A new type speed meter - Application of the Karman phenomenon to the design of a speed meter

ARCHIEF

A NFW TYPE SPEED METE1

.PPLICATION OF THE !CARNA?7 V

TEX PHCMC1

TO THE D3IGN OF A SPEED 1'ETFR

Hi88Jflit*U

ST-UBA, DR.ng.

rectr.Techn1ca1 Reee&rch Laboratory,

NIPPON KAIJI rLOAI

EE{:II _4i

_n

_H

H

.

ScheepLo.

Technische Hogescho e1L J j? - l.I I I t I.e) a aiaa talai

TABLE OF COìTLS

A BSTRA C T

Page

i.

INTRODUCTION 1

II .

VORTEX STREET TÀRTING FRCL i BOL'

IN FL

4

III.

ÂLIC

L IFITIC

OF

KARAN VORTEX TiET T

?ED 1kT

ô

_I i

Iv.

CYLINDER PRODUCING L

Ai' VOkThÀ STReT

10

Iv-1.

3ectional form and size

10

IV-2.

Length )f the square cylinder

10

IV-3.

.nd plates and side p1tes

11

1)

End plates

11

2)

side plates

13

3)

Length of end plates

15

V. MLTHOD FOR PICKI1G UP TIlE VORTEX -Ii 18

VI.

SPD INDICATOR AND TL

iCOiU)IIG

VI-1.

Outline of the research work

2)

VI-2.

Jetails of the indicator and the

rii

CABLJ FR A TOVJ::G TYPE SFEiI

2ik 25

VIII.

TÒST RESULTE OF TIE SiEED METER 26

VIII-1.

Distance of tbe preliminary

r'in ìt

a mile post speed

tri1

26

VIII-2.

Error in the rnile-r'ost disterce

and the shallow water

effects

29

viIi-3.

L:easìreient of sea waves

29

VIII-3-i.

*aves ruade by the ship

30

wave length

30

wave height

31

VIII-3-2.

Sea waves

32

VIII-3-3.

Informations

34

hJIII4.

Lerith of the twing

cable

36

I:L.

Ci:LLUI3N

40

It is of fundamental importance to measure accurate speed of a

ship when we investigate

more precisely into

_her

_sea-going

per-forrnences. It Is also expected to become quite necessary to obtain

a reliable information

_on

_{the ship speed from view point of a more}

progressed research on the strength

and

_{stability of ships, to}

which the bydrodynamic action due to the ship's motion is

closely

related.

Be that as it may, most of the modern ships are

equipped with

speed meters of various types. These speed meters are calibrated

generally on the occasion of speed trials in a mile-post course.

However, it is very difficult to evaluate the

true

_{speed of a ship}

from such trial results which inevitably include influences of tide,

wind and sea wave. _{Moreover, even if the speed meter is calibrated}

at a particular condition, for example, at a trial condition, these

calibrated resu1t _{are effective only for the specific condition}

and not useful for _{any other ones.}

This is because due to a fact

that the value indicated by an ordinary type speed meter is closely

related to the variation in trim and loading condition _{of the ship.}

So far as the accuracy is concerned, lt has _{therefore been unable to}

put full confidence upon a speed meter of usual _type.

In order to solve _{these problems, the following two points}

should

be considered; _{firstly, ;o obtain a speed meter}

sufficiently accu-rate in itself, and

secondly, to find out a new method of getting a

true ship speed under any conditions required instead _{of performing}

the mile-pcist _{course speed trials.}

If a speed meter of high accuracy be available the latter

becomes a problem of minor importance, because a calibration of a speed meter attached to the ship can be made satisfactorily by means of a towing type speed meter of high accuracy working at a distance far behind the ship, where the local disturbances due to the ship hull become extinct and the speed meter indicates a true

value of the ship speed, ( the wave caused by the ship does exist,

however, its effect on the speed measurement can be excluded by

methods as described later ) . In this paper, therefore, the problem

on a speed meter of high accuracy will primarily be discussed.

Generally speaking, necessary conditions for an ideal speed meter can be summarized in the followings;

it must have high accuracy,

it must be free from such effects as wear, corruption and temperature variation,

constant relationship between the indicated values and the speed must be maintained, a linear relation through the origin being preferable.

