Steering and manoeuvring of ships. Full scale and model tests, Part II

V

ÂRCHi

PARE YAW TEST

YAW AND DRIFT ANGLE TEST

1

STRG AD MAOUVG C

1PS

-AN

OL TESTS

by Leif Wagner Smitt*)

PART II

Planar-motion mechanism technique

The PMM can be used in two modes of oper-ation, designated "static" and "dynamic". In the static n-iode the model is constrained to move

along a straight path while drift angle and/or rudder angle are varied as shown in Fig. lo.

The unique feature of a PMM, however, is

its ability

to generate cyclic motions when

operating in the dynamic mode. Cyclic motions

are imposed on the model in such a way as to produce "pure sway" or "pure yaw" motions.

STATIC DRIFT AND RUDDER ANGLE TEST

'N

GTUtS 3.0. MOtiOURSWUNENUNd b PIIC DIArAUg iSREGC CeNt,.

PARE SWAT TEST

.3

Fig. 11 Motions generated by PMM during dynamic

tests.

) _{Research Naval Architect at the Hydro- and} Aero-dynamics Laboratory, Lyngby, Denmark.

b.

y.

Scheepbouwkud

Technische Hogeschool

Deift

SULL SCL

In "pure sway" tests sway velocity and sway acceleration are produced while the model

mo-ves with its centre-line parallel to that of the tank as shown in Fig. 11.

In "pure yaw" tests yaw velocity and yaw

accelerations are produced by causing the mo-del to move along a cyclic path with its centre-line always tangent to the path as shown in Fig. 11. A constant drift angle and/or rudder angle

can be superimposed on the pure yawing

mo-tion.

Force measurement and analysis

Modular force gauges connect the model to

the PMM. The gauges are sensitive to forces in one direction only and are orientated to record forces in the transverse and longitudinal

direc-tions in the horizontal plane. The total

side

force is obtained by summing the side-forces

measured at the forward and aft attachment

points and the turning moment is

obtained

from their difference together with the distance

between the attachment points.

The signals from the gauges are processed differently in the static and dynamic testing modes. In the static mode, the gauge signals are recorded directly by pen-recorders, but in the dynamic mode, the signals are integrated under the control of one of three alternative

programmed sequences.

The cyclic forces acting at the side-force

gauges are composed of velocity-dependent and acceleration-dependent components which are,

by the nature of the motion, 90 deg.

out-of-phase with each other. These components can

be separated by integration between time limits as illustrated in Figs. 12 and 13. It is seen from the figures that by switching polarity and

inte-grating over the relevant time intervals,

in-phase, out-of-phase and/or constant components can be either measured or eliminated.

A much more detailed description of the force

measurement and analysis technique is given

in [7]. 21 MEl 1972uropean Shipbuilding» No. i - 1971

t'1y'.

5-rk-STATIC RUDDER STATIC DRIFT ANGLE TEST ANGLE TEST

I

s

e

I

Present PMM

The first HyA PMM [7] was commissioned in 1964 and has since bee5 used to make over 55

steering and manoeuvring tests with some 35

models. The mechanism was the first PMM to

be built for testing large-sized models in the horizontal plane and has proved to be of great value in determining course stability qualities and for obtaining data enabling predictions of manoeuvres to be made.

The first PMM has an amplitude of sway

oscillation of ±100 mm, maximum amplitude of oscillatory heading angle of ±5'/2 deg. and

maximum static drift angle capability of 20 deg; (14/ deg. n combination with oscillatory tests). The frequency of oscillation can be

continuous-ly varied from 2 to 40 cycles per minute.

An idea of the mechanical arrangement may

be obtained from Figs. 14 and 15.

The mechanism consists of a horizontal frame of welded angle sections on which is mounted a main shaft driving a Scotch yoke at each end. The Scotch yokes transform the rotary motion of the shaft to cyclic lateral motions which are

transmitted to the model via the forward and

aft sets of force-gauges.

Fig. 12. Integration with periodic polarity reversals.

