Hydrodynamic and computer simulation studies of ship behavior during transit in harbor channels

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I NTRODUCTI ON

The dynamic response of ah!p ntrq, ç9rmas frm,the bridge is determined.by the ship's hu,ll.characteristics, its rudder and propeller characteristics, and also by factors xtrnJ o the ship, that is, by.the

wind, the current, the water depth under the kee, and _by the width Qf the

channel,

Extensive research and development work hes been done in recent years to define mathematicaJly the.,effects of thsevriables and their

relation-ships. This, re.ul;te pnat,hematic1node1s which predict dynamic re

sponseof ships with a fai.rly good degree of accuracy, and thus provide a

sodnd bai'fo evaliátng controilabil'itybf different type ships under

various conditions ir bo'hopn'and èstiôted waters. The digital

corn-putei- 'is. the means asthe tool'by wh'ichthes'emath simulation models are

"operated" to obtain the analyses desired.

The present study Was undertaken to examine and evaluate 'the dynamic behavior o.f tankers proceeding through Head Hàrbor.P'assage from the Bay of

Fundy to Eastport, Maine; The:con.troHability of typical 250,000 DWT and

80,000 't'-tankers wa'.to be established uderthe côñdftlons'of' tide,

cur-rents and w:ind expected, and with thesec:ificconfiguraion of that channel and the surrounding water and 'land.. The controllability was tobè expressed

interms of'deviation,of the. computed track from the ieal track.

A mathematical rnod'erwas formulatëdthàt wdurd apply realistically to

the Head Harbor Passage sil:qation. Incorporated into the model were the

following inputs spec.ific to this situation:' (a) hydrodynamic force

coef-ficients determined in tank tests, on 250,000 NT--tanker models in deep and

in shallow waters1; (b) actual current patterns in Head Harbor Passage

and (c) , CS Chart data on the depths and lengths in Head Harbor Passage..

-

28, 1979

tab.

v. Scheepsb'oliwkmJe

ARCHEF

_{SYMPOSIUM ON ASPECTS OF} NAVIGABILITlec'iSche

Hogeschool

HYDRODYNAMIC AND COMPUTER-SIMULATION STUDIES

Deift

OF SHIP BEHAVIOR DURING TRANSIT IN HARBOR CHANNELS

by Dr. HaruzoEda '

Senior Research Engineer

Davidson Laboratory, Stevens Institute-of Tchrioloy oboe, New Jersey 07030, U.S..A.

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8

BASIC MATHEMATICAL MODEL

a. Background

During the past ten years, considerable research and development work has been carried out throughout the world to define the factors and the relationships which determine a ship's maneuverability and its response

to its own contrOl systems and commands under real conditions in both open

waters and restricted waters. The advent of the larger tankers and bulk

carriers, has provided the irientive for such development, the results of which are being applied in the design ofship hull.s ai,d ship

controi'.sys-tems, in training, in setting navigatiOnal 'requirements and'operating

limitations, and in the design'Of channels and other waterways. This work

has encompassed three principal topics:

any location tions in the

various ships through model testing and full-scale ship sea

trials. (Ref Tables 1 and 2, Figure 1 through _.)

Hydrodynamic effects of waterway configuration and environmental

effects of such as wind. (Ref. Figure 5.)

. Digi talcomputer calculation or simulation as an analytical tool.

b. Waterway Configuration Input

The waterway configurations of the passage through Head Harbor Passage to Eastport were intrOduced into the basic math model in digital form from CGS Chart 801 (Figure-5), together with environmental data such

as water current speed and direction. The data so introduced include:

(a) desired ship trajectory in Head Harbor Passage; (b) water depth at in the passage; (c) water current velocity at various

loca-waterway, related to tide state; and (c) land map.

2

This waterway cohfiguration i's one of the primary inputs to the

digital computer simulation model. The other primary input is the

charac-teristics of the tanker under consideration.

Changes in water depth 'as the ship proceeds along the channel were

an important inclusion in the model. As water depths change, a substantial

change in sh p maneuvering characteristics occurs. This effect has been

adequately allowed for in the model by modifying the values of major

hydro-dynamic coefficients as a function

of

water depth.