2

Any one of the usual speed meters, such as the resistance type, whirling blade type, Pitot tube and heat wire types, does not

fulfill these conditions. The

author has

been trying to get an

accurate speed meter for many years, and finally noticed to utilize

the relationship between flow speed and frequency of

vortices

started

behind a body running through a fluid. An extensive investigation

onthe trial production of this new type speed meter has then been

carried out,

and the results were reported in the congress held by

the Ship Experiment Tar

in Tokyo at the end of World War II.

Later, in 1951, some of the results appeared in the publication,

Tank Report No.?.

The first time 'when the new speed meter was

tested on an actual ship was on the occasion of the maiden voyage

of the single screw Cargo ship "NISSEI MAiTJ" from Yokohama to

Vancouver, where an investigation Into the sea-going performances of

ship was carried out from Dicember, 1951 to May, 1952.

Since then,

a large number of exDerlmental tests h've been conducted on speed

trials at sea in order to assure of a general use, succesive

im-provernents being made for obtaining sufficient durability and

satis-factory functioi of the pick-up as well as the recording part of the

speed meter.

Since lt is believed that the newly designed speed metei

can be used without any anxiety in an ship the results obtained from

the authors study will be presented in this report.

1

II VORTEX ST1EZT STARTING FROk

A BODY IN FLOW

Since the original Investigations on the vortices associated _with

a moving body In flow was performed quite a long time ago, lt _seems

very difficult to remember an exact date or person of the discovery

on the periodic phenomena of the vortices. _{The first experimental}

observations may be due to STROUHAL who showed that the frequency depends on the relative velocity of fluid, and thereby the following

non-dimensional number being called STROTJHAL Number,

tj

_V

where

n ::: number of vortices starting from one side of a body

in flow within an unit time

B :::: breadth of the body, V :::: speed of flow

RAYLEIGH also performed similar experiments, and he pointed _out

that the STROUHAL Number S is a function of _{REYNOLDS Number.}

In 1911, KABMAN presented his famous _{theory on the vortex street,}

and the vortex street is then called KRMiN _{Vortex. It may be said}

that no substantial advance _{in the theoretical treatment f the problem}

, , ,

has been made since the KARi1ANs _{paper was published, however, a large}

number of experimental works have been carried out for a further

de-velopment of the study. _{Experimental investigations by FAGE,}

hOVASZNAY and H.BL1NKE, for instance, _{would be the typical ones.}

4

From the results of these experimental studies lt can be

con-vinced that

there exslst

three cheracteristic ranges In REYNOLDS

Number,

namely,

"stable"

C R.No. about 40 to 150 ),

"transition" ( R.No. about

150 to

OO ), and

"irregular" range (R.No. about 300 to 10,000 ).

In the stable range,

vortices which

are caused alternately from

both sides of a body are stable and quite

periodical to a point

somewhat far behind a body,

_and

they

finally

disappear due to

vis-cosity of the fluid. In the

transition

range,

vortices

are

unstable

and sometimes it is even impossible to

find out

_{their periodicity.}

In

the

irregular range, vortices are not so stable as in the case of

the stable range, however, a remarkable periodicity can again be ob-served, and they quickly disappear by the effect of the turbulence

in flow.

The STROUHAL Number,

increases

_{considerably with the}

in-crease In the

_{REYNOLDS NO. In the}

_{stable range, while In the}

irregu-lar range it becomes almost constant irrespective _{of the REYNOLDS No.}

In the transition range, the STROtJHAL No. is scattered _{and sometimes}

even difficult to find the periodicity.

III APPLICATION OF Th CHARÂCThRISTJCS OF

KRMAN VORTEX STREET TO . SPEED METER

As can be seen from

the exp1antion In the previous article, the

STROTJHAL No. varies with the REYNOLDS No.

lfl

e very complicated

manner.

In general, the

TFOUHAL No. S may

be expressed in the following;

çconfiguration, R.No., roughness, turbulence

and quantity of gas desolved in the water

)

If we neglect the effects of

roughness of the surface of a body

as well as turbulence and

content of gas in flow when the

desolved gas

becomes separated in the flow behind a body, it gives

n effect equivalent to e change in the form and

the size of a

body

the sbove reiation becomes as follows;

( R.N))

In the case of a circular

cylinder, TYLER gave a formula,

=

_.çq8

_(i

₎

for R.No. lower than 500, and concluded

that S becomes

constant when

R.No. Is higher

than 1O (

_{the maximum R.No. in}

_{his experiments was}

4x

fO

).

