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Instrumentation for free running self-propelled model research on ship manoeuvrability at the Osaka University Tank

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(1)

I,

INSTRUMENTATION FOR FREE-RJN1IG,

SELF-PROPELLED

MODEL RESARChES

ON

SHIP

MANOEUVRABILITY AT

THE OSAKA UNIVERSITY TANK

b1

Kensaku Nomoto

The Osaka University Tank

(2)
(3)

i

GENEAL DESCRIPTIONS OF THE

RADIO-CONTROL

INS'ThUMEN TATI ON FOR FREE-RUNN IN G, SELF-PROPELLED

MODEL

The, radio-control device is composed of a set of

radio tran.smitter and receiver, and relay circuits conductin individual operations.

Th.e 'bperations available by the device are

1.. to go ahead and astern with a predetermined speed,

2. to set a preselected angle of helm

( ) to star-board or to port, and to. put back to am.idship when required. The angular rate of helmirig may be preset.

- control )

3; to set another preselected angle of helm

) to

starboard or to port and to keep the angle during sending the corresponding signal. Cutting off the

signal, - the -rudder returns to amidship automatically., If cutting the signal off before the' rudder reaches the angle , the rudder returns to ainidship from an angle

which it has reached when cutting off. ( 6,

-

control

)

4. to 'start and stop a sinusoidal steering with a

preelected amplitude and frequ-ency.

.5, to perform a quasi-sinusoidal steering, which means

arbitrary steerings along sinusoidal d't,, for instance, sine impulsive steering or sinusoidal hrdover to hardover

one shown on page 4. . -.

to çonduct the standard manoeuvre of Kempf with a preselected angle of helm and helm reversing heading deviation.

to start and to cut off recording of measured signals. to cut off' a motor-generator for a gyro-device for heading measurement and in some cases an

air-propeller for skin fiic,tion correction, when e test is

over.

The radio transmitter and receiver is essentially é multi-channe1, on-off switching circuit utilizing wireless radio, as is1shown in the schematic diagram on the next

page. Therefore, in order to conduct complicated controls

required for the present purpose, a lot of relay circuits

is- to follow the Tadio 'receiver.- These relay

circuits-are described part by part in the following sections.

(4)

The. tram tterand rece1vr now in use are a set of conventional radio-control devie for a toy aeroplane in the market. Süch a device of the highest

css is

we-li refined becaue of its long expé±'ence and so rè-iiable even for reseai'ching'purposes. It has also advantages of no troubles in the allotment of radio frequency as well s of much lower cost comparing any ordér-made

device.

The radio-receiver and the major part of the relay circuits are enclosed in a box of thin steel plate, which ca-rries a 1. 2 M rod antenna on the top.

Electric supply for the radio receiver is provided from laminated dry cells contained together in the box.

A 3 V, multi-tappeó battery supplies ail relay circuits, ste'e-ringmotors and a recording oscillograph. A set of 60V .and 24V batteries supplies a main propulsion motor and another set of 24V batteries supplies a 663 cycle motor-generator for a heading measuring gyro apparatus. All these batteries are assembled from 6V auto-bIcycle

batterie' widely in the market.

E1etric supply for the radio transmitter is provided through a conventional DC supply unit with a voltage

regulating tube from 100V coiuuierclaì AC supply.

Another DC unit at the pier is a battery charger

using s.e.lenium rectifiers and an adjustable auto-transformer, which .is.able to supply the tatteries lna model at the

pier. iRA NS/II r.

5*/rc/I

CHA/V2VEL A TR,A/V'S,$f/T.

s#i req

C//4IVIVEZ

/

Do. CHANNEL g Do. Cl/A NNEL D

RADIO

J /NAL5

-

OUTPUT

REL4 Y

CIfANIVEL A ¿70. C//ANtVEZ

I

Do.

z

Po.

Switchin, channe1 A transmitting switch, channel A output relay closes, and so on.

(5)

2.

RADIO TRANSMITTER AND RECEI(ER . . .

Fig. 1, 2 & 3.

Swit'çhing one of the transmitting switches,b voltage is impressed on a multi-vibrator oscillator (OAS) and a set of R and C is connected to the grid circuits. Then

corres"ponding Ludio frequency signal is excited end tran'smi'ted through the 27. 120 MC carrier, which is provideò by a grid-tunning, cristal radio frequency

oscillator (3A5) . The transmitter has ten channelS of audio fequency signal, viz, channel A, 1, 2, , 4, b,

6, 7, 8. and B. It is possible to send either the channel 7 or 8 signal simultaneously with either 1,

2,

6 or 4

signal.