European Shipbuilding» No. 1

- 1971

The main shaft is driven by a 21/2 hp syn-chronous electric motor via a i : 50 worm and

wheel and 1 :2 belt drive. A magnetic toothed

coupling connecting the two ends of the shaft

enables a phase

ngle to be set between the

forward and aft

Scotch yokes for use when

yawing motion is to be generated.

Pure yaw is produced when the phase angle

between the forward and the aft Scotch yokes is çhosen such that

40' (Od

tg

Uc os "I' or for small "I', when

cos "1' 1 40 od

tg-=

Uc where 40 phase angle Û) circular frequency = 2 ir n

d 1/2 distance between attachment points

Uc = speed of carriage

= course angle relative to tank centre

line.

9

PR002AMII

2 C,tNT.Integrotoon aver One 012C12._{intedrotion over One period With} OS' Lii.

- period with no chango _{chongo or polarity otter atoll} tert t t'cnr one period with chungos of _öii

at polarity. (Son h (Ceo & Corot. niiminatcd, co,att atve/2 arO atom/S. (Sin, h Coontr.

Coo elxmartoteo, Sin. meotured(. flotifldted, Coo measured).

Colt'0. rnvuoured).

KTNJ.

(/J.\

_1/1t)

O 21T o ir air _{1'2 31V2 air}

e 2e eiS 5v/i 2"

J

:t)

S faut' t s(t)- folio at d(ot)°ou Jui,Lt l(sÙ- filio at dlwt)ofalin at d)at')oi

o (t e/i 30/5 -

N\J

141

2 o 2ir O ir ail' t ¿o O ¶' jir,2 _Sir 0/2 20/5 50

foCos at i(wt('U focos at d(atj-fmCoa at SCatted faCen at d(wt>-foCoi wt 5)50)0faCci _t

U ti t, O 0/S ¿0/. -'

I.

-t -t o 21l' o 2 2h' ir liT' '2 2v 0/2 3v/i 5v

fa Cwt2e, 2w OCwO.) - fu d(wt)eQ _{fu d(at) - fa d(wt) e fu J(wt)O}

POSITION SHOWN WI

/2

3TU/2

- --Sin -wco(w

ANGULAR DISPLACEMENT OF ORIGIN, 4,

(uil

INPUT I

(POLARITY)

INPUT 2 (RESE T) MARGIN PEN INTEGRATION HOLD CONDITION RESET CONDITION P OL AR IT T WI /2 FORCE COMPONENTS MOTION RELATED TO MEASURED FORCE COMPONE NT

4k

4k

4k 4IAJI

hdii"

W

VELOCITY

CORRESP TO POSIT IVE VELOCITY

OUT Q

YAW TEST ANALYSIS.

ACCELERATION

VELOCITY

CORRESP. TO NEGATIVE ACCN

IN Q

FIG.

13

CORRFSP TO NEGATIVE VELOCITY

OUT Q

CORRESP to POSIT IVE ACCN

IN Q

VE LO C ITT CORYESP TO POSITIVE VELOCITY

OUT Q

Nil WI uil

/2

MEASURED FORCE DESIGNATION OF FORCE TYPICAL RECORD FORD GAGE HF

MEASURED FROM o 2TL 4) .- --co(Wt *

TYPICAL RECORD FROM

1'. ---in-wir(wI -) AFT GAGE YA CO S. SIN Cou SIN. COR El I MINATED EL I T-IINATED ELIMINATED ELIMINATED ELIMINATED SIN MEASURED COS. MEASURED SIN MEASURED COR. MEASURED SIN MEASURED

Mounted on the main shaft is a synchronous switch that controls the integrator circuits used

in conjunction with the force measurement

system. The switch consists of a perspex disc with four black lines that actuate photocells as the main shaft rotates. For oscillating tests

the disc is rotated relative to the main shaft

and set at half the phase angle between the

forward and aft Scotch yokes.

The mechanism was originally built with the

intention of maintaining draught and trim in-dependent of speed on the principle that only one parameter should be varied at a time but

it was subsequently found to be more practical

to allow the model to sink and trim naturally

as a function of speed, drift angle, etc., and thus

automatically take account of the resultant

variation of hydrodynamic forces and moments.

