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Experimental study on the hydrodynamic forces induced by a twin-propeller ferry during berthing
ARTICLE IN PRESS
Ocean Engineering 35 (2008) 323–332 www.elsevier.com/locate/oceaneng
Experimental study on the hydrodynamic forces induced by a twin-propeller ferry during berthing Teresa Abramowicz-Gerigk Faculty of Navigation, Gdynia Maritime University, Al. Jana Pawla II 3, 81-345 Gdynia, Poland Received 25 May 2007; accepted 25 October 2007 Available online 1 November 2007
Abstract The paper presents the experimental study on the influence of wall effect on the hydrodynamic forces induced by the propellers and thrusters of a ferry during the berthing. The program of the model tests was developed for the twin-propeller, twin-rudder, man-manned model of a car–passenger ferry in 1:16 scale, equipped with two bow thrusters. The different combinations of the operational settings of bow thrusters and propellers operating in the push–pull mode allowed to observe and quantify the variation of the hydrodynamic forces due to the changes of the water depth to draft ratios and distances to the quay. The results of model tests are introduced and discussed in the paper. The difference between the measured total hydrodynamic force and superposition of the component forces induced by the propellers and thrusters has been investigated. According to the structure of the generally accepted modular manoeuvring model, the proposition of the weight factors for the component forces comprising the interaction effects has been introduced and discussed. r 2007 Elsevier Ltd. All rights reserved. Keywords: Twin propeller; Twin-rudder ferry; Berthing; Unberthing; Wall effect; Model tests; Modular manoeuvring model
1. Introduction The decreasing manoeuvring space and increasing traffic have a big impact on the risk of damage to vessels and port facilities. Because the main safety options: training of seamen, implementation of navigational aids and planning of harbour operations are based on the simulation of ship motion, the modelling of ship motions at slow speed in the constrained space is now essential to enhance safety. The investigations on the modelling of the berthing forces aim at the improvement of efficiency and increase of the vessels’ turn around speed in ports. Because of a complex turbulent flow generated around the ship, a general mathematical model that aims to describe the ship motions close to the quay wall is difficult to formulate with respect to both the methods based on CFD and model tests. Due to this fact there are few experimental results of self-berthing available (Shin and Lee, 2004; Qadvlieg and Toxopeus, 1998; Yoo et al., 2006). Tel.: +48 58 6901120.
E-mail address: [email protected] 0029-8018/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.oceaneng.2007.10.009
The modular manoeuvring models that allow for the superposition of the forces generated on the hull while accounting for extreme interactions always need a tuning usually based on the heuristic methods. However, the heuristic methods based on the opinions of experienced pilots and masters help to bring the simulation reasonably close to reality for the training purposes; the better accuracy is expected when the applications related to ship operation are considered. The open water model tests presented in the paper, carried out using the stationary model to investigate the forces generated by propulsion and steering devices, allowed to perform the quantitative analysis of the phenomena dependent on the fluid flow induced by the working propellers and thrusters. 2. Model tests The open water experiments were carried out using a large man-manned model of a car–passenger ferry in 1:16 scale. The specially designed experimental test setup shown in Fig. 1 was constructed on the shore of the Silm lake at the Ship Handling Research and Training Centre of the
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Fig. 1. Model of the car–passenger ferry and experimental test setup.
Foundation for Safety of Navigation and Environment Protection in Ilawa—Kamionka, Poland. The influence of several operational parameters on the variation of hydrodynamic forces was investigated. The program of model tests consisted of different settings of the propellers operating in push–pull mode in combination with the different rudder angles and settings of the bow thrusters, different depth to draft ratios and model distances to the quay wall. The main assumptions regarding the classification and hierarchization of the parameters influencing the interaction forces had followed from the engineering study based on the previously published results (AbramowiczGerigk, 2006a; Shin and Lee, 2004; Qadvlieg and Toxopeus, 1998).
Table 1 Main particulars of the car–passenger ferry model Length overall (m) Length between perpendicular (m) Breadth (m) Draft (m) Displacement (m) Block coefficient (–) Scale
10.98 9.64 1.78 0.42 4.89 0.687 1:16
x z
2.1. Model and experimental test setup The large man-manned model in 1:16 scale was adopted to the stationary tests to allow the measurements of the hydrodynamic forces generated on the hull only by the propellers, rudders and bow thrusters (AbramowiczGerigk, 2006b). The main particulars of the car–passenger ferry model are presented in Table 1. The model presented in Figs. 1 and 2 was equipped with two, four blades, controllable pitch propellers of the inward direction of revolution, two rudders and two bow tunnel thrusters. The quay model was a tight vertical wall. The water depth was adjusted by the movable horizontal flat plate. The dimensions of the experimental test setup were as follows: 12 m length, 5 m width and 1.25 m of the maximum adjustable water depth. The model was stationary in the horizontal plane and free to the pitch, heave and roll motions. The position of model, relative to the wall, was fixed using the bow and stern pantographs (Fig. 1). The setup of the propellers’ thrust, bow thrusters and rudder angles was done using the onboard controls. The RPM and pitch of the propellers for the settings of the on-board engine telegraphs were measured by the on-board meters. The rudder angles were measured by the on-board meters as well. The measuring system of the bow and stern transverse and longitudinal forces consisted of two (bow and stern) tensometer-type dynamometers AMTI (Advanced Mechanical Technology,
x
η y Quay Fig. 2. Coordinate system.