According to the BLENKF-FUCHS-LIEEERs

_{test results, it is also}

said that S increases until R.No. reaches about lO, and lt remains

constant, 0.202, in a range of

R.No.

between 1Oand

whereas 1f

1- _t

R.No. exceeds 10 it shows a tendency _of

_{decreasing sl1ghly but again}

starts to Increase a little.

-6

j

Most of the experiments

_{conducted up to this}

time bave been

on

the specimens of

_{circular cylinder, for}

_{which it is considered that}

as R.No. increases the position

_{of the tr1tion}

_{point of the flow}

separated from the body moves forward, causing

_{unstable fluctuation}

in its position, and

_{when further increasing}

_{the R.No. the}

trans-ition point reaches

_{the laminar separation point on the body}

(

i.e.

at the critical

_{REYNOLDS Number ), end}

_{a so-called turbulent}

sepa-ration starts to take

_place.

_{since the viscosity}

_{of the fluid}

influ-ences del1ctely upon the characteristics of flow around the circular

cylinder where pressure

_{gradient varies gradually from positive to}

negative along its surface,

_{the STAOURL No. should}

_{very quite}

complicatedly with a change

_{in the REYNOLDS No.}

It seems, however,

_{that the characteristics}

_{of Karman Vortex}

Street

in a fluid would most

_{suitably be applicable to}

_{the principle of}

speed meter, provided

_{that one could find out a body of special}

form

for which the

_{STROUBAL NO. becomes}

_{a constant value}

Irrespective of

REYNOLDS Numbers.

_{Before going into}

_{a detailed discussion}

on the

application of the

_{Karuin Vortex Street}

_{to a speed meter, the}

following general

_{considerations will}

_{first be made.}

The drag coefficient

_{of a body in flow,}

behind whicI

_{rows of}

vortices are caused, can theoretically be

_{expressed by e formula}

cx=

2

[ oJq36

0.3141

where

1space between

_{two adjoining}

_vortices,

Bbreadth of a body

_{measured perpendicularly}

to the direction

_{of flow,}

u=advance speed

_{of vortices,}

u0=-speed of a body.

8

As can be seen from Table i the c1cu1ated

_{values of C, which}

_are

obtained by using

_{experimental data of 1/B}

and u/ut

(

theoretical

ones being impossible to obtain

_{) ,}

_coincide

_quite

_{satisfactorily}

, ,

with the test results of

_C.

_{Then it may be said that, when KARiAN}

Vortex Street follows

the body

in flow, the

_{drag coefficient}

C..

takes a certain particular _value

_{depending upon}

the characteristics

of the vortices.

_{In other words, the}

_{experimental fact of}

e

constant

drag coefficient

C. in a certain

_range

of R.No. means that

, ,

the characteristics of KARMAN Vortex

_{street also have remained}

unchanged in that range. From this

point of

_{view, it}

_{would be}

useful

to observe

_{the experimental results shown in Figs i and 2.}

Figure 1

showing experimental date _{on e circular cylinder}

_obteined

by E.F.RELF illustrates _{the relation of C.}

and ' to R.No. As can

be seen from the

figure,

the curve of

_the

_{drag coefficient C}

,

as

'well as of

_v'

_{indicates a complicated}

_{form with a variation}

of R.No,

and they show an abrupt change after

_exceeding

_{a critical R.No,}

where the periodic phenomena of vortices _can

_{hardly be observed.}

In

Fig.2 shown are the _{test results on}

a sphere and a circular _{disc as}

illustrated in

_Gottingen

_{Report, representing}

the relation between

drag coefficient

_{and R.No.}

_{It can be seen}

from Fig. 2 that the drag

coefficient curve for a sphere looks similar

_{to that}

_{for a circuler}

cylinder shown in _{Fig. 1, while in the case of}

a circular disc the

drag coefficient

is almost constant throughout the tested range Of

R.No.

( from 3</Q-.-

i6

).

Considering these _{test results, the}

author presumed that

_{there would}

be no effect of viscosity _{on the separation of flow around}

a

separation point of flow locates always at both eges

of the cylinder at any

values of R.No.

If

_{lt is so, the drag}

coef-ficient or the S value which represents characteristics of vortices

would become constant when R.No.

exceeds a certain value.

