Experimental methods of estimating ship maneuvering qualities

10th INTERNATIONAL TOWING TANK CONFERENCE

ManeUverability Committee

Experimental Methods of Estimating

Ship Maneuvring Qualities

(Official Report)

by G.A. FIBSOFF

A B S TR A C T

This report covers the techniques used to investigate maneuverability of ship and presents the methods of

estimat-ing controllability or response to rudder most common in the USSR, A description is also given of the experimental faci-lities enabling to obtain the data necessary for putting these methods into practice.

(a) Curve of Controllability

To predict turning ability and directional stability, wide use is made in the USSR of the curve of controllability where steady atate values of the drift angle

ft

or non-di-mensional angular velocity j are plotted against the rud-der angle

S

(see Fig,l).

The curve plotted for a stiip in question enables to clear up the following points:

Find put whether the ship has theoretical stability in straight motion. A positive value of or

de

rivative in the origin of coordinates is indicative of stability. It is easy to show that these values have identical polarity and are proportional to the Rauss-Furwitz criterion.

Determine critical valuew of the rudder angle drift angle and radius of gyration that is, the values specific to the easiest steady circular path of

--3

ship's motion,

Cc) Estimate the ranges of rudder angles,'drift _{a1gles and}

radii of gyration making stabl.e steady motion impossible. The curves lyingwithin these unstable _{regions are, shown} in Figl indotted line,

(d).wlth

fl=f3 ,

evaluate the coiponents:ot ship's steady motion, When the rudder isñot.applied,

(e) Determine the components of ship's steay turning at any

rudder 'angle including: the maximum' one.

(1') Ascertain a relation between the critical rudder angle

and the minImum' one which is necessary to eliminate _ship's yawing under full-scale operating conditions, that is,' to

estimate in an indirect way service stability 1'

motion. .. . .. '._

The methods used for plotting the curve of controllabi-lity are as follows:

1.. _{A calculation based on the use of. nàn-1ineir theory for a}

-- low aspect-ratio wing and the résülts of systernatic model

testing.. .

' :

.2.. _{Direct simulation of free turning from non-selfprope].led}

models using the rotating arm facility (seé Appendix No.1). Direct simulation of, free turning for self-propelled _ 'dels using the rotating arm facility (see Appendix No.2).

A calculation incorporating: experimental 'dta'on the ship's hull hydrodynamic,properties obta1ned:bymodel testingin a wind tunnel. and using the rotating arm

-5. Testing of seIf.propelled integrated,

models.

- 6. FulI..aO ale ship- trials.

For directionally unstable

ships, methods 3, 5 and 6

enable

to plot the curve Only in ité practicable region,

while methods 1, 2 and 4.

permit: this to be carried through

in fUll, scope including

the regions of unstable values.

Me-thods. 1;and 2 are the major ones. now in use,

(b;) Transfer Functions of Controllability

To investigate transient conditions of Shipts motion for a given laW of rudder shifting1 the frequency response method

is used in the USSR..

..-The transfer functions. necessary for putting-this methàd into practice are: determined by:

- calculations incorporating, the data

of model

tests 1 a wind tunnel and using the rotating arm Lao ility, directly, i.e. by simulating free oscillatory rnotiofl;

of the model caüsed.by harrnonic shifting of the rudd'r 'at various frequencies (see Appendix No.3).

Both; methods yeld the results which, as a

rule,close

age.ernent. A possibility of using the frequency res-,ponse method for estimation of transient conditions inherent

in ship's motion has been pro.ved.by extensive studies Into t errors due to non-linearity of the hydrodynamic factor curvs. The studies have been carried out with the aid ot electronic cOmputers0 - At present the possibility of applying the fre-quency response method is questionable in exceptional cases

Experime

_{Device Permitting to}

Simulate Model Pree Turning

_{by Means}

of Rotating Arm.

8

The data obtained from free self-propelled model

tests eóñd toted in calm water and waves are insufficient and unreliable.

In thia.óonnectiOfl turning tests with a rotating ar-rn faoiiItyUsed'arefl103t effective.

Layout of the Device..

In Pig.1

theiajOUt

of forcea acting on a model moving over a circle, in a horizontal plane 'is shown.

'The letter -" '

indicates the point in wiah tbe

model is attached to the rotating-, arm turi1. ruu.ud the

center at constant,

angular velocity

- Since the radius o

the circle,

over which the

pjnt

" Q " is moving, is equal to the rotating arm length -and can be considered to be fixed ,,and known in experi'meflt beforehand the

'posii'tiofl'

o a model 'on

the

drawing is

de-termined by the rotating arm turning angle and model drift angle ..- The latter lies e'tween

tLe d.L'tiUL.

of the linear veloit

vector of 0

nd-th

U

If a model can turn freely around " Q 1 _{its p}

sition about

₇

_{varies in accordance with changes of} the forces acting _{upon it.}

These _{orcei are as follows:}

R1,ii,

-

_{centrifugal. foro.e of model ineti,a and}

its moment about " 0

4

R2,M2

-

total hydrodynamic force acting on the submerged part of. the model when _rudder angle is-zero and. -moment of this. force about ti- U

-- hydrodynanzic force induced by.rudder

-shif-ting.- and

M2 -.

moment of this forOe

- _{attachment response between the thodel}

and the rotating arm in "0".

thrust. of mode-i screw propeller _,aot:ing

in model. centerline...

