Feasibility study of employing the rudder as an anti-rolling device

TECHNISCHE HOGESCHOOL DELFT

.AFDELING DER SCHEEPSBOUW- EN SCHEEPVAARTKUNDE LABORATORIUM VOOR SCHEEPSHYDROMECHANICA

/

Feasibility Study of

Employing

\ the Rudder as An Antirolling Device

K. Huang

Report no. 518 April 1981

Deift University of Technology

Ship Hydromechanics Laboratory Mekelweg 2

2628 CD DELFT

The Netherlands Phone 015 -786882

Contents

Summary 1

Introduction 1

Rolling Motions Excited by the Rudder 3

Equation of Forced Rolling Motions and

Open-loop Responses 5

Roll Velocity Feedback to the Rudder 7

Roll Angle Feedback to the Rudder 11

Combined Feedback of Roll Velocity and

Roll Angle to the Rudder 16

Roll Acceleration Feedback to the Rudder 17

Concluding Remarks 18

Acknowledgement 19

References

21

Summary

Model tests and subsequent analysis of measurements in an attempt to

employ the rudder as an antirolling device have been carried out in the Ship Hydromechanics Laboratory

of

the Delft University of Tech-nology, the Netherlands.

The experimental results showed that in addition to steering a rudder has considerable potential for roll stabilisation at or near the

reso-nant roll frequency, and the feasibility of combining steering and roll

stabilizing by using only rudders exists undoubtedly. Up to now it seems that roll velocity feedback gain is the most effective among various types of feedback.

1. Introduction

In the light of conventional conceptions rudders on surface ships are rrrely

able to control the ship heading only. It was not until

1967

when an Arrerican

containership fitted with a rudder steering/stabiliser system was tested on

a

voyage crossing the Atlantic that naval architects realized that it may well

be possible to use the rudder to reduce undesirable rolling motions of the ship

without affecting its course-keeping capabilities (1.

Subsequently, in

1972 W.E.Cowley and T.H .Larnbert (2.)

pointed out that

the

side force generated by a ship's rudder generally acts beloi the centre of

gravity and thus exerts roll in addition to yaw rrorrents on the ship. When

the

roll rrorrent caused by the rudder is in phase with the exciting roll

morrent

considerable rolling would be set up. But if a correct phase relationship

can

be

established between the rudder roll morrent and the external excitation,

it

is reasonable to suppose that the rudder may be used as a rreans of

reducing

roll amplitudes.

The feasibility of roll stabilisation by rudders was also discussed by F.F.

Gunsteren (3) with full scale craft experirrents and the results were

pub-lished

in 1974.

The author held that rudder stabilisation of

small craft seems

to be promising.

In

1975,

W.E.Cowley and T.H.Larnbert pointed out once again that the

intro-duction of negative roll velocity feedback gain to the rudder enables the

dirren-sionless damping ratio in roll to

be

increased C 4)

.

At the sane tirre, a study

made by J . B .Carley (5)

showed that. effective stabilisation by rudders

is

limited to a narrow band in the proximity of the natural roll frequency.

In order to coiipletely develop the idea concerning rudder antirolling devices

a series of model tests involving

Ljt(

-2 -)

rolling rrtions excited by the rudder,

open-loop responses to exciting rrorrents generated by oscillators fixed in the model,

various types of closed-loop responses including variations in feedback gains such as roll angles, roll velocity, roll acceleration, and the corrbination of roll angle and roll velocity

were conducted by moans of a Todd 60 model with C=0 .7 ( Table 1 ) in the ship

model basin, Delft University of Technology, the Netherlands. On the basis of these tests a discussion on the principle of rudder antirolling devices was made

in brief and it was concluded that

among the various feedback gains given in this paper, it sens to be that

the velocity feedback is the best one which enables the rudder to reduce unde-sirable rolling motions at frequencies higher than 2.3 rad/sec, with a maximum reduction percentage more than 50% in peak roll angles as shown in Fig .12 (E).

