47
1 INTRODUCTION
Safe manoeuvring implies knowing all characteristics
which may influence ship behaviour. Ship
manoeuvring is influenced by changeable and
unchangeable forces. Changeable forces are mostly
external forces of wind, waves, sea currents and
interaction. Unchangeable forces are mostly ship
dimensions and its manoeuvring system (engine,
rudder, etc.). This paper analyses influence of wind
force on ship manoeuvrability, more specific the
influence of ship lateral wind force on ship above
water areas. That wind force is pronounced on
specific types of ships like cruise ships, Ro-Ro
passenger ships, car carriers, container vessels, etc.
Similar analysis was conducted by other authors-
Authors Seong-Gi.S., Mahbub M. [5] point out that the
great importance of safe manoeuvring lies in knowing
where pivot point is and author Kalinovcic H. [1]
described different methods to assess ship
manoeuvrability, standards and criteria for ship
manoeuvrability. The effect of wind force is analysed
by authors Pratama Putra M., Aisjah A.S. [4] where
the wind effect was modelled, and wind disturbance
changed initial actual heading yaw at different attack
angles. Authors Ueno et al. proposed a simple method
to estimate wind load coefficients. Using ship
structural parameters and specific ship type give
simple and reliable method for estimating wind loads.
Author Zelazny K. [6] provides analysis of wind load
on moving ship. This paper also analyses wind load
coefficients which represent the unknown part of
wind load.
2 WIND LOAD EFFECT ON SHIP MOTION
Wind force effect on ship motion can be observed
through three basic situations: when wind force acts
longitudinally towards the ship bow or stern and
Wind Influence on Ship Manoeuvrability – a Turning
Circle Analysis
M. Novaselic
1
, R. Mohovic
1
, M. Baric
2
& L. Grbić
2
1
University of Rijeka, Rijeka, Croatia
2
University of Zadar, Zadar, Croatia
ABSTRACT: Ship manoeuvrability is a wide term which consist of number of various parameters. Knowing the
influence of these parameters on ship manoeuvrability is a first condition to ensure and maintain safe
navigation. However, many of these parameters are external forces and, in some cases, cannot be calculated and
prediction may be complicated. Analysing the influence of external forces can give as an insight into ship
manoeuvrability when such external force occurs. The main purpose of this paper is to analyse the influence of
wind on ship manoeuvrability. The best way to make such analysis is during turning circle because in this case
wind acts in all 360°. Analysis is made using empirical equations and in situ with the real vessel. The results
provide the better understanding of vessel trajectory and show that in some cases vessel may respond in
unexpected manner.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 15
Number 1
March 2021
DOI: 10.12716/1001.15.01.03
48
when the wind force act transverse in regard to ship
centreline. Beside these three basic situations, wind
force may act on ship from any other direction. Ship
motion, regardless on wind force, depends on several
different factors as:
− Above water surface and its layout (including deck
cargo),
− Location of pivot point,
− Ship trim.
If the ratio of above and underwater surface is in
order that above water area is greatly larger than
underwater area, influence of wind force will be large.
In case when ship underwater area is larger than
above water area the influence of wind force will be
smaller and in that case wind force has to act longer to
overcome ship moment of inertia in order to archive
ship drift.
Wind force effect depends on if the ship is carrying
any deck cargo, such as containers, where fore and aft
area ration may affect location of ship pivot point.
That means if the ship pivot point is not in line with
the wind force acting point the result is turning
moment.
When the ship is not moving and is at even keel,
the pivot point will be located near the ship gravity
centre which is approximately around the midship. If
the fore/aft above ship area is such that wind force
acting point in in the line with the pivot point, the
ship will position parallel with the wind force and
there will be no turning momentum. In case that
above water area is larger at stern/bow, the wind force
acting point will be located closer to the stern/bow
and there will be turning momentum.
However, if the ship is moving through the water,
the pivot point will move towards the direction of
moving. If the ship is moving forward the pivot point
is also moving forward, approximately to the ¼ of the
ship length from the bow. In that case if the wind
force acting point is located on the stern the turning
moment will turn ship bow toward the wind. If the
ship is moving backward the pivot point will move
toward the stern, approximately ¼ of the ship length
from the stern. If the wind force acting point is on the
bow the turning momentum will turn ship stern
towards the wind.