At given

₇

and C17 _{the values -of}

-R1 ,M4

and

R2JV72 _{depend only on the model drift}

ankle-(- ;

I0-drift and rudder angles together.

Thus, model iquilibrium about is determined by the combined set of equations:

R

(j3)+ R2 (j)

R

(8).-R4

where _y transverse axis connected to a model.

The difference between the equations given above

and those of model free turning is in the presence of the transverse projection of attachment esponse R

in

4he first one. Therefore, among many combinations of

and.. satisfying the equations written above there

is only one corresponding to model free running at whi?h

It meanspractioa1ly that in order to

simui-te model frea ±unning under a rotating arm facility itis

necessary, to choose such a rudder angle at which the

trais-verse component of attachment response of a model to

arc-tating arm would be equal to zero. The selection of a rud-der angle can be performed either manually or automatically

.bymeanaof aservosystem. The latter must turn a rudder

until thecondition

RQ

is satisfied. In principle, Such a aervosystem solves the problem about model free

turning under a rotating _{aria. Having the servosystea in} the model turning studies _{in calm water and waves it is} possible to obtain records of the model drift angle _/W and rudder angle

_6'

_{at a given curvature radius of the} p0-mt of model attachment _{Z0 and .eirouinferentlai.ve].o...} city of this point

The fulfilment of the second condition _{of model free}

running depends onthe choice of model

_{screw thrust T}

I

at which longitudinal component of the attachment respon-se would become zero l?4x=O The oho±cé of thiust _{can be} made. by means of the servosy8tem which responds to the indicator reading

R.

- and controls a model screw

pro-peller speed.

It should,be born in mind that the fulfilnaentof the aecond condition for model free turning is not necessary for carrying out the first one. lut it maybe necis8ary only in the case if it is supposed to.determine:engmne power increasing for maintaining a given thodel speed or to simulate screw prOpeller effect on ±oróes

R2

and

. As to model heeling when turning or its motion in

carry--12

-ing out the first condition only. Therefore, in moat cases only model resistance

teatscan be condu.ctediü

which propulsion equipment and the second servosystem are not required.

The experimental device consists of the following five principal parts:

1. The rame

0eótedtOtherOtatiflg arm

and havink:

structural axis ofmodèl turning in

the horizOÜ

tal plane about the rotating arm,.

force indicators - R4 and

R4

transferred

by. amodel on the structara1axiS'Pf

.turning,

- (c) transducer of model drift angle.,

i.e. model

-turning angle in the horizontal plane about the vector of circumferential velocity of the model attachment point or

about a rotatingarth.

2.'Measuring hèad mounted on a model and'designed for transferring tb-wing force without 1i.mitatio of freedom of thödel.up' and down motfon. ft has: :- -.

(a)tanducerOf -heeling angl& br

oling,

(b) transducèr of trim angle or pitching.

Automatic rudder drive gear having: (a) transducer of rudder angle,

13

(b) dynaniometer for moment _{measurements on a} rudder stock as well as for measuring the component of hydrodynamic force of water pressure acting on a rudder which is normal to the model centerline,

4. Components of electrical circuit combining _{a force} indicator end automatic rudder drive gear into a servo-system providing compensation of side response of a

mo-del attachment to a rotating arm.

.5. Recording unit. .

-A more detailéd description of the principal elements is given below:. . .

§2

Model Attachment to Rotating m

The principal structural component providing the mo del attachment to the movable _{arm of the rotating unit} 18 a frame Which is. fitted on the _{arm from its face.}

The following components are mounted. _{on the. lower} ho-rizontal platform of the frame: the model turning struc-tural. axis, an indicator of forces.. transmitted to the

above-said components in assembly.

Box (1) which is accessible from top and connected .rigidly to the frame

i8

used. as a base incorporating all

the components of attaàhment. Upright sleeve (2) Ia con-nected to the base. Bush (3) used as a structural axis in the model turning rotates inside the sleeve in bea-rings (4) with loosely arranged balls. The bush is ptè.

-vented from

shifting down by tbeflaflge and the sleeve

rim

x1 its bottom, while from shifting up it iaprevefl-,

ted by the.upPer flange and ring mut (.5)

whichia'scré-wed

up inside sleeve

(2)

from its upper face0

The turning angle of bush (3) limited

within

20

deg. in the horizontal

plane is restieted by means

of stop screw (6)

secured to the sleeve

(2), and lugs

pro-vided on the bush itself. Bush (3), if required, may be

locked by u.psetting.prOfile clip (7)

while turning screw

(8).

Tapered toothed

sector (9) is mounted on revolving

bush (3) from uwards.

