Ship turning trajectory in regular waves

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Reprinted from

TRANSACTIONS

OF

THE WEST-JAPAN SOCIETY OF

NAVAL ARCHITECTS No. 60 AUGUST 1980 TECHNISCHE UNIVERSITEIT Laboratonum voor Scheepshydromechanlca Archlef Mekelweg 2,2628 CD Deift Tel.: 015-786873- Fax: 015- 781838

Ship Turning Trajectory in Regular Waves

Masayoshi HIRANO. Member, Junshi TAKASHINA. Member, Yoshifumi TAKAISHI and Toshihiko SARTJTA

( 55 5 , 60

icC)

Ship Turning Trajectory in Regular Waves

Masayoshi HIRANO*, Member, Junshi TAKASHINA*, Member, Yoshifumi TAIÇAISHI** and Toshihiko SA RUTA***

Summary

This paper presents the results of the study on the turning trajectory in reg-ular waves. Using a 5.Om long and self-propelled roll-on/roll-off ship model. extensive model experiments of the turning motion in regular waves were carried out, and the wave effects on the turning trajectory in regular waves were investi-gated from a view point of the wave drifting forces. The deviation of the turn-ing trajectory in regular waves from that in calm water may generally have the tendency to become larger as the wave length becomes shorter with constant wave height. The effects of the rudder angle and the ship speed on the above mentioned deviation are also clarified. Furthermore theoretical approach was made. The turning trajectory calculation in regular waves was attempted consid-ering the wave drifting forces. The computed results are compared with the experimental results, and show satisfactory agreement with those. The calcula-tion method proposed here, would be very useful for the analysis of the turning trajectory in regular waves.

1. Introduction

The study on the maneuverability in waves is one of the important subjects to be investi-gated in the maneuverability field, as recommended by ITTC Maneuvering Committee's. One typi-cal motion, among many patterns of the maneuvering motion in waves, is the turning motion in regular waves, and it is of much interest to have knowledge of the wave effects on the turning trajectory in regular waves,

A pioneering approach to this problem vas made by Dr. H. Eda et al.2 about 20 years ago. They carried out model experiments of the turning motion in regular waves under the conditions of the wave length to ship length ratio of IlL =1.0-2.0 and the wave height to wave leoght ra-tio of 1I./ll/50 (constant), using a 2.5m long and self-propelled cargo ship model. The conclusion obtained by their experimental study was that the turning trajectory in regular waves would hardly change from that in calm water.

However, several years later, it vas pointed out by Prof. S. moue et al.3 that both the turn-ing trajectories in regular waves and in calm water would not necessarily be identical. Carrying

out model experiments using two kinds of 1.0 ra long and self-propelled cargo ship models, they found out an interesting phenomenon that in certain regular waves, which corresponded to the roll resonant point at beam sea condition during turning motion, the turning trajectory made some amount of deviation to leeward comparing with that in calm water. Furthermore they made theoretical investigation on this phenomenon, and concluded that the deviation of the

turn-* Akishirna Laboratory. Mitsui Engineering and Shipbuilding Co.. Ltd. Oceanographical Engineering Division, Ship Research Institute Ship Dynamics Division, Ship Research Institute

.' =dimensionless ship speed in y-axis direction (=v/V) W =displacement of ship

X ='total force in x-axis direction

.r2 =x-coordinate of point on which rudder force Y2 acts Y = total force in y-axis direction

:2 =z-coordinate of point on which rudder force YR acts

R =effective rudder inflow angle

a,. =wave encounter angle =rudder angle

=dimensionless linear damping coefficient of roll

.1 =aspect ratio of rudder

a = wave length

=roll angle

= wave amplitude (=H,./2)

2. Model Experiments

2. L Ship Model

A 5. 0m long and self-propelled roll-on/roll-off ship model was used in this study, and the principal particulars of hull, propeller and rudder of the model are shown in Table 1. The major characteristics of hull geometry of the ship model used in this study are large beam to draft ratio and large KG (high position of the center of gravity) as can be seen in Table 1. and due to these characteristics she performs large roll (heel) in her turning motion in calm water as re-ported in the previous paper7'.

Table 1. Principal Particulars

Hull Propeller

Ship Turning Trajectory in Regular Waves 19

L B d C3 0.660 LIB i 6.57 Bld 3.59 GM 0.040 (m) KG 0.327 Cm) TR 0.308 (sec) 5.000 (m) ¡ 0.761 (m) 0.212 (m) t

2. 2. Method of Model Experiments

The model experiments were carried out at the square basin of Ship Research Institute of Japan (S. R. I.). The ship model was run with a radio control device. The ship motions (yaw and roll angle, yaw rate) were measured with gyrosensers equipped in the model, and the tra-jectory of the turning motion was obtained by the ship position detecting system with supersonic

waves.