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c. Basic Equations

Fig A-i shows the coordinate system used to define ship motions

with major symbols Which follow the hornenclature. used ii _{previous papers.}

Longitudinal and transverse horizbntal axes of the hip aie1epresented

by the x- and y-axes

with

origin fixed at the center of gravity. By

reference to these body axes, the equations, of. motion of a ship in the horiontal plane can bWritteñ iñ the form

I N ' (Yaw)

m(+ur) V (Sway) (A-I)

m(i-yr)= X (Surge)

where N, Y, and X _{represent total hydrodynamic terms generated by ship}

motions, rudder arid propeller.

-Hydrodynarnic forces are expressed in terms of dimensionless quari-t-ities N.', Y', and X' based on'non-dimensionaliing parameters p

(water density), U (resultant shlp velocity reladve. to 'th water), and

A , i.e. -N' .N , VI V etc. (A-2) .U2AL

Up

Hydrodynamic coefficients vary with positiop, attitude, rudder angle,

propeller revolution, and velocity of the ship For t.xampIe, in the case

of hydrodynamic yaw moment coefficient,,

N' = N'(v',r',ô,y',',',n',u') .;. _(A-3) where v . .0 , o n

v=u, r =r.y =--.,n =-,

u'=-Finally, the fo.Flowing polynomials we.re obtained for predictions of

ship dynamic motions:

3

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2 3 3

N' = r' +a8v' +a9 r' +a&

+a1jy3+a12r'4-a3V' bi+bv+b3rI+b4Ô+bsy+b5v12rI+b?vIrI2+bevi3+bgrI3+bLoó3 _(A-u) +b1y'3+b,2t'+b3'"

= Cj+C2V'

r'+c3v'2+c4o3+c5:i'+X' 0 F I G.

A-Oricntaiioñ (J( cóôdinate axes fixed in ship

d Pilot and Anticipatory Control Chracteristics

Representation of pilot control characteristics was also included

in this mathematical simulation mOdel. _{A ruddet conimand is generated}

_f

the ship track shows deviations _{in heading and distance of the ship from}

the desired trajectory, indicated _{as follows:}

6d a(4r + b'i' + c'L'

where

6d = rudder command

ji= ship heading angle

1r _{chanhei direction}

C

= distance between the ship and the desired trajectory relative

to the ship length = gain cOhstants

Anticpatoi control inhëgotiating turns in the waterway was

in-cluded. For. thi situation, rudder action starts in advàñce of reaching

the actual location of the turi in. the waterway.

Anticipatory control to counteract the effects of cuhënt and wind,

however, was not included.

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RESULTS AND DISCUSSION

Ship trajectories were obtained from the computer simulation model

to examine the response of a _250,000 4T fully-loaded tanker moving u.p

Head Harbor Passage under various sets of conditions. In addition, the

response of a fully-loaded 80,000 v1T tanker wa evaluated for some of

those conditions in order that a comparative evaluation could be made..

Tug assistance was not involved because the objective was to study the

response of the ship to its, own control system.

A series o.f computer simulation runs was made with changes in the following parameters:

ship speed

current speed

direction of current, ebb or flood

(Li) _{Wind speed and direction}

(5) tanker sue

1ypical examples of computer simUlation results are shown in the

following tables:

Case Ship Tide Tide Speed, knots

No. MDWT Knots. Type Knots. Dir. Thru Water Overground

1' 250 0

-

,0

-

6-'2

62

2 250

2.7

Ebb 0 -

8.7k.7

62

3 250

2.7

Ebb 20 315°

8.7L4.7

62

80

2.7

Ebb 0 -

8.7-.4.7

.

These cases were dsigne to bracket the planned passage. conditions. The

wind direction of 3150 was taken for evaluation purposes since this is the

most adverse, direction as .regards the ship. The results for each case are

given in the computer-plotted charts, Figures. 6 through 9, each of which

gives the computed ship trajectory and also shows how much and where that

trajectory deviates frOm the desired tanker track. In addition, each

chart shows the limits of the channel which is defined here

as 75

feet, or.

deeper, at mean low water. In these plots, the mid-ship locatiOn of the

tanker is plotted at 30 second intervals, and the ship form is plotted at

ten-minute intervals during the passage.

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Figure 10 shows an example of computer-plotted time history of

rudder activity and heading angle.

Pertinent finings from computer-plotted results are as follows:

(lj With currents up to 2,7 knots (which is app.roxirnatelè the

màximufi current expected durih any passage), the tankers

considered in this tudystày on the desired track wit:h

relativey small deviations.

(2) Winds of 20 knots from the mot adverse direction, the north"

west, had relatively small effect on the ship behavior during

transit.