This

sector

is in engagement with

bevel-gear (10) through whIch the extended driving shaft of selsyn (10) is driven. The selsyn is used as a tranadtiee oer to indicate model turning to the

rotating arm

rela-- I.

tieii-.e

it is a drift angle transducer,

--InId the revolving bush (3) hole there is inserted on a keya thick-walled tube (13). The tube slides along the inner bush surface and may be-fixed in any positioi on its height by means of look (14).

Head (15) of a vertical driving bar (16) is

coec-ted rigidly to the upper part of tube (13),. Abovesaid loading bar (16) designed-to transfer forces from the ro-tating arm to a model is made of a whole piece of metal. Except the head, a long the bar length there are: flat spring (17), flat spring (18),. a stoppjng flange (19) and a prismatic (three facets) part (20). Between the flange (19) and the internaltube (13) surface there is annular

clearance of. about .1 mm.-

-Thick-walled tube (13), flange 19 and springs 17añd

18 comprise an indicator system of. forces traüsférrid-to

model.

-Since t-he

rotation of the

driving bar prismatic, part in the horizontal plane takes place together with the mo-del, the orientation, for springs (17) and (15) about. model-. is maintained the-same.

1:6,

Whenthe initial 2ètt

gofbár (16)

reIative to a

model is selected prope ly,:..the smail.st-stiffness-'pl9ne

of. spring (17) 'conforms to the, longitudinal force

R2.+R2

, and the sthalIeat8tif

easpiane'Of spring

(18) is in

conformity with

theforce

which. is

normal to the oenter]±ñe. .herefori, wiéatrai

gaLige

atioked on 'spring (17)

practically,'arè' hé in'itôri

Of lon.gituAinal force, ãnd'thO3 stlôked on spring'(18)

±eindicators otranTsverse (normal) force..

PaBSage8

provided for strain gauge wiresin head

(15) of driving

bar (16) are shown In Pig.2.

As the springs with atr4n gauges

stioked on them

are applied as sensitive elements of compensating servo-eyatems, the measurement of forces I anstrred 'through

the springs is not a problem in this ease. Thus, it i3 'enáugh only to state t.he fact itself how the foro,e arises

and t determine its sign. This circumstance enablee the indicator to be extremely sensitive owing to loosing of springs (17) and (l) 'to the limits tolerable by struotu-ral and service

consideratiOnS.

Since

in -this case the

springs cannot be.

used

'to transfer considerable bending stresses, their deformation is restricted by the aize

O:

-

I?

annular clearance between flange (19) and tube (13). After load imposal on the springs, this clearance is chosen, and the bending moment on the springs resulting

from response in the point of contact between details (13) and (19) practically stops increasing. In this case forces are transferred from driving bar (16) to base (1) directly through flange (19) and tube (13) but without the action of springs (17), (is) and head (15). As it was mentioned above force action on the springs is about zero.

§3

Megsuring Jiead

The measuring head is illustrated in Fig.3. As a bgs of the head T-shape bracket (i) is applied, which is

attached to a model. P-shape

bracket is connected to shaped element (2) which turns up to ± 50 deg. angle in the vertical plane normal to the drawing. vertical small carriage (4) which can turn up to + 20 deg.angle in the drawing plane is connected o the shaped element by means of axis (7). From its underside small carriage (4) is se-cured with pinion (8) having the identical axis of

rota-18

tion (7) with the small carriage. This pinion is in enga-gement with pinion (9) fitted on selsyn (10) driving shaft. Thus the turn of small carriage (4) in the drawing plane with bracket (1) while small carriage (4) has the

constant orientation in space, results in selayn (10) rotor turning. As the measuring head is mounted in a mo-del in such a way, that the plane of the right hand part drawing in Pig.3 to be the centerline plane when the ver-tical

positiOfl

of small carriage (4) is maintained con -stant, the device just discussed, enables to make a re -cord of model trim and pitch angles.

An equivalent device to record both heeling and rol-ling angles, besides constantly oriented small carriage.

(4),

compriSes:

shaped element (2), pinion (5) c onnecte

to it, pinion (ii) fitted on the selsyn (6) driving shaft, and the selsyn itself. Clearly, bracket (1) turns about

axis (3) in the plane normal to the drawing and in common with a model undergoing heeling and rolling while element (2) is maintained stationary, but pinion (ii) runs in

pi-nion (5) and turns selsyn (6) rotor.

In order to fit the

head in a modelmOre

conveniently, piniona (8) and (5) are detented by means of pins (12).

19

Small carriage (4) is fitted on thdriving bar of

the indicator of forces acting betwe,ena mcdel an4a

structural axiá of model taning. This bar is marked with index (16) in Pig.2. The small carriage should not only transfer the above forCes, but also ensure freedom of. mo del emersion or its heave. This recjuirement is met with the aid of lying in ball bearing rollers (13) whioh are grouped by three and located in two points along the small carriage height,; the small carriage itself is sup-ported by these rollers. The roller axes are running pa-rallel to the facets of the driving bar at 12O _angle...: The precise adjustmint of rollers contact to facets of the driving bar is ensured by ecoentricity.o the struc-tural axes of rollers (14).

In non-self-propelled (towed) model tests, small

carriage (4),

directly responding to lateral towing

for-àe of drivng bar, transfers this force through

axis (7)

onto element (2) and then, by means of axis (3)...to:

bracket(1)and a model.

