R
5
con-
cerning sea wave we use the methods which are ap-
409
proximated, and show us only outline of the real sit-
uation.
In order to describe difference of draught ∆T
5
for
sluggish vessel on wave we often use empirical for-
mula prepared by Dand and Ferguson (1973) and
recommended by Nowicki (1999) - Method 1:
f5
hkT ⋅=∆
[m] (11)
where: k - coefficient depending on the relation be-
tween beam and length of ship with respect to length
and course angle of the wave, the coefficient ranges
from 0,33 to 0,66; h
f
- height of wave [m].
Coefficient k depends on relation between beam
and length of ship with respect to length and course
angle of wave. In case of the ship, which is situated
board to wave and whose beam constitutes less than
half length of wave, the coefficient is the biggest
one. For huge vessels in relation to size of wave this
coefficient has minimum value. The following rules
apply to the huge vessels:
− Sea wave direction is equal to the ship’s head-
ing line (q ≈ 000° or 180°) and length of the
vessel is bigger than length of the wave (L ≥ λ);
− Sea wave direction is perpendicular to ship’s
heading line (q ≈ 090°) and ship’s width is big-
ger than half length of sea wave (B ≥ 0,5λ);
where: λ - wave length [m]; B
- ship’s beam [m];
L
- ship’s length [m].
When the vessel is on the way the value of re-
serve must be increased (Jurdzinski, 1998) with re-
spect to the vessel speed:
12,5 % when speed v ≤ 10 knots;
25,0% when speed v > 10 knots.
The next method which enables us to count verti-
cal parameter of navigational reserve for the vessel
on the wave is the method of L.E. van Houten
(Nowicki, 1999) - Method 2. However, this method
is limited to the vessels whose size ranges from
15000DWT to 65000 DWT. In case of vessels
smaller than 15 000 DWT this method can be mis-
leading and inaccurate due to mistakes concerning
amplitude of waves for vessels on the way.
From the point of view of safety of navigation we
could consider the additional element with respect to
formula (11). The case of navigating obliquely to
wave direction is presented in table as the value of
total difference under keel clearance on the bow and
aft, amidships and height of bow and aft part of the
vessel. Parameter R
5
is: either
( )
5
Z
p
∆
δ
, that is the
error which results from defining the change, or
change in draught
55
TZ ∆=∆
increased by error
( )
5
Z
p
∆
δ
:
( )
5
55
ZTR
p
∆+∆=
δ
[m] (12)
In real conditions vessel on the wave makes very
complicated movement, which is combination of
simple movement in one direction. Usually one type
of movement results in another. These two types
mutually interact, as it is in the case of scenting
which is in fact combination of heaving and rolling.
In case of ship’s movement on the wave the progno-
sis of changes in complex movement is based on
usual accumulation of results. On the other side, ad-
ditional increase of safety contour, especially in very
bad weather condition, has positive influence on re-
ducing risk of navigation, and increasing safety of
navigation. For example, according to “Report of
Working Group IV of the Pianc International Com-
mission for The Reception of Large Ships”, for traf-
fic lane exposed to huge swelling minimum of the
under keel clearance must constitute 15% of maxi-
mum ship’s draught (Method 3).
Similar solution is described by Gucma and
Jagniszczak, (1997), in which minimum reserve for
wave in the open sea area on the straightforward
traffic lane without dredgering, with sea wave height
up to 3,0m is assumed as 40% of maximum ship’s
draught (Method 4).
Table 4. Numerical value of coefficient m dependent on the
ship’s particulars (v, B, L, C
B
) and wave parameters (λ, h
f
, q).
___________________________________________________
m For the wave from bow or For the wave from board
aft (q ≈ 000° or 180°) (q ≈ 090°)
___________________________________________________
0,500 When: v = 0, and L > λ When: v = 0, and B > λ
1,000 When:v≥10w, and L ≥ λ When:v≥10w, and B≥ 0,5⋅λ
1,125 When: v<10w, and L<0,5⋅λ When: v<10w, and B<0,5⋅λ
≥1,250 When:v≥10w, and L<0,5⋅λ When: v≥10w, and B<0,5⋅λ
___________________________________________________
Rutkowski (2000) gives us another solution for
reserve R
5
(Method 5):
f5
hm66,0R ⋅⋅=
(13)
where: R
5
- reserve for wave [m]; h
f
- height wave
[m]; m - numeral coefficient (factor), dependent on
ship’s particulars (v, B, L, C
B
) and parameters of
wave (λ, h
f
, q).