This procedure is also in accordance with the

recommendations of the ITTC Manoeuvrability

Committee

Some initial difficulties were experienced during the first tests with the mechanism due to resonant transverse surface waves induced

in the towing tank by the oscillating model but these were elminated by reducing the

frequen-cy of oscillation. This reduction of frequenfrequen-cy

meant that the maximum value of yaw velocity

was lower than planned, which in turn neces-sitated extrapolation ai some of the test data

when predicting radical manoeuvres especially

for modern supertankers with their extremely

tight turning circles.

New PMM

As a result of the experience gained during

the last six years and in view of the present

trends in

the development of new ships

-particularly large tankers - a new PMM has

been designed in cooperation with A.E.W. *

The new PMM, which was expected to be

ready for use in October 1970, can generate

con-siderably larger motions than the present PMM,

and is also more versatile and efficient for

setting up a test and the measurements made

will be automated to a greater extent than was

previously possible.

The new PMM can generate:

max. sway-amplitude ±750 mm Dynamic mode

max. yaw-angle ± 27 deg.

Static mode max. drift angle ±180 deg. (also in combination with dynamic tests).

A.EW. = Admiralty Experiment Works, Haslar, Gosport, England.

Fig. 14. The HyA PMM shown suspended over a 6 m wax model for photographic purposes. «European Shipbuilding» No. 1 - 1971

Fig. 15. The HyA PMM mounted on the towing

carriage during testing.

The frequency of oscillation can be varied

between 0.5 and 10 rpm.

The mechanism is driven by a 2'/ HP motor

via a 1 : 200 reduction consisting of spur and

worm and wheel gears.

The principal difference between the new and

the present PMM is the ability of the new

mechanism to generate large yaw velocities at small frequency, thereby diminishing some of the problems previously mentioned.

Although based on the same principles as the

present PMM, the new PMM is radically dif-ferent in its physical realisation.

In order to enable the drift angle to be varied

±180 deg., the motions are transmitted to the

model through a single strut with axis through

origin in the model. The swaying and yawing

motions are produced by transverse motion and

rotation of the strut respectively. Due to the limited height under the towing carriage, the

new mechanism will be bolted onto the aft end

of the towing carriage, and in order to reduce the dimensions as well as the number of

slid-ing parts, a special linkage was used suggested by O'Dell from A.E.W.

«Europc'an Shipbuil.ding» No. i - 1971

110 tor

Of,. Osd of T0,.10 eorrl,,.g.

Model Support Strut

Tangoot Generator b Coo ut tan ,) -C Gear So Sway Crank ( Sway kmpl. - a) X

=Ut

o e y0 = 2a ainLit ta _{'.) =} ±l _{.. = 2a} -dt dz Yo

Fig. 19. Definition of "pure yaw".

p1ino ..hn!t

Fig. 16. O'Dll linkage for generation of simple

harmonic swaying motion.

oT Model Subcarriage (Sway: y 2 a a.Uwt) o (=oonatant) Sub-aubcarria5e (Motion Rlativ to Subcarriae b co8ot) Yaw Crank (Ampi. - b) Ampi. A4uatment tern o Model

Fig. 17. Generation of Yawing Motion.

Mechanism seen from below.

Gos wt

This linkage consists, in this case as shown on Fig. 16, of two gearboxes, of which one is fixed relative to the carriage, and the other is

mounted on a subcarriage driving on horizontal

rails perpendicular to the tank centreline. The

vertical output shafts of the gearboxes arc each,

at the upper end,

fitted with a sway-crank

which turns with the same r.p.m., but in

op-posite direction. The sway cranks are connected by a cross-arm, and when the same amplitude is set on both sway-arms and'they are rotating, a harmonic sway motion of the subcarriage will

result (Ysubcarriage = 2 a sin t, where a is

the amplitude set on each sway-crank). The gearboxes are driven via a splined shaft. The

movable gearbox has another crank on its lower

output shaft - the "yaw-crank". This crank is

angled 90 deg. relative to the sway-crank, and

it is used to produce the yaw motion as

illus-trated in Fig. 17. When the "yaw-crank" is

rotating, a harmonic motion of the subcarriage

will result, and by means of the

"tangent-generator" this motion is transformed into an

angular motion of the model support strut and thereby of the model.

