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Roll damping characteristics of a small fishing vessel with a central wing
Ocean Engineering 28 (2001) 1601–1619
Roll damping characteristics of a small fishing vessel with a central wing H.H. Chun
a,*
, S.H. Chun a, S.Y. Kim
b
a
b
Department of Naval Architecture and Ocean Engineering, Pusan National University, 30 Changjeon-dong, Keumjeong-ku, Pusan 609-735, South Korea Department of Control and Mechanical Engineering, Pukyung National University, Ham-kin, Keumjeong-ku, Pusan 609-737, South Korea Received 23 February 2000; accepted 19 March 2000
Abstract The roll damping characteristics of three models of a 3-ton class fishing vessel representing the bare hull, hull with bilge keels, and hull with bilge keels and a central wing are investigated by the free roll decay tests in calm water and also in uniform head waves in a towing tank. Speed and roll initial angle and OG (distance between the centers of gravity and roll) are varied to check their dependence on roll damping. The experimental results are compared with the numerical results of mathematical modeling by the energy method and the energy dissipation patterns are also compared for these three models. The bilge keel contributes significantly to the increment of the roll damping for zero speed but as speed increases, the lift generated by the central wing contributes significantly to the roll damping increase. In addition, it is shown that the roll damping is more or less influenced by the regular head waves. 2001 Elsevier Science Ltd. All rights reserved. Keywords: Roll damping; Fishing vessel; Bilge keel; Central wings; Energy method
1. Introduction Small fishing vessels of size less than 20 gross tons comprise the majority of offshore fishing vessels. The accidental loss of these small fishing vessels is due mainly to capsize which occurs mostly by an excessive roll motion or its coupling
* Corresponding author. E-mail address: [email protected] (H.H. Chun). 0029-8018/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 9 - 8 0 1 8 ( 0 0 ) 0 0 0 6 6 - 4
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with other mode of motion. In order to decrease the roll motion, various methods have been adapted, such as hull form improvement, the attachment of a bilge keel or stabilizing fin, and the installation of an anti-rolling tank, etc. Good descriptions of these can be seen in the literature, e.g. Lloyd (1978). In order to improve the roll motions of offshore fishing vessels, a retractable central wing-flap system was developed by Chun et al. (1999). This paper describes the numerical and experimental roll damping characteristics of a 3-ton class fishing vessel with a central wing-flap system. Numerous studies on the roll motion or roll damping of small fishing vessels have been carried out (see, for example, Tanaka et al. 1983, 1984; Bass and Haddara, 1989; Haddara and Bennett, 1989; Haddara and Bass, 1990). Tanaka et al. (1983) investigated the effect of hull form and appendage on the roll motion together with OG (distance between the centers of gravity and roll) and speed variations, showing the strong dependence of the roll damping moment on hull form, speed, initial angle and OG. They concluded that since the correlation between the model and full-scale data was in fairly good agreement, the scale effect on the roll damping was negligible. Bass and Haddara (1989) investigated the roll and roll–sway damping characteristics of three small fishing vessels by the free roll decay test at a towing tank, revealing a strong dependence of the roll damping on the initial angle and the OG which was also shown by Tanaka et al. (1983). Haddara and Bass (1990) studied the form of the roll damping moment for three small fishing models and derived four linear and nonlinear (angle and speed dependent) mathematical models for the damping moment by the energy method, showing good correlation with the experimental data depending on the cases. The roll damping characteristics of a 3-ton class fishing vessel with a central wingflap system attached are investigated experimentally and numerically in this paper. The roll damping moment coefficients for three models 1/4 scaled from the 3-ton class fishing vessel representing the bare hull (model 1), hull with bilge keels (model 2), and hull with bilge keels and central wing-flap (model 3) are measured by free roll decay tests in calm water and uniform head waves in the towing tank of Pusan National University. The speed, initial angle and OG are varied to check the dependence on the roll damping moments of these three models. Among the four mathematical forms for the roll damping moment suggested by Haddara and Bass (1990), two forms (the linear and quadratic speed-dependent form, and the linear and cubic speed-dependent form) are used to compare the numerical results with the experimental results. In addition, the roll motion energy level variations for these three models as a function of time are compared to understand their roll damping moment characteristics.