It should be mentioned that the secondary but highly significant role of the

measuring

head is aimed to make

20

springs of the force indicator free from the moment

act-ing on a model in

the transverse plane. Due to availabi-lity of the head, this moment can be compensated by the

model reStoring

moment, but it

ouJ.d be

transf erred on

the component of model attachment to a

rotating arm.

uitomatio Rudder Dri.vingq

The design of a driving gear is shown in Fig.4. Bracket (1) supports actuating

rudder

shifting motor

(2);

the motor is

incorporated in common housing with

reduction gear (3). The bracket is connected rigidly to shaped element

(9)

having

the

lower f see

resting

on a

pair of bronse springs (7), arranged so that their pla-nes to be parallel to the centerline of the model.Lowex base.s of springs (7) are connected to the base of

8et

(8).

Through a set of cylindrical wheels (107 and

toothed sector (ii) the actuating motor drives bush (4) which

iB

turning inside element (9) lying in bearings

(12) with loosely arranged balls, Four transversely set flat springs

(5) are

linked rigidly to a lower face of

21

bash (4). Springs (5) _{are made integral with their solid} beaes; their upper base is used for springs _{to be} connec-ted to rotatable bush (4), _{and a lower base is designed} for rudder-stock attachment. _{The selayn driving}

_{shaft is}

fixed in the upper part of bush (4) by rubber bushing

(13). The complete _{et ia enclosed in}

_{casing (15) suffi..}

ciently ample to ensure unhindered displacements

_{of its}

components when the set undergoes some deformation

_of

sup-porting springs (7).

Corresponding clearances are provided

_{at the points}

of casing intersections with the working

_parts

_{of the}

Set.

The set is mounted in a model so that the actuating motor (2) axis

(6) to be lying

_{in the plane parallel}

to centerline. The mounting is carried

_out

_{by means of base} (8) which is connected to model deck invariably.

BLldder _{lifting is executed by driving the actuating}

motor which turns toothed sector (ii), rotable bush (4) as

well as the rudder-stock linked

with rotatable bush (4) through transversely set springs (5). Since springs

₍₇₎

_are

the only link between the components of the set _{and its} base, the hydrodynamic load imposed on a rudder is finally

compensated only by

intrinsic elasticity of these spriflgs.

In partculsr, their transverse

elastic deformation is

use4 for the determination of the rudder hydrodynamio for-.

cecomponent normal to a model

centerline plane. Variation.,

of this component resulting from rudder is dhown in Fig.1

it1

the symbol. R

Budder-stock moment is deterniine4 by use of

'deforma-tion in.transversely set springs (5) transferring torque from rudder-stock. (6) onto the support springs of set (7) through rotatable bush (4), toothedsectOr. .(ii),.motor (2), braóket (1) and shaped element (9). The records of elaatic dèfbrmatiOfl of springs (5) and (7)- are taken with the- help

of wire strain gauges.

Since selsyn (14) driving shaft is connected rigidly to toothed sector (ii) or rotatable bush (4), the angle:t0 whiCh this shaft turns is

equ-ivaleflt

to rudder angle.. .Po

the latter visua-1 read.ng toothed sector .(i.:i

fitt4

itb the scale, arranged opposite a glazed slot in- the: casing of set (16). .

- 2

§ 5.

Servosystem to Compensate Side iesponse

on Model Attachment

to Rotating Arm

In accordance with discussed above, side re8ponae unbalance is detected by spring (18) comprising _an ele-ment _{of the force indicator which design is described} in § 2 and illustrated in Pig.2. A _{electric signal of} wire strain gauges aticked to this spring after

ainplifi-cation affects actuating

motor (2) in the automatio rud-der driving gear (see § 4). With the aid of the actua-ting motor the rudder is executed to right or to left in order to decrease the side _{response, and to restore the} balance.

As an advance amplifier of the _{servosystem a channel} of typical strain gauge instruments is used. The required efficiency for voltage amplification is attained by a stage connection of an amplifier channel with a constant current amplifier. A constant current amplifier _has out-put onto a polarized relay operating for two power re

-lays, which are thus

_{poer amplifiers. The actuating}

mo-tor which is a two phase inductIon _{alternating current,} mo-tor is Controlled by contacts of _{relay. Such a type of}

24

the .motor is 8eleoted owing to

it8

working condition close to a starting one.

As t is apparent from the structural seheme,given

above a

model is Incorporated Inservosystem as oe of

its component elements, Due to

this, model inertia

pro-parties

affectsinifioatly servosystem properties as

a whole. Hencé, it follows the iznossibilityto make

fox

variousmodel types the

systen resembling the opt-. mum system. HOwever, b Selecting reQui.re

effcienoy of

Bmpl±fiáation for riidderquick-reponse a'piifier good

results may be reaohed In testing

modS1s cf most variou.s

types .

cordin Element

Records of angles. of rudder, heel, trimaS. wellas drift should be

taken.

As angular

displacement converters to

electric sinl

inall.the

OaSes

oontaotless

selsyns sre adopted.

