Sea trials on a roll stabiliser using the ship's rudder

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SEA TRIALS ON A ROLL STABILISER

USING THE SEIP S RUDDER

W.E. Cowley and T.H. Labert*

T

Stheem

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Meketweg 2, 2828 CD Deift

& U1 - Fa 018 181838

Dopartant of Mechanical Enginoorinq, Univereity College London

TNI'RODUCTION

The behaviour of a ship in roll is complex due to cross

coupling and non-linear effects. _{By making simplifying and} linear-izing assumptions, however, the behaviour can reasonably be described in most cases. by a linear second order _{differential equation}

I, P

X$ +.e +

f(t)

a

where c is a damping coefficient associated with _{viscous effects}

around the hull, K is the restoring force per unit heel angle and f(t) is the external forcing function.

The centre of pressure of the ship's rudder is normally Situated below the roll axis and thus side forces produced _{by rudder} deflections will contribute moments about the roll axis. If rudder deflections proportional to roll rate are introduced with the correct sign relationship, the right-hand side of the equation is

modified

-P1 I

14i + c$ + K = f(t)

This may be rewritten in the form 2

+ 2ve + w F(t)

where a is the natural frequency of roll and v, the damping ratio

c+k

is given by _Y7ii

-Thus the introduction of negative roll rate feedback to the rudder enables the damping ratio in roll to be increased.

For an harmonic forcing function FCt. w02a sin at the

2-196

amplitude response is given by

(C )2]2

42

a

and maximum response occurs when a - w0/l 2w2 and is_{given by}

For light damping this approximates to

_-

_{and the thaximu}

amplitude ratio is inversely proportional to the damping rati

Although th _{sea excitation is a random process, the sharply}

bined resonance characteristic of_{a lightly damped ship means that} most of the larger roll oscillations _{occur at or near the roll}

resonant frequency, and severe rolling can be expected when the sea spectrum also contains high energy components at or near this

frequency. _{For the lightly, damped ship, therefore, any means of}

increasing the damping ratio _{will give a proportional reductin in peak}

'roll amplittdes.

A signal proportional to roll rate can readily be obtài+d from a rate gyro but if applied directly to the _{rudder control gear,}

would be unsatisfactory due _{to the phase shifts caused by the}

delays in the rudder actuating _{mechaniam. It is important that the}

phase relationship between _{rudder deflection and roll rate be}

maintained at or close to 180 _{degrees otherwise unacceptable rudder} excursions will be required to _{increase roll damping.}

A phase

rolationship which doviated by 45 degrees from the required value

of 180 degrees would

neceositato an increase or /2 in the rudder

1.

* amplitude to achieve the same alteration in damping ratio

POor ships which operate with _{a low G.M. and have a reasonably}

fast rudder gear, compensation for rudder _{delays can. be satisfactorily} obtained by simple phase lead compensation _{in the feedback path.}

or 'stiff' vessels with ponderous rudder _{actuating mechanisms,}

more complicated techniques would have to be employed to achieve phase

compensation, but in such cases it may well _{rov impossible to}

achieve sufficient rudder amplitude at the roll resonant frequency to make significant improvements in the roll damping_ratio.

The system employed in the tests described below is shown in

fig.l.

SEA TRIALS

Tests of the rudder .stabiliser system have been carried out on the container ship Manchester Concorde. This vessel, of 14810 torines displacement, L.G.P 151,8 m and beam 19.4 m, normally operates between Manchester and Montreal. _{Due to Operation in the Manchester}

Ship Canal and the Gulf of St. Lawrence under icing conditions the

ship is not fitted with bilge keels and is therefore lightly damped

in roll.

Roll reduction can be obtained from passive stabiliser tanks

fitted at the aft end of the Ship. Due to the operating requirements

S.'

* _{Active fin stabiliser systems sometimes use roll angle and roll} acceleration feedback as well as roll rate feedback. In such systems all three coefficients in the left-hand side of the roll equation are modified and the natural frequency Wn as well as the

damping ratio u is affected. It tnustbe recognised, ho,ever, that

such systems are capable of generating much greater moments about the roll acis than the rudder is, and that rudder activity is

really only capable of modifying the smaller of the three

coeff-icients, namely that of .