2. Mathematical models by the energy method The analysis of the roll decay curves can be made using the energy method. Haddara and Bass (1990) derived the four linear and nonlinear mathematical (angle and speed dependent) forms for the damping moment by the energy approach. Among
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them, two forms are used to compare the numerical predictions with the experimental results: linear and quadratic speed-dependent form, and linear and cubic speeddependent form. A brief outline of the analysis is introduced here but more details can be obtained from Haddara and Bass (1990). The equation of motion for a free roll model about a point O (the roll center) can be written as: f¨ ⫹B(f,f˙ )⫹D(f)⫽0 (1) where f is the roll angle, B(f,f) is the damping moment per unit of the virtual moment of inertia, and D(f) is the restoring moment per unit of the virtual moment of inertia. Dots over the variables mean the differentiation with respect to time. To separate the effects of roll and sway, B(f,f) can be written in the following form: (2) B(f,f˙ )⫽BG44⫹OG(BO42⫹BG24) where OG is the signed distance between the centers of roll and gravity (positive upwards). BG44 denotes the pure roll damping moment, and other two coupling damping moment coefficients BG24 and BO42 are due to the moments by roll and sway velocities, respectively, induced by the restrained roll about O. Multiplying Eq. (1) by f˙ and rearranging, the following is obtained: d [0.5f˙ 2⫹G(f)]⫽⫺B(f˙ ,f)f˙ dt
(3)
冕 f
where G(f)⫽ D(x) dx. 0
The energy V(t) and the energy difference h(t) can be defined as follows: V(t)⫽0.5f˙ 2⫹G(f) h(t)⫽V(t⫹dt)⫺V(t)
(4) (5)
Then, Eq. (3) becomes
冕
t⫹dt
h(t)⫽⫺
B(f˙ ,f)f˙ dt
(6)
t
The different forms for the damping moment for a rolling ship can be found in the open literature and the following two forms are used by Haddara and Bass (1990): (i) Linear plus quadratic speed-dependent form: B1(f˙ ,f)⫽2z1wf(1⫹e1兩f˙ 兩)f˙
(7)
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(ii) Linear plus cubic speed-dependent form: B2(f˙ ,f)⫽2z2wf(1⫹e2f˙ 2)f˙
(8)
where wf is the natural frequency, z1,z2 are the nondimensional linear damping coefficients, and e1,e2 are the measures of nonlinearity. Substituting any of the two forms into Eq. (6), the following is obtained: h(t)⫽zku1(t)⫹ekuk+1(t), k⫽1,2
(9)
where
冕
f˙ 2 dt
冕
兩f˙ 兩f˙ 2 dt
冕
f˙ 4 dt
t⫹dt
u1(t)⫽⫺2wf
t
t⫹dt
u2(t)⫽⫺2wf
t
t⫹dt
u3(t)⫽⫺2wf
t
From h(t) and uk(t) at each time t, a least-squares technique can be used to determine zk and ek. Eq. (9) explains that the loss of the ship’s energy is equal to the energy dissipated by the damping moment during a time interval dt. Eq. (9) is usually averaged over a half-cycle by the averaging technique. Therefore, it can be seen that the damping coefficient values obtained from Eq. (9) would reflect the actual energy dissipation mechanism.
3. Experiment The vessel used for the study is a typical small fishing boat which is largely used in Korean offshore fishing. The hull form with a hard chine and a large skeg is shown in Fig. 1 and its main dimensions are given in Table 1. In order to improve the roll motion of this offshore fishing vessel, a retractable central wing-flap system was developed by Chun et al. (1999), showing by model tests a large reduction in the roll motion in severe waves when the flap is active (more detailed results are presented in the reference). The model with the central wing-flap system which is retractable from the cabin is shown in Fig. 2. The chord of the wing is 1 m at the center and 0.8 m at the tip
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Fig. 1.
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Body plan of fishing vessel with bilge keel and central wing (model scale, units in meters).
Table 1 Principal dimensions of the fishing vessel (full scale) Disp. volume (m3) Length in Water Line (m) Beam (m) Draft (m) Longitudinal Centre of Buoyancy (m)
7.56 7.9 2.35 0.73 ⫺0.44624
with a span of 0.75 m. The wing section is NACA0015. In order to control the roll motion, the left and right flaps with 0.2 m chord in common are used. The wing is attached in parallel with the bottom of the skeg to minimize the lift generated by the wing with the zero flap angle at all speeds. The central wing is attached lengthwise at the point where the center of the lift generated at the design speed and LCG (⫺0.1 m from the midship) coincide with each other. Since the central wing system is retractable, the height of the wing can be varied, but is fixed at 0.38 m from the bottom of the bilge keel for the present study. In addition, the flap is fixed as zero angle of attack. The bilge keel starts from the stern and ends at station no. 8. The breadth and height of the bilge keel are 0.07 m and 0.06 m uniformly up to station 5 and then its height is tapered linearly up to station 8. The position of the bilge keel is below the chine and its outer edge is flush with the vertical side of the hull along the length. The 1/4 scaled model of this vessel was made of wood and the model tests were done at the towing tank of Pusan National University. The size of the towing tank is 86 m in length, 5 m in width and 3 m in water depth. The test conditions are
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Fig. 2.
Fishing vessel with a central wing.
shown in Table 2. The free roll decay records were measured for various parametric variations such as five different OGs, six different initial angles and six different forward speeds, resulting in a total of 37 test conditions in the still water. Although the roll motion is known to be independent of the uniform head waves, it would be interesting to see how the roll damping is affected by the head seas. Therefore, the Table 2 Test conditions for the fishing vessel Fn*
Test no.
OG/d
Initial angle (deg)
25
0.142
4, 8, 12, 16, 20 0
Speed in calm water
12
0.510 0.674 0.811 1.058 0.142
12
0, 0.1, 0.18, 0.2, 0.3, 0.4
Stationary in waves
20
1.058 0.142
12
0
Speed in waves 12
1.058 0.142 1.058 0.142
Stationary in calm water
2.42, 2.73, 3.14, 3.7, 4.5
4, 8, 12, 16, 20 0
3.14
12
3.14
0, 0.1, 0.18, 0.2, 0.3, 0.4
1.058 *
w (wave frequency rad/s)
Fn = U/√gL: U = model speed, g = gravity acceleration, L = LWL.
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free roll decay tests for the three models were conducted in regular head waves whose condition is shown in Table 2. A six-component motion measuring device is used free of heave and roll with the other all modes restrained. The OG is varied by changing the roll center (O) where the motion measuring device is attached.
4. Discussion 4.1. For zero speed The free roll decay records were measured for the three models with the bare hull (model 1), hull with the bilge keels (model 2), and hull with the bilge keels and the central wing-flap (model 3) by varying OG/d (where d is draft) and initial angle as shown in Table 2. These results were analyzed and some important results and pertinent discussions are included in this paper. Figs. 3–5 show the typical results of the three models showing the comparison between the experimental result for OG/d=0.142 and the predicted roll response by the two mathematical models discussed in Section 2. Among the three models, for the bare hull case which has less roll damping compared with other two models, the numerical results predicted by the linear plus nonlinear speed-dependent form for the roll damping moment agree well with the experimental results, as seen in Fig. 3. However, for the case of model 3 that has the largest damping among the three models, some discrepancy can be seen between the numerical and experimental results as seen in Fig. 5. Haddara and Bass (1990) reported that the angle-dependent form fit the experimental data better than the speed-dependent form for the heavily
Fig. 3.