Inc.) MC3-100. The signals from the dynamometers were amplified using the AMTI amplifiers and sent to A/D converter in the computer. The data collection software (VBasic) had been developed for data collection and processing. The total sway force and yawing moment were calculated on the basis of the measurements. 2.2. Results of experiment The results of berthing and unberthing experiments are presented in the form of non-dimensional sway force and yawing moment plotted as the functions of non-dimensional distance b (1) between the hull centreline and the quay wall for the water depth to draft ratios h/T ¼ 1.2 and 3: b¼
Z , B
(1)
ARTICLE IN PRESS T. Abramowicz-Gerigk / Ocean Engineering 35 (2008) 323–332
where Z is the distance between the wall and model centreline and B is the model breadth. The non-dimensional sway force (2) and yawing moment (3) are made non-dimensional and based on the length between perpendiculars and draft (Yoo et al., 2006): Fy0 ¼
Fy , 0:5rgL2 T
Mz0 ¼
(2)
Mz , 0:5rgL3 T
(3)
where Fy is the measured sway force, r is the water density, g is the acceleration of gravity, L is the model length between perpendiculars and T is the model draft. The propellers were operated in the push–pull mode to generate the yawing moment opposite to the moment produced by the bow thrusters. The coupled rudders were put 351 to port for the berthing and 351 to starboard for the unberthing. The non-dimensional sway forces and yawing moments induced on the hull by the bow thrusters are presented in Figs. 3 and 4. The non-dimensional sway force and yawing moment induced by the propellers in the push–pull mode and coupled rudders put 351 to starboard or 351 to port for the unberthing and berthing, respectively, are presented in Figs. 5 and 6. The non-dimensional sway force and yawing moment due to the combined action of the bow thrusters, propellers and rudders are presented in Figs. 7 and 8 for
the berthing, and in Figs. 9 and 10 for the unberthing, respectively. The settings of the engine telegraph of port and starboard propeller correspond to the following values of the non-dimensional effective thrust in open water conditions: dead slow ahead: 6.57E5, slow ahead: 22.36E5, dead slow astern: 3.81E5 and slow astern: 13.67E5. The settings of the bow thruster controls correspond to the following values of the non-dimensional thrust in open water conditions: 100%: 11.26E5, 75%: 5.47E5 and 50%: 2.22E5. Thrust values are made non-dimensional in the same way as the sway force (2). 3. The influence of the wall effect on the forces induced by the propellers and rudders and on the forces induced by the bow thrusters The influence of the wall effect on the sway force and yawing moment is different in the berthing and unberthing cases. In both the berthing and unberthing cases at h/ T ¼ 1.2, the strong suction is induced by the starboard propeller. It results into an attraction between the stern and wall during the berthing and attraction along the whole length of the hull during the unberthing. For example, at b ¼ 0.75 the force measured at the bow was 12% of the total sway force in the berthing and 57% in the unberthing case, respectively. The sway force and yawing moment induced by the bow thrusters are strongly dependent on the
Berthing
Fy'x103
0.35 0.3
h/T=3.0 BT 50%
0.25
h/T=3.0 BT 75%
0.2
h/T=3.0 BT 100%
0.15
h/T=1.2 BT 50%
0.1
h/T=1.2 BT 75%
0.05
h/T=1.2 BT 100%
0 0.5
1
1.5
2
b Berthing
Mz'x103
0.16 0.14
h/T=3.0 BT 50%
0.12
h/T=3.0 BT 75%
0.1
h/T=3.0 BT 100%
0.08 h/T=1.2 BT 50%
0.06 0.04
h/T=1.2 BT 75%
0.02
h/T=1.2 BT 100%
0 0.5
1
1.5
325
2
b Fig. 3. The lateral force and yawing moment induced by the bow thrusters during the berthing.
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Unberthing 0 h/T=3.0 BT 50%
Fy'x103
-0.05
h/T=3.0 BT 75%
-0.1
h/T=3.0 BT 100% -0.15 h/T=1.2 BT 50% -0.2
h/T=1.2 BT 75%
-0.25
h/T=1.2 BT 100%
-0.3 0.5
1.5
1
2
b Unberthing
Mz'x103
0 -0.02
h/T=3.0 BT 50%
-0.04
h/T=3.0 BT 75%
-0.06
h/T=3.0 BT 100%
-0.08
h/T=1.2 BT 50%
-0.1
h/T=1.2 BT 75%
-0.12
h/T=1.2 BT 100%
-0.14 0.5
1.5
1
2
b Fig. 4. The lateral force and yawing moment induced by the bow thrusters during the unberthing.
Berthing 0.5
Fy'x103
0.4
h/T=3 DEAD SLOW
0.3
h/T=3 SLOW
0.2 h/T=1.2 DEAD SLOW 0.1 h/T=1.2 SLOW 0 -0.1 0.5
1
1.5
2
b Berthing 0.02
Mz'x103
0 -0.02
h/T=3 DEAD SLOW
-0.04
h/T=3 SLOW
-0.06
h/T=1.2 DEAD SLOW
-0.08
h/T=1.2 SLOW
-0.1 -0.12 -0.14 0.5
1
1.5
2
b Fig. 5. The lateral force and yawing moment induced by the propellers in the push–pull mode and coupled rudders put 351 to port during the berthing.
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Fy'x10
3
Unberthing 0.15 0.1 0.05 0 -0.05 -0.1
h/T=3 DEAD SLOW h/T=3 SLOW h/T=1.2 DEAD SLOW h/T=1.2 SLOW
-0.15 -0.2 0.5
1
1.5 b Unberthing
2
0.12 0.1
h/T=3 DEAD SLOW
0.08 Mz'x10
3
h/T=3 SLOW
0.06
h/T=1.2 DEAD SLOW
0.04
h/T=1.2 SLOW
0.02 0 0.5
1
1.5
2
b Fig. 6. The lateral force and yawing moment induced by the propellers in the push–pull mode and coupled rudders put 351 to starboard during unberthing.
distance between the wall and model side only during the unberthing due to the blockage of the outflow stream from the bow thrusters by the wall. 3.1. Berthing The sway force and yawing moment induced on the hull by the thrusters during the berthing, presented in Fig. 3, are not much influenced by the distance to the quay and water depth. The biggest decrease of the sway force, about 15%, is observed in the shallow water conditions at h/T ¼ 1.2, for the 100% settings of the bow thrusters, at the distance between the wall and model side less than a quarter of the model breadth. The changes of the moment have the same character and they do not exceed 10% of the maximum value at h/T ¼ 3. In the shallow water conditions the slipstream, of the starboard propeller acting ahead, generated a suction force at the aft part of the model. However, it was not observed for the dead slow settings of the propellers (Fig. 5). When the model was close to the wall, at bo0.8, the bow away moment in shallow water was significantly greater than the moment measured at h/T ¼ 3. The maximum difference, about 30% of the value at h/T ¼ 3, was observed at b ¼ 0.6. When the sway force was generated by the propellers and coupled rudders (starboard/port propellers engine telegraph settings slow ahead/slow astern, the coupled rudder angle 351 to starboard), the changes of the sway force and yawing moment both at h/T ¼ 1.2 and 3 were general in the same level of values, except for the change of berthing at h/T ¼ 1.2 and b less than 1.0 (Figs. 7 and 8). At h/T=1.2
the additional attraction force raised linearly with the decreasing distance to the wall. At b=1 it was about 10% greater than at b=2.1 and then at b less than 0.75 it was 100% greater then at b=2.1. This means that at b=1 the sway force at h/T=1.2 was 70% greater than the force generated at h/T=3. In the shallow water only, when the model was positioned close to the wall, at b=0.6, there was 10% decrease of the suction force in comparison to the value at b=0.75. 3.2. Unberthing The results of investigations carried out by Yoo et al. (2006) confirm that the thrust of the bow thrusters which are located near the centreline is not affected by either the water depth to draft ratio or the distance to the quay. However, the sway force and yawing moment induced on the hull by the bow thrusters during unberthing, presented in Fig. 4, were dependent on the distance of the model to the quay and the water depth to draft ratio especially when acting with the 100% thrust settings. In general, the negative (repulsion) sway force was decreasing with the decreasing distance to the wall. The outflow stream from the bow thrusters reflected from the quay area was pushed along the wall in both the stern and bow directions, what is clearly illustrated by the visualization experiment published by Nielsen (2005). At h/T ¼ 1.2 and b ¼ 0.75 the strong rise of the repulsion force was induced and then at b ¼ 0.6 the repulsion effect disappeared. In the unberthing condition—coupled rudder angle 351 to starboard, slow ahead/slow astern propeller settings— the suction force in the deep and shallow water conditions
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Be rth in g h /T=3 0.6 0.5
DEAD SLOW BT 50% s SLOW BT 50% s
Fy'x103
0.4
DEAD SLOW BT 100% s SLOW BT 100% s
0.3
DEAD SLOW BT 50% SLOW BT 50%
0.2
DEAD SLOW BT 100% SLOW BT 100%
0.1 0 0. 5
1
1. 5
b Berthing h/T=3 0.15
DEAD SLOW BT 50% s
0.1
Mz'x103
SLOW BT 50% s DEAD SLOW BT 100% s
0.05
SLOW BT 100% s DEAD SLOW BT 50% 0
SLOW BT 50% DEAD SLOW BT 100%
-0.05
SLOW BT 100%
-0.1 0.5
1
1.5
b Fig. 7. Lateral force and yawing moment induced by the bow thrusters, propellers in the push–pull mode and coupled rudders put 351 to port for the depth to draft ratio h/T ¼ 3. s denotes the superposition of the forces induced separately by the bow thrusters and propellers with rudders during the berthing.