The first stage of the receiver is a self-excited super-regenerative detector usin a subminiature tube (TkG4 orXFY-34). Three audio-frequeney transistors which constitute an audio frequency amplifier follow it.

The last transistor drives the coil of the reed-selector, which is-eserLtialiy a e.lectro-megret with multiple reeds

of thin steel. A natural frequency of an individual reed is selected so ss to synchronize with either one of

u.dio sinals. Then receiving a radio signal, one or the reeds, which synchronizes with the audio frequency, osci.11at.es and closes its contactor intermittently.

This intermittent contact keeps the corresponding outpt relay close by help of a smoothing RC circuit. Undei a proper adjustment, it is easy to receive, either channel 7. or 8 simultaneously with either 1,

2,

3 or 4.

3E MAIN MOTOR CONTROL C

i

)

.Fï.4

RL -'1, & 4 Radio receiver output relays.

No. Indicates each channel number.

RL -' il io Micro switches driven by electro-,

magnets.

breaking capacity ....DC l, 100V. RL - 12. . . . ... . . . Midget relay (a kind of m.iniature

relay) breaking capacity ... 0.3 A.

Oce "AHEAD" sIna1 comes and then RL-4 closes,

RL-ll closes and keeps close untill "STOP" or "ASTER" signal comes. This action is similar for "ASTERN" operation.

It is not preferable, however, to execute reversing the motor without sending "STOP"; because an abnormally

large -rush current may appear when abrupt reversing.

When starting for a test run, it is deSIred to reach testapeed in a short travel. A.time relay circuit Iown atthe top of the figure-isof this..p.,urpose, the p.incIp1e of which is merelf o raise propeller revolution

during -acceleration. -

Accorin

to experience, excè'ss

oitage of 10V and accelerating duration determined thxough sveral trial runs provide ssti8factory results. The

duration us usually 1O-l5 sec. and the travel is less

than .30 -M for 6M models.

(6)

4.

AUMLNT CONTROL

Fig. b

RL - A & B

Radio

receiver output relays

RL - 28

Small size relsy, breaking capacity

.b A

RL - 29 Midget relay

G Mirror type alva.nomeer in a

recording oscillograph.

Once "MLASURENT ON" signel comes and then RL-B closes, RL-lB closes and keeps close untill "MEASUREMENT OFF'! signal comes and RL- 29 breaks the locking of RL-28,

Once RL-28 keeps close, any more repet of MEASURE. ON signsl does not affect RL-28; measurement still

conti-nues. 5the "synchronism signal" is, however, cut at each repeat a.d it is recorded by the recording oscillograph. The signai is utilized as s synchronism signal between a record tEcen b, the oscillograpli in a modcl and traverse angle records for running pith drawing provided from a pair of tracking transits at the shore.

b.

Th'EING

CONTROL ( 1 )

Fig. 6.

The steering gear now in use has two different steering systems, one of which yields a constant rate steering

and another a sinusoidal one. The latter provides a 'ontinuous sinusoidal stêering as well as a

quasi-stnusodai one, which means an arbitrary steering along a sinusidal ö(t); for instanóe, sine impulsive steering and sinusoidal hardover to hardover steering s1own below. These types of steering may be Valuable for ship manoeuv-rahility researches ( refer to a contrIbution for i.S.p.

1957,.Nr., 35, by the author ). it) / ' I

S/ne impulse

/

---

,--,

s. , 4 - ._-.s

/

fi,w'/da/ Hopdoiì7'

u/apoyp

(7)

The ccnpositIon of the steering system is shown-beow

a black diagram.

,rhe sinusoidal steerIng motor, drives

the tiller sinusoidally

itb a preselected amplitude and

-

frequency through the sinusoidal motfo

mechanisirr ernployin

2 Scotch-oke.

The constant rabe steering motor is fixed.

upon. the tiller and turn the tiller disk which Is secured

to. the rudder, with a preselected constant rete.

Ac.c.-ordirigly this steering motor yields a relative rotation

between the tiller and the rudder.