Comparison between experiment and prediction by energy approach (bare hull, OG/d=0.142).
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Fig. 4. Comparison between experiment and prediction by energy approach (hull with bilge keel, OG/d=0.142).
Fig. 5. Comparison between experiment and prediction by energy approach (hull with bilge keel and wing, OG/d=0.142).
damped case and, therefore, it can be seen that an improvement can be made for the heavily damped case of the hull with the bilge keels and central wing-flap if the angle-dependent forms for the roll damping moment are used instead of the present speed-dependent forms. Nevertheless, it is worthwhile mentioning that the present
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Fig. 6.
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z vs. initial roll angle for various OG/d (bare hull).
mathematical modelings for the roll damping moment shown in this paper can fit quite reasonably to the experimental data for the present fishing vessel even for the hull attached by the bilge keels and the central wing-flap which has a large damping as will be seen later. Figs. 6–8 show the nondimensional linear roll damping coefficient (z) of the three models as a function of the initial angle for five OG/d variations. Where
Fig. 7. z vs. roll angle for various OG/d (hull with bilge keel).
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Fig. 8. z vs. roll angle for various OG/d (hull with bilge keel and wing).
z=B/(2wf), wf is the natural frequency of roll. As seen in the figure, z increases as the OG increases and z also increases with an increase in the initial angle. The reason for the increase in z due to the increase in OG is as follows: the increase in OG results in the extension of the moment arm lever and also the increase in the local velocity around the bilge and accordingly, the generation of the vortices and eddies is increased, resulting in the increment of the viscous damping. This was also observed and mentioned in Tanaka et al. (1983). The figures also show that the experimental points are well approximated by a linear regression for each case. These regression lines intersect the vertical axis (f=0) at certain values of z, which are indicative of the wave-damping component of the total damping for each roll center. It can be seen that the viscous damping becomes smaller as the OG decreases. This was also indicated in Bass and Haddara (1989). Another noticeable point of the figures of z against the roll angle is the increase in slope for higher roll centers. The slope of the regression line is a measure of the increase of viscous effect with both roll angle and roll center height. Fig. 9 shows z as a function of OG/d at an initial roll angle of 8° for the bare hull. The figure shows a regression curve which shows a strong nonlinearity on the roll center height. This regression line intersects the vertical axis (OG/d=0) at a certain value of z, which is the roll damping coefficient BG44 for OG=0. This value can be obtained at other initial roll angles and is plotted against roll angle in Fig. 10 for all the three models. From the figure, it can be clearly seen that the roll damping increases in order of the bare hull, the hull with the bilge keel, and the hull with the bilge keel and the central wing. Also, it can be seen that the roll damping coefficient is linearly proportional to the roll angle, as shown by other research such as Tanaka et al. (1983), Bass and Haddara (1989), Haddara and Bennett
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Fig. 9.
Fig. 10.
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z vs. OG/d (bare hull, f=8°).
Comparison of BG44 vs. initial angle for the three models.
(1989), and Haddara and Bass (1990). The energy level variation versus time, over the period of one cycle, for these three models is shown in Fig. 11 for OG/d=1.058 and initial angle of 8°. The presence of the bilge keel largely increases the energy dissipation compared with the bare hull case, but the further addition of the central wing does not change much in the energy dissipation. However, this pattern is
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Fig. 11. Energy level variation vs. time for the three models (f0=8°).
changed significantly for the forward speed case and also in waves, as will be discussed later. 4.2. For forward speed Fig. 12 shows the comparison between the experimental data and the predicted roll responses by the two mathematical modelings discussed in Section 2, for the
Fig. 12. Comparison between experiment and prediction by the energy approach at Fn=0.2 (hull with bilge keel and wing, OG/d=1.0).
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model 3 at OG/d=1.058 and Fn=0.2. Since the damping may increase due to the speed effect, some discrepancy can be seen compared with the cases for the zero speed. For this kind of heavily damped case, the angle-dependent forms for the roll damping moment would be promising as mentioned earlier. Fig. 13 shows z against speed for the bare hull at two OG/d and the initial angle of 8°. In general, as speed increases, the lift generated contributes to the damping increment. However, it was reported by Tanaka et al. (1983) that the result could be different depending on the hull form and the roll center height. As seen in Fig. 13, z increases considerably with the increase of speed for OG/d=1.058, but is almost constant (slightly increasing) for OG/d=0.142. z against speed for the three models at OG/d=1.058 and the initial angle of 8° is shown in Fig. 14. z increases considerably with the increase in speed for all the cases and the slope increases in the order model 1, model 2 and model 3. It can be understood that the significant increase in the damping for the hull with the central wing is due to the lift force generated by the wing at higher speeds. The change in the energy level with time is shown in Fig. 15 for the three models at OG/d=1.058, the initial angle of 8° and Fn=0.2. Comparing with the result for the zero speed seen in Fig. 11, it can be seen that the drop in energy level during the first quarter cycle for the bare hull is very sharp and the presence of the bilge keel does not contribute much to the energy drop compared with the bare hull case. However, the presence of the central wing at forward speed contributes significantly to the energy drop compared with the zero speed case. Therefore, it is worthwhile mentioning that the central wing attached to the hull can reduce the roll motion at higher speeds.
Fig. 13.
z vs. speed at two values of OG/d (bare hull, f0=8°).
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Fig. 14. Comparison of z for the three models vs. speed (f0=8°).
Fig. 15. Energy level variation vs. time for the three models (f0=8°, Fn=0.2).