Exemplary values of navigational depth reserve
R
5
for wave estimated by means of the above meth-
ods for different type of ships on shallow water in
Stolpe gutter are presented in Table 5. The calcula-
tion considers various methods for the vehicles pro-
ceeding with 10 knots speed along traffic lane
straight to wave with height 3,0m and length 150m
in the open sea area, exposed to sea waves and cur-
rent, with no dredging requirement.
410
Table 5. Hypothetical value of navigation depth reserve R
5
for
wave calculated with the above described methods for different
type of ships for shallow water in Stolpe gutter. In calculation
we assume that every unit sails along traffic lane with 10 knots
speed straight to wave whose height is 3,0m and length 150m.
___________________________________________________
Type of Vessel Value of reserve R
5
[m] for wave
(L; B; T; C
B
) calculated with different methods
1 2 3 4 5
___________________________________________________
VLCC
(350m; 60m; 15m; 0,85) 1,00 3,15 2,25 6,00 1,98
Container ship
(250m; 32m; 12m; 0,70) 1,50 2,52 1,80 4,80 1,98
Passenger ferry
(140m; 16m; 7,5m; 0,65) 2,00 1,58 1,13 3,00 2,23
Fishing boat
(40m; 8,5m; 4m; 0,63) 2,00 0,84 0,60 1,60 2,48
___________________________________________________
Due to big discrepancy of results we use the data
from method 5 for further research. This method as-
sumes that the reserve R
5
depends on the wave pa-
rameters and gives us result similar to methods 1,3
and 4. Methods 2 and 4 are very general and do not
include interaction between ship’s particulars and
wave’s parameters.
Long term observation of waves near Polish coast
in area of Stolpe gutter in south part of Baltic Sea
confirms that period with high frequency of storm
and gale appears in winter time between November
and February. In this period one can observe sea
waves with height of about 3m. Sea appears to be
calm in summer time from May to September. Max-
imum of wind speed in the given area is up to 32m/s.
The maximum values of wave height are observed in
winter time and they are up to 7m in western part of
Polish coast and up to 8m in eastern part of Polish
coast. Maximum waves are observed during the
strong and long-lasting winds from W, N and NE.
The maximum waves amount to 160m of length in
eastern coast and about 120m length in western
coast. Predominantly the frequent waves are up to
3,0m high and 40m long. More than 90,85% of all
waves in the area near the eastern coast and about
96,53% of all waves in area near the western coast
are the waves whose height H
5%
equals or is less
than 1,5 m. Maximum sea waves whose heights H
5%
reach more than 3,00m are hardly ever observed.
The probability that we can expect extreme weather
condition (H
5%
>3,00m) in researched area is less
than 0,3% in eastern coast and less than 0,01% in
western coast.
Table 6. The frequency of wave height in % on the South Bal-
tic Sea. Paszkiewicz, 1989.
___________________________________________________
Wave’s height Eastern part of Western part of
H
5%
[m] coast coast
___________________________________________________
H
5%
< 1,0 m 75,26 88,64
1,0m – 1,5m 15,59 7,89
1,5m – 3,0m 8,85 3,46
H
5%
> 3,0 m 0,30 0,01
___________________________________________________
Reserve R
6
for the increasing ship draught when
manoeuvring in breaking waters near the Polish
coast on Baltic Sea established by means of the for-
mula:
R
6
= 0,025 x T
c
(14)
where: T
C
- the maximum draught of the vessel
loaded on even keen, [m].
The reserve R
6
applies to all vessels proceeding to
the Baltic Sea from the North Sea. This reserve
concerns the increase off the ship’s draught when
manoeuvring in water near Polish coast. The density
of sea water in Baltic sea equals from γ
1
= 1,00525
g/cm
3
to γ
2
= 1,00250 g/cm
3
what with relation to
density of sea water in the North Sea (γ
3
= 1,025
g/cm
3
) can increase the draught of each vessel which
enters the Baltic Sea from the North Sea.
For the example the value of reserve R
6
estimated
by means of the formula (14) for different type of
the vessel are presented in Table 7.