Gear

ra-tios

for driving gears are selected In, such a way, that,

with nonlinear characteristic above 4, permits

to fix

-

25

-rudder angle O.-60°,

drift angle _{0_150!} heel angle 12°,

trim angle

t

12g.

Channels for recording all

_{the valuesare}

assemb-led In accordance with diagrams of a Similar.type. -

-A4Q0cps signal modulated in

_{amplitude and phase}

under recording parameter change _{Aaw Is ±e.d from the} sel-syn to a phase-discriminator. Three beam _{winding is} acorn-ponent part of the :selsyn.

At a complete utilization of linear portions, the-selsyn rotor turns up to

,

300 _{angle and it leads to}

emergence of a reversed sign signal at output if a conven-tional phase discriminator is adopted. As the recording element enables to take records of only identical sign, the circuIt of the phase-discriminator provides output value bias towards

one polarity br means of some pedestal voltage ihlch is taken off a

i,5jcc

_{resistor. Such a}

circuit enables to maintain the symmetry

_in

_{discriminator} arms and its characteristio _{at a sufficiently high}

pe-destal voltage and _{a rather low bias voltage.}

- 26

The signal is fed from the phase discriminator at a filter and a diviser in which the circuit sensitivity is

also adjusted by

5G

FCS? potentiometer. Filtered out

sig-na]. voltag, is fed at an electronic potentiometer which makes records of a measured value.

If required, the record may also be made by a loop osoillograph after replacement the diviser.

In designing the system contact].esa elements (sel-syna,

8.0.

electric motor) were selected. This provides high reliability of equipment.

2?

EXPERIMENTS VONDUC TED JY MEANS

CF. A. ROTATING -_{ARM FAC ILITY}

Experiments conducted by. means of a rotating arm- _be

divided into 3 groups:

investigation into elements oi model sidy turnlng -in

calm water, .

investigation into model behaviour when turning in a

sea-way,

investigation into model -rudder-hull Interaction.

The first group of experilents _{deals with plotting a.} dia-gramof ship steering.. _{If it Is admitted by the size of a} rotating arm, a steering diagram can be plotted for ships having the course stability as well as without it. _When car-rying.out turning trials in calm water the _{experimentalde...} vice under consideration secures rather favourab's conditions for studying heeling when turnin

_and

_{different measures to} be taken to decrease it.

The second group of experiments consists of reproducing model free turning in regular _{waves generated by a. wavemaker}

In the course of turning experiments the following records

are made:

rolling and heeling angle, pitching and trim angle, drift angle and yawing angle,

-,2e--rudder

angle and its fiuctuat:ions,

turning radius,

-(f7) rudder stock. moment.

- EXperien.ts are conducted at. differen.t speeds and waves. - During experiments. observations are made over ShIpping of

la-ter of a. model and its: super-structureS and 'separate parts.

--Recordso.f moment on a rudder stock is of

special

interest.

dnce they sho.w those

overloadings of rudder drive which

occur in a seaway.

-The. third group of experiments can be carried out

toge-:ther' with. the second one.

DirIng these experiments 'measurements of rudder normal

force are 'màdö and riadder-fluIl- interaction. effect. is predict-ed. Date obtained from these. experiments can be

applied fr

determining. steering qualities of ships with. cavitating

rud-ders. Moreover they can be used to make correct1os for re-suits obtained in. experiments in.

ca1im water

in the case when

a rudder of a model experiences cri'si.s.,of lifting forcé:which

'is not charac:teristic of a ship,,

in experiments of any group a. model is. attached .to ,a ro

'tating arm so as model pivoting axis would be. located in the forward. perpendicular or even some before it. B this way a

model i.s. imported with statical stability about drift angle

required. for tests and which is absent in the, case with full-scale, ship.. If there Is no statical stability, an experiment cannot be conducted since in this case a model will have, a.

tendency to be

across

the flow. after beginning of runniflg6

In ship trials

it

_{does not take place due to the possibility}

of progressive transverse

shifting which provides ynamica1

stability.

As to model since it has a fixed radius of gyra

tionin experiments the notions of dynamical and statical stabilities coincide for it. Thus the experimental device under consideration reproduces completely the state of ship. relative equilibrium at steady turning but it does not simu-late her real stability0

Naturally, all the values measured in experiments (bee sides force end moment on.a rudder) refer to the point of model attachment to a.rotating arm. However, it is evident

that. the

transition from this point to model center of

34

Simulation of Free Turning

for. SelfPropelled Models

Tested under Rotating Arm

byA,Sh0 AFREMOFF

- 36 -.

l The experiment layout is presented in Fig.1. Ship's model I is towed by rotating boom 3 of the arm facility with

the aid of light rope 2. Rudder 4 is put over in. advance to a pre-set angle Towing rope 2 is fitted to the model through. d3mamometric ring 5which measures thrust 5 applied to the models Model screw 6 is.driven from electric motor7,

Electric supply is delivered from a power pack ins.tafled io

rigidly fixed girder 9 of the rotating arm facility through cable 8 suspended to rope 2 using commutator rings and

brush-es0 Readings of pickup 5 indicating thrust applied tO the mOdel are transmitted in the same manner to a recording instrument.