4.3. For uniform head waves Although the roll motion is known to be independent of the uniform head waves, it would be interesting to see how the roll damping is affected by the head seas. Therefore, the free roll decay tests for the three models were conducted in regular head waves whose condition is seen in Table 2. The maximum heave and pitch
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motions of the model at the maximum design speed of 10 knots would occur at the wave period of around 2 s and, therefore, the wave periods tested are 1.4, 1.7, 2.0, 2.3, and 2.6 s which are equivalent to the wave frequencies of 4.5, 3.7, 3.14, 2.73 and 2.42 rad/s, respectively. Fig. 16 shows z against the nondimensional wave frequency for the bare hull with two OG/d at the initial angle of 8° and zero speed. The zero value on the x-axis indicates still water with no waves. As in the cases of calm water in the previous sections, the damping is increased at the larger OG/d value. It can be seen from the figure that the waves affect the roll damping moment which is increased compared with the still water. It can be also seen that the damping increases (almost linearly) as the wave frequency increases (in other words, the wave length decreases) within the test range. Fig. 17 shows z against the nondimensional wave frequency for the three models with OG/d=1.058 at the initial angle of 8° and zero speed. The damping increases as the wave frequency increases within the test range for the three models. The energy level variation versus time, over the period of one cycle, for the three models is shown in Fig. 18 for OG/d=1.058, initial angle of 8° and wave frequency of 3.14 rad/s. As compared with the case in the still water shown in Fig. 11, the drop in energy level during the first quarter cycle for the bare hull is very sharp in the presence of the waves whereas the drop is gradual in the still water. Furthermore, it is noticeable that the energy drop of model 2 with the bilge keels in the waves becomes much less compared with the case in the still water. The presence of the waves (even head regular waves) would cause the changes of the local velocities around the hulls, resulting in different formations of the vortices and eddies. Therefore, it can be seen that the roll damping is more or less influenced by the head waves. Figs. 19–21 show the comparison of z in calm water and wave (frequency of 3.14) as a function of speed for the three models. The initial roll angle is 8° for all
Fig. 16. z vs. nondimensional wave frequency (bare hull, f0=8°, Fn=0.0).
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Fig. 17.
Fig. 18.
z vs. nondimensional wave frequency for the three models (f0=8°, Fn=0.0).
Energy variation vs. time for the three models (f0=8°, Fn=0.0, w=3.14 rad/s).
the cases. For the bare hull case seen in Fig. 19, the wave effect on the roll damping increases with the speed. This change was just observed from the energy dissipation pattern changes in comparing Figs. 18 and 11. However, it can be seen to be of little difference for models 2 and 3, as seen in Figs. 20 and 21. This suggests that the heavily damped cases of models 2 and 3 due to the presence of the bilge keels and the central wing would not be affected by the waves.
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Fig. 19. z vs. speed for bare hull with and without waves (f0=8°).
Fig. 20. z vs. speed for hull with bilge keel with and without waves (f0=8°).
5. Conclusions Based on the present study, some conclusions can be drawn as follows: 앫 The speed-dependent forms for the roll damping moment can fit quite reasonably with the experimental data for the present models. However, it can be seen that
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Fig. 21.
앫 앫
앫
앫
H.H. Chun et al. / Ocean Engineering 28 (2001) 1601–1619
z vs. speed for hull with bilge keel with central wing with and without waves (f0=8°).
an improvement in the angle-dependent forms for the roll damping moment can be made for the heavily damped case of the hull with the bilge keels and the central wing, as suggested by Haddara and Bass (1990). The damping increases as the OG increases and also increases with the increase in the initial angle by the increased viscous damping due to the much-generated vortices and eddies. At zero speed, the presence of the bilge keel increases the energy dissipation compared with the bare hull case, but the further addition of the central wing does not cause much change in the energy dissipation. However, this pattern is changed significantly for the forward speed case and also in waves. At speed, the drop in energy level during the first quarter cycle for the bare hull is very sharp and the presence of the bilge keel does not contribute much to the energy drop compared with the bare hull case. However, the presence of the central wing at forward speed contributes significantly to the energy drop compared with the zero speed case. Therefore, the main contribution of the damping moment at forward speed can be seen as the lift force generated by hull or wing if any. The damping of model 3 with the central wing significantly increases as speed increases. The pattern of the energy dissipation in the roll decay motion in calm water is changed significantly by the presence of the waves for the lightly damped model 1, resulting in the increase of the roll damping. The shorter the wave length, the larger the damping. However, the heavily damped models are not influenced by the head waves.
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References Bass, D.W., Haddara, M.R., 1989. Roll damping for small fishing vessels. In: Proceedings of the 22nd American Towing Tank Conference. St John’s, Canada, pp. 443–449. Chun, S.H., Chun, H.H., Kim, C.H., Kim, S.Y., 1999. Development of a stability system to prevent the capsize of a small fishing vessel. J. Ocean Eng. Technol. 13 (1), 130–137(in Korean). Haddara, M.R., Bennett, P., 1989. A study of the angle dependence of roll damping moment. Ocean Eng. 16 (4), 411–427. Haddara, M.R., Bass, D.W., 1990. On the form of roll damping moment for small fishing vessels. Ocean Eng. 17 (6), 525–539. Lloyd, J.M., 1978. Seakeeping: ship behaviour in rough weather. Ellis Horwood Limited, Chichesterpp. 343-397. Tanaka, N., Ikeda, Y., Okada, H., 1983. Study on roll characteristics of small fishing vessel. Part 1. Measurement of roll damping. J. Kansai Soc. Nav. Arch. 187, 15–23 (in Japanese). Tanaka, N., Ikeda, Y., Okada, H., 1984. Study on roll characteristics of small fishing vessel. Part 2. An approximate method of solution for nonlinear lateral equations. J. Kansai Soc. Nav. Arch. 189, 43– 51 (in Japanese). Tanaka, N., Ikeda, Y., Okada, H., 1985. Study on roll characteristics of small fishing vessel. Part 3. Effects of over-hung deck. J. Kansai Soc. Nav. Arch. 194, 43–52 (in Japanese).