When the sinusoidal steering motor is, and then

also the.tiller is et rest, the constant rate steering

motr governs steering.

In this case, the elecromagnetic

bTóak.secures the tiller to prevent the sinusoidal motion

mecharLism. from a counter driving.

On the contrary, when the constent rate steering

motor is at rest, the sinusoidal steering motor governs

steerIn&.

Counter driv-ing of the constánt rate stering

rnechan

is avoided by using a worm gear in Its gear

train...

Steering control, viz, to put a certain angle 'of

he-im and.' to return helm amidship, may be provided ty

4aci of.the two steering systems following radio

signals,

while the. sinusoidal system can not yield a helm angle larger

than a predetermined amplitude of sinusoidal steering.

Fig,. .&- Shows the steering control circuit.

However in

th.e figu.xe only the constant rate system is described for

easy explanation, the steering control circuit In the

-figure may govern also the sinusoidal system 1j sWItching

to t.he latter syatem.

This switching, viz, selection

betwean the two sstems iaa

be also controlled Ly radic

signa.ls.

. The following section and Fig. 7 relates to

this control.

SIA/I/SO/DAL

STEER.

MO TOR.

RADIO-PECEIt'E1<

S/N. ii'O 110M

M(CH1N/5H

fJEEPiN,

CONTROL. RELAIS

TILLER

A ELECTRO -MAo.

IREA 1<

ECHL1'IE OF SThERIi'G GEAR,& CONTROL SYSTEM

I STEER. cONT2OL t

SHA ¿70

W

H PHOTO-

4-1

,I7RAN5/STO. PIE CE5

t

1 CO'VJi. RATE STEER.

MOTOR

TILLER

P151<

,UODER

(8)

JWAP0W PIECE f

NOTATION IN FIS. 6

}t&d10 receivtr output re1

Midget relay

-electrolytic, workir voltse. .10V:

DC Micro-motor with permarìen.t

magnet field, 2 W, 3600 rpm.

1: 60 self-contained reduction gear. Audio frequency tiansistor

photo-transistor

small. pieces of brass, fixed to the tiller disk. Theirfunctions are to cut off the rays from a lamp into a photo-transistor at predetermined positions cf the

rudder. (refer to the figure below) 1. Suose the rudder is e.niidship. As the shadow piece 2

covèrs the photo-transistor PD3L (1), RL-20 is opened. When a sIgnal "+ôz" comes and RL-5 closes, a chí.rge

current of 400p..F condenser runs through RL-14 during a short time, which depends on a capacIty of the condenser and a resistnc.e of the relay coil. Then RL-19 and RL-23 are actuated successively and the steering motor turns to

starboard. Provided a proper adjustment of the condenser capactt,. the shadow piece 2 leaves PD3L(l) before RL-14 opens'and:then the rays shoot into PD3L and RL-20 closes. Iow RL-19 does no more open even if RL-14 opens and

the

mo.tor keeps turn to starboard. As soon as a helm angle of

reaches, the shadow pIece i cut off the rads and RL-20, 19 and 26 opens succ;essivel and then the motor

stops irediate1y by dynarIc

reakin.

This is "hardover

to strbparc11.

As RL-14 have to open before

this instatit, too

1rge coñdenser capacity must

be voIded. 0bvious1 the

higher is a steering speed, the smaller is an optimum

condenser capacity. According to experience, this adjust-ment is easy and enough relIable once it is done.

flL-b,-6,-7&d....

F1 -14 to 26

.

400 p.F condenser

. *

Steering Motor ...

2SB-116. PD3L - y...

Shadow

Pi,'eces T/LLE Dí5/< CO/iT4/NE ¿F

/j7-

7A/IS/STa

PD3L-(I)

fHA804'//ECE 3

-JHAPOIVP/ECE 2

SLIT ON CON4/NER TO

CHTAINER

'T

P/'OTO- 74,$/ST

PD3L -(2)

N

S//ADOIV/'/ECE

4

6

(9)

In ordrtò

return

the rudc'er to arnidship,

theirJ

" ta to be sent. One more "- "

fter-he

,ruer

res c)es a:nidshi-

¡ields "hardover to_port". .V

ThIs "hardover"

or " " contrpl is usually emplored

or.l- fo turning trial snd "ftce about" after a test

run. The extents of z and-az may be selected easily

by shíftin the shadow piece i and 6. A sicht shIft of the shadow piece 2 provides "neutral helm adjust".