Beside the turning momentum, the wind force will
cause the ship heel angle. The turning and heeling
momentum lever can be calculated using following
expression [3]:
1
1000
w
P A Z
l
g
=
where:
P – wind pressure (N/m²),
A – lateral ship surface (m²),
Z – vertical distance between surface point of gravity
and underwater area centre of gravity (m),
∆ - displacement (t),
g – earth acceleration (9,81 m/s²).
Wind pressure can be determined using following
expression [3]:
( )
2
1
2
zv
va
P C Vr
=
where:
Cv(a) – ship resistant coefficient. Its value depends on
which angle wind acts on ship hull. For the Ro-Ro
passenger ships its value is 0,85 for wind acting on
lateral area and 0,95 for wind acting on frontal area
[2].
ρz – air density (kg/m³),
Vrv – wind relative speed (m/s).
Beside turning moment wind force may case
following effects:
− Speed increment, if the ship is moving downwind,
− Speed decrement, if the ship is moving upwind,
− Drift angle, if the wind force acts lateral to the
centreline. Drift angle is angle between the ship
heading and course over ground.
3 WIND FORCE CALCULATION
Influence of the wind force, acting on the above water
ship surfaces, will depend on wind speed and attack
angle. In most cases the greatest impact wind has at
angles between 60° - 120° in regard to ship centreline.
In order to archive correct lateral above water
surface ship side view plan can be used. Ship side
plan silhouette is then divided in 1 meter height parts
(Figure 1). That enables easier calculation of each part
square surface area, where imperfections at bow or
stern are negligible and to include different wind
effect at different heights.
For the purpose of this paper in research Ro-Ro
passenger ship Dubrovnik was used (Table 2). Using
ship side plan lateral surface was calculated and
specific wind impact at different height was
calculated using dimensionless coefficients obtained
from Schoeneich research.
Figure 1. Ship side view plan division into 1 meter height
parts to calculate longitudinal area (Source: authors)
Calculation process is shown in Table 1, where the
used wind speed is 20 knots (10 m/s), air pressure
1013 hPa and 0 °C air temperature. In Table 1
following abbreviations were used:
1. Ah (m
2
) – dissected part of ship side plan lateral
area (1 meter in height · LOA),
2. h(m) – height from ship bottom to dissected part
centre of gravity,
3. Ah∙h (m
3
) – represent momentum of each dissected
area,
4. Pmid (N/m
2
) – wind pressure median,
5. MvVL (Nm) – wind momentum at each dissected
area and total sum of this column is wind lateral
momentum (obtained by multiplication of Ah∙h
and Pmid),
49
Table 1. Wind force and momentum effect calculation (Source: authors)
__________________________________________________________________________________________________
Height above 𝐴ℎ ℎ 𝐴ℎ 𝑥 ℎ 𝑃𝑠𝑟𝑒𝑑 𝑀𝑣
𝑉𝐿
𝐹𝑣
water line (𝑚
2
) (𝑚) (𝑚
3
) (𝑁/𝑚
2
) (𝑁𝑚) (𝑁)
__________________________________________________________________________________________________
0-1m 118,5 0,5 59,25 17,75 1051,69 2103,38
1-2m 119,0 1,5 178,5 26,91 4803,44 3202,29
2-3m 119,5 2,5 298,75 33,09 9885,64 3954,26
3-4m 119,8 3,5 419,3 37,91 15895,66 4541,62
4-5m 120,2 4,5 540,9 42,13 22788,12 5064,03
5-6m 120,5 5,5 662,75 45,93 30440,11 5534,57
6-7m 120,9 6,5 785,85 49,30 38742,41 5960,37
7-8m 121,1 7,5 908,25 52,28 47483,31 6331,11
8-9m 112,5 8,5 956,25 54,88 52479,00 6174,00
9-10m 103,0 9,5 978,5 57,12 55891,92 5883,36
10-11m 100,0 10,5 1050 59,01 61960,50 5901,00
11-12m 92,0 11,5 1058 60,64 64157,12 5578,88
12-13m 91,0 12,5 1137,5 62,09 70627,38 5650,19
13-14m 86,0 13,5 1161 58,72 68173,92 5049,92
14-15m 85,0 14,5 1232,5 64,65 79681,13 5495,25
15-16m 82,0 15,5 1271 65,80 83631,80 5395,60
16-17m 64,0 16,5 1056 66,89 70635,84 4280,96
17-18m 57,0 17,5 997,5 67,91 67740,23 3870,87
18-19m 26,5 18,5 490,25 68,88 33768,42 1825,32
19-20m 21,0 19,5 409,5 69,79 28579,01 1465,59
20-21m 11,5 20,5 235,75 65,42 15422,77 752,33
21-22m 8,8 21,5 189,2 71,47 13522,12 628,94
22-23m 8 22,5 180 72,23 13001,40 577,84
23-24m 3,5 23,5 82,25 72,96 6000,96 255,36
24-25m 2 24,5 49 73,65 3608,85 147,30
25-26m 0,8 25,5 20,4 74,30 1515,72 59,44
26-27m 0,7 26,5 18,55 74,92 1389,77 52,44
27-28m 0,5 27,5 13,75 75,51 1038,26 37,75
28-29m 0,35 28,5 9,975 76,08 758,90 26,63
29-30m 0,2 29,5 5,9 76,63 452,12 15,33
__________________________________________________________________________________________________
𝛴𝐴
ℎ
=1915,85 𝛴𝐴
ℎ
·ℎ=16456,33 𝛴𝑀𝑣
𝑉𝐿
=965127,52 𝛴𝐹
𝑣
=95815,93
__________________________________________________________________________________________________
6. Fv (N) – wind force at each dissected part and total
sum of this column is wind lateral force
(obtained by multiplication of Ah and Pmid).
