Ship control during two-way traffic in channels

10 JAN. 1974

_Lab.

_v.

_{Scheepsbouwkurd}

A

RCHIEF

_Fechnische

_Hogeschaci

THIRD

ieek v.

e

_Deift

PAPER IX B-I SHIP DOCUMENtATIft.

CONTROL

_Ondera4de

- - .sbouwkunde

SYSTEMS

_{nisce Hogeschoo}

SYMPOSIUM DOCUMENA1tE

j:

'(6).)

DATUM: MINISTRY OF DEFENCE FOX HILL BATH SOMERSET UK

1tL

SHIP CONTROL DURING TWO-WAY TRAFFIC IN CHANNELS (CASE OF LARGE FULL-FORM SHIPS)

SHIP CONTROL DURING NO-WAY TRAFFIC IN CHANNELS (CASE OF LARG,E FULL-FORM SHIPS)

by Dr. Haruzo Eda, Senior Research Engineer Davidson Laboratory

Stevens lhstitute of Technology Castle Point Station

Hoboken, New Jersey 07030 U. S. A.

ABSTRACT

A non-linear digital simulation model was formulated to examine the dynamic behaviQr of large full-form tankers during meeting and passing

in restricted channels. Computer-printed trajectories obtaihed in a series of digital simulations indicated basic patterns of ship behavior.

Performance of various control systems was evaluated in terms of devia-tions in ship trajectory and rudder angle Comparisons with previous measurements obtained in full'- and model-scale tests verify realistic

modeling of' t'he system.

I NTRODUCTION.

During meeting ard passing in restricted channels, hydroynamic inter-actions between two ships are fairly significant, thereby introducing

a problem i'n' ship operations. Previous studies of the subject' generally utilized the free-running model test technique.16 From 1970-1971, ef-forts were made at Davidson Laboratory to examine the problem through digital simulations for the case of cargo ships. ' Encouraging results were obtained employing this approach Since a much greater problem was anticipated for larger ships in similar operations, the simulation study was extended, in this paper,to the case of large full-form tankers. The objective of this study was to examine dynamic behavior of tankers during two-way traffic in channels and to evaluate effects of various control system characteristics Using recently obtained hydrodynamic data5'7'8 for tanker forms, the mathematical model was formulatid on a digital computel- and a series of computer runs were carried out.

Results revealbasic patterns of ship behavior and rudder activity, which' were compared with records previously obtained from full-scale tests and manned-model tests during North Sea Canal studies in, the Netherlands..

Al-though there exist differences in ship and canal configurations' between those of simulations and these tests, fairly similar trends in ship be-havior are shown Furthermore, performance of various control systems were evaluated in terms of deviations in trajectory and rudder activity.

gravity. Byreference tO' these body axes, the equations of motion of a ship in the horizontal plane can be. written in the form

I N z m ("+ u r) m( -v r) (Yaw) V (Sway) = x (Surge) (1)

where N, Y, and X represent total hydrodynamic terms generated by ship motions, rudder., propeller, and effects of banks and bottom of narrow waterWays.

Hydrodynamic force are expressed in terms of dimensionless quantities N' Y', and X' based on non-dimensionalizing parameters p (water density), U (resultant ship velocity relative to the water), and A ,, i.e.,,

N"

N

,, Yt , etc. (2)

U2A2 :2.U2A.

Hydrodynami.c coefficients va-y with positiOn,, attitude,. rudder angle, propeller revolution, and velocity of the ship For example, in the case of hydrod'namic yaw moment coefficient,

N' = N'(v',r',Ô,y,*' where

U,

,u') y U = - ,

n' = -

, u' = - , etc.. (3)

Finally, the fbIlowing polynomials were obtained 'for predictions of ship dynamic motions:

N' =

Y"' (4)

X''c +cv'r'+cv'2-i-c82+c±X'

ol

_2.

3 4 p

where coefficients of rudder force and moment are functions of propeller slip as fol'lbw:'° , .