By proper choice of amplitude ratio and

r.p.m. in relation to the speed of the towing

carriage, the pure yaw motion defined in Fig. 19 can be produced without making

approx-imations of the type cos 'l' 1. This

approx-imation which was acceptable in the old PMM

Zub-aubca.rriae

u.

t

Coupling Releaoe Am

Spiine Shat Driving Gear Sox

Tancent Generator (Yaw-angle)

Couplio Permittin Prenetting o Dritt Angle .o to -150 deg. in

Stepe o 2 deg.

AlignneGt o Model

Trim & Siukae Linkages Dyo.amometere

Fig. 18. Principles of new PMM. Side view.

Sway Crank

design, when '1'max = 5I

deg., is of course

invalidated when '1'max = 27 deg.

A tooth coupling between the model support strut and the "tangent generator" enables a

pre-setting of drift angles from O to ±180 deg. to be made. A horizontal beam is bolted to the lower end of the model support strut, which,

via trim and sinkage links and force

dynamo-meters, transmits the motions to the model

(Fig. 18).

Quasi-stationary drift angles can be made by

setting the sway-crank amplitudes to zero and

the yaw-crank amplitude to its max. value, and

then letting the mechanism rotate at very low

r.p.m. In this way drift-angles from ßo 27 deg. to /3o + 27 deg. can be made continuously

dur-ing one run through the tank.

The new PMM also permits measurements of

"added mass" in surge to be made (X ). In

order to do this, the drift angle is set at 90° and

the yaw crank is set at zero amplitude. The

model is then made to surge perpendicular to

the tank centreline by means of the

sway-cranks. The towing carriage must of

course

stand still during this test.

All measurements can be made using the

pre-sent electronic equipment;

a number of

im-provements are, however, planned, e.g. the

pre-sent pen recorder will be replaced by a digital voltmeter (data logger), with punch tape

out-put, which can be processed directly in the

HyA GIER digital computer. Statistics from PMM tests

About 55 complete Planar Motion Mechanism

tests have been carried out on 35

different

models ranging from trawlers to supertankers. The results of all these tests enable a statisti-cal study to be made of some of the coefficients

(derivatives) in the mathematical model. It is hoped to develop empirical formulae for

the estimation of coefficients, on the basis of ship dimensions, thus enabling a preliminary

estimate of steering and manoeuvring qualities of new designs to be made.

Since most of the tests have been made for

customers, no details can be given here on ship particulars, etc. Nevertheless, the figures 20 to

27 shown here may be of some interest.

The collected coefficients

here are those

governing the stability criterion

(C' = Y'v(N'rm'x'Gu')N'v(Y'rm'u') > O

for stability) and each point in the diagrams is

the result of a complete static drift angle test or pure yaw test, the coefficients representing

the slope at zero of the measured data.

-000 -2000 -3000 4000 - 000 ,000 -1 000 -3000 -'000 - s000 - 200 - 400 - 600 - £00 bOO Fig. 0' 6 bIab

«European Shipbuilding» No. I - 1971

-7qr 3

GflGaG

Fig. 21. Col1eced coefficients: Y\,, tankers and

bulk carriers.

22. Collected coefficients:

BQLLGSt 1042.9

Trimm.d Gad WNJSUGL V.SS.L

-so(VLPP

9 0

9 bO

Fig. 23. Collected coefficients: N'y, tankers and

bulk carriers.

13

Fig. 20. Collected coefficients: Y,v, all ships.

V1pp0' 9 b0

<Europcan Shipbuilcling» No. i 1971 soc 800 900 200 N N -,00_._ N N - 300 s -0001 - ooslt8j0 - Bsllsst -F Lood.d Trimmed Qndrsnu100ty.668I

Fig. 27. Collected coefficients:

(N'r _niGXU), tankers and bulk carriers.