But it can be seen, from Figs.9 and 13, that for the considered case at fre-quencies lower than 2.3 rad/sec roll angle feedback is better than roll velocity

feedback as viewed fran the reduction in peak roll angles,

after introducing roll velocity feedback gain to the rudder it appeared that the peak roll angular velocity decreased with a maximum reduction of about 50% as shown in Fig.11.

Table 1 Main particulars of the model

2 Todd Series 60

model scale 1/54

Items Ship Model

Length, design waterline Length, beeen

perpen-diculars Breadth, molded Draft, loaded Volwne

of

displacement, loaded Service speed

Natural frequency

of

roll

123.962m 121.91Gm 1?.416m 6.968m 10364m3 14 knots 0.335 rad /sec 2.295Gm 2.257?m 0.3225m 0.1290m 65.?48n3 0.99m/sec 2.464rad /sec

S

S

2. Rolling Motions Excited by the Rudder

Making the rudder angle be changed in a sinusoidal manner

5=S 5mw t

a o

where Sa= rudder angle amplitude

= frequency of rudder swing

the model would be excited in still water into a steady rolling motion

= sin ( w t +

a 0

where = roll angle excited by the rudder = roll amplitude or peak roll angle

= phase angle by which the rolling motion lags the rudder deflections. The still water responses

a to an harmonic excitation by the rudder and

10.8

0

0

_ó =10° 6 =20

a a

Fiq.1 Still water roll responses to a

harmonic excitation by the rudder

phase angle at given Vm ( model speed ) and are shan in Figs.l and 2 res-pectively.

The similar results obt:ined from a fast containership model tests (2) _are shown in Fig.3.

The fact that considerable roll moments can be generated by rudders is veri-fied by the test results of a full scale 16,900-ton containership (1) running on a voyage of Atlantic crossing, as shown in Fig.4 from which two points are

)CL -t--) er ) 1

V =

14 m

V=Q.99m/sec

knots

4I

-s_

'C.-1.0 2.0 rad. /sec) 3.0

9 0 3 30 0) 0) 20 10 0.2 2 0 40 80 120 160 (degree) =10° ____.

a20U

a

Fig.2 Phase angle

0.3

Wa

0.4

Fig.3 _{Rolling angles excited by}

the rudder

noteworthy:

Wnen the rudder reaches

an

angle of 20 deg to port or to starboard,

the

swing extremities reach angles of attack to the propeller race where stall

begins and the side forces fall off drastically. Therefore, it is

unnecessary

to make the maximum rudder angle greater than 20 deg.

As far as a full scale ship is concerned, there exists an

unsyImTtrical

distribution of side forces to left and to right because of the corrbined effects

of wake distribution, changes in propeller race, and so on.

(Hz) 0.5 ) 4

V-l4knots

Vm=0.99m/sec

-0 S

=20° a =100 a

/\

,

°5A

8O0 40 0 0 10 20 30 (3 (degree) a

Fig.4 Rolling moment excited by the rudder

In view of the above-mentioned statemants it may well be imagined that since rudder can excite roll it also has potential value as an antirolling device.

3. Equation of Forced Rolling Motions and Open-loop Responses

By making simple and linear assumptions, the forced rolling motions of ships in waves can reasonably be described in rrost cases by a simple linear equation

in one degree of freedom

AtBtC=M(t)

(1)

where A = inertial rrorrent of mass including virtual mass B = damping coefficient

C = restoring mcment per unit heel angle

M ( t ) = roll exciting morrent which is produced by a gyro-oscillator fitted in the model and changed in a sinusoidal manner

M ( t ) = Msinuit

(2)

in which Ma = amplitude of the exciting morrent

w = frequency of the roll exciting mcinent, i.e., the angular fre-quency of the oscillator.