BASIC MATHEMATICAL MODELS

Figure 1 shs' the coordinate system used to define ship motions in narrow waterways with major symbols (which follow the nomenclature used in pre-vious papers9) Longitudinal and transverse horizontal axes of the ship are., represented by the x and y-axes with origin fixed at the enter of

and

where

8d = rudder command :

8e = rudder at equilibrium condition

8 'actual rudder angle = gain constants

and t

= 0.1',

_{II 2.7 deg/sec}

, 181 35 deg in 'the imulatiOn.

PRINCIPAL DIMENSIONS OF SHIP AND CANAL Table I gives the principal dimensions of large full-form

tankers

ex-amined in this study _{Figure 2 shows the geometry of the canal and the} courses of two ships A and B _{Major hydrodynamic coefficients of Ship A}

in this canal were determined from presently available data,5'7'8 and _are shown in Table 2 _{The dynamic motions of Ship A were simulated due to the} interaction with Ship B while meeting and passing _{Ship A proceeded at a} speed of 6.1 knots, and Ship B at a speed of 9.1 knots. _{Interaction forces} and moments during meeting and passing, previously measured by Moody in

captive model tes.ts,35 were applied to this case.,

a6 (I + ksLS)

(1 +kse5)

(l +

ks5)

(1 _{+ kse'5')} $ propeller p propeller n . propeller

k=3.60

subscript e a, (5) etc..

The hydrodynamic force coefficients of X' differ in form from the lateral force coefficients Y' in Eq.(1+), e.g.,

C X1

0

0,

=X'

, etc. ₍₆₎

and X' = _{propeller thrust depending on Kt., Kq and J (i.e., u' and n').} Torque constant characteristics _{were used assuming a steam} turbine for the ship in this paper.

The following rudder control characteristics _{are employed:'}

b"4r' ₈

_t8'

'(7)

si ip =

,pn

p itch

revolutions per second

SHIP TRAJECTORIES

Simulations of ship motions were carried out on the digital computer in the following manner:

Initially, the ship moved from the canal centerline course, to the off-centerline course and maintained the off-off-centerline straight course with a rudder angle 'required for retaining the equilibrium condition. Then,

time histories of hydrodynamic interactions in yaw moment and side force were applied to the ship. A series of simulation runs was continued for 1000 secOnds in full-scale (t' 9, i.e., for a period of time to travel nine ship lengtis). The digital computer model included plotting sub-routines Which could produce ship trajectories either on a lineprinter at. the Computer Center of Stevens Institute, or on a time-sharing terminal. One of our tirne-sharing terminals had greater accuracy in plotting than that.of the linepririter.

Figures 3 and 1. show computer-plotting of trajectories (heading angle

and path deviatins, respectively) for a period of 900 seconds (ti 8) during meeting and after passing. The following control system charac-teristics were ued:

(I) no control, a = b' c' = 0 , shown by in the figures (2) t.ypicl control, a 3, b'. = 1.5., c' = 0, shown by ******

The figures showthat the ship deviates very little from the initial course during a period of meeting This small deviation is because the inertial terms of ships (inc,luding added inertial terms which are greatly increased in the canal) are relatively larger than hydrodynamic interactions, which are somewhat oscillatory with relatively short duration. This small de-viation during meeting justifies the simulation procedure in the present study, which utilizes hydrodynamic interactions measured in captive model

tests. Without control, the trajectory is divergent with slow oscillation due to bank effecp. It should be noted that potential hazards are still great after passiig, and that adequate control must be continued for a long time after passing until the disturbance due to meeting diminishes.

In order to understand the basic behavior of a ship, detailed trajectories are shown for 250 seconds (t' 2.3) in Figures 5-10. Yaw acceleration, heading angle, path deviation, yaw rate, drift angle, and rudder angle, respectively, are shown in these figures.

Figure 5 shows predicted yaw acceleration for the case without control. This Figure illustrates four major peaks in yaw acceleration as follows:

Immediaely after the time of the bow-to-bow encounter, the two bows tend to turn away from each other (i.e., they tend to turn\to the near bank).. This is due to the water elevation

near the bows. .

Shortly before. the midship-to-midship encounter, the bows tend to move toward each other (i.e., they tend to turn to the

canal centerline). _{This is due to the drop in water level} between twohulls (mainly fore half portions). _{At this time,} the magnitude of the peak is at its greatest.