Table 7. The value of reserve R
6
for increasing ship’s draught
in breaking sea water near Polish coast on the Baltic Sea estab-
lished by means of the formula 14 for different types of vessel.
___________________________________________________
No. Type of ship (L; B; T; C
B
) R
6
[m]
___________________________________________________
1. VLCC (350m; 60m; 15m; 0,85) 0,38
2. Container Ship (250m;32m;12m;0,70) 0,30
3. Passenger Ferry (140m;16m;7,5m;0,65) 0,19
4. Fishing Boat (40m;B=8,5m;4m; 0,63) 0,10
___________________________________________________
Reserve R
7
, depicted in meters, for trim (pitch) up to
2° and list (roll) up to 5° established for all floating
units by means of the following formulas:
1 reserve for trim due to pitch up to 2°:
R
I
7
= 0,0016
ּ
◌ L
c
(15)
where: L
c
– ship’s overall length, [m].
2 reserve for list (roll) up to 5°:
R
II
7
= 0,008
ּ
◌ B
c
(16)
where: B
c
– maximum ship’s beam, [m].
In order to examine the depth of water we assume
that the biggest value of reserve R
7
is bigger than
two values a) and b) but not smaller than R
7
=0,15 m.
The value of reserve R
7
can be estimated also by
means of the formulas (6) and (7).
Reserve R
8
for trim to aft for all vessels proceeding
with speed over ground when dredging channels,
approaching fairways, proceeding in interior fair-
ways and channels, basin and port waters
In this case as the area which we are discussing is
the open sea with natural sea bottom the value of re-
serve R
8
can be ignored.
411
Reserve R
9
for ship’s squat when proceeding in re-
stricted sea area across the shallow water
When studying professional publications there are
many methods for estimating reserve R
9
for ship’s
squat when proceeding in restricted sea area across
the shallow water. In practice we can use only one of
the following methods:
1 C.B.Barrass precise method for estimating ship’s
squat in sea area (Method 1) (with limitation:
0,5≤C
B
≤0,9; 0≤ t/L≤ 0,005; 1,1 ≤ h/T ≤ 1,4):
08,2
3
2
9
30
1
v
BTbH
BT
CR
B
⋅
−
⋅⋅=
[m] (17)
2 C.B.Barrass simplified method (Method 2) for es-
timating ship’s squat in:
− shallow water (with limitation: 1,1≤ h/T ≤ 1,2):
2
9
01,0 vCR
B
⋅⋅=
[m] (18)
− narrow channel (with limitation:
3,006,0 ≤
⋅
⋅
≤
hb
TB
):
2
9
02,0 vCR
B
⋅⋅=
[m] (19)
3 N.E.Eryuzlu and R.Hausser method for estimat-
ing ship’s squat in sea area (Method 3)
8,1
27,0
9
Hg
v514,0
T
h
B113,0R
⋅
⋅
⋅
⋅⋅=
−
[m] (20)
(with limitation: C
B
≥ 0,7;
78,208,1 ≤≤
T
h
)
4 G.I.Soukhomela and V.M.Zass method for esti-
mating ship’s squat in shallow unrestricted water
(Method 4):
⋅⋅⋅⋅=
− 11,1
2
9
049047542,0
B
L
H
T
vlR
[m] (21)
(with limitation:
95,3 ≤≤
B
L
)
where: B,L,T
max
, C
B
- ship’s particulars: beam
B[m], length L[m], maximum draught T[m],
block coefficient C
B
[-]; v- speed over ground in
knots, [kn]; b,H,h
f
- area characteristics: depth
H[m], wide b [m], wave’s height (swell) [m]; l-
numeral coefficient (factor) (1,1 ≤ l ≤ 1,5) de-
pendent on ship’s length L and ship’s beam B, [-
].
Ship’s squat (reserve R
9
), estimated for vessel
proceeding with 5knots speed and 10 knots speed in
shallow water whose depth Hn=17,0m and minimum
width b=1000m is presented in Table 9.
Table 8. Relation between numeral coefficient (factor) l from
formula (21), ship’s length L and ship’s beam B.
___________________________________________________
Value of numeral coefficient (factor) l dependent on ship’s
length L and ship’s beam B
___________________________________________________
9
B
L
7 ≤≤
75 <≤
B
L
55,3 <≤
B
L
1,10 1,25 1,50
___________________________________________________
Table 9. The value of ship’s squat (reserve R
9
) estimated by
means of formula 17 to 21 (Method 1,2,3 and 4) for different
types of vessel proceeding with 5kn and 10 kn speed in shallow
water with depth Hn=17,0m and wide b=1000m.