increased when the interval between the model side and wall decreased. The decrease was observed only at b ¼ 0.6 for the slow settings and for dead slow at h/T ¼ 3 (Fig. 6). The repulsion—negative sway—force induced at b ¼ 2.1 was changing into the positive—attraction, when the distance between the wall and model side was less than a half of the model breadth. The maximum attraction force appeared in shallow water at b ¼ 0.75 and it had the same absolute value as the negative sway force at b ¼ 2.1. At h/T ¼ 3 the negative sway force was greater then the sway force induced at h/T ¼ 1.2 and suction effect at b ¼ 0.75 was smaller than that in shallow water. The increase of the suction force was less than 50% of the force at b ¼ 1.5, so there was no change in the sign from the repulsion to attraction. The significant rise of the stern away moment was observed at b ¼ 0.6. Due to this rise of the moment in
shallow water, at b ¼ 0.6 the moments for both the depth to draft ratios were almost equal. 4. Superposition of the forces induced by the propellers, rudders and bow thrusters In Figs. 7 and 8 the non-dimensional sway force and yawing moment due to the combined action of the bow thrusters, propellers and rudders are compared with the force and moment obtained by the superposition of the forces generated by the propellers with the rudders and bow thrusters separately for the berthing case. Figs. 9 and 10 illustrate the results of measurements and superposition for the unberthing case. In the shallow water conditions during the berthing at slow ahead/slow astern action of the propellers, the character of the sway force and yawing moment functions
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329
Berthing h/T=1.2 1 0.9 DEAD SLOW BT 50% s
0.8
SLOW BT 50% s
Fy'x103
0.7
DEAD SLOW BT 100% s
0.6
SLOW BT 100% s
0.5
DEAD SLOW BT 50%
0.4
SLOW BT 50%
0.3
DEAD SLOW BT 100%
0.2
SLOW BT 100%
0.1 0 0.5
1
1.5 b Berthing h/T=1.2
2
0.15 DEAD SLOW BT 50% s
0.1
SLOW BT 50% s Mz'x103
0.05
DEAD SLOW BT 100% s SLOW BT 100% s
0
DEAD SLOW BT 50% SLOW BT 50%
-0.05
DEAD SLOW BT 100% -0.1
SLOW BT 100%
-0.15 0.5
1
1.5
2
b
Fig. 8. Lateral force and yawing moment induced by the bow thrusters, propellers in the push–pull mode and coupled rudders put 351 to port for the depth to draft ratio h/T ¼ 1.2. s denotes the superposition of the forces generated separately by the bow thrusters and propellers with rudders during the berthing.
for the coupled action of the bow thrusters and propellers is similar to the force and moment induced by the propellers and rudders but the values are dependent on the settings of the bow thrusters. Up to the distance between the model side and wall over a half of the model breadth, for the full power of bow thrusters, the measured sway force was about 15% less than the resultant force obtained by the superposition of the component forces induced by the thrusters and propellers separately. This phenomena was due to the interaction of the thrust stream from the port propeller, acting astern, with the outflow stream from the bow thrusters. If that distance decreased, the attraction force increased. Between the values at b=1 and 0.75 the sharp rise of the attraction force, about 50% of the value at b=1, was observed. Then at b=0.6 the force dropped of about 10% of the maximum sway force at b=0.75. If the 50% settings of the bow thrusters were applied the measured force was closer to the superposition; however, if b was less than 1.5 the same effects appeared. The bigger differences between the measured sway force and superposition of the component forces induced by propellers and thrusters separately were observed in the
shallow water conditions during the unberthing for 100% of the bow thruster settings applied. This is illustrated in Fig. 10. The strong repulsion force was due to the overpressure induced by the blockage of the thrust stream from the starboard propeller acting astern by the bow thrusters outflow. For the slow ahead/slow astern and 50% of the bow thruster settings combination the stern away moment was induced. The bow away moments were induced only for the dead slow ahead/dead slow astern combined with 100% of the bow thruster settings and for the slow ahead/slow astern combined with 100% settings of bow thrusters. However, for the slow ahead propeller action combined with 100% settings of the bow thrusters the bow away moment was decreasing with the increasing distance and at b ¼ 2 was equal to zero. In combination with the bow thruster action the bow away yawing moment, which already occurred in shallow water and close to the wall at the zero propeller rate, at b less than 1 was amplified by the propeller action. The greater was the distance, the closer to the superposition of the component moments was the measured value.
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330
Unberthing h/T=3 0 DEAD SLOW BT 50%
Fy'x103
-0.1
SLOW BT 50% DEAD SLOW BT 100%
-0.2
SLOW BT 100% -0.3
superposition measurement
-0.4 -0.5 0.5
model
0.7
0.9
1.1
1.3
1.5
b Unberthing h/T=3
DEAD SLOW BT 50% 0.05
SLOW BT 50%
Mz'x103
DEAD SLOW BT 100% SLOW BT 100% -0.05
superposition measurement model
-0.15 0.5
0.7
0.9
1.1
1.3
1.5
b
Fig. 9. The lateral force and yawing moment induced by the bow thrusters, propellers in the push–pull mode and coupled rudders put 351 to starboard for the depth to draft ratio h/T ¼ 3.