Roll damping characteristics of a small fishing vessel with a central wing H.H. Chun
a,*
, S.H. Chun a, S.Y. Kim
b
a
b
Department of Naval Architecture and Ocean Engineering, Pusan National University, 30 Changjeon-dong, Keumjeong-ku, Pusan 609-735, South Korea Department of Control and Mechanical Engineering, Pukyung National University, Ham-kin, Keumjeong-ku, Pusan 609-737, South Korea Received 23 February 2000; accepted 19 March 2000
Abstract The roll damping characteristics of three models of a 3-ton class fishing vessel representing the bare hull, hull with bilge keels, and hull with bilge keels and a central wing are investigated by the free roll decay tests in calm water and also in uniform head waves in a towing tank. Speed and roll initial angle and OG (distance between the centers of gravity and roll) are varied to check their dependence on roll damping. The experimental results are compared with the numerical results of mathematical modeling by the energy method and the energy dissipation patterns are also compared for these three models. The bilge keel contributes significantly to the increment of the roll damping for zero speed but as speed increases, the lift generated by the central wing contributes significantly to the roll damping increase. In addition, it is shown that the roll damping is more or less influenced by the regular head waves. 2001 Elsevier Science Ltd. All rights reserved. Keywords: Roll damping; Fishing vessel; Bilge keel; Central wings; Energy method
1. Introduction Small fishing vessels of size less than 20 gross tons comprise the majority of offshore fishing vessels. The accidental loss of these small fishing vessels is due mainly to capsize which occurs mostly by an excessive roll motion or its coupling
* Corresponding author. E-mail address: [email protected] (H.H. Chun). 0029-8018/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 9 - 8 0 1 8 ( 0 0 ) 0 0 0 6 6 - 4
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with other mode of motion. In order to decrease the roll motion, various methods have been adapted, such as hull form improvement, the attachment of a bilge keel or stabilizing fin, and the installation of an anti-rolling tank, etc. Good descriptions of these can be seen in the literature, e.g. Lloyd (1978). In order to improve the roll motions of offshore fishing vessels, a retractable central wing-flap system was developed by Chun et al. (1999). This paper describes the numerical and experimental roll damping characteristics of a 3-ton class fishing vessel with a central wing-flap system. Numerous studies on the roll motion or roll damping of small fishing vessels have been carried out (see, for example, Tanaka et al. 1983, 1984; Bass and Haddara, 1989; Haddara and Bennett, 1989; Haddara and Bass, 1990). Tanaka et al. (1983) investigated the effect of hull form and appendage on the roll motion together with OG (distance between the centers of gravity and roll) and speed variations, showing the strong dependence of the roll damping moment on hull form, speed, initial angle and OG. They concluded that since the correlation between the model and full-scale data was in fairly good agreement, the scale effect on the roll damping was negligible. Bass and Haddara (1989) investigated the roll and roll–sway damping characteristics of three small fishing vessels by the free roll decay test at a towing tank, revealing a strong dependence of the roll damping on the initial angle and the OG which was also shown by Tanaka et al. (1983). Haddara and Bass (1990) studied the form of the roll damping moment for three small fishing models and derived four linear and nonlinear (angle and speed dependent) mathematical models for the damping moment by the energy method, showing good correlation with the experimental data depending on the cases. The roll damping characteristics of a 3-ton class fishing vessel with a central wingflap system attached are investigated experimentally and numerically in this paper. The roll damping moment coefficients for three models 1/4 scaled from the 3-ton class fishing vessel representing the bare hull (model 1), hull with bilge keels (model 2), and hull with bilge keels and central wing-flap (model 3) are measured by free roll decay tests in calm water and uniform head waves in the towing tank of Pusan National University. The speed, initial angle and OG are varied to check the dependence on the roll damping moments of these three models. Among the four mathematical forms for the roll damping moment suggested by Haddara and Bass (1990), two forms (the linear and quadratic speed-dependent form, and the linear and cubic speed-dependent form) are used to compare the numerical results with the experimental results. In addition, the roll motion energy level variations for these three models as a function of time are compared to understand their roll damping moment characteristics.
2. Mathematical models by the energy method The analysis of the roll decay curves can be made using the energy method. Haddara and Bass (1990) derived the four linear and nonlinear mathematical (angle and speed dependent) forms for the damping moment by the energy approach. Among
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them, two forms are used to compare the numerical predictions with the experimental results: linear and quadratic speed-dependent form, and linear and cubic speeddependent form. A brief outline of the analysis is introduced here but more details can be obtained from Haddara and Bass (1990). The equation of motion for a free roll model about a point O (the roll center) can be written as: f¨ ⫹B(f,f˙ )⫹D(f)⫽0 (1) where f is the roll angle, B(f,f) is the damping moment per unit of the virtual moment of inertia, and D(f) is the restoring moment per unit of the virtual moment of inertia. Dots over the variables mean the differentiation with respect to time. To separate the effects of roll and sway, B(f,f) can be written in the following form: (2) B(f,f˙ )⫽BG44⫹OG(BO42⫹BG24) where OG is the signed distance between the centers of roll and gravity (positive upwards). BG44 denotes the pure roll damping moment, and other two coupling damping moment coefficients BG24 and BO42 are due to the moments by roll and sway velocities, respectively, induced by the restrained roll about O. Multiplying Eq. (1) by f˙ and rearranging, the following is obtained: d [0.5f˙ 2⫹G(f)]⫽⫺B(f˙ ,f)f˙ dt
(3)
冕 f
where G(f)⫽ D(x) dx. 0
The energy V(t) and the energy difference h(t) can be defined as follows: V(t)⫽0.5f˙ 2⫹G(f) h(t)⫽V(t⫹dt)⫺V(t)
(4) (5)
Then, Eq. (3) becomes
冕
t⫹dt
h(t)⫽⫺
B(f˙ ,f)f˙ dt
(6)
t
The different forms for the damping moment for a rolling ship can be found in the open literature and the following two forms are used by Haddara and Bass (1990): (i) Linear plus quadratic speed-dependent form: B1(f˙ ,f)⫽2z1wf(1⫹e1兩f˙ 兩)f˙
(7)
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(ii) Linear plus cubic speed-dependent form: B2(f˙ ,f)⫽2z2wf(1⫹e2f˙ 2)f˙
(8)
where wf is the natural frequency, z1,z2 are the nondimensional linear damping coefficients, and e1,e2 are the measures of nonlinearity. Substituting any of the two forms into Eq. (6), the following is obtained: h(t)⫽zku1(t)⫹ekuk+1(t), k⫽1,2
(9)
where
冕
f˙ 2 dt
冕
兩f˙ 兩f˙ 2 dt
冕
f˙ 4 dt
t⫹dt
u1(t)⫽⫺2wf
t
t⫹dt
u2(t)⫽⫺2wf
t
t⫹dt
u3(t)⫽⫺2wf
t
From h(t) and uk(t) at each time t, a least-squares technique can be used to determine zk and ek. Eq. (9) explains that the loss of the ship’s energy is equal to the energy dissipated by the damping moment during a time interval dt. Eq. (9) is usually averaged over a half-cycle by the averaging technique. Therefore, it can be seen that the damping coefficient values obtained from Eq. (9) would reflect the actual energy dissipation mechanism.