2-1.98

the ship is fitted with a powerful rudder with fast actuation and

the rudder delay can be approximated to by a Simple exponential

lag of time constant 3 a.

The ship normally operates with a G.M. between 0.3 and 0.9 m giving rolling periods between 15 and 18 seconds.

Satisfactory compensation .for the rudder delays can b achieved

with a simple phase lead network of the form ( 1 + T5

1 +

CALM WATER TRIALS

Calm water tests were carrred out to determine the r011

response of the vessel to harmonic rudder excitation. _{Sirni oidil} inputs at varying frequencies were injected into the rudder servo

amplifier and the steady state roll angles produced were me sured.

The results of these tests are shown in fig.2 where the do le amplitude

of roll is plotted against frequency for two ship speeds with

different amplitudes of rudder angle. _{The smaller rudder gle}

corr-esponded to peak deflections of 7½°; the higher angles be ng 15°.

It can be seen that the resonance peaks occur at an excitát en frequency oE 0.065 lIz and that the ratio of roll angle to rudder angl at

resonance- is aprroximately 0.5 for the larger rudder angles and _0.67

for the smaller rudder angles. The effect of speed reducti n on

the amplification factor is very pronounced _{at low speed, t ratio of}

roll to rudder angle being only 0.25. _{It was observed dunn the tests} that, in the region of resonance, differont _{amplitudes of osillation}

were obtained dopending en whether the frequency was increaskng or

decroa@jng _{This La indicated by the curves shown on fig.2}

md is

wtj the jp recnanc-s

_{or.omer.on observed duinj model}

:-testing (ref _{1) which is due to a hard spring characteristic of the} restoring moment versus heel angle curve.

Further tests were carried out to determine the damping ratio

of the hull and to investigate the effects of roll _{rate feedback}

to the rudder on this damping ratio. In these tests sinusâidal

excitation at resonant frequency was fed to the rudder in order to create a forced oscillation in roll and when steady state conditions had

been reached the excitation was switched out and roll rate feedback was switched in. The decaying transients were recorded and the

damping ratio obtained from the logarithm decrement. _{Typical transients} are shown in ig.3, and the results of the tests are shown plotted

in flg.4. Due to small amounts of natural sea excitation producing

random roll of 1 or 2 degrees amplitude and due to the difficulties

of measuring the more heavily damped transients, some appreciable scatter of the results occurs. Nevertheless they indicate a

substantially linear relationship between damping ratio and roll rate

feedback gain. Although the phase advance parameters in the controller

were varied during the test, the effects of scatter caused the

variation of damping ratio with these parameters to be not statistically significant and a single line based on the best least squares'

fit is shown on fig.4.

By reversing the sign of the roll rate feedback, self-sustained (unstable) roll oscillations with peak to peak amplitude of 15 degrees were obtained with a roll rate feedback gain of =3.

TRP.NS-ATLATIC TESTS

With the co-operation of- the ship's officers, measurements of

roll and rudder activity encountered under a variety of ce states

during seven voyages were recorded. Ths ship is fitted wih passive

tank stabilisers which-are normally filled during very rough weather

and so results were- obtained with the passive tanks both empty -and

filled.

The normal procedure in every case was for recordings to be made over consecutive one-hour periods with and without the rudder

stabiliser switched on. The results of these tests are shown in Figs.5 to 8. An analysis of the rudder records showed thai roll

reduction was achieved without any measureable increase of rudder

activity, when the stabi-liser was used with the passive t S unfilled. When the passive stabiliser tanks were filled the situation is sOmewhat different. Much smaller reductions in roll amplitude were obtãinCd

- from the use of the rudder stabiliser and the reductions which did occur carried the penalty of increased rudder activity.