2. With the boom moving at a constant velocity, the mo-del makes turning circles the centre of which lies on the boom rotation axis Turning diameter

_2R

Sand drift angle

/3 are registered visually at a moment when the model pas-ses by under platform 10. The reduction inthrust

T

is

carried out by inOreasing gradually the voltage delivered to

motor 7..

Plotting

2R

and /3 versus. 7'.

for constant angular

rotation velocity of boom 3 and its extrapolating for

T 0

enables to obtain the values of

2R

and corresponding with such conditions of the model motion when the rope effect is eliminated

-3?-boom rotation velocity,

It is noteworthy that the position of point f7

_where

tow rope 2 Is fixed to the boom, _{should be in fair agreement} with

the

_{value of the turning diameter to be}

expected

(with-in the rope

length accuracy). _{If the initial position proves}

to be unsuccessful, it

_{should be altered, the latter}

proce-dure involving no difficulties because the rope is fixed not

to the boom directly but 'to _{a frame (not shown in the layout)}

which can be shifted by means of remote control to any posi-tion along the boom0

3, _{The above method of determining the model turning}

qualities identical to the method of testlng integrated self-propelled models possesses anumbér of advantages Over the latter one from the viewpoint _{of final results', Supply of} the model electric motor from

_{apowerpack installed}

onri-gidly fixed girder _{enables to test the model.s of ships} hav-ing high pcwer loadhav-ing for which _{self-contaiaed models cannot} be built at all or the use

of

_internal

_âombustion

_{engines is} necessary, this making the tests much more complicated,

Other advantages of the abovesaid method are high accu-racy of speed pre-setting, great simplicity and _{precision of} registering the path components,

-38-APPENDIX 3

A Test Facility for Plotting Directly

the Transfer FunctionsofShips'

Controllability

- kO

it is well kno that an analytical investigation. Into ship's controllability can be reduced to the integration o! a system of linear differential equations, which have constant coefficients and their right-hand side given as a.certain function of

timE

specific for the law of rudder movements,

It is also common knowledge that a spectrum method enabl-ing to avoid a labour-consumenabl-ing operation of extractenabl-ing the rpots. of a characteristic equation can be used to seek a so-lution to the system of linear differential equations .prOvd-ad the assumptions m.prOvd-ade are sufficiently general In theirn

ture0 However, the use. of the spectrum method in itself does not save one from the necessity of making up differential

equations of ship's. motion and determining the values of con-atant coffficients confistent

with a case under investigation,

This procedure results. in a labour-consuming nature of the operations preceding the controllability studies and. involies

a pure1 theoretical estimation of major hydrodyxiamzc proper-ties of a ship related to the liquid inertia as well as a strictly experimental evaluation of all hydrodynamic proper-ties due to viscosity.

In the latter case estimation of characteristiCs for a ship in forward motiqn Should be carried out separately from that of damping characteristics, and, therefore, obtaining the whole set of data related to viosity makes it necessary

- 41

to set up at least _{tWo different series}

of experjwenja In most cases. the

experiments aimed at estimating the forward motion characteristics _{are' performed in}

a wind tunnel, while the tèsts.designed _{to determine turnng}

properties are con

ducted in a'éxperime].

modelbasin. Thus, the differen tial equations related to the _{otioñ of a body cover the data} much differeüt _{as to the methods. used}

to _{btajn it and often}

--posSèssing an.ut.teHydjfferent degree of certainty. _This leads to the fact that the differential _{equations of. motion} simulate actual _{properties of a ship Under}

investigation With insufficient accuracy; _{and the rsults of}

analysis of these equations invariably contain an element of _uncertainty.

Making up a :system of differential

equations covering ship!s motion can be avoided ad the. _{errors due to the method} of independent determination of individual _{terms of this}

sys-tern elilninated'by

cOnducting an experiment ènábling direct recording-or the reactiOn _{of a freely moving mode].}

to an

in-stantaneous deflection

_{of-rudders and to the retaining of the} deflection angle o%er _{a long period of time (jump),}

to an

in-stanteneous defleetfon of _{rudders and their momentary return to} to the initial _{positjon(pulse) or, finally,}

to steady harmo-nic Oscillations of rudders occurring at various

_frequencj,

The latter kind of maneuvering most

suitable for simulation In any mehañjca1 _{system possessing}

apprecigblë lnertia.i' In.

addition to that, Whenapplied _{to a case of Investigating}

ship's controllability,

_I'thasa

assoclat

-ed With 'the features of the rudder hdrodynainiC lift forms-'tion and the effect of the.rudder and huIivorticity

-iaCr0

Adescription is giveniñ this paper.of anexpérimental :faclli'ty enabling the recording oV the model Oscillatory

mo-tion caused by harWonic shifting of rudders 'and making it

-possible to plot 'the model amplitude and phase frequency

re-,.,sponses, as related to, the yawing angle f/J and -lateral :ehifting

?'

thus yielding data for calculation of the body maneuvering by the frequenoy response method.