The open-loop responses to the manent given in Eq. ( 2 ) is as follows

= sin( wt +

(3)

iderin (op cijfe

i (op cijfer-2 -) lijn)

1'

0---6

swing swing

10

Left Right

/fi

I

where

_{= phase angle by which the roll motion lags the exciting manent}

= peak open-loop response or roll arrplitude.

The nondimensional danping ratio is given by

0 150 w w a) 100 50 C 0

2.0

* = B

2JAC

3.0 _(rad./sec) U)

Fig.6 Phase angles

(4)

4.0 6 dllI

-V V =14 5 rn knots =0.99rn/se/

/

I//n

p

A-

M=O.O47kg-rn

1.5

2.0

2.5

3.0 3.5 w (rad. /sec) O__Ma .071kg-rn .047kg-rn

S

2 -)

n I

In this case the open-loop responses and phase angles have been obtained

fran

the tests and are given in Figs.5 and 6 respectively.

4.

Roll Velocity Feedback to the Rudder

Various types of closed-loop responses have been tested

, with the

feedback

control system in Fig.7 and the results given in the subsequent sections.

At

first the roll velocity feedback to the rudder will be taken into consideration

in this paragraph.

If rudder deflections proportional to the roll velocity, i.e., cS=c2q

( where

is a coefficient dependent on the roll velocity feedback gain

) are introduced

with correct phase relationship, a negative roll morrent

M()

-k2

(5)

will

be

caused by the rudder, and the right-hand side of Eq. (1) is rrodified

A+B+C=M(t)-k2

(6)

The equation above may be rewritten in the form

+c2=M(t)

in

n

where

Wn = natural frequency of rolling rrtions

= nondimensional damping ratio which is given by

B+k

₂

2JAC

k2 = a moirnt coefficient in kg-m-sec/de, which is also proportional to

the roll velocity feedback gain and is chosen in accordance with

the rudder swinq extremities.

For such an harmonic force function as is shown in Eq. (2), the closed-loop

resrcnses would be

= ai" wt +

(

in which

a1

= peak closed-loop response

or roll amplitude

= phase angle by which the rolling motion lags the exciting manent.

But we only show interest in

, the phase angle difference between

the rollng

motion and the rudder swing, instead of

The phase relationship among M,

S

rudder servo

u eceive

'4

.7 Block diagram measurement with Todd 60 mode1,C=.7O

power suply

for battery charger transmitter remote control rudder mot or control motor power s u ppl y battery

L

roll-gyro roll oscillator rudder amplifier

batt ery course- I

gyro I

50HZ

50HZ

oscillator

period time u . v . paper

recorder

carriage speed counter

printer

cal ibrat ion

amplifier low-pass filter 00HZ generator for all gyro' s

amplifier unit for

50HZ summation, inversion, differentiation to r 50HZ d emodul s 50HZ

servo remote charge

rate-c0n t r ol cont rol Os c ill at or regulator gyro I I I I-L

b

_{E=EM_EM}

a

20 10 5 0 M

Fig.8 Phase relationship

Contrasting Eq. (4) to Eq. (9) shows that the negative roll velocity _feedback to the rudder enables the daniping ratio in roll to be increased. This is

ye-1.5 2.0 2.5 3.0 3.5

(rad ./sec)

(A)

Fig.9 _{Peak roll responses}

. 0

A

V =14 5 knots V =0.99rn/sec rn M =0.047kg-rn a

/

. k2=0.24 / C'' /

/

/

\

\\

_

Open-loop L-- Closed-loop

0--Reduction percentage of peak roll respon

I I I I I I 40 a) cd 4J C a) C) a) 30 C 0 4J C) 0 a) 20 10 e 0

I

rified by the

open-loop and closed-loop responses shown in Fig. 9, with the

phase

angle difference

E2

and peak rudder angles given in Fig. 10.

It is noteworthy that in general the roll rate would reduce after

introducing

the roll velocity feedback and under certain circumstances this reduction

is

rather large as shown in Fig. 11.

