Maneuvring performance of high speed ships with effect of roll motion

Ocean Engng. Vol. 7, pp. 379-397.

Pergamoa Press Ltd. 1980. Printed in Great Britain

379 TECHNISCHE UNIVERSITEIT Laboratoilum voor Scheepshydromechanlca Archief Mekeiweg 2, 2628 CD Deift TeL 015.788873-Fax: 015-181838

MANEUVERING PERFORMANCE OF HIGH-SPEED

SHIPS WItH EFFECT OF ROLL MOTION

HARUZO EDA

Stevens InstituteofTechnology, Hoboken, NJ 07030, U.S.A.

AbstractEquations of yaw, sway, roll and rudder motions are formulated to represent realistic maneuvering behavior of high.speed ships such _{as destroyers. Important coupling} terms between yaw, sway, roll and rudder were included on the basis of recent captive model test results of a high-speed ship. A series of computer runs was made by using_{the equations.} of yaw, sway, roll and rudder motions. Results indicate substantial coupling effects between yaw, roll, and rudder, which introduce changes in maneuvering characteristics and_reduce course stability in high-speed operation. These effects together with relatively small GM (whIch is typical for certain high-speed ships) produce large rolling motions in a seaway as frequently observed in actual operations. Results of digital simulations and captive model tests clearly indicate the major contributing factors to such excessive rolling motions at sec.

NOMENCLATURE

A _{reference area (A = iN, i, orBK)} a yaw gain constant

B ship beam

b yaw-rate gain constant

c sway gain constant

d sway-rate gain constant

D,,. water depth

e subscript e indicates the value at the equilibrium condition

F, Froude number (UI v'gi) g acceleration due to gravity H ship draft

1, moment of inertia referred to :-axis ship length

'n mass of ship

N hydrodynamic and aerodynamic yaw moment

N; _{derivative of hydrodynamic yaw moment with respect to yaw acceleration}

N; _{derivative at' hydrodynamic yaw moment with respect to sideslip velocity} n oropeller revolutions per second

Na derivative of hydrodynamic yaw moment with respect to rudder angle r yaw rate

t, time constant of rudder in control system

U ship speed (U = v1uz + )

u component of ship speed along x-axis

v componentofship speed along y-ais

X hydrodyriamic and aerodynamic force component in x-axis direction hydrodynamic force component along .r-axis due to propeller

r _{derivative of hydrodynamic force component along e axis with respect to surge acceleration}

X_. second derivativeof_{hydrodynamic force component along x-axis direction with respect to sideslip} velocity and yaw angular velocity

X,. total resistanceralong x-axis

Y _{hydrodynarnic and aerodynamic force component along y-axis}

Y, derivativeof_{hydrodynamic force component along y-axis with respect to yaw rate}

Y. _{derivative of hydrodynamic force component along y-axis with respect to sideslip velocity} Y; _{derivative of hydrodynamic force component along y-axis with respect to sideslip acceleration}

TI3T313V! 1 wov rmi ei

na 03 8

ct8t-ero x

3HHT

byr!qeii2

£ 'M

- C38-rC :iT

Length _YJI

Force Y

Y'=Y/

Moment N N' NI 4/U'

Mass m

Angular velocity r r' ri/U

Static force rate Y, Y', - Y,/ .- AU

Sta:ic rnoeru rate N. _{N', = NJ} A/U

Rudder force rate Y5 Y'5 Y/ - AU2

Damping force rate Y, Y', Y,/ -j-A1U Damping moment rate N', N', NJ 4 APU Inertial coefficient Y

Y'; = Y;f f Al

Inertial coefficient N, _{N'; N;/ 4 Al'}

Moment of inertia 1, 1., _{1,1 4 4(3}

Velocity u U' u/U

Time t t'= rU/i

I. INTRODUCTION

WH _{a ship is proceeding at a high speed in a seaway, serious rolling motions are frequently} observed in actual ship operations and in model testing in waves (Taggart 1970, DaIzell and Cluocco, 1973) Anomalous behavior of rolling and steering was clearly evident for example, in full-scale tests of a high speed container ship during cross-Atlantic operations

(Taggart 1970).