The modular approach in mathematical modelling of the ship manoeuvring motions means that each force and moment acting on the ship can be expressed as the sum of a hull, propeller, rudder and thruster modules based on their effective hydrodynamic characteristics. In the case when the fluid flow around the ship is disturbed by the vicinity of another object, a module of the interaction forces is added. However, the model of the additional forces due to the interactions can be formulated on the basis of the model tests; in the case of self-berthing due to the complex fluid dynamics the sub-models must be introduced to obtain a reasonable estimation of the interaction forces. The constraints of the sub-models are dependent on the character of variation of the measured values in the particular ranges of influencing parameters. For example, in the shallow water conditions at h/T ¼ 1.2 the model must describe the phenomena not observed or neglected at h/T ¼ 3. In this case a global model combined with a sequence of partially overlapping sub-models which could be largely unrelated to each other and constrained gives substantially better results. The simple linear superposition of the component forces induced by the propellers and bow thrusters acting separately can be applied for h/T ¼ 3. To get a better agreement with the experimental results, the
weight factors ai and bi, i ¼ 1, 2, comprising the interaction effects were implemented in the models of the total sway force and yawing moment in Eqs. (4) and (5), respectively: Fy0 ¼ a1 Fy0PR þ a2 Fy0BT ,
(4)
Mz0 ¼ b1 Mz0PR þ b2 Mz0BT ,
(5)
where ai, bi are the weight factors, the subscript PR denotes the action of propellers in the push–pull mode with the coupled rudders and the subscript BT denotes the action of the bow thrusters. Fig. 9 illustrates the results of measurements of the total sway force and yawing moment, results of fitting a simple superposition and fitting the multiple linear regression model to describe the relationship between Fy0 , Mz0 and two independent variables Fy0PR , Fy0BT and Mz0PR , Mz0BT , respectively. The coefficients ai, bi and R2 statistics describing the fitting of the models for h/T ¼ 3 and 1.2 are presented in Table 2. 5. Concluding remarks The study is the basic research to obtain quantitatively the hydrodynamic forces induced during the self-berthing.
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Unberthing h/T=1.2 0.2 0
DEAD SLOW BT 50% s SLOW BT 50% s
Fy'x103
-0.2
DEAD SLOW BT 100% s SLOW BT 100% s
-0.4
DEAD SLOW BT 50% SLOW BT 50%
-0.6
DEAD SLOW BT 100% -0.8
SLOW BT 100%
-1 0.5
1.5
1
2
b Unberthing h/T=1.2 0.15 0.1
DEAD SLOW BT 50% s SLOW BT 50% s
Mz'x103
0.05
DEAD SLOW BT 100% s SLOW BT 100% s
0
DEAD SLOW BT 50% -0.05
SLOW BT 50% DEAD SLOW BT 100%
-0.1
SLOW BT 100%
-0.15 0.5
1.5
1
2
b Fig. 10. The lateral force and yawing moment induced by the bow thrusters, propellers in the push–pull mode and coupled rudders put 351 to starboard for the depth to draft ratio h/T ¼ 1.2.
Table 2 Coefficients of linear regression models of the sway force and yawing moment, R squared statistics: R2a for the sway force model and R2b for the yawing moment model h/T
a1
a2
b1
b2
R2a (%)
R2b (%)
1.2 3
0.121 0.700
2.882 1.238
0.776 0.839
1.277 1.023
97.83 98.83
78.24 97.54
The influence of water depth and distance between the berth and ship side on the forces generated on the hull due to the action of propulsion and steering devices has been studied. The main conclusions have been formulated with respect to the application of the interaction forces into the modular model of ship motion. The research was carried out using the large manmanned model in 1:16 scale. The uncertainty in prediction of the interaction forces due to not fully recognized scale effect and uncertainty connected with the measurements of the small forces were less than that for the smaller models. However, they could not be avoided. The results obtained for the bow thruster action, in deep water conditions, at
h/T ¼ 3, were close to the measurements published by Yoo et al. (2006) for the model in scale 1:30. However, at h/T ¼ 1.2, for the distances between the wall and model side less than one ship breadth, the significant difference appeared. In almost every case the measured forces were not constant and fluctuated due to the unsteady turbulent flow field pattern. Therefore the mean values, averaged over the time, were computed and used in the analysis. The practical benefits of the project are mainly connected with the modelling of hydrodynamic forces. The completed model of interaction forces, formulated on the basis of a sequence of the sub-models, is further investigated. The limitations of the model are the constraints of the experimental parameters. Acknowledgements The paper presents a part of results of the research project no. 4T12C01029 entitled ‘‘The influence of the berth type and water depth on efficiency of the steering and propulsion devices during the ship berthing and unberthing’’, sponsored by Polish Ministry of Science and Higher Education, currently conducted at Gdynia Maritime
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University, Poland. The open water model tests were carried out in collaboration with Ship Handling Research and Training Centre of the Foundation for Safety of Navigation and Environment Protection in Ilawa— Kamionka, Poland. References Abramowicz-Gerigk, T., 2006a. Identification, classification and hierarchization of parameters influencing interaction forces between quay and berthing vessel. Journal of KONBiN 1 (1). In: Proceedings of the 4th International Conference on Safety and Reliability, Krakow, Poland, 2006, pp. 97–104. Abramowicz-Gerigk, T., 2006b. Determination of safety factors for ship berthing operations. In: Proceedings of European Safety and Reliability Conference ESREL 2006, Estoril, Portugal. In: Guedes
Soares, C., Zio, E. (Eds.), Safety and Reliability for Managing Risk. Taylor & Francis, London, 2006, pp. 2737–2741. Nielsen, B., 2005. Bow thruster-induced damage. A physical model study on bow thruster-induced flow. /http://www.citg.tudelft.nl/live/ binaries/4de0d195-5207-4e67-84bb-455c5403ae47/doc/2005Nielsen. pdfS. Qadvlieg, F., Toxopeus, S., 1998. Prediction of crabbing in the early design stages. In: Oosterveld, M.W.C., Tan, S.G. (Eds.), Practical Design of Ships and Mobile Units. Elsevier, Amsterdam, pp. 649–654 /http://www.marin.nl/original/publications/Prads1998-Prediction OfCrabbingS. Shin, H., Lee, H., 2004. Crabbing test of 3 m ferry model. Journal of Naval Architects of Korea 41 (1). Yoo, W.-J., Yoo, B.Y., Rhee, K.P., 2006. An experimental study on the manoeuvring characteristics of a twin propeller/twin rudder ship during berthing and unberthing. Ships and Offshore Structures 1 (3), 191–198.