100 95 90 1.5 2.0 2.5 3.0 3.5 (rad. /sec) w

Fig.10 Phase angle difference and

oeak rudder angles

The effects of k2 on rolling motions are shown in Fig.12,

from

which it is found that as k2 increases the peak roll angle

_a1

would decrease and the peak roll angular velocity decreases

too,

with

ranging from 95 deg to 106 deg. in making choice of

k2

special attention should be paid to the fact that when the

rudder

swing reaches angles of attack to the propeller race where stall

begins the side forces fall off drastically. Therefore, there seems

to be no need to make the peak rudder angle excessive.

30 5 0 15 10 10

/

/

/

V =0.99m/sec k2=0.24 knots 0.047kg-m -\\ V =14 5 / m M I / \ a / / -0 I I U

5 4C ! 3Q 0 4J U 0 c 20 0 10 2.0 V _l6knots S 2.5 M _0.047kg-m a Vm=l.l3m/sec k2=0.175

Fig.11 _{Peak roll rate}

5. _{Roll Angle Feedback to the Rudder}

If the rudder is controlled by an automatic pilot system with a roll angle signal 5=c1 ( c1 is a coefficient dependent on the roll

angle feedback gain ) , a negative roll moment

M() =-k

will be caused by the rudder, and the equation of rolling motion will be

A + B _{+ ( c+k1}

) = M ( t ) (10)

The nondimensional damping ratio is given by B

- 2JA(c+k1)

3.0 (rad. /sec) (1) -U S 0

oio

__I'

F _K'

0,_

-

o

/

\ 00

\O

C) rtj _5Q .1J 0 C) 0 C) 40 0 0 4J 0 0 20 10 -20 -1 0 15 5

0 0

0.1

0.2

0.3

0.4

(A)

Peak roll responses

Fig.12

Effect of roll velocity feedcack gain

on rolling motions

0.5

k 2 12

-

a1

V=14 knots

M0.047kg-m

IV=O.99m/sec

I

Open-loop

G

Reduction

Closed-loop

I I

percentage

of peak roll responses

i I I i

_V=14

I I I I

knots

M=O.O47kg-m

50 C) C) 10 C) 40 10 30 95 20

0.2

0.3

0.4

0.5

k2 (B)

50 .4J U) 0 U) 40 0 0 o 30 U) 20 10 0

-20

15 10 5

0.1

(c)

Peak roll responses

U) ZL .

V =14

5

=0.99m/sec

knots

M a

=0.047kg-m

=2.46rad/sec

V m

0

I

Open-loop

Closed-loop

Recuction

I I

percentage

1

--of peak

1 I I I

roll responses

50

40,

30

:iU1.i.

F__

40 -100 30 95 20 10 90

0.1

_0.2

_0.3

_0.4

_0.5

0.2

0.3

_0.4

(D)

Fig.12

_{Effect of roll velocity}

_{feedback gain}

on rolling motions

a

U) U)

)

bf

blan.

cij fer

W (t: 50 -4J C) C) C) 40 0 C) 0 30 20 10 (S a 50 40 30 20 -20 15 10 5 0_ 0 0.1 105 100 95 10 90 0.1 0.2 0.3

Peak roll responses

0.2 0.3 0.4 k 2 0.4 k 2

Fig.12 _{Effects of roll velocity feedback gain}

on rolling motions 0.5 0.5 14 IW a1

//

N

/

N N V =0.99rn/sec knots a M =0.047kg-rn w=2.70rad/Sec V =14 5 -0-Open-loop C losed-I Reduction I

loop

Dercentage 1 rn

of peak roll responses

WI

-0

C) (I) 50 30 20 -.

___________

U

U\f

i....140

-VV

S=14 V =0.99rn/sec knots M a w=2.7Orad/sec =0.047kg-rn rn I I I I I I I

I

and the closed-loop responses would be

wt + ₍₁₂₎

where

a2 = peak closed-loop response with roll angle feedback

gain

k1 = moment coefficient dependent _{on the roll angle} feedback gain.