Certain naval ships have the following hull form characteristics which have major impacts on ship performance in particular, maneuvering and rollingbehavior:

yav anc Sifli bee ff0 330 H. EDA

Y5 derivative of hydrodynamic force component niong y-axis with respect to rudder angle drift angle ( Sjflt v/U)

8 rudder angle

w heading angle of ship.

Dimensionks: forms

Most dimensionless expressions in this paper follow SNAME nomenclature. The dimensionless_{form of} a quantity is indicated by the prime of that quantity. Examples are shown bólOw:

Quantity Typical symbol Typical

f

Maneuvering performance of high-speed ships with efTect of roll motion 381

..t .-...

F,G. I. Body plans ol rcprcscntative naval ships.

(I) High speeds with large i/B ratio and relatively small GM.

Fore-and-aft asymmetry (e.g. with a sonar dome at the bow, see Fig. 1)

(Baitis er al., 1976). Relatively large rudder.

This particular hull form characteristics introduces the possibilities of fairly significant yawswayrollrudder coupling effects during high-speed operations.

The major objective of this study is to examine the coupled 'notions of yaw, sway, roll and rudder for high-speed ships (e.g. hull forms similar to destroyers) through digital

simulation studies.

Due to lack of available hydrodynamic data, no extensive digital simulation effort has been made previously, in the area of maneuvering performance with inclusion of roll

382 _{H. EoA}

Recently, under another simultaneous research program at Davidson Laboratory, a

high-speed ship was extensively tested in the rotating-arm facility with inclusion of _{roll motion}

effect Test results clearly indicated fairly significant couplings between _{yawswayrofl_} rudder motions Accordingly a mathematical model was formulated on the basis of these

expenmental results combined with analytical estimations, for a 500 ft long hull form which

is similar to that of high-speed naval ships.

A series of computer runs were made by using equations of_{yaw, sway, roll and rudder}

motionS on a digital computer.

Results indicated substantial coupling effects between _{yaw, sway, roll and rudder}

which introduce changes in maneuvering and rolling behavior For_{example, coupling}

terms introduce destabilizing effects on course stability and increase turning performance

at high-speeds These coupling effects together with relatively small GM produce _large rolling motions in operations in seaways Effects of_{yawswayrollrudder coupling on} the possibility of yawroll instability were clearly demonstrated th simulation _results.

2. HULL CONFIGURATIONS

A high-speed hull form to be considered in this study includes the following_charac teristics as shown in the table below:

(I) High lengthbeam ratio and relatively small GM for high-speed operation. Fore-and-aft asymmetry, wh.ich is more pronounced for naval ships with

áppeni-dages than that for commercial ships.

Relatively large rudder.

Length, 1,,,, ft 500.0

Beam at WI., B, ft 60.0 L '

Draft, H, ft 17.0

/7

2 2

Rudder area ratio, Ar/lB 1/40 Block coefficient, Cb 0.56

The above mentioned hull-form characteristics introduces _{a fairly substantial} hydro-dynamic coupling effects between yawswayroll-rudder _motions.

Figure 2. shows two curves Which indicate the distance of CG of the local sectional area from the longitudinal centerline at roll angle p = 0 and 150. The curves can be con-sidered to be equivalent to camberime of the wing section

Figure 3 shows the other example of the camberline for the hull form shown in the top

of the figure.

When roll angle is not zero, the cãmberl Inc is not astraight line, as shown in these figures

introducing hydrodynamic yaw moment and side force. This trend is pronounced by the fore-and-aft symmetry cf hull form, in particular, during _{high-speed operation.}

Figure 4 shows, for example, captive model test results of yawroll coupling effect,

indicating hydrodynaxnic yaw _{moment to port introduced by roll angle to starboard.}

0

was realis

Maneuvering performance of high-speed ships with efFect of roll motion ₃₈₃

t

'I

/

I

Aft perpendicular _{Aft perpendicular}

-2 -I 0 I 2'/.L.