In order

to

confirm the

_truth

of

_the

_{presumption, a}

literature

survey on the experimental work was made. _{Nevertheless, none of the}

test results on a triangular or square formed

_{cylinder was found,}

since most of the experiments were conducted on circular

_cylinders

although a few

canses on

_{flat plates or aerofoil shapes vere also}

reported. Only F.DURALL

explained in his

_"Aerodynamic

_{Theory" that}

in the

case

of a body having

sharp edges

_{nB/V was}

_{constant throughout}

the whole range of R.No. in his experiments except at its low values.

It is therefore impossible to determine _exactly

_{an upper}

_{limit of}

R.No. to which tile

nB/V value stays

_{constant, but it may be estimated}

from the

above-mentioned test

results on a circular disc that

_S

remains

constant up to lOof R.No.

Under these circumstances, _{tests 'were carried out on}

triangular

cylinder, and

their results

_{seemed quite}

_{satisfactory for applying the}

characteristics of Karman Vortex

phenomena to the

principle of a newly

designed speed meter.

( See the

Report No.? of the Ship

Experiment

Tank in

_Tokyo

_{) .}

_Further

investigations were then made

on such

problems as determination of

a suitable form and size, pick-up _system,

integrating method,

recording

_{set-up, towing cable, etc.}

that must be

considered toward

its realization into a practical use.

U

Iv _{CYLINDER PRODUCING KA1AN}

VORTEX STREET

Iv-1. _{Sectional form and size}

Although lt is not necessarily _limited

to a

triangular or square

cylinder that can be

utilized for a

_{speed meter (}

see the previous

article ), a square cylinder

_{is currently used simply}

_{because of its}

easy production and

convenient fitting.

When a required

speed

range for

_{measurement is given,}

say from

0.5 to 50 knots ( 0.26 to 26 rn/s _{), the minimum size of the}

square

cylinder should be deteruilned _{from the}

_{lower limit of the}

speed. If

we take

the allowable minimum R.No. _{conservatively to}

_{be about}

then the minimum breadth of a square cylinder is determined by the

following

relation; 1/2

_)'

where B is

the

breadth of a square cylinder

measured

perpendicularly

to the direction of

flow (

length of the

diagonal line

) and Is

kinematic

coefficient of

viscosity.

_{Taking that V=O.26 rn/s}

and

) =j.Aò( salt water at 15Th

_),

_{becomes 2.23 ein, namely,}

_{a square}

cylinder of 1.6

_{cm in each side.}

_{Thus, taking into}

consideration

the

convenience for its _{fitting a square}

_{cylinder of about 2}

cm in each

side is now

used as a standard

_type.

_The

corresponding range of _R.No.

is from _{6.3 - 63 x}

IV-2. _Length

of the square cylinder

It is said that

_{the end effect of}

_{a cylinder upon the}

flow is

re-markable within a

range of e

length five times the

_{breadth, but lt}

lo

diminishes at a distance of about eleven _{times breadth from the end.}

Nevertheless from the test results on a square cylinder of a 1.85 cm

In each side _{( see Photo. i}

) , a regular periodicity of the vortices

could hardly be observed even with a voriation in the length _{up to}

fifteen times the breadth, unless fitting end plates on both ends _of

the cylinder. 3ince these experiments

_were

_{carried out in aiming at}

an investigation of a log attached to the bottom of e ship without fitting the end plates, further tests were suspended in view of the

above-mentioned results. _{It is thus decided to fit end plates on}

both top and bottom of a cylinder for any kind of speed meter Irre-spective of whether a towing type or a ship bottom attachment type.

Suiteble length of the cylinder with _{the end plates is considered to}

be approximately equal to

twice Its breadth, but in the actual case

the length could be varied as long as a regular periodicity be

available.

IV-3 End plates and side plates

1) End plates

The Irregular motion of vortex rows that has been observed in the case of a cylinder alone would be

due not only to the end _{effect of}

_FLOA'

a cylinder but also to the

f

,

\

unstb1eness of vortex line _{as it}

PLAT-R'ECTPAN(JULA _CYLiNDER

4f

is not always straight _{along its} S1tE PLATE

ength. _{To avoid these effects,}

it is therefore

preferable to make the cylinder length as shorter as

possible and to fit end plates at both ends, thereby realizing an

(2)

12

ideal two-dimensional flow. _{The 8uitable distance between the two}

end plates ( which Is equal to the length or a cylinder ) has also

been found to be about twice the breadth of _{a cylinder.}

The effect of the

breadth of end plates upon the

_{characteristics}

or vortices is not so

simple.