3. Experiment The vessel used for the study is a typical small fishing boat which is largely used in Korean offshore fishing. The hull form with a hard chine and a large skeg is shown in Fig. 1 and its main dimensions are given in Table 1. In order to improve the roll motion of this offshore fishing vessel, a retractable central wing-flap system was developed by Chun et al. (1999), showing by model tests a large reduction in the roll motion in severe waves when the flap is active (more detailed results are presented in the reference). The model with the central wing-flap system which is retractable from the cabin is shown in Fig. 2. The chord of the wing is 1 m at the center and 0.8 m at the tip
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Fig. 1.
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Body plan of fishing vessel with bilge keel and central wing (model scale, units in meters).
Table 1 Principal dimensions of the fishing vessel (full scale) Disp. volume (m3) Length in Water Line (m) Beam (m) Draft (m) Longitudinal Centre of Buoyancy (m)
7.56 7.9 2.35 0.73 ⫺0.44624
with a span of 0.75 m. The wing section is NACA0015. In order to control the roll motion, the left and right flaps with 0.2 m chord in common are used. The wing is attached in parallel with the bottom of the skeg to minimize the lift generated by the wing with the zero flap angle at all speeds. The central wing is attached lengthwise at the point where the center of the lift generated at the design speed and LCG (⫺0.1 m from the midship) coincide with each other. Since the central wing system is retractable, the height of the wing can be varied, but is fixed at 0.38 m from the bottom of the bilge keel for the present study. In addition, the flap is fixed as zero angle of attack. The bilge keel starts from the stern and ends at station no. 8. The breadth and height of the bilge keel are 0.07 m and 0.06 m uniformly up to station 5 and then its height is tapered linearly up to station 8. The position of the bilge keel is below the chine and its outer edge is flush with the vertical side of the hull along the length. The 1/4 scaled model of this vessel was made of wood and the model tests were done at the towing tank of Pusan National University. The size of the towing tank is 86 m in length, 5 m in width and 3 m in water depth. The test conditions are
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Fig. 2.
Fishing vessel with a central wing.
shown in Table 2. The free roll decay records were measured for various parametric variations such as five different OGs, six different initial angles and six different forward speeds, resulting in a total of 37 test conditions in the still water. Although the roll motion is known to be independent of the uniform head waves, it would be interesting to see how the roll damping is affected by the head seas. Therefore, the Table 2 Test conditions for the fishing vessel Fn*
Test no.
OG/d
Initial angle (deg)
25
0.142
4, 8, 12, 16, 20 0
Speed in calm water
12
0.510 0.674 0.811 1.058 0.142
12
0, 0.1, 0.18, 0.2, 0.3, 0.4
Stationary in waves
20
1.058 0.142
12
0
Speed in waves 12
1.058 0.142 1.058 0.142
Stationary in calm water
2.42, 2.73, 3.14, 3.7, 4.5
4, 8, 12, 16, 20 0
3.14
12
3.14
0, 0.1, 0.18, 0.2, 0.3, 0.4
1.058 *
w (wave frequency rad/s)
Fn = U/√gL: U = model speed, g = gravity acceleration, L = LWL.
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free roll decay tests for the three models were conducted in regular head waves whose condition is shown in Table 2. A six-component motion measuring device is used free of heave and roll with the other all modes restrained. The OG is varied by changing the roll center (O) where the motion measuring device is attached.
4. Discussion 4.1. For zero speed The free roll decay records were measured for the three models with the bare hull (model 1), hull with the bilge keels (model 2), and hull with the bilge keels and the central wing-flap (model 3) by varying OG/d (where d is draft) and initial angle as shown in Table 2. These results were analyzed and some important results and pertinent discussions are included in this paper. Figs. 3–5 show the typical results of the three models showing the comparison between the experimental result for OG/d=0.142 and the predicted roll response by the two mathematical models discussed in Section 2. Among the three models, for the bare hull case which has less roll damping compared with other two models, the numerical results predicted by the linear plus nonlinear speed-dependent form for the roll damping moment agree well with the experimental results, as seen in Fig. 3. However, for the case of model 3 that has the largest damping among the three models, some discrepancy can be seen between the numerical and experimental results as seen in Fig. 5. Haddara and Bass (1990) reported that the angle-dependent form fit the experimental data better than the speed-dependent form for the heavily
Fig. 3.