Based further tes

on these results, it is presently planned that .a series of

t runs be made on shiphandling simulators with. inctUsibn of

an actual human pilot for the purpose of further data collection and

training.

REFERENCES

Eda, H., _{"Directional Stability and Control of Ships in Restricted}

Channels," presented at the Annual Meeting, New York, _N.Y.,

Novem-ber 11 and 12, _{1971, of the Society of Naval Architects and Marine}

Engineers, Transactions, SNAME, Vol.79, 1971. CGS Chart 801.

Eda, H., 31Digital Simulation Analysis of Maneuvering Performance,"

paper based on research supplied by Naval Ship Systems Command, the Corps of Engineers, the Society of Naval Architects and Marine Engineers, presented at the 10th Naval Hydrodynamics Symposium held

at MIT, iJ.i1y 1974. -.

Eda, H.;- 'Maneuvering.Characteristics of Large Tankers," paper based

on studies sponsored under the General Hydrodynamics Research

Pro-gram and by the Sun Shipbuilding and Drydock Company, Proceedings, Super Ocean Carrier Conference, held in New York, January 1974.

Eda, H., 'Dynamic Behavior of Tankers During Two-Way Traffic in

Channels," Marine Technology, Vol 10, July 1973

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L_

Ounel ne

TABLE 2, PRINCIPAL DIMENSIONS OF A 80,000 DWT TANKER

Length between perpendIculars, L

763 ft Beam, 8 125 ft Draft, H . 39.9 ft Block coefficIent, Cb 0.80 f/B 6.10 B/H 3.13 1./H 19,12 Rudder area /LH 0,017 m' 0.0137 TABLE I.

PRINCIPAL PARTICULARS OF THE 250,000

.JT TANKER Lap 1085' fleem 170' Depth 84' Draft 65' 5-3/4 Draft, molded 65', 4-3/4' Displacement, tons 285.944 Midship coefficient 0.995 Prismatic coefficient 0.834 Block coefficient 0.830 Waterline coefficient 0.909 KG 45.4' LCG. forward amidships 23.4'

Gyradius. ye.. % LaP

23.8 Rudder erea/(ien8th'drsft) 0.0193 -27 0 25' 52'

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8 II

FIGURE I . THE 250,000 DWT TANKER MODEL BEING TESTED IN SHALLOW WATER IN THE ROTATING-ARM FACILITY.

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FIGURE 2. THE 80,000 LMT TANKER MODEL BEING TESTED IN SHALLOW WATER

IN THE ROTATING-ARM FACILITY OF DAVIDSON LABORATORY

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-FIGURE 5. EASTPORT CHART (From CGS Chart

801 ,i.e.

. NOAA Chart 13328) ..-.

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N

FIGURE 6. COMPUTED SHIP TRAJECTOR'r

Sea MFlei 250,000 DJT TANKER Full Load No Current No Wind Speed: 62 knots N 250.000 DT TANKER Full Load Ebb Current(2.7 kt) No WInd Speed: 8.7 L.7 knots

FIGURE 7. COMPUTED SHIP TMJECTORY

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1200 900 3000 600

0-.ln SPYEÔ. u

TANKER(250TYPE). FULLY LOK0LD

APPROACH SPUR U 5KI

RADOER MULE b.l.0 0UREES

PREDICTION FULL$CALE TRIAL -0 -. ''311, B ,.i (LII / I .2 3

LATERAL DISTANCE TRAVULLD/SNIP-,LNGTN. y.y'Z P buRl -3. TIIRAIRATRAJECTORY CORREI.AT IONS

TANKER )50 ho).FULLY LOADED

ST0PPNG MIIEUVLR SPUR (PREOCTI0)

DISTANCE (PREDICTION) HEADIIIC )PREOICTION)

10

PICURU 4 STOPPINU TRAJECTORY COAR(1.AT.IOIIS

FULL SCALE TRIALS

5. 20 25

TIME, t .

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250,000 DWT TANKER

Full Load

Ebb Current (2.7 k) WInd 20 knots 315° Speed: 8.7 ..7 knots

COMPUTED SHIP TRAJECTORY

Sea Miles 80,000 OWl TANKER Full Load Ebb Current(2.7 kt) No Wind Speed: 8.74.7 kE

FIGURE . COMPUTED SKIP TRAJECTORY

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8

250!000 lT TANKER Full Load No Current lo Win Speed: 6 to 2 knots 6,deg 10 20 30 50

FIGURE 10. TIME HISTORY OF RUDDER ACTIVITY AND HEADING ANGLE 60