Ocean Engineering 35 (2008) 323–332 www.elsevier.com/locate/oceaneng
Experimental study on the hydrodynamic forces induced by a twin-propeller ferry during berthing Teresa Abramowicz-Gerigk Faculty of Navigation, Gdynia Maritime University, Al. Jana Pawla II 3, 81-345 Gdynia, Poland Received 25 May 2007; accepted 25 October 2007 Available online 1 November 2007
Abstract The paper presents the experimental study on the influence of wall effect on the hydrodynamic forces induced by the propellers and thrusters of a ferry during the berthing. The program of the model tests was developed for the twin-propeller, twin-rudder, man-manned model of a car–passenger ferry in 1:16 scale, equipped with two bow thrusters. The different combinations of the operational settings of bow thrusters and propellers operating in the push–pull mode allowed to observe and quantify the variation of the hydrodynamic forces due to the changes of the water depth to draft ratios and distances to the quay. The results of model tests are introduced and discussed in the paper. The difference between the measured total hydrodynamic force and superposition of the component forces induced by the propellers and thrusters has been investigated. According to the structure of the generally accepted modular manoeuvring model, the proposition of the weight factors for the component forces comprising the interaction effects has been introduced and discussed. r 2007 Elsevier Ltd. All rights reserved. Keywords: Twin propeller; Twin-rudder ferry; Berthing; Unberthing; Wall effect; Model tests; Modular manoeuvring model
1. Introduction The decreasing manoeuvring space and increasing traffic have a big impact on the risk of damage to vessels and port facilities. Because the main safety options: training of seamen, implementation of navigational aids and planning of harbour operations are based on the simulation of ship motion, the modelling of ship motions at slow speed in the constrained space is now essential to enhance safety. The investigations on the modelling of the berthing forces aim at the improvement of efficiency and increase of the vessels’ turn around speed in ports. Because of a complex turbulent flow generated around the ship, a general mathematical model that aims to describe the ship motions close to the quay wall is difficult to formulate with respect to both the methods based on CFD and model tests. Due to this fact there are few experimental results of self-berthing available (Shin and Lee, 2004; Qadvlieg and Toxopeus, 1998; Yoo et al., 2006). Tel.: +48 58 6901120.
E-mail address: [email protected] 0029-8018/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.oceaneng.2007.10.009
The modular manoeuvring models that allow for the superposition of the forces generated on the hull while accounting for extreme interactions always need a tuning usually based on the heuristic methods. However, the heuristic methods based on the opinions of experienced pilots and masters help to bring the simulation reasonably close to reality for the training purposes; the better accuracy is expected when the applications related to ship operation are considered. The open water model tests presented in the paper, carried out using the stationary model to investigate the forces generated by propulsion and steering devices, allowed to perform the quantitative analysis of the phenomena dependent on the fluid flow induced by the working propellers and thrusters. 2. Model tests The open water experiments were carried out using a large man-manned model of a car–passenger ferry in 1:16 scale. The specially designed experimental test setup shown in Fig. 1 was constructed on the shore of the Silm lake at the Ship Handling Research and Training Centre of the
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Fig. 1. Model of the car–passenger ferry and experimental test setup.
Foundation for Safety of Navigation and Environment Protection in Ilawa—Kamionka, Poland. The influence of several operational parameters on the variation of hydrodynamic forces was investigated. The program of model tests consisted of different settings of the propellers operating in push–pull mode in combination with the different rudder angles and settings of the bow thrusters, different depth to draft ratios and model distances to the quay wall. The main assumptions regarding the classification and hierarchization of the parameters influencing the interaction forces had followed from the engineering study based on the previously published results (AbramowiczGerigk, 2006a; Shin and Lee, 2004; Qadvlieg and Toxopeus, 1998).
Table 1 Main particulars of the car–passenger ferry model Length overall (m) Length between perpendicular (m) Breadth (m) Draft (m) Displacement (m) Block coefficient (–) Scale
10.98 9.64 1.78 0.42 4.89 0.687 1:16
x z
2.1. Model and experimental test setup The large man-manned model in 1:16 scale was adopted to the stationary tests to allow the measurements of the hydrodynamic forces generated on the hull only by the propellers, rudders and bow thrusters (AbramowiczGerigk, 2006b). The main particulars of the car–passenger ferry model are presented in Table 1. The model presented in Figs. 1 and 2 was equipped with two, four blades, controllable pitch propellers of the inward direction of revolution, two rudders and two bow tunnel thrusters. The quay model was a tight vertical wall. The water depth was adjusted by the movable horizontal flat plate. The dimensions of the experimental test setup were as follows: 12 m length, 5 m width and 1.25 m of the maximum adjustable water depth. The model was stationary in the horizontal plane and free to the pitch, heave and roll motions. The position of model, relative to the wall, was fixed using the bow and stern pantographs (Fig. 1). The setup of the propellers’ thrust, bow thrusters and rudder angles was done using the onboard controls. The RPM and pitch of the propellers for the settings of the on-board engine telegraphs were measured by the on-board meters. The rudder angles were measured by the on-board meters as well. The measuring system of the bow and stern transverse and longitudinal forces consisted of two (bow and stern) tensometer-type dynamometers AMTI (Advanced Mechanical Technology,
x
η y Quay Fig. 2. Coordinate system.