Comparison between experiment and prediction by energy approach (bare hull, OG/d=0.142).
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Fig. 4. Comparison between experiment and prediction by energy approach (hull with bilge keel, OG/d=0.142).
Fig. 5. Comparison between experiment and prediction by energy approach (hull with bilge keel and wing, OG/d=0.142).
damped case and, therefore, it can be seen that an improvement can be made for the heavily damped case of the hull with the bilge keels and central wing-flap if the angle-dependent forms for the roll damping moment are used instead of the present speed-dependent forms. Nevertheless, it is worthwhile mentioning that the present
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Fig. 6.
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z vs. initial roll angle for various OG/d (bare hull).
mathematical modelings for the roll damping moment shown in this paper can fit quite reasonably to the experimental data for the present fishing vessel even for the hull attached by the bilge keels and the central wing-flap which has a large damping as will be seen later. Figs. 6–8 show the nondimensional linear roll damping coefficient (z) of the three models as a function of the initial angle for five OG/d variations. Where
Fig. 7. z vs. roll angle for various OG/d (hull with bilge keel).
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Fig. 8. z vs. roll angle for various OG/d (hull with bilge keel and wing).
z=B/(2wf), wf is the natural frequency of roll. As seen in the figure, z increases as the OG increases and z also increases with an increase in the initial angle. The reason for the increase in z due to the increase in OG is as follows: the increase in OG results in the extension of the moment arm lever and also the increase in the local velocity around the bilge and accordingly, the generation of the vortices and eddies is increased, resulting in the increment of the viscous damping. This was also observed and mentioned in Tanaka et al. (1983). The figures also show that the experimental points are well approximated by a linear regression for each case. These regression lines intersect the vertical axis (f=0) at certain values of z, which are indicative of the wave-damping component of the total damping for each roll center. It can be seen that the viscous damping becomes smaller as the OG decreases. This was also indicated in Bass and Haddara (1989). Another noticeable point of the figures of z against the roll angle is the increase in slope for higher roll centers. The slope of the regression line is a measure of the increase of viscous effect with both roll angle and roll center height. Fig. 9 shows z as a function of OG/d at an initial roll angle of 8° for the bare hull. The figure shows a regression curve which shows a strong nonlinearity on the roll center height. This regression line intersects the vertical axis (OG/d=0) at a certain value of z, which is the roll damping coefficient BG44 for OG=0. This value can be obtained at other initial roll angles and is plotted against roll angle in Fig. 10 for all the three models. From the figure, it can be clearly seen that the roll damping increases in order of the bare hull, the hull with the bilge keel, and the hull with the bilge keel and the central wing. Also, it can be seen that the roll damping coefficient is linearly proportional to the roll angle, as shown by other research such as Tanaka et al. (1983), Bass and Haddara (1989), Haddara and Bennett
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Fig. 9.
Fig. 10.
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z vs. OG/d (bare hull, f=8°).
Comparison of BG44 vs. initial angle for the three models.
(1989), and Haddara and Bass (1990). The energy level variation versus time, over the period of one cycle, for these three models is shown in Fig. 11 for OG/d=1.058 and initial angle of 8°. The presence of the bilge keel largely increases the energy dissipation compared with the bare hull case, but the further addition of the central wing does not change much in the energy dissipation. However, this pattern is
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Fig. 11. Energy level variation vs. time for the three models (f0=8°).
changed significantly for the forward speed case and also in waves, as will be discussed later. 4.2. For forward speed Fig. 12 shows the comparison between the experimental data and the predicted roll responses by the two mathematical modelings discussed in Section 2, for the
Fig. 12. Comparison between experiment and prediction by the energy approach at Fn=0.2 (hull with bilge keel and wing, OG/d=1.0).
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model 3 at OG/d=1.058 and Fn=0.2. Since the damping may increase due to the speed effect, some discrepancy can be seen compared with the cases for the zero speed. For this kind of heavily damped case, the angle-dependent forms for the roll damping moment would be promising as mentioned earlier. Fig. 13 shows z against speed for the bare hull at two OG/d and the initial angle of 8°. In general, as speed increases, the lift generated contributes to the damping increment. However, it was reported by Tanaka et al. (1983) that the result could be different depending on the hull form and the roll center height. As seen in Fig. 13, z increases considerably with the increase of speed for OG/d=1.058, but is almost constant (slightly increasing) for OG/d=0.142. z against speed for the three models at OG/d=1.058 and the initial angle of 8° is shown in Fig. 14. z increases considerably with the increase in speed for all the cases and the slope increases in the order model 1, model 2 and model 3. It can be understood that the significant increase in the damping for the hull with the central wing is due to the lift force generated by the wing at higher speeds. The change in the energy level with time is shown in Fig. 15 for the three models at OG/d=1.058, the initial angle of 8° and Fn=0.2. Comparing with the result for the zero speed seen in Fig. 11, it can be seen that the drop in energy level during the first quarter cycle for the bare hull is very sharp and the presence of the bilge keel does not contribute much to the energy drop compared with the bare hull case. However, the presence of the central wing at forward speed contributes significantly to the energy drop compared with the zero speed case. Therefore, it is worthwhile mentioning that the central wing attached to the hull can reduce the roll motion at higher speeds.
Fig. 13.
z vs. speed at two values of OG/d (bare hull, f0=8°).
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Fig. 14. Comparison of z for the three models vs. speed (f0=8°).
Fig. 15. Energy level variation vs. time for the three models (f0=8°, Fn=0.2).