Records of yaw were only taken during one voyage but no discernable

difference between the stabiljser and unatabilised tests was observed. This is a predictable result since the yaw resonant frequency is-an order of magnitude lower this-an that in roll is-and during tris-ansient testing it was found that rudder excitation producing some 20

degrees of roll oscillation caused less than 1 degree of yawIng. Fig. 9 shows a plot of stabilised amplitude versus unstabilised amplitude taken from all the tests. _{Least squa±es fit striight lines}

are shown for the conditions with and without the passive _stabiliser tanks filled.

SIJMMART OF RESULTS

From the stary of transient results shown in fig.4 .t may

3 and 4 give rise to an increase In damping ratio of about 70%.

For the light dming conditions obtained it is reasonable to assume that the peak amplification factor at roll- resonance is inversely proportional to damping ratio and that a reduction in peak roll

amplitude of about 40% should be obtained with this increased damping ratio. Reference to fig.9 shows that under random sea

disturbance conditions a reduction of this magnitude is obtained

without the passive tanks filled and the agreement between the prediction from transient tests and the actual roll response results is quite

remarkable.

The results of the trials with the passive tanks unfilled are

also consistent with the analogue and model experiments previously reported. The results of the trials with the stabiliser tanks filled are not consistent with those obtained from model experiments where the two systems were found to be entirely compatible and the rudder. stabiliser produced -additional worthwhile reductions in peak roll

angles without increased rudder activity. A complete explanation

has yet to be found for the difference between the model and ship

results with the passive tanks filled, but the unsatisfactory behaviour of the rudder stabiliser in these circumstances is thought tobe due

to phase changes which occur with the tanks filled as a result of interaction between yaw and roll in the hull dynamics. This was

suggested by observations made during trials where it was noted

that rudder and yaw activity with the tanks filled was generally less than the activity in corresponding sea states without the tarl)s

filled, thus suggesting that the stabiliser tanks act as yawdampers

as well as roll dampers. This is consistent with the positioning of the tanks which are mounted well aft in the ship and thas inertia

2-202

forces due to the lateral acceleration of the water -in the tanks

will produce quite large momonts about the yaw axis of the ship.

Further investigation of this hypothesis Is taking place. Anothe

factor which may well influence the response with the tanks fille is non-linear behaviour of the water within the tanks. It Is apptrent that wave breaking effects commonly known as 'sloshirig' occur in he

tanks particularly at larger roll amplitudes and in these conditi?ns the simplified theory of the tank acting as a linear tuned absorber is no longer valid. Operating experience showed that it was advantageous

to modify the shaped roll rate feedback signal with the introducton

of a small dead zone and amplitude limiting. The former had the 4ffect of fIltering small amplitude high frequency noise signals from the

rate yros which caused undesirable clatter of the autopilot rela's. The amplitude limit had little effect With the passive tanks empty.

but helped to reduce excessive rudder activity when the tanks wer in operation.

cONCLUS IONS

The results show that, for the particular ship used for the

trials, the rudder stabiliser was successful in reducing roll.

one particular voyage (86 West) the stabiliser enabled the ship

maintain speed .and course when emerging from the eye of a storm b

when the stabiliser was switched off at the end of the test pen

the increased violent rolling necessitated a reduction in speed a

change of course while the passive tanks were filled.

The successful application of the -system depends upon the

capacity of the rudder to excite significant -angles of roll. For

is probably ma1l. For new designs, naval architects may care to assess the economic advantage of using a slightly larger and faster

rudder instead of passive tanks or other means of stabilisation. and

also the benefits to be obtained from avoiding the undesirable

features of passive tanks.

AcNowLEDCEMcNr

Ta authors acknowledge the Support given for this work by the

Department of Industry and are indebted to the Superintendent of

Ship Division, National Physical Laboratory for permission to

publish this paper.

They are also grateful to Manchester Linors Ltd. for offering

the facilities for sea trials and to the officers and in particular

the two captains of the C.S. Manchester Concorde, Captain J.E. skcw and Captain P.N. Fielding, for their care in taking records in the

arduous conditions of the N.. Atlantic in winter.