Inc.) MC3-100. The signals from the dynamometers were amplified using the AMTI amplifiers and sent to A/D converter in the computer. The data collection software (VBasic) had been developed for data collection and processing. The total sway force and yawing moment were calculated on the basis of the measurements. 2.2. Results of experiment The results of berthing and unberthing experiments are presented in the form of non-dimensional sway force and yawing moment plotted as the functions of non-dimensional distance b (1) between the hull centreline and the quay wall for the water depth to draft ratios h/T ¼ 1.2 and 3: b¼
Z , B
(1)
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where Z is the distance between the wall and model centreline and B is the model breadth. The non-dimensional sway force (2) and yawing moment (3) are made non-dimensional and based on the length between perpendiculars and draft (Yoo et al., 2006): Fy0 ¼
Fy , 0:5rgL2 T
Mz0 ¼
(2)
Mz , 0:5rgL3 T
(3)
where Fy is the measured sway force, r is the water density, g is the acceleration of gravity, L is the model length between perpendiculars and T is the model draft. The propellers were operated in the push–pull mode to generate the yawing moment opposite to the moment produced by the bow thrusters. The coupled rudders were put 351 to port for the berthing and 351 to starboard for the unberthing. The non-dimensional sway forces and yawing moments induced on the hull by the bow thrusters are presented in Figs. 3 and 4. The non-dimensional sway force and yawing moment induced by the propellers in the push–pull mode and coupled rudders put 351 to starboard or 351 to port for the unberthing and berthing, respectively, are presented in Figs. 5 and 6. The non-dimensional sway force and yawing moment due to the combined action of the bow thrusters, propellers and rudders are presented in Figs. 7 and 8 for
the berthing, and in Figs. 9 and 10 for the unberthing, respectively. The settings of the engine telegraph of port and starboard propeller correspond to the following values of the non-dimensional effective thrust in open water conditions: dead slow ahead: 6.57E5, slow ahead: 22.36E5, dead slow astern: 3.81E5 and slow astern: 13.67E5. The settings of the bow thruster controls correspond to the following values of the non-dimensional thrust in open water conditions: 100%: 11.26E5, 75%: 5.47E5 and 50%: 2.22E5. Thrust values are made non-dimensional in the same way as the sway force (2). 3. The influence of the wall effect on the forces induced by the propellers and rudders and on the forces induced by the bow thrusters The influence of the wall effect on the sway force and yawing moment is different in the berthing and unberthing cases. In both the berthing and unberthing cases at h/ T ¼ 1.2, the strong suction is induced by the starboard propeller. It results into an attraction between the stern and wall during the berthing and attraction along the whole length of the hull during the unberthing. For example, at b ¼ 0.75 the force measured at the bow was 12% of the total sway force in the berthing and 57% in the unberthing case, respectively. The sway force and yawing moment induced by the bow thrusters are strongly dependent on the
Berthing
Fy'x103
0.35 0.3
h/T=3.0 BT 50%
0.25
h/T=3.0 BT 75%
0.2
h/T=3.0 BT 100%
0.15
h/T=1.2 BT 50%
0.1
h/T=1.2 BT 75%
0.05
h/T=1.2 BT 100%
0 0.5
1
1.5
2
b Berthing
Mz'x103
0.16 0.14
h/T=3.0 BT 50%
0.12
h/T=3.0 BT 75%
0.1
h/T=3.0 BT 100%
0.08 h/T=1.2 BT 50%
0.06 0.04
h/T=1.2 BT 75%
0.02
h/T=1.2 BT 100%
0 0.5
1
1.5
325
2
b Fig. 3. The lateral force and yawing moment induced by the bow thrusters during the berthing.
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Unberthing 0 h/T=3.0 BT 50%
Fy'x103
-0.05
h/T=3.0 BT 75%
-0.1
h/T=3.0 BT 100% -0.15 h/T=1.2 BT 50% -0.2
h/T=1.2 BT 75%
-0.25
h/T=1.2 BT 100%
-0.3 0.5
1.5
1
2
b Unberthing
Mz'x103
0 -0.02
h/T=3.0 BT 50%
-0.04
h/T=3.0 BT 75%
-0.06
h/T=3.0 BT 100%
-0.08
h/T=1.2 BT 50%
-0.1
h/T=1.2 BT 75%
-0.12
h/T=1.2 BT 100%
-0.14 0.5
1.5
1
2
b Fig. 4. The lateral force and yawing moment induced by the bow thrusters during the unberthing.
Berthing 0.5
Fy'x103
0.4
h/T=3 DEAD SLOW
0.3
h/T=3 SLOW
0.2 h/T=1.2 DEAD SLOW 0.1 h/T=1.2 SLOW 0 -0.1 0.5
1
1.5
2
b Berthing 0.02
Mz'x103
0 -0.02
h/T=3 DEAD SLOW
-0.04
h/T=3 SLOW
-0.06
h/T=1.2 DEAD SLOW
-0.08
h/T=1.2 SLOW
-0.1 -0.12 -0.14 0.5
1
1.5
2
b Fig. 5. The lateral force and yawing moment induced by the propellers in the push–pull mode and coupled rudders put 351 to port during the berthing.
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Fy'x10
3
Unberthing 0.15 0.1 0.05 0 -0.05 -0.1
h/T=3 DEAD SLOW h/T=3 SLOW h/T=1.2 DEAD SLOW h/T=1.2 SLOW
-0.15 -0.2 0.5
1
1.5 b Unberthing
2
0.12 0.1
h/T=3 DEAD SLOW
0.08 Mz'x10
3
h/T=3 SLOW
0.06
h/T=1.2 DEAD SLOW
0.04
h/T=1.2 SLOW
0.02 0 0.5
1
1.5
2
b Fig. 6. The lateral force and yawing moment induced by the propellers in the push–pull mode and coupled rudders put 351 to starboard during unberthing.
distance between the wall and model side only during the unberthing due to the blockage of the outflow stream from the bow thrusters by the wall. 3.1. Berthing The sway force and yawing moment induced on the hull by the thrusters during the berthing, presented in Fig. 3, are not much influenced by the distance to the quay and water depth. The biggest decrease of the sway force, about 15%, is observed in the shallow water conditions at h/T ¼ 1.2, for the 100% settings of the bow thrusters, at the distance between the wall and model side less than a quarter of the model breadth. The changes of the moment have the same character and they do not exceed 10% of the maximum value at h/T ¼ 3. In the shallow water conditions the slipstream, of the starboard propeller acting ahead, generated a suction force at the aft part of the model. However, it was not observed for the dead slow settings of the propellers (Fig. 5). When the model was close to the wall, at bo0.8, the bow away moment in shallow water was significantly greater than the moment measured at h/T ¼ 3. The maximum difference, about 30% of the value at h/T ¼ 3, was observed at b ¼ 0.6. When the sway force was generated by the propellers and coupled rudders (starboard/port propellers engine telegraph settings slow ahead/slow astern, the coupled rudder angle 351 to starboard), the changes of the sway force and yawing moment both at h/T ¼ 1.2 and 3 were general in the same level of values, except for the change of berthing at h/T ¼ 1.2 and b less than 1.0 (Figs. 7 and 8). At h/T=1.2
the additional attraction force raised linearly with the decreasing distance to the wall. At b=1 it was about 10% greater than at b=2.1 and then at b less than 0.75 it was 100% greater then at b=2.1. This means that at b=1 the sway force at h/T=1.2 was 70% greater than the force generated at h/T=3. In the shallow water only, when the model was positioned close to the wall, at b=0.6, there was 10% decrease of the suction force in comparison to the value at b=0.75. 3.2. Unberthing The results of investigations carried out by Yoo et al. (2006) confirm that the thrust of the bow thrusters which are located near the centreline is not affected by either the water depth to draft ratio or the distance to the quay. However, the sway force and yawing moment induced on the hull by the bow thrusters during unberthing, presented in Fig. 4, were dependent on the distance of the model to the quay and the water depth to draft ratio especially when acting with the 100% thrust settings. In general, the negative (repulsion) sway force was decreasing with the decreasing distance to the wall. The outflow stream from the bow thrusters reflected from the quay area was pushed along the wall in both the stern and bow directions, what is clearly illustrated by the visualization experiment published by Nielsen (2005). At h/T ¼ 1.2 and b ¼ 0.75 the strong rise of the repulsion force was induced and then at b ¼ 0.6 the repulsion effect disappeared. In the unberthing condition—coupled rudder angle 351 to starboard, slow ahead/slow astern propeller settings— the suction force in the deep and shallow water conditions
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Be rth in g h /T=3 0.6 0.5
DEAD SLOW BT 50% s SLOW BT 50% s
Fy'x103
0.4
DEAD SLOW BT 100% s SLOW BT 100% s
0.3
DEAD SLOW BT 50% SLOW BT 50%
0.2
DEAD SLOW BT 100% SLOW BT 100%
0.1 0 0. 5
1
1. 5
b Berthing h/T=3 0.15
DEAD SLOW BT 50% s
0.1
Mz'x103
SLOW BT 50% s DEAD SLOW BT 100% s
0.05
SLOW BT 100% s DEAD SLOW BT 50% 0
SLOW BT 50% DEAD SLOW BT 100%
-0.05
SLOW BT 100%
-0.1 0.5
1
1.5
b Fig. 7. Lateral force and yawing moment induced by the bow thrusters, propellers in the push–pull mode and coupled rudders put 351 to port for the depth to draft ratio h/T ¼ 3. s denotes the superposition of the forces induced separately by the bow thrusters and propellers with rudders during the berthing.