The turning tests in regular waves were carried out under the following combinations of wave condition, rudder angle and ship speed, placing emphases on the effects of the wave drift-ing forces, which would have large value in the region of relatively short waves, on the turndrift-ing trajectory.

wave length: a/L=0,35, 0.50. 0.75. 1.00 and 2.40 wave height: H,.=lOcm (constant)

wave direction before entering the turning motion: fr,.O (at head seacondition) 0. 167 (m) PID h055 Z 5 Rudder A3/Ld 1/56.5 'z 1. 55

Fig. 5 Turning Trajectory in Regular Waves

Fig. 3 Turning Trajectory in Regular Waves Fig. 4 Turning Trajectory in Regular Waves

Fig. 6 Turning Trajectory in Regular Waves

angle of 8_35. 25 and l0 with the ship speed of Fn=0.26 are shown in Figs. 7. 8 and )

respectively. It can be seen from these figures and Fig. 5 that the deviation of the turning

tra-jectory becomes smaller and the direction of the deviation approaches to the wave direction as rudder angle becomes larger. The turning trajectories in regular waves of /L=0.35 for the ship speed of Fn=0.30 and 0.21 with the rudder angle of $=-15 are shown in Figs. 10 and 11

respectively. It can be seen from Figs. 6. 10 and 11 that the deviation of the turning trajectory

becomes larger as the ship speed becomes slower. On the other hand the speed effects on the a I III. LOO IL 0.75 I 5 s .15. a F. 0.26 j F. 0.26

- cCI.

- Cal.

in Figs. 14 and 15 respectively. It can be seen from these figures that the time histories of the yaw rate and the roll angle obtained in the model experiments consist of two kinds of components. One is the high frequency variation due to the oscillatory forces of reg-ular waves in which the ship model advanced changing her heading every moment. The other is the low frequency variation due to the wave drifting forces. Noticing this low frequency variation in Figs. 14 and 15. the variation of the yaw rate may be seen to have each two maxima and minima during one round turning, while that of the roll angle has each one maximum and minimum during the same one round turning. This phenome-non may be interpreted as follows: The yaw rate would vary under the influence of the wave drifting yaw moment, which has each two maxima and minima during one round

turning, as well as under the influence of the lateral wave drifting force.

;'hile the variation of the

roll angle would not be influ-enced by thewave drifting yaw

moment. In the study of the

turning motion in wind5' Prof. S. moue et al. discussed the re-lation between the time history pattern of the yaw rate during one round turnig (with respect to the number of maxima and minima) and the direction of the deviation of the turning

trajecto-ry. Considering the analogy of the characteristics of the wave

drifting forces to those of the

wind forces, similar discussion to

that cited above for the turning trajectory

regular waves. ilL 0.35 s F. 0.21

- Cal.

- Cal.

Fig. IO Turning Trajectory in Regular

Waves

-Fig. Il Turning Trajectory in Regular Waves in wind would be possible on the turning trajectory in

3. _Calculation

3. I. Basic Equations

A ship in waves is generally subjected to the oscillatory forces with relatively high frequen-cy corresponding to the passage of individual waves, and to the second-order steady forces, so-called the wave drifting forces, in addition. From a macroscopic point of view, the deviation of

rCe.g s.c I 20 -.10 70 (d.q) .lL 0.50 S .15' 0.25 t t

'.

Fig. 16(a) Coordinate System (1)

Fig. 15 Time Histories of Yaw Rate and Roll Angle

lOO t t t t 630 fl0 810 900 i t i L 100 t (sic) z t (sic) Ezp.

FIg. 16(b) Coordinate System (2)

Cal.

Cal

Where the terms with subscript H, R and D represent the hydrodynamic forces produced by the motions of ship hull (without propeller and rudder) and acting on it. the rudder forces including the hydrodynarnic forces induced on ship hull by rudder action, and the wave drifting forces

re-spectively.

3. 2. _{Hull. Propeller and Rudder Forces}

The longitudinal force X,, and the propeller effective thrust Xp can be written

X,, = ₍₂₎

X,. = (.t,).T(4)

Where X(u) represents ship resistance _{as a function of u. and T(J,.) can be obtained by making} use of propeller characteristic in _{open water as a function of 4.}

wave drifting force coefficients has riot been made from both theoretical and experimental aspects yet. On the other hand, with respect to the effects of wave length and wave encounter angle on the wave drifting force coefficients at zero ship speed, many studies have been made theoretically and experimentally. Especially some experimental data of the wave drifting forces are available for the drilling vessels.