From Table 1 additional data following data were
obtained:
1. 𝛴𝐴
ℎ
·ℎ – total above water surface momentum (m3),
2. 𝛴𝐴
ℎ
– total above water lateral surface (m3),
3. 𝛴𝑀𝑣
𝑉𝐿
– wind lateral momentum (Nm),
4. 𝛴𝐹
𝑣
- wind lateral force (N).
Beside before mentioned data, additional data is
calculated:
1.
h
lat
- Lateral above water surface centre of gravity
(m):
16456,33
1915,85
8,59
h
lat
h
Ah
hm
A
= = =
2. hwind – centre of gravity of acting wind force (m):
96512
3
10,07
7,52
95815,9
VL
wind
v
Mv
hm
F
= = =
3. Pmid – average wind fore pressure (N/m
2
):
2
95815,9
5
191
3
0,01 /
5,85
v
mid
h
F
P N m
A
= = =
4. Analysis of wind influence on ship
manoeuvrability
In order to gather reliable data for this research Ro-
Pax ship Dubrovnik was used. The Ro-Pax ship
Dubrovnik data is shown in Table 2.
Table 2. Ro-Pax ship Dubrovnik technical data
_______________________________________________
Ship name Dubrovnik
Year built 1979
Summer deadweight 1310
LOA 122 m
LBP 116 m
Breadth 18.83 m
Draught 4,8 m
Max. speed 21 knots
Number and type of propellers 2 controllable pitch
propellers
Number of rudders 2
Passenger capacity 1200
Cars capacity: 300
_______________________________________________
The experiment consisted of making turning circles
(over port and starboard side) on two different
conditions. First experiment was conduced 21 nautical
mile out of port Ancona and second experiment in
Croatian territorial waters 1,5 nautical mile off coast.
Ship instruments were used to collect data such as
ship speed (speedometer for ship speed through
water and GPS for speed over ground), ECDIS for
plotting ship position and anemometer for wind
speed and direction. To analyse influence of wind
following conditions had to be met: sea state bellow 1
of Beaufort scale, sea current under 0.5 knot and wind
speed of 20 knots. That conditions were obtained on
second experiment position where experiment took
place. First experiment was conducted on conditions
where wind, sea current speed were 0 knots and sea
were calm, to obtain control data.
50
Both experiments were made in following order
and procedure. First, ship speed and curse had to be
constant and stabilised. Then, rudder was turned full
to port/starboard (35°) until full circle was made. For
every phase of turning circle ship speed and time was
recoded as well as turning circle data such as advance
(AD), tactical diameter (TD) and transfer (TR).
First experiment took place at 20. December 2018
in the morning and recorded data is shown in Table 3
and Figure 2.
Figure 2. Turning circle first experiment recorded trajectory
In theory turning circle over port or starboard side
should be the same. However, in this experiment
minor differences were recorded. For example,
turning circle over port side have advance shorter for
3,7 %, transfer smaller for 2,7 % and tactical diameter
shorter for 8,6 %. Also, total time needed for making
turning circle over port side is faster for 9,6 seconds
than over starboard side. Those differences are minor
and are result in differences in port and starboard
engine.