(3) After the midship-to-midship encounter, the _{sterns tend to} move toward each other (i.e.,.they tend to turn to the near

bank) The following two important factors introduce _this tendency:

The drop in water level, between hulls (aft half. portions). Strong suction force between hulls introduces sideSlip velocity (i.e., .drift angle), generating large yaw moments

in this direction.

(4i.) _{At the time of stern-to-stern encounter, the bows tend} to turn to the canal centerline. _{This is due to the water} eleva-tion near the sterns. Of the four peaks, this one i.s the least pronounced.

In Figure 5, the basic behavior of the interaction _{yaw moment measured in} captive model tests is also shown by _{a dotted line fOr comparison. Although} a great similarity is shown between predicted yaw acceleration and _measured yaw moment, it should be noted that the No _{3 peak of the measured yaw} mo-ment is relatively much lower than that of yaw acceleration (whose scale

is chosen for direct comparison with the yaw moment coefficient), indicating that significant portions of _{yaw acceleration are generated by the sideslip} (i.e.,, drift angle) as mentioned in the above

_(3.

Figures 6 and 7 show heading change 'and path deviation in enlarged scale for 250 seconds. _{Similar to Figures 3 and i, these figures show that the} ship moves very little from the initial _{course during meeting (i e , less} than 3 degrees in heading, and less than 3% of ship length in path

devia-tion). _{Large deviations in heading and path start .after passing.}

Figures 8 and. 9 illustrate yaw 'angular velocity and drift angle (i.e., sideslip velocity). _{Figure 8 indicates similar behavior of yaw rate,} regardless of the preSence of the control system. _{It should be noted,} hOw-ever, that the difference in yaw rate slowly starts to _{increase near the}

end (at t > 200 seconds) in the figure _{This difference indicates that} the rudder force and moment are much smaller than the _hydrodynamic inter-actions during meeting, and that the rudder _{is only effective in a long run}

In Figure 9, very little difference is seen in drift angle (sidelip _velocity) between those with and without control _{Comparing Figures 8 and 9, it is} clear that the rudder is directly effective, controlling _{yaw and yaw rate} and not path and sideslip velocity.

Figure 10 shows rudder activity during meeting. _{The straight dotted line} delineates the initial rudder angle required _{to maintain the off-centerline} equilibrium course. _{It is interesting to note that three major peaks shown} in yaw acceleration (i.e., _{cjI , ,} 'and in Figure5) appear with a time lag in yaw rate _{in. Figure 8, and with a further time lag in rudder angle}

in Figure 1.0. \These three peaks are nOt very pronounced in heading angle in Figure 6. The greatest similarity in the behavior of time history is shoWn betwen rudder angle and yaw rate, which indicate a much greater weight of yaw rate control than of yaw control.

EFFECT OF CONTROL SYSTEM CHARACTERISTICS

A series of simulation runs was made with changes in control gain constants a, b', and c'. Since the previous s.tudy indicated that control due to path deviation is somewhat redundant,8 it is'not included in this study. To evaluate the performance of the system, root-méan-square of heading angle, path deviation, and rudder angle relative to the initial equilibrium con-ditions were obtained. Furthermore., the following performance index was considered to. eialuate the system:

erms

+ X2(y + X3(ô6e)rms

Table 3 shows a typical example of. results, i.e., a series of digital sim.-ulations for 1000 seconds (t' 9) In this particular case, X=A3= 1 and

= 1+3 are used A relatively large value of X2 is due to a small path deviation coefficient, y' , which is based, on ship length. Table 3 shows examples of adequate values in control gains' to be those of Run Nos. 8, 9,

10, 12,

and. 13 (i.e., a=3to 1+, and b' 0 to 1.5).

COMPARISON OF SIMULATION TRAJECTORIES WITH FULL- AND MODEL-SCALE TESTS

During

l960-l962

an extensive series of full- and model-scale tests carried out in the NetherlandsG for the North Sea Canal studies included measurements of two-way traffi\c in narrow canals. Comparisons are made here between

simulation trajectories and test results.