Contrasting Eq.(11) to Eq.(4) shows _{that roll angle feedback gain} to the rudder enables the damping ratio to be decreased. When _the

damping reduces to such _{an extent that the rudder is made as a}

roll-exciting device, the peak roll responses are to be increased cor-responding to some frequencies of _{external forces, as shown in Fig.}

13. Therefore, roll angle feedback to the rudder seems to be

un-practical. 30 20 a2 10 0 (rad. /sec) w V =14 knots M =0.047kg-rn 5 a

V=0.99m/sec

k1=0.358 _.Q_ Ooen-loop -- closed-loop

Reduction percentage of the peak roll responses

Fig.l3 Peak roll responses

-2 0 0

USL.

w cd w ci 20 W 0 4J C-) 10 c 0 0 2.0 2.5 j. -10 20

b1c

b lant

ci3f 2

3

6. _{Combined Feedback of Roll Velocity and}

Roll Angle to the Rudder If a combined signal

- c2 + c1

where c1 and c2 are coefficients previously mentioned is _received by the rudder from an automatic pilot system, a negative roll mo-ment

M() =-( k2++ k1

will be caused by the rudder, and the equation of _{rolling motion} is

A + (B+k2) + (c-f-k1) _{= M(t) (13)}

The nondimensional damping ratio is given by B + k2 lerin (opcijfer (op cijfer -2 -) ''erbrokenlijn) (enkel 16 2/A(c+k1) (14)

and the closed-loop responses would be

= a35ifl t+,i ) (15)

where = peak closed-loop responses

Ic1 and k2 = moment coefficients m&itioned in Sections 4 and

5 respectively.

Contrasting Equation (14) to Equation (4), it is difficult to de-termine whether the damping ratio increases or decreases after

in-troducing a combined feedback. The experimental results given in Fig.14 shows that the reduction percentage in peak roll responses is less than in the case with roll velocity feedback shown in Fig.9, and this reduction percentage will be very small at higher frequen-cies of external moments.

It can be concluded that the combined feedback is inferior to that mentioned in Section 4.

)

20 a3 10 30 2.5 3. (rad. /sec) w 0

2.0

V =14 knots S V 0.99m/sec m k1=0.358

k2=0.24

-0 Open- loop -ta- Closed-loop

Reduction percentage of the peak roll responses

Fig.14 Peak roll responses

7. _{Roll Acceleration Feedback to the Rudder}

If a roll acceleration signal

= -k

where k3 is a coefficient dependent on the roll acceleration feed-back gain is given to the rudder by a automatic pilot system, a negative roll moment

M() = -k3

will be caused by the rudder, and the equation of rolling motion is as follows Ma=O .071k g-rn 30 20 10 0 (opcijfer-)cijfer-2)

)

)

(17)

(18)

en lijn) A+k3)

+ B q + C q = M(t)

The nondimensional damping ratio is given by

B

-

_2J(A+k3)C

and the closed-loop responses would be

= a4r(

wt +

)

(19)

where

a4

= peak closed-loop response

k3 = moment coefficient dependent on the roll

acceleration

feedback gain.

By contrasting Eq. (18) to Eq. (4)

,

it is evident that

4 I

and especially in the proximity of resonant frequency the recuction

percentage in peak roll responses shown in Fig.9 is much greater

than that in Fig.15. This proves that a roll velocity feedback to

the rudder is superior to a roll acceleration feedback at or

near

the resonant frequency.

8.

Concluding Remarks

So far, the contribution of rudder antirolling devices to

re-duce

peak roll angles at or near the resonant roll frequency

has been explained. In automatic systems of combining steering

and roll stabilising by using only rudders, a roll velocity

feed-4

back seems to be the best among all the feedback types put forward

in this paper.

As for the effectiveness of rudder antirolling devices when cariparing

them

with other stabilisers, Fig.16(2)

may be a good representation to shcw their

relative merits.