___________________________________________________
Method Method 1 Method 2 Method 2 Method 4
Speed [kn] 5 10 5 10 5 10 5 10
___________________________________________________
Ship’s type The value of ship’s squat (reserve R
9
) [m]
___________________________________________________
VLCC 0,12 0,50 0,21 0,85 0,36 1,25 0,20 0,81
Container 0,05 0,23 0,18 0,63 0,12 0,46
Passenger 0,08 0,32
Fishing Boat 0,16 0,64
___________________________________________________
To sum up, navigational reserve of depth R
t
de-
scribed as a sum off all parts from R
1
to R
9
estimated
for shallow water in Stolpe gutter should be depend-
ent on size and type of a ship and actual weather
condition; in Stolpe area the value should range
from 4,61m to 5,57m.
Table 10. Maximum ship’s draught Tc in shallow water esti-
mated by means of formula (4) and navigational reserve of
depth Rt as a sum of all parts from R
1
to R
9
in normal and bad
weather condition (h
f
=3m, λ=150m, H
N
=18,00m) estimated for
different type of vessel proceeding with speed 10 kn and 5 kn.
___________________________________________________
Good weather condition, Ship’s speed 10 knots
___________________________________________________
Ship’s type R
1÷4
R
5
R
6
R
7
R
8÷9
R
t
Tc
[m] [m] [m] [m] [m] [m] [m]
___________________________________________________
VLCC 1,75 1,98 0,38 0,56 0,81 5,38 12,62
Container vessel 1,75 1,98 0,30 0,40 0,46 4,79 13,21
Passenger Ferry 1,75 2,23 0,19 0,22 0,32 4,61 13,39
Fishing Boat 1,75 2,48 0,10 0,15 0,64 5,02 12,98
___________________________________________________
Bad weather condition, Ship’s speed 5 knots
___________________________________________________
Ship’s type R
1÷4
R
5
R
6
R
7
R
8÷9
R
t
Tc
[m] [m] [m] [m] [m] [m] [m]
___________________________________________________
VLCC 2,45 1,98 0,38 0,56 0,20 5,57 12,43
Container vessel 2,45 1,98 0,30 0,40 0,12 5,25 12,75
Passenger Ferry 2,45 2,23 0,19 0,22 0,08 5,17 12,83
Fishing Boat 2,45 2,48 0,10 0,15 0,16 5,34 12,66
___________________________________________________
In this case the highest acceptable ship’s draught
T
c
(see Table 10), which could guarantee safe navi-
gation near the Stolpe gutter with maximum swell
and wave’s height about h
f
=3m and length about
λ=150m, should not exceed the value T
c1
=12,43m in
bad weather condition for VLCC when proceeding
with 5 knots speed and T
c2
=13,39m in normal
weather condition for Passenger Ferry when pro-
ceeding with 10 knots speed. Otherwise, the Decree
of Minister of Transport and Maritime Economy will
be not accepted.
412
What is more, in extreme weather conditions,
such as winter time, wave (swell) which equals
about h
f
=5m and whose length is about λ=160m)
one can expect higher value of navigational reserve
of depth Rt, that is to say about 1,32m.
Probability that we can expect extreme weather
condition (H
5%
>3,00m) in this area, i.e. S of Stolpe
Bank is less than 0,3% (See Tables 6 and 11). Ex-
treme weather conditions can be expected only dur-
ing winter from November to February with strong
and long-lasting winds from W and NE.
Table 11. Maximum ship’s draught Tc in shallow water esti-
mated by means of a sum of all parts of the navigational re-
serve of depth Rt from R
1
to R
9
in extreme weather conditions
(h
f
=5m, λ=160m, H
N
=18,00m.