Second experiment was conduced on 26. December
2018 when required conditions were met. At site
recorded wind speed was 20 knots (10 m/s) from
NNE, sea state was 1 and there was no sea current.
Recorded data is shown in Table 4 and Figure 3.
Figure 3. Turning circle second experiment recorded
trajectory
As in the second experiment wind direction was
NNE starting course was approximately NNW, so the
wind was acting lateral at the beginning of the turning
circle. Turning circle over port side was down wind
so the tactical diameter is larger for 54 meters, as well
as advance which is larger for 68,52 meters and
transfer which is larger for 24 meters. Total time for
turning circle over port side is longer for 24 second
than turning circle over starboard side. To analyse
wind influence data from both experiments were
compared (Table 5).
It can be seen from Table 5, that downwind turning
circle is a lot greater than upwind turning circle as
well as time needed. One of the reasons is that this is a
ship with quite large above water area and small
displacement where drift is pronounced. Recorded
data was compared with ship Trials report which
were conducted by Verolme Cork Dockyard in
January 1979. At the time of trials wind was 6-7
Beaufort from SW. Sea state was moderate with sweel.
These conditions are approximate to our experiment.
Data from trials turning circles are shown in table 6.
Table 3. Turning circle first experiment recorded data
__________________________________________________________________________________________________
Turning Rudder engine Starting ΔKp 90° ΔKp 180° ΔKp 270° ΔKp 360° AD TR TD
side angle RPM course (s) (s) (s) (s) (m) (m) (m)
__________________________________________________________________________________________________
Port 35° 250 rpm 292° 55,5 78,2 122,8 147,8 351,88 194,46 346,32
Stbd 35° 250 rpm 240° 55,5 89,5 125,6 157,4 364,84 199,64 375,96
__________________________________________________________________________________________________
Table 4. Turning circle second experiment recorded data
__________________________________________________________________________________________________
Turning Rudder engine Starting ΔKp 90° ΔKp 180° ΔKp 270° ΔKp 360° AD TR TD
side angle RPM course (s) (s) (s) (s) (m) (m) (m)
__________________________________________________________________________________________________
Port 35° 250 rpm 292° 84,3 136,1 184,3 233,5 590,78 266,68 498,19
Stbd 35° 250 rpm 283° 72,0 115,8 160,7 209,5 522,26 242,61 444,48
__________________________________________________________________________________________________
Table 5. Differences in turning circle between first and second experiment
__________________________________________________________________________________________________
Turning side ΔKp 90° (s) ΔKp 180° (s) ΔKp 270° (s) ΔKp 360° (s) AD (m) TR (m) TD (m)
__________________________________________________________________________________________________
Port +51,9% +74,0% +50,1% +58,0% +67,9% +37,1% +43,9%
Stbd +29,7% +29,4% +27,9% +33,1% +43,1% +21,5% +18,2%
__________________________________________________________________________________________________
Table 6. Trial run turning circle data
__________________________________________________________________________________________________
Turning Rudder engine Starting ΔKp 90° ΔKp 180° ΔKp 270° ΔKp 360° AD TR TD
side angle RPM course (s) (s) (s) (s) (m) (m) (m)
__________________________________________________________________________________________________
Port 35° 24.3 080 54 113 178 233 250 245 500
Stbd 35° 17.95 085 63 120 170 237 325 180 350
__________________________________________________________________________________________________
51
It can be seen that starboard circle was done with
lower starting speed and upwind, while port circle
was done downwind. Since the port turning circle is
downwind that larger starting speed can be ascribed
to that phenomena. Data from table 6 shows that this
vessel is prone to drifting and that effect is
pronounced with larger wind speeds.
4 CONCLUSION
This paper analyses in situ the wind influence on ship
manoeuvring. For the purpose of experiment and to
comply with safety standards ship turning circle was
analysed. The experiment had to be executed on
appropriate conditions, one with no wind and sea
influence and one with wind speed of 20 knots and
minimal sea state.
The results show that this type of ship, Ro-Ro
passenger, is due to larger above water surface
accelerated downwind and deaccelerated upwind.
Also, lateral wind will cause significant ship drifting.
Data analyses show that turning circle is greater than
one without external forces and that influence should
be considered when making turning circle. That drift
should be also considered when making turning up to
180°.
Since the safe ship manoeuvring implies knowing
all ship manoeuvring features this type of
experiments should be conducted on other ship types.
That data enables safer ship manoeuvring in
conditions where navigational dangers are close to
fairway or when manoeuvring in port.
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