0 3 7 8 9 10

Fig. 24. Collected coefficients: Y'r, all ships.

T000

oo (v.2)'

Ir j ,nm.d s nO I VOI ,e 1.01.

Fig. 25. Collected coefficients: 'r' tankers and

bulk carriers. .. -l00 -200 - 300 - ODO }.l0 g 0 N N

N

:°

N.N 8 T000 800 600 600 000 e.

/

/

/

/

o

/

__...___l.02

T,rmnmd O.1 %SU4L WOMLO.

(Y'

= (i)

etc.). V' = O

The coefficients are shown non-dimensionally and plotted against (T/Lpp)2, where T is mean 'draught, (TA + TF )/2. The parameter (T/Lpp)2

has been chosen since low aspect ratio wing

theory suggests a linear variation with

this

parameter of force and moment coefficients. Using 2 T/Lpp for aspect ratio the following

theoretical values for the coefficients can be

obtained: Y,v = (T/Lpp)2

=

_{-i-- (T/Lpp)2}

=

_{j- (T/Lpp)}

N'r =

- (T/Lpp)2 (See e.g. [8] or [9].)

Figure 20 shows the non-dimensional side

force coefficient Y'

6Y' Y

(Y,

V

y' v'O'

where Y' -- 1/2f) Lpp2U2'

=

-The theoretical value, Y'v = r(T/Lpp)2, is

also shown.

Further the line 2- (T/Lpp)2 and the curve corresponding to the classical lift curve slope

equation,

60L

-

2

. or

' te=o

1+2/Aspect Ratio

- T/Lpp+ 1

(T/Lpp)2,

are shown.

Of these "theoretical" lines, the "classical"

one comes closest to the measured data, alt-hough none of them is really accurate, which is not surprising considering the influence of friction and the difference between a ship and

a flat plate.

Considering the quite large variation of hull

geometry, speed, trim, etc., the scatter of the

measured coefficients is surprisingly small.

The effect of trim is, generally, to increase the numerical value of the coefficient, which

may be explained partly by the effectively

larger aspect ratio associated with trim (a more

correct measure of aspect ratio than 2T/Lpp

would be 2 x (max. draught)/lateral area

2TA2/T Lpp).

Speed also influences the

coefficients

-although not apparent in the figures - and,

generally, for the displacement vessels tested, the numerical values of the coefficients increase

N

- soc

N

_(r)

N

eÑ sr.soI wn..I..

Fig. 26. Collected coefficients:

(N'r ni' x'Gu'), all ships.

5 _n,8.

r

slightly with Fx:oude number, possibly partly

due to the associated sinkage, which causi's an

increase of lateral area as well as aspect ratio.

In Fig. 21 the same coefficient, Y', is

plot-ted for tankers and bulk carriers only. In this case the scatter around the mean line is very small when neglecting trimmed and unusual vessels. The smaller scatter here is of course due to similarity of ship hulls in this group.

Figs. 22 and 23 show similar 'trends for the

moment coefficient, N'y, except that in this

case the effect of trim astern is to reduce the numerical value of the coefficient, due to the

centre of action of the side-force moving aft.

Figs 24 and 25 show side-force coefficient,

Y'1. obtained from pure yaw tests.

In a pure

yaw test the side-force, within the linear range,

can be exprssed by Y'(r) = (Y'r m'u')r',

where m'u'r' is the centrifugal force which is

always, at least in deep water, numerically

larger and of opposite sign than the

hydro-dynamic component Y'rr.

For a larger tanker the

non-dimensional

mass, m', in loaded condition, is usually about

1700 l0, whereas for a typical fast container

- , 2A

vessel, it is around 700 l0

(m -

_Lpp

Non-dimensional speed in the X-direction, u',

equals (IJcos )/U i in the linear range.

Considering the large variation of m' with

ship type, the hydrodynamic coefficient,

_'r

in figures 24 and 25, shows surprisingly small scatter.