Table 1+ presents ship and canal dimensions for three cases (i.e., simulations, full-scale tests,k and manned-model tests).' Figures 11 and 12 compare time histories of yaw rate and rudder activity. In digital simulations, yaw and yaw-rate gains of\3 and 1 5 were employed Time and yaw rate in test results are scaled to Case 1 (i e , simulations) in these figures A fairly good

correlation in behavior of yaw rate and rudder activity is shown in three cases All casesindicate three major peaks in yaw rate and rudder activity at corresponding time. Since the canal size relative to the. ship is the

largest in Case I (shown in Table 4), the time history Of yaw rate and rudder activity is the least pronounced in Figures II and 12.

COnsiering the difference in '5hip and canal configurations in these cases, the comparisons presented in the figures are encouraging It is considered that the results fairly well verify realistic modeling of the ship-waterwa' systeni in this s'tuy.

COMCLUS ONS

A real istic niodelihg has been hieved on a digital computer to represent dynamicbehaviOr of large full-form ships during two-way traffic inre-stricted channels Based on results obtained from a series of simulation runs, major findings may be summarized as follows:

1. The shipdeviatés ohly slightly from the ihitial course during the period of meeting because the ship's inertial terms (includ-ing added inertial terms whichare greatly mci-eased in the canal) are relatively larger than the hydrodynamic interactions. Potential hazards arestill great, however, after the passing, because the motions of the ship may diverge with slow oscilla-tions if not adequately controlled. Until.the disturbance due to meeting diminishes, adequate control must be continued for a relatively long time after meeting (e g , t' 5 time to

travel five.ship lengths).

2 During meeting, there exist four major peaks in yaw

accelera-tioh. The most important one occurs shortly before the midship-to-midship encounter when the two bows tend to move

toward each other.

Subsequently, the second important peak occurs after the midship-to-midship encointer when the sterns tend to move

toward eachother. The drift angle, generated by a suction force between the two hulls, greatly contributes to this

tend-ency.

3. Results from a series of simulation runs indicate-that adequate control can be achieved utilizing errors in yaw and yaw rate

(For example, adequate values of yaw and yaw-rate gain constants are a 3 to 4, and b' 0 to 1.5.)

.1+. A good correlation is shown between simulation trajectories and full- and model-scale.test records. It is considered that the

results verify realistic modeling of the ship-waterway system. 5. The relatively small deviations of.trajectory. during.the period

of meeting justifies the simulation procedure in this study, which utilizes dynamic interactions measured in captive model tests with fixedheading angle and path. The abovementioned en-couraging correlation of simulation results with teS.t records

ACKNOWLEDGMENTS

This paper i' an extension of previous studies supported by the

Atlantic-Pacific Interoceanic Canal Study Commission, Corps of Engineers,.and

Panama analConipahy.. The author wishes to acknowledge their sponsorship, which made thi paper possible..

The author al1so wishes to thank Dr. J.P. Breslin, Director, Dr. D. Savitsky, Assistant Dir1ector, and many members of Davidson Laboratory for their valu-able suggesti1ons during the preparation of this paper

REFERENCES

1. Gárthune,\R.S., Rosenberg, B.,Cafiéio, D. and Olson, C.R., "The Performnce of Model Ships in Restricted Channels in Relation to

the Design of a Ship Canal," DTMB Report 601, 191+8..

- 2. Lee, A4A.. and Bowers, G.E.., "Ship Performance in Restricted Channels,"

Proc of American Society o.Civil Engineers, Aril 191+8.

MoOdy, C.G., "The Handling of Live Super Ships Through Gaillard Cut of the Ianama Cahal," DTMB Report 1277, 1958. .

li. _{Moody, C.G.,} "The Handling of Ships Through a Widened and Asymmetrically

Deepened Section of Ga.illard Cut in the Panama Canal.," DTMB Report No.

1705, 1961+.

Moody, C.G., "Study of the Performance of Large Bulk Cargo Ships in a :Proposd lnteroceanicCanals,'1 Naval Ship Research &. Development

Center Report .371+-H-Ol, 1970.