2.

.Su.p-ose

again he1m midship".

When a signal "+"

comes,RL-17,

16, 17 end 23 close successively nd then the' steering motor turns to starboard. The shadow piecs,2leaves PD3L(l)

soon

after and RL-20 closes.

Thri

cutting off

the signal "+,", RL-7 and 16

open

inedi-ate1, while RL-17 still keeps close because RI-20 already

.keps close.. Accordingly RL-26 opens and RL-22 closes.

The

motor reverses to port. As soon as the

rudder

r.eaohèsamidship and theshadow piece 2 covers PD6L(1), V

RL-2O,l-7

and 22 open successively and the rudder stops. jth.ese actions mean in a word that the rudder turns

to

s.tártrard during transmitting the signal "+" and ±eturns.to amidship automatically when cutting the sigani

off. The ±udder does not

turn

to starboard Iñfinitely, however. 'When the rudder reaches the angle

+g

and

theshadow

piece 4 leaves the photo-transistor PD3L(2), RI-21

is.. ac.tuated and RL-23 opens. Then the rudder stops at

the angle +ö

,.even

if keeping still t?ansmitting the signal . Also in

this case, cutting off the

signal1

theruddè.'r r&turns toamidahp.

Transmïttin the signs.i -ô1 during the

rudder

is

urtin, to aiic.shi, from , the r'idder ptes amidship

id turns to port.

When the rdder pses amdship,

RL-l'T opens and all 01-circuits are restored to Ìest.

PZ2.ctica1lj this opôration is performed by sending

"-3,

irmiediately after cuttin

off "+b

" and it is.used

for the

tandard manoeuvre of Kampf.

Th

extent of ôj

is selected

by changin trie shadow

piece 4.

This

ô

- control is used for coarse keeping in

straight running and other gener1 purposes 23 well as for

the

standsrd manoeuvÍe and npulsive steering teste.

6. .

STIRING

CONTROL ( 2

)

Fi.7

RL -

24, 25, 2

&27 . . .

Midget

relays

inusoiás1 steering motor . . the same as the constant

rate steering motor, 2 W.

SW i & 2 Snap switches.

Sinusoidal and quasi-sinusoidal steering are enera1ly called for only in a test

run,,

while they are not always celled for even In a test

run.

(10)

If 5W-2 is closed manually beforeleaving, RL-27

closes

snd keeps cloae when the siGnal "MEASUEIENT Or:"

aones

and RL-28 cibses.

Then-911 steer1ns are gorerned no

moré by RL-22 & 23 and the constant rs'te steering motor

Lit by RL.-24, 2b and the.sinusoidai steering

motor.

62

and

6,

-

control described in the isst section

is now performed through the sinusoidal steering system.

Ts i. ",qusi-sinusoida1 steeringtt.

The electromagnetic

break releases the tiller when every steering is

executed

md either RL-24 or 25 is actuated, and secures it

again

when -e.very steering finishes.

On the contrary, if SW-2 is not closed when leaving,

the con&tsnt rate steering astem is still ready for

all

stee-ringsigna1s even when measurement is executed.

Cutting a measurement off, RL-27 opens tmmeditely

if the sinusoidal steering motor Is in-

no Qperstion

(both RL-24 & 25 open) at that time.

If the motor is

in operation, RL-27 keeps stili close until? the

operation

-is over.

.

Thus the sinusoidal steering

systemreturn$the

place..of steering control to the constant

rate system

-when a measurement is over, after finishing

a steering

already in hand.

-Closing manually both SW-i & 2 before leavirg,

also

L-2.t keeps close as RL-27 during

a mea suremen:t.

The tWo contactors o

RL-20 are both short-circuited and

sccordingly.the steering motor keeps turning

even when the

shadowcieces 1, 2 and .3

cover the photo-transistor PD3L(l),

once

5a- or -ô2

is executed.

This yields a con1;inuous

sinnaoldal sterirìg.

Its frequency and amplitude must

be adjusted before leaving.

Executing "I

ASURE.INT O1F',

RL -2ò opens irnraediatel

while RL-27 keeps still close ecuse either RL-24 or

25 is benerall- still closing.

If

and -2

are

adjusted to be outside of an amplitude of

sinusoidal

steering, the motor stops and RL-27 opens when the

rudder

comes to amidship for the first time after

a measurement

ia çut off.