The experimental data of the wave drifting force coefficients reported in the References 5) and 6) are shown in Fig. 17 where MES experimental data of the drilling vessel are added. It can be seen from Fig. 17 that these experimental data of three ships show similar tendency with respect to the effects of wave length and wave encounter angle on the wave drifting force coefficients. In this study the mean values of these experimental data drawn with solid lines in sig. 17 are empioyed in the wave drifting force calculation. not giving any consideration to the effects of the wave encounter frequency due to non-zero ship speed on the wave drifting forces. Ship Turning Trajectory in Regular Waves 27

Fig. 17 Wave Drifting Force and Moment Coefficients

3. 4. Numerical Results

Solving the equations of motion (1). the turning trajectories can be calculated by the follow-ing expressions.

xo=J (ucosØipsin)d:

(10)

Yo =Lcusin±vcos dr

A series of computations corresponding to the contents of the model experiments were carried out, and the computed results are shown in Figs. 1-15 with solid lines. It can be seen from Figs. 1. and 2 that the computed results of the turning trajectories in calm water show good agreement with the experimental results. Satisfactory agreement between the computed and the experimental results generally can be seen for the turning trajectories in regular waves shown in Figs. 3-11. although some discrepancy is seen in the direction of the deviation of the turning trajectories in Figs. 3 and 4. As concerns the drifting distance during one round

Fig. 19 Turning Trajectory in

Regular Waves (Simplified Calculation)

Fig. 20 Turning Trajectory in Regular Wave s

(Simplified Calculation)

V 'V=3.0 with zero wind direction before entering the turning motion for the rudder angle nf ¿=-15'. which is obtained supposing the projected areas above the waterline of A,/Ld= 0.52 and A5/Ld =2.06 which correspond to the full scale value of the roll-on/roll-off ship model at full load condition, and using the wind force coefficients of a container carrier'". Comparing the result shown in Fig. 21 with those shown in Figs. 5 and 6, it can be understood that both the turning trajectories in regular waves and in wind recemble each other, and that the wave condition of 1/L=0.50-O.35 in the model experiments of this study approximately corresponds to the wind condition of JÇ/V0=3.O for the turning trajectory of the roll-on/roll-off ship model.

4.3. Maneuvering Limitation in Regular Waves

Referring to the study of the turning motion in wind" made by Prof. S. moue et al., an at-tempt to examine the maneuvering limitation in regular waves was made. In the above-cited study8), the maneuvering limitation in wind was discussed introducing the concept of the wind speed of maneuvering limitation which is defined as the maximum speed of wind in which a ship can turn to any desired direction. In regular waves of given wave length the wave drifting forces are determined by the wave height, as mentioned in 3.3, which has the same meaning as the wind speed in the wind force calculation. Therefore the concept of the wave height of ma-neuvering limitation, which is defined as the maximum height of regular waves in which a ship can turn to any desired direction. may be introduced on the turning motion in regular waves. Fig. 22 shows the computed results of the maneuvering limitation in regular waves obtained in the same manner as that in wind taking the dimensionless form of the wave height to ship speed rajo of H/2F, in ordinate and the rudder angle in abscissa. In the model experiments uf this study the ship model was not able to turn only at the condition of 2/L=O.35. à-5' and F0.26, the point of which is shown by the solid circle in Fig. 22. and one can see this Peint in the unmaneuverable range obtained by the calculation. Furthermore it can be seen from Fig. 22 that the regular waves of 2/L=0.5 give the most severe limitation under the con-dition of constant wave height to wave length ratio.

w 1-je -y j. ri 1-e e

Ship Turning Trajectory in Regular Waves 31

References

The 15th ITTC Maneuvering Committee Report. 1978

H. Eda and H. Shiba; On the Turning Experiments by the Free-Running Models (in

Japa-nese). Monthly Reports of Transportation Technical Research Institute. Vol. 11. No. 12. 1962

S. moue and T. Murahashi; A Calculation of Turning Motion in Regular Waves (in Japa-nese). Transaction of the West-Japan Society of Naval Architects. No. 31. 1965

F. Tasai; Ship Motion in Beam Seas (in Japanese). Transaction of the West-Japan Society of Naval Architects. No. 30. 1965

Y. Tomonaga and K. Hatanaka; Measurements of the Drifting Force and Moment on

Float-ing Type Offshore Structures in Waves (in Japanese). Transaction of the West-Japan Society

of Naval Architects. No. 59. 1980

ti) H. Eda; Dynamic Positioning Control of Drilling Ships. The 3rd International Ocean Devel-opment Conference. Vol. jI. 1975

7) M. Hirano and J. Takashina; A Calculation of Ship Turning Motion Taking Coupling Effect

Due to Heel into Consideration. Transaction of the West-Japan Society of Naval Architects. No. 59. 1980

S) S. moue and Y. Ishibashi; The Effects of Wind on the Ship Manoeuvrability (I) (in Japa-nese). Transaction of the West-Japan Society of Naval Architects. No. 44. 1972

A. Ogawa; The Drifting Force and Moment on a Ship in Oblique Regular Waves. Report

No. 155. Technishe Hogeschool. Delft. 1966

T. Tsuji. Y. Takaishi. M. Kan and T. Sato; Model Test about Wind Forces Acting on the Ships (in Japanese). Report of Ship Research Institute. Vol. 7. No. 5. 1970