As would be expected,

the effect of trim

astern is to increase the hydrodynamic force

coefficient,

Finally Figs. 26 and 27 show the moment

coefficient (N'r m'x'Gu'). In this case the

centrifugal moment coefficient, m'x'Gu', has

been included, partly because it is usually very small compared to the hydrodynamic part, and

partly because the exact centre of gravity is

L.C.B.

not always known. (X'G

_{- Lpp}

L.C.B.

measured from '(f5, positive forward).

The linear variation with (T/Lpp) predicted

from theory is not supported by actual measure-ments, and cannot be explained by the inclusion

of m'x' u' either. A better approximation

would be (N'r m'x'

u')

0.001-0.65

(T/Lpp)2

Approximate calculation of C

The stability criteri6n, C', is

C' =

'v (N'rm'X'GU') - N'v(Y'r

m'u') > O

for stability.

and by inserting m'u'

-6 5 4 3 2

Zuropean Shipbuilding» No. i - 1971

L.Jnsthble

St a bi e

10 20 30 40 Lpp,/1

Fig. 28. Trends of course stability variation with Lpp/T,

B/T and Cb.

The curves shown correspond to the stability

criterion C' = 0. C' approximated by C' - (T/Lpp)4 [5.23-3.88 Cb B/T + 0.0050 (Lpp/T)2] T = draught Cb block coefficient. 15

For untrimmed vessels in the range

i

-- (T/lpp,'

t:' c.''

icierit.s cÑn be

ap-pxuXilTiated loi it,'iis:

c

5.0 (T/Lpp)2

N'

- 1.95 (T/Lpp)2

1.02 (T/Lpp)2 (N'rm'X'GU') - 0.0010-0.65 (T/Lpp)2 2

2CbLppTB

and _{Lpp: Lpp:} u

= cosß

1

Only a very iough estimate can be expected

from thee approximated

coefficients, e.g.,

here the ratio N'vIY'v is 0.39 which is quite

reasonable, corresponding to the centre of

action of hydrodynamic side-force during pure

drift angle (oblique tow) located at 0.39 Lpp forward of amidships; however for quite

nor-mal untrimmed vessels this centre of action has

been found to vary as much as from 0.25 to 0.46

Lpp.

It may still be of interest to carry ou

the

calculations to get a rough idea of the influence

of T/Lpp, Cb and BIT on the stability

criter-ion C.

Substituting into C we get:

C' 5.0(T/Lpp)2 (-0.0010-0.65 (T/Lpp)) --1 .94(T/Lpp)2(1 .02(T/Lpp)m'u') 2 CbLpp TB Lpp1 C' (T/Lpp)4 5.23-3.88 Cb B/T±0.0050 (Lpp/T)

Using this formula for the stability criterion, Fig. 28 has been prepared.

«European Shipbuilding» No. i - 1971

This diagram should be regarded only as an

indication of trends. Several cargo vessels test-ed have been found stable on course when this

diagram would suggest

that they were

un-stable. The opposite has also happened once, although in this case the vessel was only

mar-ginally unstable.

The following trends are immediately

appar-ent:

Increasing length improves stability (B, T

and Cbkept constant),

Increasing breadth reduces stability (Lpp, T and 0b kept constant),

Increasing Ch reduces stability (Lpp, B and T kept constant),

and less pronounced:

Increasing draught improves stability (in the

range 14 < Lpp/T< 32), (Lpp, B and Cb

kept constant).

To this list may be added:

Trim astern improves stability,

Increased rudder area and skeg area aft im-proves stability.

Several other properties probably influence

the stability, such as type of lines, rounding of

bilges, bilge keels, L.C.B., speed, type of rudder,

single or twin screws, single or twin rudders,

etc.

When try.ing to estimate C it must be kept

in mind that C is the unsually small difference between two positive products, and hence fairly

small errors in the individual coefficients ma

change the sign of C. It will therefore be some time before formulae can substitute model tests.

Steering large ships

Hand steering of super tankers is difficult for two reasons. Firstly because these ships often have bad steering and manoeuvring properties,

which result from these ships' large Ci,, small

Lpp/T etc., rather than from their size directly.