___________________________________________________
Extreme weather conditions. Ship’s speed 5 knots
___________________________________________________
Ship’s type R
1÷4
R
5
R
6
R
7
R
8÷9
R
t
Tc
[m] [m] [m] [m] [m] [m] [m]
___________________________________________________
VLCC 2,45 3,30 0,38 0,56 0,20 6,89 11,11
Container vessel 2,45 3,30 0,30 0,40 0,12 6,57 11,43
Passenger Ferry 2,45 3,71 0,19 0,22 0,08 6,65 11,35
Fishing Boat 2,45 4,13 0,10 0,15 0,16 6,99 11,01
___________________________________________________
3 SIMPLIFIED METHOD FOR ESTIMATING
MAXIMUM SHIP’S DRAUGHT WHEN
NAVIGATING IN SHALLOW WATER BY
MEANS OF THE MODEL OF THE SHIP’S
DOMAIN.
In this chapter we present methods that can be used
for estimating maximum ship draught of a vessel.
One must take into consideration safety of naviga-
tion, i.e. navigational risk in the restricted sea areas
by means of the model of the ship’s domain.
Figure 1. Presentation of navigational risk for ship passing
shallow water and bridge.
According to the ship’s domain (Rutkowski,
2002) definition, every ship will be safe (in naviga-
tional meaning) as long as she is the exclusive object
which can generate danger within her domain.
With reference to vertical plane of the three di-
mensional co-ordinates established down from the
central point of the local ship’s reference system we
can affirm unambiguously, that every ship will re-
main safe as long the value of G
D
is smaller than the
real value of the sea depth H. Therefore, component
R
NG
of R
N
can be referred to as vertical component of
navigational risk that concerns keeping under keel
clearance, or risk concerning under keel clearance.
The component mentioned above can be depicted by
means of the following formulas:
≤
≤<÷
≥
=
max
max
when1
when10
when0
TH
GHT
GH
R
D
D
NG
[-] (22)
According to the formula (22), assumption
D
GH ≥
can be defined as the guarantee of the safe
shipping (navigation) with reference to all underwa-
ter objects or obstructions immersed on the depth
smaller than H. If sea depth H is smaller or equal to
the ship’s draught T, that is
max
TH ≤
, according to
the formula (22) sea passage can be unfeasible
2
or
highly risky. In that situation the value of naviga-
tional risk R
NG
will equal one, and in all probability
it will signify unquestionable (100%) risk of colli-
sion with some underwater objects immersed on the
depth less than H. Furthermore, we can also say that
the value of navigational risk R
NG
for the sea depth h
limited between T
max
and G
D
(T
max
<H≤G
D
) will be
limited between zero and one (R
NG
∈[0,1]) (see for-
mula (22) middle line). General formula, which can
be used to estimate navigational risk R
NG
, depend-
ing on H factor from the range (
D
GHT ≤<
max
), is
presented below:
max
TG
HG
R
D
D
NG
−
−
=
[-] (23)
Additionally when we not only accept Barrass
method, recommended by shipyards and ship’s own-
ers for estimating ship’s squat, but also take into
consideration ship’s particulars, Pilot Cards (ma-
noeuvre characteristic) and other information (mete-
orological, navigational warnings and etc.) freely
available during normal sea passage, simple formula
for depth of the ship’s domain according to Rutkow-
ski (2002) can be presented as follows:
− Using precisely Barrass method for estimating
ship’s squat: (with limitation: 0,5≤ C
B
≤ 0,9; 0
≤ t/L ≤ 0,005; 1,1 ≤ h/T ≤ 1,4):
⋅
−
⋅⋅⋅+⋅⋅+⋅=
08,2
3
2
max
30
1
66,0
dBfD
v
BTbh
BT
CkhmTnG
[m] (24)
2
In our analyses we exclude the situation, when the ship can change her
draught due to for example deballasting operation.
H
413
− Using simplified Barrass method for estimating
ship’s squat in shallow water (with limitation:
1,1 ≤ h/T ≤ 1,2):
( )
2
max
.01,066,0 vCkhmTnG
BfD
⋅⋅+⋅⋅+⋅=
[m](25)
where: G
D
- depth of ship’s domain calculated
vertically down from water line (line showing actual
ship’s draft) [m]; B,L,T
max
, C
B
- ship’s particulars:
beam B[m], length L[m], maximum draught T[m],
block coefficient C
B
[-]; v - speed over ground, [kn];
b, H, h
f
- area characteristics: depth H[m], wide b
[m], wave’s height (swell) [m]; n - numeral coeffi-
cient (factor) (1,1 ≤ n ≤ 1,3) dependent on type of
sea areas and sea bottoms, which determines ship’s
static vertical navigational reserve. In this paper n =
1,2 (see table 17); m - numeral coefficient (factor)
(0,5 ≤ m ≤ 1,5) dependent on ship’s particulars: v, B,
L, C
B
and waves characteristics: λ,h
f
and q. See ta-
ble 13; k- numeral coefficient (factor) (1,0 ≤ k ≤ 2,0)
dependent on ship’s particulars, type of sea areas
and navigational situation (overtaking, crossing,
sailing in ice, navigating in restricted sea areas or
shallow waters and etc.). The fact that in normal sea
passage we cannot exactly estimate all ship’s or ar-
ea’s parameters, such as for example ship’s squat,
depth etc. results in this factor. In this paper k = 1,0.