To port To stbd

Distance.of CG of sectional area from centerline

FIG. 2. _{Longitudinal asymmetry due to roll (destroyer).}

3. BASIC EQUATIONS FOR _{YAW-SWAY..ROLL..RUDDER MOTIONS} On the basis of captive model test results _{together with analytical estimations,an effort}

was made to formulate the equations of yawswayrollrudder motions to represent

realistic maneuvering and rolling behavior_{of a high-speed ship.}

OWL

Appendages ore not Shown in lines draw rig. I / I I

/

I I I I I I I .1 I Forwdrd perpendicular \ \ \

'

I I I I I I / I Forward perpendicular I \I I I I I I I I I I I t

'

'¼ I I I I \

'

' I I /

Distrrbution of sectional area '¼ '¼

'¼ '¼

I

384 H. EUA Forward P.

I'

I'

/ \

I'

/ \ I I lI 'S Forward P.

\

' CG of sectional

area-'

I I,

I'

I whereN, I rudderan

'I

Distribution of sectional area I /

I

/

//

"I

II Aft

:

Aft P. -'.0 -0.5 0 -0.5 1.0 /. L I I To port To slbd. Distance of CG of sectional area

from centerline FIG. 3. Longitudinal asymmetry due to roll (high-speed container ship).

Figure A-I shows the coordinate system used to define ship motions with major symbols

which follow the nomenclature used in previous papers. Longitudinal and transverse

horizontalaxes of the ship are represented 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 hori-zontal plane can be written in the form:

Hydrd

and X' b

velocity r Roll angleO Roll angle 15°

Martcuvcring performance of higii-spcd ships with cifect of roll motion

35

Ftc. 4. _{Yaw moment coefficient due to roll angle.}

1/ = N (Yaw),

lcj, = K(Roll), _(I)

!n(v =ur) = Y(Sway),

ft - vr) = X (Surge),

where N, K, Y, and X represent total hydrodvnamic terms generated by ship motions, rudder and propeller.

Figure A-I. Orientation of Coordinate axes tixed in ship

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

N V N'

=

,

y' = --

, etc. (2) --U2A/ 6.0 zO -4 4.OxtO 2.OxIO N' - 1/R -0.197 .oe 0

°r

th,

386 _H.EDA

Hydrodynamic coefficients vary with position, attitude, rudder angle,_propeller

revolu-tion, and velocity of the ship. For example, in the áase of _{hydrodynamic yaw moment}

coefficient,

N' N' (v', r', 8, y, v ', r ', iz', u', i, _'4,', 4)), ₍₃₎

where

I , YO fl U

V

=Ur =r,y0=-7,n

=,U =-,etc.

Finally, the following polynomials _{were obtained for predictions of ship dynamic} motions:

N' =

a1

± av' ±

a3r' ± a38 ± a5y + a6v'2r' ±a7v'r'2 ± asv'3 + a9r'3 + a1063

± ay'3 ± a12I,: + a13;i'' + a1

+ a1i' + a164i',

= b1 + b2' ±

b3r' ±

b45 ± b5y ± b6"2r' + b7v'r'2 + bv'3

_±

_{b9r' +}

b1053

+ b11y.3 ± b12r' + b13' + b14) ± b15' ± b16',

= C1 ± CVt'

_±

L3Y2 _{+ C. ± C5}

_{± X;}

(4)

3. ROLL-YAW COUPLED INSTABILITY

Figure 5 shows roll extinction curves obtained in simulation _{runs on a straight course} at 30 knots having GM values of 3 and 2 ft. This particular result was obtained in the roll equation uncoupled from yaw and sway equations. The roll response shown in the figurc can be considered to be realistic on the basis of comparison with results obtained_from model tests of a similar high-speed ship shown in thesame figure.

When roll extinction curves were obtained in simultion

_{runs in equations of}

roll-yaw-sway coupled motions, an important change in rolling and yawing behavior was

taking place. Roll-yaw coupled instability was clearly indicated in test rtins. Figure 6 shows time history of roll and yaw motions starting on a straight course at 30 knots with an initial roll angle of 100. The roll extinction curve is approximately the same as that shown in the previous figure at the initial portion of the_{run. However, subsequent roll and} yaw motions are divergent, indicating roll-yaw coupled instability. When an autopilot is adequately included in these yaW-sway-roil coupled motions, stability characteristics of

sh

the ship system is improved as shown in Fig. 7, where _{the above mentioned roll-yaw}

to th instability is eliminated.