Secondly, purely on account of their size and

relatively low speed,

these ships have yaw

rates and accelerations which are very small

and diffcu1t to discern quickly enough to avoid large rudder angles and course deviations.

When these conditions occur simultaneously,

as is normally the case for super tankers, the steering deteriorates further resulting in speed loss and unnecessary activity of the steering gear and consequent helmsman fatigue.

Course stability and manoeuvring qualities

can only be improved by significant changes of hull form and rudder, which are scarcely

ac-ceptable for economic reasons. However, im-proved navigational aids lead to speedier per-ception of the ship's movements and can thus

improve the steering considerably.

It has become clear that a sensitive rate gyro is o1 considerable help to the helmsman and it

is also becoming more and more common to

install them onboard. Instruction and training, possibly with the aid of a manoeuvring

simul-ator, improve the helmsman's knowledge and feel for the ship's steering dynamics and thus

improve his ability to anticipate

the ship's

response to the helm. An onboard manoeuvring simulator, a so called "predictor" [10], [11], has

been tested on the 'Sea Sovereign' *) and has

proved to be of considerable help to the helms-.man.

Manoeuvring with large ships is difficult for the same reasons as are mentioned above, and

the problem of the perception of the small

ac-celerations and yaw rates is accentuated by the

low speed.

The use of precision navigational instruments will probably become increasingly common as

an aid to making faster and safer harbour

manoeuvres, etc.

"Hi-Fix", "Doppler Navigation" as well as

"inertial navigation" can be mentioned as

ex-amples and the "predictor" has also shown it-self to be of great help in these situations.

In addition, the "leader-cable" system could be used in difficult harbour approaches.

Autopilots

A good, well-adjusted autopilot steers better

than is possible with hand steering.

Autopilots will probably be developed for use in nearly all situations, also those which

have traditionally been reserved for hand

steer-ing, such as course alterations, harbour

ap-proaches, collision avoidance, etc.

The development of new autopilots and

op-timalisation of existing autopilots is greatly

facilitated by the use of computers. Analogue

computers which for example can calculate 100

times faster than "real time" can be useful. As long as it is a question of optimalisation

of steering on a straight course the techniques

used in system control analysis can be used

(Bode-diagrams, etc. 12), and equation (2)

to-gether with equations for steering gear and

S) _{A computer which can also function as a}

"predic-tor" has been installed in the Salén Lines 210,000 DWT tanker 'Sea Sovereign' by Stiftelsen Svensk

autopilot and possibly a simple equation for speed loss as function of yaw-rate and rudder

angie [1] will be quite sufficient, even for un-stable ships.

If there

are large disturbances, e.g. from

waves (which can for example be simulated by a noise generator), equation (3), (Bech) will be preferable for simulation of small course alter-ations. Finally if large changes in speed, mark-ed course alterations or other radical

manoeuv-res are to be simulated, more complete

non-linear equations uch as (10) must be used, and

optimalisation of the autopilot must, at least partially, be made by a trial and error process.

Adjustment of existing autopilots is a problem in itself. In the author's opinion there are many

ships sailing with unnecessarily large speed

losses as a result of incorrectly adjusted

auto-pi]ots.

The autopilot manufacturers are aware of

this problem and are continuing to improve

their adjustment procedures.

<European Shipbuilcking» No. I - 1971 A reduction in the number of accessible ad-justable knobs by means of built-in initial set-tings for individual ships would also be of great advantage (it is apparently quite usual for each navigator to have his own theory about how the knobs should be. adjusted, with the result that the autopilot is

always out of adjustment).

Work is also proceeding in this area, and the author is aware of an example where a large tanker is equipped with an autopilot having

only two external knobs:

.1. Variation from loaded to ballast conditions, and

. Weather adjustment.

'The aim must be a self optirnising autopilot

which can take regard of water depth, speed,

loading conditions, waves, etc.

Both full scale and model tests are of great value in these endeavours, even though such

use of the test data has so

far been rather

limited.

Note: References are included in part I.