Table 12. Numeral coefficient (factor) dependent on type of sea
areas and sea bottoms, which determines ship’s static vertical
navigational reserve.
___________________________________________________
n Type of the sea area Type of the
sea bottom
___________________________________________________
1,1 Port area, internal and inshore channels Mud
1,15 Road, Approaching channels to the port, Sand
inshore area
>1,2 Open sea Rock, Stone
___________________________________________________
Additionally when we accept that navigational
risk R
NG
will equal zero when G
D
=H
N
then after
transformation of the formula (24) or (25) compara-
tively to unknown T, we can estimate maximum
ship’s draught in restricted sea area. As an example
using simplified formula (25) with limitation: 1,1 ≤
h/T ≤ 1,2, the maximum ship’s draught in shallow
water can be presented as below:
( )
n
vCkhmH
T
BfN
2
max
.01,066,0 ⋅⋅−⋅⋅−
=
[m] (26)
where: T
max
- maximum draught of the vessel T [m];
H
N
-navigational depth of the sea H [m]; C
B
- block
coefficient C
B
[-]; v - speed over ground, [kn]; h
f
-
wave’s height (swell) [m]; n - numeral coefficient
(factor) (1,1 ≤ n ≤ 1,3) dependent on type of sea ar-
eas and sea bottoms, which determines ship’s static
vertical navigational reserve. In this paper n = 1,2
(see table 12); m - numeral coefficient (factor) (0,5 ≤
m ≤ 1,5) dependent on ship’s particulars: v, B, L, C
B
and waves characteristics: λ, h
f
and q. See table 13;
k - numeral coefficient (factor) (1,0 ≤ k ≤ 2,0) de-
pendent on ship’s particulars, type of sea areas and
navigational situation (overtaking, crossing, sailing
in ice, navigating in restricted sea areas or shallow
waters and etc.). The fact that in normal sea passage
we cannot exactly estimate all ship’s or area’s pa-
rameters, such as for example ship’s squat, depth
etc. results in this factor. In this paper k = 1,0.
Table 13. Numeral coefficient (factor) dependent on ship’s par-
ticulars: v,B,L,C
B
and waves characteristics: λ,h
f
and q.
___________________________________________________
m Sea wave direction equal with Sea wave direction
ship’s heading line (waves perpendicular to ship’s
from ahead or astern of the heading (waves from
vessel q ≈ 000° or 180°) the port or starboard
beam of the vessel,
q ≈ 090°)
___________________________________________________
0,500 When: v = 0 and L > λ When: v = 0 and B > 0,5⋅λ
1,000 When: v ≥ 10 kn and L > λ When: v≥10 w and B > 0,5⋅λ
1,125 When: v < 10 kn and L< 0,5⋅λ When: v < 10w and B<0,5⋅λ
≥
1,25 0 When: v ≥ 10 kn and L < 0,5⋅λ When: v≥10w and B < 0,5⋅λ
___________________________________________________
Table 14. Maximum ship’s draught in shallow water estimated
by means of formulae (26) for average (h
f
=3m, λ=150m, ∆h=
±0,30 m, H
N1
=17,70m) and extreme (h
f
=5m, λ=160m, ∆h=
±0,60 m, H
N2
=17,40m) weather condition, with limitation: 1,1
≤ h/T ≤ 1,2, for different ship’s type (her block coefficient C
B
)
and different ship’s speed v. ( n=1,20; m=1 and k=1,0).