tics beh2

4. PREDICTIONS OF RESPONSE TO TURNING AND_Z-MANEUVERS

is g Figures 8 and 9 show response to 20°-20° Z-maneuver having GM of 3.0 and 25.0 ft. dire

to GM - 3 ft 0l 0 0 T port 3 2 To starboard 50

Maneuvering performance of high-speed ships with effect of roll motion 387

U -30 kt GM - 3 ft and 2ff

Time, s

Roll iesponse to initial angle of 0' (Simulation run on straight course)

Roll response t _{initial roll angle}

(6.29 ft model tests) FIG. 5. RoIling characteristics.

shown in Fig. 8, which clearly indicates a greater overshoot angle with GM of 3.0 ft relative to that with GM of 25.0 ft. It is clearly evident in this figure that cOurse stability characteris-tics are deteriorated with reduction in G1t-f. Figure 9 shows a substantial difference in rolling behavior with GM of 3 and 25 ft. rt should be noted in this figure that the largest roll angle

is generated for the case of GM of 3.0 ft when the rudder angle is shiftedto the other

direction. This clearly indicates that the rudder angle has a counteracting effect to outward heel angle during steady turning

00 ISp

Syr. Saeed, Displ.

knOt3 ') C) kcavy . 28 Heavy 28 Ligflr I -0 0.5 .0 .5 .2.0 2.5 3.0 4.0 4.5 5.0 Number of cycles

388 H. EDA 20 20 I0 5 U 0, C

0O

0 5 To Starboard

j

Roll angle. GM 3 ft star und hyd seq angl boa The

As

ma sub syst 00 ISO Time, s Heading angle, GM 3 ft To port

Fio. 6. _{Roll-yaw instability (with lO Initial isturbance)}

Figures 10 and 1.1 show computer-plotted turning and rolling characteristics in deep water. The major parameter changes in computer runs were as follows:

Rüddér angle 350 Gii'I = 20, 3.0 and 25.0 ft.

Roll angle during enter-a-turn is shown, for example, in Fig. 11, whichconfirms very well previous full-scale observations.

Figures 10 and 11 clearly show the ffect of GM on turning and rolling characteristics.

Substantial changes in maneuvering characteristics (i e, reduction in course-keeping and

increase in turning performance) are clearly evident in these figures with a decrease in GM.

S. YAW-SWAY-ROLL-RUDDER COUPLED MOTIONS WITH _AUTOPILOT Roll-yav coupled instability was clearly indicated in_{yaw-sway-roll coUpled motions} in the previous test runs. In actual ship operations, rudder is actively used, introducing important effects on yaw-sway-roll motiotis

Let us consider the ship dynamic behavior under the following conditions:

When the ship is proceeding on a straight course, a certain external disturbance (e g _the

)

3 0 0

=₀

where 20

Maneuvering performance of high-spccd ships with etlect of roll motion 389

To starboard

To port

soIlangle, GM 3 tt

= a ( -

) + b'.#',

= desired rudder angle, = desired heading angle,

a = yaw gain,

= yaw-rate gain.

Fo. 7. Roll extilietion curve (with autopilot).

starboard, for example, due to beam wind from the port, an asymmetri is formed in the underwater portion of the hull as shown in the previous figure (i.e. Fig. 2). As a result,

hydrodynamic yaw moment is generated to deviate the ship heading to the port. Sub-sequently, the rudder is activated by the autopilot to the starboard to correct heading

angle deviation. This starboard rudder angle produces the roll angle further to the star-board. Under this condition, the possibility of instability exists in the ship systems.

Accordingly, simulations were carried out under the following conditions:

The 500 ft long ship was proceeding on a straight course at n approach speed of 30 knots. A stepwise roll moment (e.g. due to beam wind from the port) was given to the ship. The

magnitude of the moment is equivalent to a statically generated roll angle of 5. The

subsequent dynaiiic response of the ship was computed with inclusion of an autopilot system, which can be represented as:

I0 20 50 Rudder angle 100 ISo Time. s

:

GM 2 ft :: .

:

20 -

..