Waterthopkudig Laboratorium, "Noordzeekanaal, Part I to III."

Eda, H., "Directional Stability and Control of Ships in Restricted thannels,' TSNAME, Vol.79, 1971.

Eujino, M.,\ "Experimental Studies on Ship Maneuverability in Restricted

Waters, Prts I and II," International Shipbuilding. Progress, No. 168,

1968 and 1970, respective1'. --..

-Eda, H. and Crane, C.L., Jr., "Steering Characteristics of Ships in Calm Water and Waves," TSNAME, Vol.73, 1965.

Fujii, H. add Tsuda, T., "Experimental tudy of Rudder Performance," Journ. ofSoc. .of.N.A. in Japan, Vol.1.10, 1961.

L/B L/d C p LCG/L forward amidship, % Yaw gyradius.,

t/L

_, L', Ship A (250,000 4T Tanker , ft

L, Ship B (similar form), ft

RU'JNØ

1

WI Dm

4. 75000 I.ZPRIM

0 00350

NV

0.0 450 6

Yv

-0.12270

NVVV

0.90350

.Yvvv

-13.54000

PRINCIPAL PARTC1JLARS OF TANKERS

DEPTH

1.20000

MYPRIM

0,06927

N R

-0.00855

YR

0.00646

NDDD

0 . 00000

YDDD

0. 00000.

TABLE 1 TABLE 2

MXPRIM

0.0i 69

ND

-Oo 00282.

YD

0.00535

N ETA 3

0.O4247

Y ETA 3 0. 1O020

6.k

16.6

0.995 O.83L 0.830 2.2 23.8 1 085 965

MPRIM

0.01 566.

N ETA

-0.00250

YETA 0.01 617

TABLE 3

EFFECT OF CONTROL GAINS

TABLE 4

SHIP AND CANAL DIMENSIONS

Test Description CASE 1 ComputerSimulation CASE 2 Full-Scale Test CASE 3

Manned Model Test

Canal CANAL 1 CANAL 2 CANAL 3

- Width at. the bbttOm, W Width at the surfac, W2 Water depth, D 810 ft . 810 ft 78 ft 75m 160m 12.5m 135m 235m 15m

Ship SHIP A SHIP B SHIP A SHIP B SHIP A S P B

Description of-Ship -Tanker 250,000 T -Tanker 170,000 T ASTYANAX . -WILLEM BARENDSZ .. Tanker 70,000 DWT 1/50 Scale Tanker 70,000 UWT Ship length, L Beam, B Fore draft, Hf Aft draft, Ha Speed, U 1085 ft 170 ft. 65 ft 65 ft 6;1 kt 965 ft 151 ft 58 ft 58 ft 9.1 kt 137 2m 18.9m. 4.3m 5.9m 6.1 kt 190m 27.6m 7.Om 7.9m 5.2 kt 241m 34.6m 13.3m 13.3m 6.1 kt 241m 34.6m 11.Om tmean 6.5 kt RATIO /H

475

1 2

536

1 35

40

2 45

27

1 68

39

1 13

39

1 36 Run No. Yaw Gain a Yaw aie b' Yaw Acc. Gain ci

Headi hg Path Rudder Deviation Deviation Angle (8-s \ rms O '0e'rms' 'rms Perform-ance Index j 1 0.0 0.0 0.0

6.73

0. 1 5.7

0.00

13.45

2

1.0

0.0

0.0

2.91

o 060

2.89

8.38

3

1.0

0.5

0.0

2.1 5

0.045

2.58

6.66

4

1.0

1.0

0.0

_I 78

0.036

2 9.1

6.23

5

2.0

0.0

0.0

1 o 58

0.027

3014

5.87

6

2.0

1.0

0.0

_1.07

_0.022

2.93

_4.96

7

2.0

2.0

0.0

0.92

0.022

3093

5.78

8

3.0

0.0

0.0

1.01

0.018

3.01

4.79

9

3.0

1.0

0.0

0 78

0,017

3.01

4.52

10

3.0

1.5

0.0

0.72

0.017

3.51

4.96

11

3.0

3.0

0.0

0.71

0.020

4.58

6. 1 7

12.