FERENCE

1. Cowley, W.E. and Lambert, T.H. "The use of the rudder as a

roll stabiliser" 3rd Ship Control Systems Symposium, Bath, 1972.

2-204

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Frequency (Hz)

11,Skts, Rudder.±12,5°

Disp. 13290 Tonne

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17.5kts, Rudder ±15°

o 17,5kts, Rudder ± 7,5°

Forced Rofl Responses to Rudder Inputs.

Fig.2

G.M. 0,87 m 2-20 6

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2-207 I'.

Fig.3 _{Transient Roll Decay}

(The arrows indicate the start of each transient) /

(b) Roll rate gain 2

(a) Roll rate gain 1

0,15 0,10

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+ 4: + + 2 1. 6 8 10

Roll Rate Gain

Results of Transient Tests in Calm

Wate

11. December 197!..

+

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(LEast sqJares fit tind

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Fig.!.

10 8 2 2100 2200 2300 SP 18 KTS.

SEA Mainly fellowing or quarterly

WIND _{Force 5 increaoing to 8}

SPEED 17 KTS

SEA Mainly iy

WIND Force 'IS

V0V7CE 85Z .5 0100 3 DEC 74 I I I

.

0200 1600 2?'3 30 25 20 15 10 S

ROLl. RESPONSE RECORDS OF VOYACE 85 N £

o UNSTABILISD STABILISED TANKS IN I I I-8 I I I 8 I I-

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1 I I WEST 0 4 a + + + ₊ 27 NOV 74 I I 26 NOV 74 I I I I

1.1

1000 1100 1200 1300 1400 1500

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32

12 jo

17 )CFS SEA Heavy bees sea

A weil .n eye of low WIXD Force 5/6

F-

31 DEC 74 1000 1200 1400 VOYAGE 865 2-2O .4 3 .JM 75 4 a EAST 4v I I I I I 7O0 1.900 2100 17.5 KTS

-- Heavy 'cund swell Force 1/2

2/

6

ROLL. RZSPONSC RECORDS OF VOYAGE 88 E

0

1 I I I- I I 24 Feb 75 £ I I I I I I I I I I EAST I I

Moderate quarterly sea and swell Force 6 2-211 Pig .8 UNSIABILIS £ STABILISED o TANKS IN 1500 0800 1000 1200 1400 1600 800 2000 Reducing )4odcrat. beam sea Force 8

SPEED SEA WIND

Increasing

Moderate beam sea

Passing thróug) depression

O IJNSTABILISED

4 STABILISED o TAN1(S IN

ROLL RESPONSE RECORDS OF VOYAGE 86 W

2000 2200 0000 0200 1000 1200 17 KTS

Beis sea & heavy swell Force 7

Reduced to 14 KTS Beam sea & swell.

Force 8

Fig.6

SPEED 17.5 KTS

SEA Rough beam sea A swell

WIND Force 7

2f 1 6 4 2 1200 SPEED SEA WIND 3.2 10

&

I I I S I I I I I - WEST 16JAN75 I I I I I

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29 JAN 75 I I SPEED SEA WIND 11.5 KTS

Rough following sea Moderate swell Force 7 VoyaoE 87 5 0800 1200 1600 17 KTS 17.5 KTS

Slight head sea

-Moderate/heavy beaa swell Moderate/heavy beam awelX

17.5 KTS

S1igt head sea

1600 2000 2200 2400 our.h hs.ie oa Heavy swell Force 7 increasing to 9 1 Feb 75 4 I V _{0700 0900} 16 KIS

Ru.b uirter1y sea

8eavy swell 6 increasing to 8

Stabilised Roll Amplitude (2

_,degrees)

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1400 1600 17 ICTS Slight sea Moderate head swell

Force 3/4 Force 2/3 Force 3/&&

UNSTABLISED

ROLL RESPONSE RECORDS OF VOYACE 81 8 _STABILISED o TANKS IN 12 jo 6 _£ £4 28 JAN 75 I

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I 1 2000 2400