2

(a).Oierating Winciile of 'perimenta'l Facility

Baèio 'diagram of the experimental facility used to plot

'the transfer functions of Shlp's :controliability B shown in

Fig.].. 'Ship!s model (i)'is placed on the water surface of a

'towing 'ta.k. Ver:tioal pin' (2) 'Invariably fixed to the .áodel

'sO that:its axis passes through the .modelcentre of gravity,.

'thus 'coupling the mode]. to small carriage (3) sliding freely along :gui'de rails (4).

The pin and small carriage joint prevents the model from any linear displacement 'with respect. to the small carriage but enables the model to turn freely in the horizontal plane.

-4,3-ensures uniform forward motion of the model in a direction -perpendicular to the guide rail axes _{Ifthere are some}

by-drodynamic forces transverse to the directiô!a of motion _and a hydrodynawic moment in the horizontal plane, the model

shifts together with small aarriage (3) from the initial centre position to a distance

7

and turns aside from the

direction of motion to an angle . The rudder of model 5

brought to harmonic oscillatory motion by space-saving drive

gear (5) built in the model hull, is the primary cause. for

for-mation of transverse forces. The amplitude and the rudder shifting frequency Ct.) can be varied within wide

li-mits. _{If the model is a'systew close to a linear one, the}

harmonic way of

7

and C4) variation corresponds to the harmonic ruddersh1f.tirig &. The recorded- variationé of

these values enable to determine the amplitudes of

7

and

oscillations as well as their phase shifting relative to the rudder oscillations and A similar expe-riment at a given towing speed V but

with

_{slightly different} values of the rudder shifting frequency 4.) enables to plot

appropriaLe curves of the autpi4.ude and phase frequency re- -spouses as follows:

to

(b

-

JT

When these curves are available., the transfer functions

sought for can be made up. Since it is more convenient to

Le(c,)

j8c)Ie

instead of

letus make use of an obviousratio

is =

tr

it follows that

have

-

4k-The amplitude and phase of frequencyresponses obtained for: several speeds can be generalized, if non-dimensional

fre-,-

cL

quency

'ic=

(Strouhal nuinber)is used as an

argu-!nent instead of the rudde' shifting circular frequency.

The model testiflgcofl'ditions

%=

from Which

y

with the aid of the experi-mental facility described above correspond to full-scale con-ditious under which the surface craft and submersible bodies move in the horizontal.plane. If the abovesaid equipment Is used to investigate the motion of submerged bodies In the. vertical, plane, the body model' centerline is located parallil

to the free water plane, while its stability moment

I1Q sin

_4'

-

(where.

_D

is the model weight,

Q

rising of the centre of buoyancy above the centre of gravity) acting on the body in Its natural position is simulated by a specially

se-lected spring, fitted between the pin and the small carriage. From, the brief d&scription presented above It follows

45--that the "ex)erimental'fac11ity consists Of two units; whlëh

are practically self-contain :

(a) drive gear for shifting the model rudders,

(b) towing gear with recording device.

It is evident that the main difficulty in the designing of the experimental facility lies in relieving the model from

the smai].carriage resistance and from power losses involved in the recording of the values to be registered.

(b) _{Drive Gear for Shifting the}

Model Rudders

To shiftthe model rudders,there is

a midget

servos-tern the block diagrm.,of which, is shown in Fig,2, where the

following notation is used:

1, low, frequency signal generator, counter, modulator, - 4.-power amplifier, S. electricmotor,' tachogenerator, steeringgear, teed-backpotentiometer

The circuit Operates as follows, Two' electrit signals

are supplied to the counter, I.e. the first signal Is deli' vered from the low frequency generator, the second one,which is proportional to the rudder angle, from the feed back

po-tentiometer, - A, non-balance signaiequalilnj

con-- 46con--

46-verted and delivered to the amplifier. The servomotOr wind-ings are used as the amplifier loading. The motor drives

the steering gear and the feed-back potentiometer kinematic-ally coupled to the former. The servomotOr rotates

ándte

model rudders ae shifted till the votage taken from the

feid-back potentiometer equals the signal voltage delivered

from the generator. Thus, the. servosystem provides a precise conformitYOf the model rudder

shifting law with

that of the low frequency generator voltage ariation.

To improve dynamic properties of the servosystem, flex-ible feed-back as related to the rudder shifting speed is used. 'n asynchronous tachometer mounted integral with the

servomotor is used as. a differentiating component.

( ) Towing Gear With Recordiflp Device

Fig.4 shows kinematic diagram

of the facility featuring

main parts of the servosystesi designed to

unload

the model from the resistance due to the

small

carriage and the

record-ing gear0 The system may be readily.imagifled as one used to follow up the transverse force applied to the model from the towing gear side.