4.0

.

0.0

0.0 o 78

0.015

3.12

4.54

13

.0

1.0

0.0

0.64

0.015

3. 1 7

4.44

14

4.0

2.0

0.0

0.59

0.016

3.96

5.23

15

4.0

4.0

0.0

0.64

0.021

5. 1 6

6.72

y

°e

CANALWIDTH W

N

tx.

r

U

FIG.

1 COORDINATE AXES

Y0-y0

PATH DEVIATION

e

12.

B1 bBA.1

I.2.HA

4r(deg) 10.

-10

-20

BOW T0 BOW

MIDSHIP TO MIDSHIP

$TERNTO STERN

0

t(sec)

200

₆₀₀

₇₀₀

₈₀₀

₉₀₀

4

4 *

_4*0

0 0

.1

S 0 0

.

0 0 OWITHOUT CONTROL 0 a

"I,

'0

0 3.Qm

-O 10_

-O.20

BOW T0 lOW

STERN TO STERN

MIDSHIP TO MIDSHIP

S S 0 0 S S S 0-5 S S

WITHOUT CONTROL

4 S S 0 S 0 0 S

t-(sec)

100

200

30.0

400

500

600

70Q

00

900

0 _S S 0 S S

0.20

O.ioJ

6 0

(rad/sec)

O.00Q2

0.000

'-0'.Op9'

O.O0O2

0.5

0. 5

(Nj %LBHU2). BOW.

TO

BOW

9'Ot '.1

1p

(MIDSHIP

MIDSHIP

I 120 181

20

-1.0_. -2 .0.

-3.04

BOW

TO

BOW

MIDSHIP.

TO

M-IDSH1P

1.

*

_{WIThOUT CONTROL}

-0 0*

.:

*

0 e

_{WITH CONTROL}

* STERN TO STERN

t(sec)

120

15.0

180

210

**40

210

0 0 -0 0 0S SS SS SS

0.14

¶71

10

* *_* * *

t.

SS.

BOW

MIDSHIP

BOW

MIDSHIP

STERN

TO

STERN

Oo

CO

0..

0. 00 30 60 90 120 150 180 210. 240

0.12

0.10

0.08

(deg/sec)

MIDSHI

0.1s

TO

MIDSHIP

0.1

0.15

BOWt

TO

0 (TT

*

*

-rrc

0 0

*

o°.*,

0

ft

* 0

0*

WITH CONTROL

0 t

0*;

=:

30 60 . 90 120 150 180

210

240 27.0 a. t(sec),

STERN

TO

STERN

*

*0

S I,

(deg) o 30 60

**

-4.0

'_-WITHOUT CONTROL

2'% t(sec)

6.0

4.0

2.0

BOW

TO

BOW

MIDSHIP

TO

MIDSHIP

o 0* -2 .0 * *

II.:

*

WITH CONTROL

STERN

TO

STERN

-10

-20

-30

40

+ BOW TO

BOW

MIDSHIP

TO

MIDSHIP

6 * o ft _ft ft ft

ft

ft

*

ft

ft

ft

STERN

TO

STERN

t(sec)

90

120 15Ô 180

210

240

270

I--

_.1clI4HIft,4,.IH,.*

ft

*

WIThOUT CONTROL

ft

*

ft

4r ('deg/s'ec)

0.2

0.1

-0.1

-0.2

-* \

60

BOW

TO

BOW

MIDSHIP

TO

MIDSHIP

* i2O STERN.

TO

'STERN

SIMULATION TEST IN CANAL I

FULL-SCALE TEST IN CANAL 2'

150 180 210 240' 270

t (sec),

6(deg)

4O

30

-20.

10

3:0

FULL-SCALE. TEST IN CANAL 2

FREE-RUNNING MODEL TEST IN CANAL 3

SIMUATION TEST IN CANAL 1

-10 0OS.

...

*

20

-t(sec)

10

2]

240

_Z1

*

*

00 o ,, , .0 0 0 0 000

STERN

BOW

_TO

-30 .,.

TO

_{. *} / STERN.

BOW

_***.j

-40k

M'iD$HIP TO MIDSHIP