___________________________________________________
Speed 4 kn 6 kn 8 kn
C
B
Average Extreme Average Extreme Average Extreme
___________________________________________________
0,5
13,03 11,68 12,95 11,60 12,83 11,48
0,6 13,02 11,67 12,92 11,57 12,78 11,43
0,7 13,01 11,66 12,89 11,54 12,73 11,38
0,8 12,99 11,64 12,86 11,51 12,67 11,32
0,9 12,98 11,63 12,83 11,48 12,62 11,27
1,0 12,97 11,62 12,80 11,45 12,57 11,22
___________________________________________________
Speed 10 kn 12 kn 14 kn
C
B
Average Extreme Average Extreme Average Extreme
___________________________________________________
0,5
12,68 11,33 12,50 11,15 12,28 10,93
0,6 12,60 11,25 12,38 11,03 12,12 10,77
0,7 12,52 11,17 12,26 10,91 11,96 10,61
0,8 12,43 11,08 12,14 10,79 11,79 10,44
0,9 12,35 11,00 12,02 10,67 11,63 10,28
1,0 12,27 10,92 11,90 10,55 11,47 10,12
___________________________________________________
4 CONCLUSIONS
To depict maximum draught of a vessel we can use
practical method which incorporates risk of naviga-
tional and three-dimensional model of ship’s do-
main.
Maximum ship’s draught in shallow water esti-
mated by means of formulae (26), with limitation:
1,1 ≤ h/T ≤ 1,2, are presented in table 14. Maximum
ship’s draught is estimated in shallow water (S of
Stolpe Bank) with navigational depth no less than
H
N
=G
D
=18,0m estimated with reference to chart da-
tum related to MSL (Mean Sea Level).
414
Additionally, maximum ship’s draught is estimat-
ed for average (wave’s height (swell) no more than
h
f
=3m and length no more than λ=150m, maximum
fluctuation of the sea water level observed in the ar-
ea ∆h= ±0,30 m, H
N1
=17,70m) and extreme weather
condition (winter time, maximum wave’s height
(swell) about h
f
=5m and length about λ=160m, max-
imum fluctuation of the sea water level observed in
the area ∆h= ±0,60 m, H
N2
=17,40m) for different
ship’s type (her block coefficient C
B
) and different
ship’s speed. Numeral coefficients (factors): n=1,20
(see table 12), m=1 (see table 13) and k=1,0.
The probability that we can expect extreme
weather condition (H
5%
>3,00m) in the researched
area (S of Stolpe Bank) is less than 0,3% (See table
6). Extreme weather condition can be expected only
during the winter from November to February with
strong and long-lasting winds from W and NE.
REFERENCES
Czesław Paszkiewicz,.,Waves on the Baltic Sea”, Polish Acad-
emy of Science, Morza, Wydawnictwo PAN, Warszawa
1989.
Ed. by J.Sundermann, „Dynamics of Coastal Waters and their
modelling”, Institut fur Meereskunde, Hamburg 2005.
„Environmental conditions of Polish Southern Baltic Sea Zone
in 2001”, Institute of Meteorology and Water Management,
Gdynia 2004.
Gucma S., Jagniszczak I., Sea Navigation for captains, (In
Polish) Wydawnictwo Foka, Szczecin 1997.
Joseph M., Assesing the Precision of Depth Data, International
Hydrographic Reviev, Monaco, LXVII (2) July 1991.
Jurdziński M., Planning navigation In coastal areas, Fundacja
Rozwoju WSM w Gdyni, 1998.
Nowicki A., Knowledge about manoeuvring vessels,
Wydawnictwo Trademar - Gdynia 1999.
Rutkowski G. “ Modeling of ship’s domain when maneuvering
in restricted areas”, Warsaw Polytechnic Department of
Transport, Warszawa 2000.
Rutkowski G. Modelling of ship’s domain when manoeuvring
in restricted areas, Warsaw Polytechnic Department of
Transport, Scientist Workbook „T”, Book 47, Warszawa
2001.
Rutkowski G., ”Practical Use of the Ship’s Domain Model for
Estimating Safety of Navigation in Restricted Sea Areas”,
(in Polish), Warsaw Polytechnical University, Transport
Department, Prace Naukowe „T”, Publication No 47, War-
szawa 2002.
Sten Blomgren, Magnus Larson, Hans Hanson: „Numerical
Modeling of the Wave Climate In the Southern Baltic Sea”,
Journal of Coastal Research, CERF, Spring 2001.