4.3. For uniform head waves Although the roll motion is known to be independent of the uniform head waves, it would be interesting to see how the roll damping is affected by the head seas. Therefore, the free roll decay tests for the three models were conducted in regular head waves whose condition is seen in Table 2. The maximum heave and pitch
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motions of the model at the maximum design speed of 10 knots would occur at the wave period of around 2 s and, therefore, the wave periods tested are 1.4, 1.7, 2.0, 2.3, and 2.6 s which are equivalent to the wave frequencies of 4.5, 3.7, 3.14, 2.73 and 2.42 rad/s, respectively. Fig. 16 shows z against the nondimensional wave frequency for the bare hull with two OG/d at the initial angle of 8° and zero speed. The zero value on the x-axis indicates still water with no waves. As in the cases of calm water in the previous sections, the damping is increased at the larger OG/d value. It can be seen from the figure that the waves affect the roll damping moment which is increased compared with the still water. It can be also seen that the damping increases (almost linearly) as the wave frequency increases (in other words, the wave length decreases) within the test range. Fig. 17 shows z against the nondimensional wave frequency for the three models with OG/d=1.058 at the initial angle of 8° and zero speed. The damping increases as the wave frequency increases within the test range for the three models. The energy level variation versus time, over the period of one cycle, for the three models is shown in Fig. 18 for OG/d=1.058, initial angle of 8° and wave frequency of 3.14 rad/s. As compared with the case in the still water shown in Fig. 11, the drop in energy level during the first quarter cycle for the bare hull is very sharp in the presence of the waves whereas the drop is gradual in the still water. Furthermore, it is noticeable that the energy drop of model 2 with the bilge keels in the waves becomes much less compared with the case in the still water. The presence of the waves (even head regular waves) would cause the changes of the local velocities around the hulls, resulting in different formations of the vortices and eddies. Therefore, it can be seen that the roll damping is more or less influenced by the head waves. Figs. 19–21 show the comparison of z in calm water and wave (frequency of 3.14) as a function of speed for the three models. The initial roll angle is 8° for all
Fig. 16. z vs. nondimensional wave frequency (bare hull, f0=8°, Fn=0.0).
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Fig. 17.
Fig. 18.
z vs. nondimensional wave frequency for the three models (f0=8°, Fn=0.0).
Energy variation vs. time for the three models (f0=8°, Fn=0.0, w=3.14 rad/s).
the cases. For the bare hull case seen in Fig. 19, the wave effect on the roll damping increases with the speed. This change was just observed from the energy dissipation pattern changes in comparing Figs. 18 and 11. However, it can be seen to be of little difference for models 2 and 3, as seen in Figs. 20 and 21. This suggests that the heavily damped cases of models 2 and 3 due to the presence of the bilge keels and the central wing would not be affected by the waves.
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Fig. 19. z vs. speed for bare hull with and without waves (f0=8°).
Fig. 20. z vs. speed for hull with bilge keel with and without waves (f0=8°).
5. Conclusions Based on the present study, some conclusions can be drawn as follows: 앫 The speed-dependent forms for the roll damping moment can fit quite reasonably with the experimental data for the present models. However, it can be seen that
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Fig. 21.
앫 앫
앫
앫
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z vs. speed for hull with bilge keel with central wing with and without waves (f0=8°).
an improvement in the angle-dependent forms for the roll damping moment can be made for the heavily damped case of the hull with the bilge keels and the central wing, as suggested by Haddara and Bass (1990). The damping increases as the OG increases and also increases with the increase in the initial angle by the increased viscous damping due to the much-generated vortices and eddies. At zero speed, the presence of the bilge keel increases the energy dissipation compared with the bare hull case, but the further addition of the central wing does not cause much change in the energy dissipation. However, this pattern is changed significantly for the forward speed case and also in waves. At speed, the drop in energy level during the first quarter cycle for the bare hull is very sharp and the presence of the bilge keel does not contribute much to the energy drop compared with the bare hull case. However, the presence of the central wing at forward speed contributes significantly to the energy drop compared with the zero speed case. Therefore, the main contribution of the damping moment at forward speed can be seen as the lift force generated by hull or wing if any. The damping of model 3 with the central wing significantly increases as speed increases. The pattern of the energy dissipation in the roll decay motion in calm water is changed significantly by the presence of the waves for the lightly damped model 1, resulting in the increase of the roll damping. The shorter the wave length, the larger the damping. However, the heavily damped models are not influenced by the head waves.
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References Bass, D.W., Haddara, M.R., 1989. Roll damping for small fishing vessels. In: Proceedings of the 22nd American Towing Tank Conference. St John’s, Canada, pp. 443–449. Chun, S.H., Chun, H.H., Kim, C.H., Kim, S.Y., 1999. Development of a stability system to prevent the capsize of a small fishing vessel. J. Ocean Eng. Technol. 13 (1), 130–137(in Korean). Haddara, M.R., Bennett, P., 1989. A study of the angle dependence of roll damping moment. Ocean Eng. 16 (4), 411–427. Haddara, M.R., Bass, D.W., 1990. On the form of roll damping moment for small fishing vessels. Ocean Eng. 17 (6), 525–539. Lloyd, J.M., 1978. Seakeeping: ship behaviour in rough weather. Ellis Horwood Limited, Chichesterpp. 343-397. Tanaka, N., Ikeda, Y., Okada, H., 1983. Study on roll characteristics of small fishing vessel. Part 1. Measurement of roll damping. J. Kansai Soc. Nav. Arch. 187, 15–23 (in Japanese). Tanaka, N., Ikeda, Y., Okada, H., 1984. Study on roll characteristics of small fishing vessel. Part 2. An approximate method of solution for nonlinear lateral equations. J. Kansai Soc. Nav. Arch. 189, 43– 51 (in Japanese). Tanaka, N., Ikeda, Y., Okada, H., 1985. Study on roll characteristics of small fishing vessel. Part 3. Effects of over-hung deck. J. Kansai Soc. Nav. Arch. 194, 43–52 (in Japanese).