Fig,3 features the block diagram of the unloading servo-system where the following notation is used:

-l sensing element,

-2. bignal amplifier, . .

power amplifier,

servomotor,

6, small carriage, 7. tachogenerátor,

The servosystem should ope±ate. so-that the servomotor

torque balances the transverse component of the loading act-.

ing on the model from the small carriage side,

Since the pin used for the model towing is coupled tO the small carriage through the sensing unit, the signal

pro-duced by the unit is always proportional to the above-mention-d transverse loaabove-mention-ding,

The signal i delivered to the pre-ainplifier and its

further passage to the servomotor does not differ from the signal transmission in an ordinary servosystem used to

simu-lat displacement,

The methods of designing the damping facilities for- ser-vosystems developed in the automatic control theory are ap-plicable in this particular case as well, The methods based on considering the transfer function of an open control sys-tem can be used to an adequate degree, particularly those

that-are ounded on the application of the logarithmical am-plitude frequency response. The only condition that the use of these methods should satisfy is that the system 'opening point is to be selected so as to ensure one-way passage of control signals, -

-The system in question incorporates the use of -flexible feed-back as related to the small carriage travel speed, - An

48

-asynchronous tachogenerator is used as a differentiating component housed integral with the servomotor.

The servosystem sensing unit in the diagram presented

in

Fig04 is Indexed as (3), the servomOtor - (6),, Sma].l

car-riage (2) is coupled to the servomotor output shaft

though

a reduction gear built in its casing, a drum and flxible

wire rope (s)...

Potentiometer (7) Is used for measuring and reeorzling

of the model transverse shifting. Potentiometer (8) coupled to the model pin through a gear drive is applied for measur-Ing and recording of the model turning angles.

The circuits of both measuring channels as well as that of the channel used for recording of the model rudder shift-ing angles are completely identical, Al]. values t. be

record-ed are registerrecord-ed by a loop o.sciliograph.

çparison of Transfer Functions Obtained by Direct Model Pestin

a.nd_Calculation

Linear differential equatioS for ship's two-d'mensiQnal motion are of the form as follows:

O:

J9

rn

c;

m

K22

'G6

_2

LjjOW5L

w

z

_2j

_2C'

,

2(1+/c22)

49

-Here

/3

-

/

2(1 2Z)

Go -- 2(1rsic6)l'

.jm'j

;

_2(1+cS)LE'

C9.

rn

2(1/c) ,

=

2(i+k66)L'

- added moment of inertia

coefficient,-non-dimensional expression for moment of inertia, - moment of inertia,

- displacement,

- drift angle ,

-

course angle,

-

rudder shifting angle,

-

normal force derivative coefficient in drift angle, - moment derivative coefficient indrift

ang].e,

- normal force derivative coefficient in

non-dimension-al. angular velocity,

- moment derivative coefficient in non-dimensional an-gular velocity,

- normal force derivative doefficlent in rudder ehifting

angle,

--

moment derivative coefficient in rudder shifting

angle,

50

-y -

principal

transverse body axis lying in the plane of

motion,

-- ditto, perpendicular to the plane of motion.

For a case when is a harmonic function of time va-rying with circular frequency

C)

and amplitude a sta-tionary solution of these equations is characterized by

rela-tive amplitude

and

phase shift

2 4

r

L (9

3)2

(zc)j

9 Sq.

(6-s (f)J

In addition In these formulas

s= a

9=

zGI S20 1

c)W't3

-

non-dimensional frequency

if

-

model speed of motion. A fully submerged streamlined body of revolution with appendages arranged in a cross-shaped way is used as an

object to compare

-

I'(W) and c _p =

functions determined by calculation with the aid of the above

formulas

and obtained as-

a result

of

tests by

eans

of the

-

51.-The body length is 2.OLI, maximum d.Iame.er 0.285m, displacement

W

= 0.0735 cu.m., moment of Inertia

l25.

The body was tested in the horizontal plane, had zero mowent of static stability, the immersion depth of its upper-most point was 102m.

The body bydrodynamic propertie,s required for the calcu-lation were determined as follows:

0,49,

c:= 0,46.

rn=-o,98,

-

by testing the body on a wind; tunnel balance;.

C'=-220, m'=-4,8O

by testing the body with the aid of the rotating arm facili-ty in a model towing tank;

K22

1,0, K

1j7.

by calculation using the

formu-V las. for ideal. stall-proof flow. The body testing involving the uee of the above

equip-merit has been carried out at the rudder shifting amplitude

= 10°

and speed

V= 1,0 m/se?c

The results of these tests compared with the calculation data are given In Figs.5

and 6. It is evident that they are in satisfactory agreement

with each other. .

The factor that has a pronounced effect on the model testing results is the crisis of. flow around its ruddçrs. which is obvious at large shifting angles within the, low

-

52

frequency range. The fact that the crisis phenomenon can-not be considered as one typical of a full-scale ship makes

it necessary to limit the experiments to the small shifting angles mentioned above0

The model testihg results obtained at greater angles of

the

rudder shifting can be used to estimate the effect of

non-.linearity of hydrodynamic

properties. However owing to

-the

abovesaid such

experiments yield trustworthy data only

at

'9>033.

The

model towing

speed cannot be raised because of an undesirable loading on the servosystem due t6 the increase

in holding power and a. limited

freedom

that the model

has in

transverse shifting.

No effect of the towing speed upon the experiment

resuit.s

has been

detected

within the towing speed

-

-1O

I

theo

0

.1erpement