increased when the interval between the model side and wall decreased. The decrease was observed only at b ¼ 0.6 for the slow settings and for dead slow at h/T ¼ 3 (Fig. 6). The repulsion—negative sway—force induced at b ¼ 2.1 was changing into the positive—attraction, when the distance between the wall and model side was less than a half of the model breadth. The maximum attraction force appeared in shallow water at b ¼ 0.75 and it had the same absolute value as the negative sway force at b ¼ 2.1. At h/T ¼ 3 the negative sway force was greater then the sway force induced at h/T ¼ 1.2 and suction effect at b ¼ 0.75 was smaller than that in shallow water. The increase of the suction force was less than 50% of the force at b ¼ 1.5, so there was no change in the sign from the repulsion to attraction. The significant rise of the stern away moment was observed at b ¼ 0.6. Due to this rise of the moment in
shallow water, at b ¼ 0.6 the moments for both the depth to draft ratios were almost equal. 4. Superposition of the forces induced by the propellers, rudders and bow thrusters In Figs. 7 and 8 the non-dimensional sway force and yawing moment due to the combined action of the bow thrusters, propellers and rudders are compared with the force and moment obtained by the superposition of the forces generated by the propellers with the rudders and bow thrusters separately for the berthing case. Figs. 9 and 10 illustrate the results of measurements and superposition for the unberthing case. In the shallow water conditions during the berthing at slow ahead/slow astern action of the propellers, the character of the sway force and yawing moment functions
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Berthing h/T=1.2 1 0.9 DEAD SLOW BT 50% s
0.8
SLOW BT 50% s
Fy'x103
0.7
DEAD SLOW BT 100% s
0.6
SLOW BT 100% s
0.5
DEAD SLOW BT 50%
0.4
SLOW BT 50%
0.3
DEAD SLOW BT 100%
0.2
SLOW BT 100%
0.1 0 0.5
1
1.5 b Berthing h/T=1.2
2
0.15 DEAD SLOW BT 50% s
0.1
SLOW BT 50% s Mz'x103
0.05
DEAD SLOW BT 100% s SLOW BT 100% s
0
DEAD SLOW BT 50% SLOW BT 50%
-0.05
DEAD SLOW BT 100% -0.1
SLOW BT 100%
-0.15 0.5
1
1.5
2
b
Fig. 8. Lateral force and yawing moment induced by the bow thrusters, propellers in the push–pull mode and coupled rudders put 351 to port for the depth to draft ratio h/T ¼ 1.2. s denotes the superposition of the forces generated separately by the bow thrusters and propellers with rudders during the berthing.
for the coupled action of the bow thrusters and propellers is similar to the force and moment induced by the propellers and rudders but the values are dependent on the settings of the bow thrusters. Up to the distance between the model side and wall over a half of the model breadth, for the full power of bow thrusters, the measured sway force was about 15% less than the resultant force obtained by the superposition of the component forces induced by the thrusters and propellers separately. This phenomena was due to the interaction of the thrust stream from the port propeller, acting astern, with the outflow stream from the bow thrusters. If that distance decreased, the attraction force increased. Between the values at b=1 and 0.75 the sharp rise of the attraction force, about 50% of the value at b=1, was observed. Then at b=0.6 the force dropped of about 10% of the maximum sway force at b=0.75. If the 50% settings of the bow thrusters were applied the measured force was closer to the superposition; however, if b was less than 1.5 the same effects appeared. The bigger differences between the measured sway force and superposition of the component forces induced by propellers and thrusters separately were observed in the
shallow water conditions during the unberthing for 100% of the bow thruster settings applied. This is illustrated in Fig. 10. The strong repulsion force was due to the overpressure induced by the blockage of the thrust stream from the starboard propeller acting astern by the bow thrusters outflow. For the slow ahead/slow astern and 50% of the bow thruster settings combination the stern away moment was induced. The bow away moments were induced only for the dead slow ahead/dead slow astern combined with 100% of the bow thruster settings and for the slow ahead/slow astern combined with 100% settings of bow thrusters. However, for the slow ahead propeller action combined with 100% settings of the bow thrusters the bow away moment was decreasing with the increasing distance and at b ¼ 2 was equal to zero. In combination with the bow thruster action the bow away yawing moment, which already occurred in shallow water and close to the wall at the zero propeller rate, at b less than 1 was amplified by the propeller action. The greater was the distance, the closer to the superposition of the component moments was the measured value.
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Unberthing h/T=3 0 DEAD SLOW BT 50%
Fy'x103
-0.1
SLOW BT 50% DEAD SLOW BT 100%
-0.2
SLOW BT 100% -0.3
superposition measurement
-0.4 -0.5 0.5
model
0.7
0.9
1.1
1.3
1.5
b Unberthing h/T=3
DEAD SLOW BT 50% 0.05
SLOW BT 50%
Mz'x103
DEAD SLOW BT 100% SLOW BT 100% -0.05
superposition measurement model
-0.15 0.5
0.7
0.9
1.1
1.3
1.5
b
Fig. 9. The lateral force and yawing moment induced by the bow thrusters, propellers in the push–pull mode and coupled rudders put 351 to starboard for the depth to draft ratio h/T ¼ 3.