In order to make rudder aritirolling devices cane into use, ships to which

these devices are to be applied must be

equipped with large rudders, powerful

steering machineries, and autcmatic control systems.

)

a4 20 10 0 0 w 2.0 V =14 knots S Vrn=O.99rn/sec k3=0.1875

-0

Onen-loon - Closed-loop

EJ-- Reduction percentage of peak

roll responses

Fig.15 Peak roll responses

9. Acknowledgement

The author is greatly indebted to Prof. Ir.J.Gerritsma and

W.Beukelman for their patient guidance due to which all the expe-riments and this report could finally be finished smoothly.

The author would like to express his gratetude to J.Ooms and

C.V.Jorens for designing and making the whole control system in the tested model. The assistance and co-operation given by _R.Brink

and E.C.Post are gratefully _{acknowledged.}

(rad . /sec) Ma=O .047kg-rn 3.0 40 30 10 0 0 20 0 0 0

)

)

)

0

0.2

0.3

0.4

_(Hz)

0.5

W

o

Unstabilised Rudder alone

0

Tank alone

+

Rudder and tank

Fig.16 Peak roll responses with

different stabilising systems

erin (opcijfer 1 -) (op cijfer -2 -)

{2J

20

:

)

(\4 60 ci) 40 20

)

)

onderin (op cijfer

-r

tfl (01.) ciiCer

-References

Robert Taggart, " Anomalous Behavior

of

_{Merchant Ship} Steering Systems " Marine Technology, vol.?, no.2, April 1970

W.E.Cowley and T.H.Lambert, _{" The Use of the Rudder as A} Roll Stabiliser " 3rd Ship Control System Symposium, _Bath, England, September 26-28,1972

F.F.van Gunsteren, " Analysis of Roll Stabiliser

Per-formance " _{I.S.P., vol.21, no.23?, May 1974}

W.E. Cowley and T.H.Lambert, " Sea Tria7s on A Roll Sta-biliser Using the Ship's Rudder " 4th Ship Control System Symposium, Oct. 1975

J.B.Carley, " Feasibility Study

of

Steering and Stabi-lising by Rudder " 4th Ship Control System _Symposium, Oct. 1975

IVomenc lature

A mass of ships including added mass

B damping coefficient

C restoring moment per unit heel angle

k,k,k

1 2 3 moment coeff-ic-ients w'i-th i-ntroducing feedback of roll angle, roll velocity and roll acceleration

respec-tively

M(t) roll exciting moment produced by the gyro-oscillator fitted in the model

Ma amplitude of exciting moments

t time

Vm speed of the model

V5 speed of the ship rudder angle

rudder angle amplitude

phase angle by which the roll motion lags the rudder deflections

phase angle by which the roll motion lags the exciting moment

phase angle by which the rudder deflections lag the exciting moment

nondimensional roll damping ratio unstabilised by the rudder

v, v2, \)3 V4

nondimensional roll damping ratio after

22 introducing feedback of roll velocity, roll angle, com-bining both, and roll acceleration to the rudder res-pective ly

roll angle excited by the rudder, _{or by the} gyro-oscil-lator with no or various _{types of feedback}

amplitude of roll angle excited by _{the rudder}

34

open-loop response to the moment produced by the gyro-oscillator

peak open-loop response

a1, a2, a3, a4 peak closed-loop responses after intro-ducing feedback of roll velocity, roll angle, combining

w _{frequency of the roll exciting moment produced}

by the

gyro-osci 1 lator

801085

AFDELING DEA SCHEEPSBOUW- EN SCHEEPVAARTKUNDE

TECHNISCHE HOGESCHOOL DELFI

LABORATORIUM VOOR SCHEEPSHYDROMECHANICA

/

Feasibility Study of

Employing

\ the Rudder

_{as An Antirolling Device}

K. Huang

Report no. 518 April 1981

Deift University of Technology

Ship Hydromechanics Laboratory Mekelweg 2

2628 CD DELFT

The Netherlands Phone 015 -786882