*

4

* 50 '. 100 50 C C * ..* _* o

! 20

- -'

40 To port

Fic. 8. Z-nianeuver response.

Figures 12 and 13 show oscillatory motions for the case where GM = 2 ft, yaw gain

= 3, and yaw-rate gain = 0. Instability of the ship systems is clearly evident in the figure. When GM is increased to 3 ft, the stability charáctéristics is improved as shown in

Figs 14 and 15.

When the autopilot is refined with addition of yaw-rate gain of 0.5, further improvement

in the stability characteristics is shown in Fig. 16 and 17. It should be noted here that the

autopilot refinement substantially improved the rolling behavior as shown in these figures. The results mentioned in the above clearly indicate the possibility of instability due _{to a}

stepwise disturbance. During actual operations in seaways, Continuous disturbances are

given to the ship due to wind and waves. Accordingly, _{even marginal yawrollrudder} instability can introduce serious rolling problems inseaways.

Such difficulties have been frequently indicated in full-scale observations and model

tests (Taggart, 1970; Dalzell and Chiocco, 1973). Figure 18 shows, for example, the

possibi-lity of yaw instabipossibi-lity obtained by J. F. Dalzell during model tests ofa high-speed ship in waves (DaIzell and Chiocco, 1973).

6. CONCLUDING REMARKS

The purpose of this study was to develop mathematical equations of yaw, sway, roll

Rudder angle . a '1 a. C a 0 0 10 20 a a. C a a 250 300 .Trne s * ".

'

. 390 _{H. EDA} To starboard _{i - 500 It, U - 30 kt} Heading angle 40 _{GM.3ft p. 20}

10 20 0 t12 .GM= 25 1.-SOOn, U-3Okt .50 IO 50

200 '250

300 Time, s

Fro. 9. Roll during Z-rnancuvcr. U0 30 kt t - 500 ft Rudder angle 35 GM- 2.Oft 4.. .4. 4._4. 4.. 4.. 4.. 4- 4.. 4.'. 4.. 4* I 2 -3 4 I.

Fia. 10. Turning trajectory. To starboard 40 Roll angle ,GM 3ff Rudder angle 20 C 0 0 5 4 3 a -t 2 391

Maneuvering performance of high-speed ships with effect of roll motion

20

392 H. EDA

20

50 100 50 200 0

0

To port

-

FIG. II. Roll angle due to turning.

and rudder to represent realistic maneuvering behavior of high-speed naval ships, and

subsequently to exairune yawing and rolling motions during high speed operations through a series of simulation runs.

Based on recent captive-model test results of a high-speed ship configuration, important

coupling effects between yaw, sway, roll and rudder motions were included in the mathe-matical model. Certain terms such as yaw moment due to roll angle were not adequately considered in previous studies It was found in this study that these terms have important impact on maneuvering and rolling behavior, introducing the possibilities of instability

and serious rolling problems during high-speed operations in seaways.

The major findings obtained in this study are summarized as follows:

Roll angle introduces asymmetry of underwater portion of hull form relative to the longitudinal centerline, which generates yaw moment due to roll (i.e. Nt4).

This particular term introduces a tendency to turn to port when the ship is

heeled to starboard, contributing to inherent yaw instability due to roll combined

together with other couplingterms such as K,.' and K5' (i.e. roll-moment due to

sideslip and rudder angle, respectively).

When GM is relatively small (which is the case for most high-speed ships), the above-mentioned coupling terms can introduce severe rolling motions in a

sea-GM- 3.Oit GM- 2.0ff I0 (4) (5) Acknowl disctissio 0 J a. C a 4 20-To storboord Rudder oriIe Li 30 Id L- 500 ft - 35 Time s 20 tO

20 l0 C _a. a

o

C o 10

5-Maneuvering performance of high-speed ships with effect of roll motion 393

Conditions: I. Beam wind moment applied stepwise

autopilOt with yaw gain of 3

Ship speed U30 kr, L500 ft

GM - 2 ft

To starboard

,,,RolI angle

._.

To part

Frc. 12. Roll-yaw-rudder coupled motion.

. - . _.-: t . . _S.. _- ..

-.

. _* ._.... .

:.