The modular approach in mathematical modelling of the ship manoeuvring motions means that each force and moment acting on the ship can be expressed as the sum of a hull, propeller, rudder and thruster modules based on their effective hydrodynamic characteristics. In the case when the fluid flow around the ship is disturbed by the vicinity of another object, a module of the interaction forces is added. However, the model of the additional forces due to the interactions can be formulated on the basis of the model tests; in the case of self-berthing due to the complex fluid dynamics the sub-models must be introduced to obtain a reasonable estimation of the interaction forces. The constraints of the sub-models are dependent on the character of variation of the measured values in the particular ranges of influencing parameters. For example, in the shallow water conditions at h/T ¼ 1.2 the model must describe the phenomena not observed or neglected at h/T ¼ 3. In this case a global model combined with a sequence of partially overlapping sub-models which could be largely unrelated to each other and constrained gives substantially better results. The simple linear superposition of the component forces induced by the propellers and bow thrusters acting separately can be applied for h/T ¼ 3. To get a better agreement with the experimental results, the
weight factors ai and bi, i ¼ 1, 2, comprising the interaction effects were implemented in the models of the total sway force and yawing moment in Eqs. (4) and (5), respectively: Fy0 ¼ a1 Fy0PR þ a2 Fy0BT ,
(4)
Mz0 ¼ b1 Mz0PR þ b2 Mz0BT ,
(5)
where ai, bi are the weight factors, the subscript PR denotes the action of propellers in the push–pull mode with the coupled rudders and the subscript BT denotes the action of the bow thrusters. Fig. 9 illustrates the results of measurements of the total sway force and yawing moment, results of fitting a simple superposition and fitting the multiple linear regression model to describe the relationship between Fy0 , Mz0 and two independent variables Fy0PR , Fy0BT and Mz0PR , Mz0BT , respectively. The coefficients ai, bi and R2 statistics describing the fitting of the models for h/T ¼ 3 and 1.2 are presented in Table 2. 5. Concluding remarks The study is the basic research to obtain quantitatively the hydrodynamic forces induced during the self-berthing.
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Unberthing h/T=1.2 0.2 0
DEAD SLOW BT 50% s SLOW BT 50% s
Fy'x103
-0.2
DEAD SLOW BT 100% s SLOW BT 100% s
-0.4
DEAD SLOW BT 50% SLOW BT 50%
-0.6
DEAD SLOW BT 100% -0.8
SLOW BT 100%
-1 0.5
1.5
1
2
b Unberthing h/T=1.2 0.15 0.1
DEAD SLOW BT 50% s SLOW BT 50% s
Mz'x103
0.05
DEAD SLOW BT 100% s SLOW BT 100% s
0
DEAD SLOW BT 50% -0.05
SLOW BT 50% DEAD SLOW BT 100%
-0.1
SLOW BT 100%
-0.15 0.5
1.5
1
2
b Fig. 10. The lateral force and yawing moment induced by the bow thrusters, propellers in the push–pull mode and coupled rudders put 351 to starboard for the depth to draft ratio h/T ¼ 1.2.
Table 2 Coefficients of linear regression models of the sway force and yawing moment, R squared statistics: R2a for the sway force model and R2b for the yawing moment model h/T
a1
a2
b1
b2
R2a (%)
R2b (%)
1.2 3
0.121 0.700
2.882 1.238
0.776 0.839
1.277 1.023
97.83 98.83
78.24 97.54
The influence of water depth and distance between the berth and ship side on the forces generated on the hull due to the action of propulsion and steering devices has been studied. The main conclusions have been formulated with respect to the application of the interaction forces into the modular model of ship motion. The research was carried out using the large manmanned model in 1:16 scale. The uncertainty in prediction of the interaction forces due to not fully recognized scale effect and uncertainty connected with the measurements of the small forces were less than that for the smaller models. However, they could not be avoided. The results obtained for the bow thruster action, in deep water conditions, at
h/T ¼ 3, were close to the measurements published by Yoo et al. (2006) for the model in scale 1:30. However, at h/T ¼ 1.2, for the distances between the wall and model side less than one ship breadth, the significant difference appeared. In almost every case the measured forces were not constant and fluctuated due to the unsteady turbulent flow field pattern. Therefore the mean values, averaged over the time, were computed and used in the analysis. The practical benefits of the project are mainly connected with the modelling of hydrodynamic forces. The completed model of interaction forces, formulated on the basis of a sequence of the sub-models, is further investigated. The limitations of the model are the constraints of the experimental parameters. Acknowledgements The paper presents a part of results of the research project no. 4T12C01029 entitled ‘‘The influence of the berth type and water depth on efficiency of the steering and propulsion devices during the ship berthing and unberthing’’, sponsored by Polish Ministry of Science and Higher Education, currently conducted at Gdynia Maritime
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University, Poland. The open water model tests were carried out in collaboration with Ship Handling Research and Training Centre of the Foundation for Safety of Navigation and Environment Protection in Ilawa— Kamionka, Poland. References Abramowicz-Gerigk, T., 2006a. Identification, classification and hierarchization of parameters influencing interaction forces between quay and berthing vessel. Journal of KONBiN 1 (1). In: Proceedings of the 4th International Conference on Safety and Reliability, Krakow, Poland, 2006, pp. 97–104. Abramowicz-Gerigk, T., 2006b. Determination of safety factors for ship berthing operations. In: Proceedings of European Safety and Reliability Conference ESREL 2006, Estoril, Portugal. In: Guedes
Soares, C., Zio, E. (Eds.), Safety and Reliability for Managing Risk. Taylor & Francis, London, 2006, pp. 2737–2741. Nielsen, B., 2005. Bow thruster-induced damage. A physical model study on bow thruster-induced flow. /http://www.citg.tudelft.nl/live/ binaries/4de0d195-5207-4e67-84bb-455c5403ae47/doc/2005Nielsen. pdfS. Qadvlieg, F., Toxopeus, S., 1998. Prediction of crabbing in the early design stages. In: Oosterveld, M.W.C., Tan, S.G. (Eds.), Practical Design of Ships and Mobile Units. Elsevier, Amsterdam, pp. 649–654 /http://www.marin.nl/original/publications/Prads1998-Prediction OfCrabbingS. Shin, H., Lee, H., 2004. Crabbing test of 3 m ferry model. Journal of Naval Architects of Korea 41 (1). Yoo, W.-J., Yoo, B.Y., Rhee, K.P., 2006. An experimental study on the manoeuvring characteristics of a twin propeller/twin rudder ship during berthing and unberthing. Ships and Offshore Structures 1 (3), 191–198.