Now the Constant rate steering system is

ready for a next radio signal.

This makes easy steering

-control. in

homing after a sinusoiaal steering

test.

7.

STh1RING CONTROL ( 6 )

Fig. 8.

-AUTOMÊ.TIC CONTROL FOR CONDUCTING THE STANDARD

rrJOEUVRE OF KEMPF.

RL - 61 & 62

Roty Rel-y

midget relaye

s special rely widely used for

telehone exchanging.

ThIs reiry

has a common coritactor

(

wi,per,

so called) which sweeps multiple

òontactors put along

a circle about

it, step by step every time the coil

is actuated.

Thus the relay is

ess-ectially a multiple contactor

rotary switch driven by electric

(11)

6 ROD/S/<

(SW- TEETi

ßIS/</.

FIi/O)

Pl/OTOCONTAINER-TRANSISTOR

9

The_sdw piece b is

fan-shaped piece of

te1

Shown helowf the anale of arc of which equals twice .

heading nt1e of h&im reversIng in the sttnrd manoeuv'e

(uaually tje saine

r

hem anleernpioyed inthe manoeuvre). Ufltti1-Thf 1andard manoeuvre opens, the piece Is ec'ired

.1 s4 b the e1ectro-miiet

-

/ÍAv11

QF ao thct its certre

/ agrees with the

E]jt,

of the photo-trntor

i

container.

JI//IDO/Y

PIECE J

Whe the

radio

signal "START THE STANDARD MANOEUVRE"

cornea R-3l closes.and keeps close untill "PAEJRE'i!EN OFF"

is exeuted.

Then the electro-magnet is diactuated and

the thedow piece is droped and, put ori the gyro disk which is. fixed to the space in spite of heading change of

model by an action of a frec-'roscooe (refer to the est

.se-ctton). Thus starting the standardmanoeuvre, the

hadow piece begins

tp shift relative to the slit by the

saine

ongle rs a

herding cbrne.

On the

other hand, when

the stsndrd rnrnoeuvre is

executed-

nd RL-1 closes, the rotary re1y beClns to

conduct

and

-

steerin

control in place of radio

s!rials 7 & . nd

Ft the some 'time ±t executes ethcr

or -os. Then

the standard manoeuvre starte. Direction of

the

first helm

is selected

by driving the "wiper" b

'reasin

the

urh button 'eore levjn.

e herding change f a model reches the hclm

reversing

the had.ow Iece ler'ves the photo-tronsistor

PD6L(3)

nd RL-62 clos.

A charging current of

600 pF

condenser rushes through the rotary relay coil durIng a short. time and the wiper advances one step. The rotary relay executes reversing the helm.

A the heading ret-irns cgin to the helm reversing n'le, PL-32 onens ard. the coreriser diechorges through 100 2 r.e.sistor to he re'dy fr the r.ext oere.tton.

The helm reversin sn:le my be ve.riatle b:,- changing

the shrd-w piece 5.

Transmitting the radio signal "EASURENT OFF",

- 61. opens ard the rotary relay does nô more conduct

seering.

According to the function of

-control,

the rudcr returns to amidship automatically arid is resdy for the radio steering control.

(12)

C-GENERAL DESCRIPTION OF

ARThG- I-TRUIVNTATIaN

Q,uantitiez to ce measured -are

sbip's heading angle as a function of time:, angle. of helm as a function of time,

rev1ution of pro.peller, running path of a free-model

rudder normal force and rudder torque

These quantities except arunn±n path are detected electrically and recorded continuously by a mirror-galvanometer type recordinìg oscilloraph put in a free-running, .seif-propelied model. The recOrding is con-ducted -through radio remote control.

-1. Time signal is provided by a portable

electric-- contact watch at each i or 0. 2 sec. and

recorded by the oscilloraph accompanied ith other measured ignais. Synchronization between this time record and

cr.other one with a running path record took at the shore is. oerforir±ed using a r.dio signai, channel b

s is sttd previously. (-Section 4)

2. Hea-ing b.ngle (course

nie

is detected using an e1eetriclly driven free-gjroscope shown in

Fig, . -A motor-generator driven byDC 9V supplies the

gyro motor 110v, cycles,

hse AC.