:

+ -IOO 150 200 25O 3O 3

\

lime. 5 Rudder angle

way. This was clearly indicated in substantial rolling motions during turning

and Z-maneuvers.

The possibility of yawroll instability exists for the ship system with autopilot

during high-speed QperatioflS with small GiI.

Refinement in the autopilot characteristics has important efTects on yawing and rolling behavior of the ship.

Serious rolling problems frequently observed during high-speed operations in waves can partly be due to inherent yawroll instability (or marginal stability).

Acknow/edgernenzs-_Theauthor wLsh to thankMr J. F. Dalzell and Dr A.. Strumpi for their valuable discussions during various stages of this study.

10

C 0 3 C 10 C

Heoing angle tip)

C a

0 0

a l0 5 H. EDA To starboard Rudder angle. (-$) zo

:

.

*

.

0 _* +

t

4 4 * 4 4 4 4 ₄ 4 4 4 * _{4 + .} + 4 ₄ S + + + Time, s

.

+ 0 To port To starboard To port

Fic. 13. _{Roil-yaw-rudder Ooupled motion.}

Conditions: i.. Scorn wind moment applied _stepwise

Autopilot with yaw gain of 3

Ship speed .1-30 kt, t-500 ft

GM3f

FIG. 14. _{Roll-yaw-rudder coupled motion.}

Roll angle 4'.,

I

.. 50 100 ISO _{200 250} 300 350 flme, s 20 l0 I0 5.

0

10

Maneuvering performance of high-speed ships with effect of roll motion ₃₉₅

To starboard

10-o _rime.

.. .¼ _- Rudder angle

.e. * . IIIgI:I,1144t*ttI,,l,n,.IJJ::. ILl

j0_.

.,/50 tOO 150 200 250 300 350

_s_.. -.-.--. s.._

Heading angle

0

10

Toport

Fio. 15. Roll-yaw-rudder coupled motion.

0'

00

0 5 To port 100 50 200 Time, s

Ftc. 16. Roll-yaw-rudder coupled motion.

Conditions: I. Beam Wind moment applied stepwise

Autopilot With yaw gain of 3 and

yaw-rate gain of 0.5 Ship speed 11-30 kt, 1.500 ft GM3ft Roll angle Rudder angle 250 300 350 To starboard 20 To I0

5. 0 5 Wave higflt .../Heove Bow V Pitch Roll angle To port

Ftc. 17. Roll-yaw-rudder coupled motion.

Run No. 285 Wave Iengrh/shi length -0.75 Wave- to-heading angle 90' (beam seas)

I0' port Rudder -5 port Roll '(OW l0 storboørd 'Yaw 3 4 Time, S

Ftc. IS. Test records of yaw, roll, and rudder of-a container ship model_{(6.29 ft long) in a beam} sea, indicating yaw instability and coupling between yaw, roll and rudder.

6 396 a 'a 'a 20 l0 I0 5

a0

a To H.ESA starboard Time, S -l.. _. Rudder angle 3.i Ds Es Es Es Es Es Ti 50 tOO ISO 200 - I N__n. 230 300 350 ..

.______.----,..__..___.._.__-.___

-.

350

Maneuvering performing of high-speed ships with efFect of roll motion 397

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NSRDC-SPD-738-01.

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heading in regular wa'es. Tech. Rep. SSC-239 (SL-7-2), prepared for the Ship Structural Committee.

EDA,H. 1968. Low-speed controllability of ships in winds. I. Ship. Res.

Eø*, H. 1971. Directional stability and control of ships in restricted channels. Trans. Soc. nov. Archit. mar. Engrs, N.Y.

EDA, _{H. 1972. Course stability, turning performance, and connect on force of barge systems in coastal}

seaways. Trans. Soc. nay. Archit. mar. Engrs, N.Y.

EDA, a 1967. Steering control of ships in waves. Davidson Lab. Rep. 1205, June 1967. (Presented_{at the} International Theoretical and Applied Mechanics Symposium in London, April 1972)

EDA, _{H. and CaANE, C. L., Sit. 1965. Steering characteristics of ships in calm water and waves. Trans. Soc.}

nov. Archi:. mar. Engrs, N. Y.