The xis of the inner irnbal is horizontal arid

the one of the gyro-rotor is also horizontal in a normal condition (viz, no precession exists). The two axes

are -aïisys perpendic-ilar to each other. The outer

gimbal is suspended by a vertical shaft so as to rotate freely about the vertical axis and thus its direction

is ftxeó to the space in spite of s;.ip's headIng change,

according to the vell-kron proprt

of a free-suspncd

gyrosccc.

Therefore an n1e of rotatIon of the outer

-gimbsi relative to a model ship indicates

Inedistc1i

-change cf- her heading. The angie is detected and recorded

by a photo..electric means decriLed hereafter.

lo

}

(13)

A c-ircular , around the outer edge o± which

- cut are w-teeth in a pitch of one deree, is secured

to the verticsl -shaft. Closely under the w-t-eeth,

ut is a. photo-transistor

shielded in a

container. on the top of the dontairier, a fine

slit

is cut in a

radiai direction of the disk and rays from a lamp put

a1ove.the disk edge shoot into the photo-transistor through the slit. The sa-teth covers a certain pprtiorì oÎ

the silt depending on n angular position of the disk and thus an intensity of light supplied to the

photo-transistor varies in a saw-teeth form at each one degree of heading change. It induces a sim±lar saw-teeth

variation ofan output current of the photo-transistor and the. current is recorded by the osciliograph as a

hàa;dir arLgle signal. The circuIt is shown belo: Practically a measured signal is somewhat of a deformed saw-teeth and a calibrated nonlinear scale is to be used in order to read up the heading angle in a fraction of one -degree.

Accuracy of this messuiement depends upon precision w.orking of tte saw-teeth for a relatively short period measurëment and upon a stray drift of a free-gyro for a

longer one. It is riot so difficult to assure an accuracy or 0.05 0.03 degrees in cutting the eeth, if a

;'eontly large radious of the disk is selected.. 0nthe other hand, a stray drift rate-of a free-gyro

-.my exceed sometimes 0.Öb0.1 degrees per min..

Tiea the,acc'aracy of heading measurement may rise to 0.03 0.0 de-rees for a short period measurement (less -thanl020 sec.),.while it is reduced. to 0..1''O.

dere&s for a. lier period, one

( lo min.)

-' -

--

LAMP

A071 1/ONO,F

SA/1'-TEET/ DISK frHOTO-TMN$/fT

(OMM! E«

SLIT

e.,,.\

/

1 / ,. .1 t1

t

11

(14)

12

3.

An. anale of heim

1s detected ana recorded

y

the

iiilar phcto-eletric means asheadingatigle.

Jrl this csetho saw-teeth are cut a1or the edge of the tiller disk (Section o) and cover ± 40 d.grees of

heim an1e.

Two indivIduai teeth, which correspond to

j 3 der.ees respective1y are of a half-depth in oDder toidentify helm amidship in a recorded saw-teeth sirLal. Also in the helm angle

iaesuremerit,

output sinal of a

photo-transistor is. amplified by usual transistor

prior to

drive s galvanometer because of much higher

frequencies and of a lower level of a helm angle saw-teeth signai comparing to heading

one.

Th

accuracyof the

j-ielrn.sngle messurement is about 0.Ob decrees for 311

cases.

4.. Propeller revolution is detected by an usual electric

eon.tactor with a reduction gear and recorded by the

osciliogr.aph,

5. Rudder forces are detected by wIre strain-gauge

-

tchnics.

A rudder i suspended by a ru&er stock,

vh ich is rnechanicall isolated from a gLdeon and shoe

piece, so that all reaction against rudder forces

are

provided throuh the rudder stock. A thin circular pipe of tee1 constitutes ari intcrrnediate part of the rdder..stock and a number of wire strain-gaues are basted or: it so as to detcct a ì:oral force acting on a

rder. ad Its moment aboit a

ruc..dr stock. An all-transistorizd stran-meter coriposed from a carrier esciiiator, two mp1ifiers and sc-lf-cortaining dry

cel1. electric source is emp1oed.

The detected and

mp1tfio

sinals

re transriltted. to the cscilloraph.

6-. runring path of a fre-mode1 is dtermined by a

pair of trsckIn transits, each of which yields

contin'ous

record of traversi angle. The receiving

antennais uualiy locted on G.G. of a model so as to

be uasd as a

tsret

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