_{When we assume a source in place of a}

cylinder which

_{Is located between two Infinite end plates, the}

ve-locity potential is given by the following

_formula,

a -' 2

)=

VZ

o9(x-)

sou i'CC

Then the velocity u at a position

of y=O Is given by

( e:

u=v1-., 3) ) from which lt can be noticed that

the effect of a cylinder _{upon the}

flow diminishes inversely proprtlonal _{to the distance from the}

cylinder.

If the breadth of end plates is _{finite, B, , it may change the}

characteristics of flow

due to a disturbance depending

_{upon the}

value of'tat both sides of the end plates. Assuming that this dis

turbance

be equivalently

_{replaced by another source at the side}

of

the end plates, the effect _{on the flow can be expressed by a'/x'}

Furthermore, with respect to the _{centre lt becomes}

''/

In the case of end plates of _B1

, it is given by 8',( L

f,

indicating

that the effect of end plates diminishes very rapidly

_{with an in-.}

crease in their breadth.

_Consequently

_{if the end plates of a}

proper-.

ly large breadth be used, then their

_{effect will become of a negli-.}

gibly small one. In other words, k value in the

following

ex-pression couldapproximately be taken as unity even in the case of

finite end plates a long as their breadth is

sufficient

large.

s= V,x%Çr

It has been found from the author _{experiments that if the breadth}

of end plates Is larger than four times the cylinder breadth, _B,

then

the

_{rows of vortices become quite regular, n/V value being}

constant. _{However, since further relevant tests for obtaining an}

exact value of Ç itself have never been carried out yet , _values

in each case are now determined through a calibration for _the

measurement of both n and V values by using a cylinder with end

plates.

2) SIde p1tes

Test results on the effect of the side plates as well as of enu

plates upon the frequency of vortices are

illustrated In Fig.3.

_It

can be seen from this figure

that the

_{frequency increases by about}

4% as a consequence of fitting side plates in addition to the end plates, of which the breadth is approximately eight times breadth of

the cylinder (compare the results marked _{i and 2 in Fig.3). On the}

other hand, there seems no significant effect _{of a variation in e}

distence between the side plates (see the test results marked 2,3

and 4 in Fig.3) It is thus obvious _{that the side plates influence}

delicately on the frequency of the vortices, _{and therefore some}

theoretical considerations will be made in the following.

Circulation of a vortex starting from a cylinder is given by

r = C

IT

dt

_T=

,

C =

COiStQlt

(4)

Moreover, the following two conditions for KiBMkN Vortex Street

must be fulfilled;

-fl2V2 u.L

=COflStQflt

-Using the definitions,

-< _L

v=vt

in case of end plates only,

v -= v0

_{in case of both end}

_{and side}

_plates,

Equation (4) becomes as follows,

=

_cÇïû1J0dt

a=*->1

7)

In the case of (B), vortices have a

tendency

_{of being attracted}

toward a wall (side plate), _that

_{means an}

_{increase in h}

_and

thereby

in i according to Eq. (6). _{This leads to an increase In}

fl also

(see Iq. (5)).

When the distance between

_{side plates decreases}

'becomes large, however, _{it can easily be expected}

_that

there

exists

a certain range of the distance _{for which.T does not}

vary so

signifi-cantly

due to the increase

_in

f . This would be the

reason why the

test results did not indicate

any

pronounced differeces in the

frequency in spite of _{the variation of the}

distance between two side

plates. ₍

_See

_{the test results marked 2,}

and 4

in Fig. 3)

Although [' decreases _{when side plates are removed}

a=Yt/y.

becomes

unity, and this Is so influential _{compared with}

_{the decrease}

in

circu-lation that T

_{must have Increased}

(

i.e. n

decreased) in _the

above-mentioned tests.

₍

_{See the test results}

_{marked i and 2 in}

Fig.

3 ).

From these

_{results it can}

_be

_summarized

that a linear relation-14

ship between n and V is always maintained, though in the _{case of e}

cylinder with both side and end plates the ratio

t

_{differs a}

little from th8t for a cylinder with end plates only. _{But the}

ratio was constant irrespective of a variation in the distaìce

be-tween two side plates within thé tested range of Bg/B from 4.7 to

7.9.

3) Length of end plates

When the circulation of a vortex initiated along the edges of a

cylinder reaches a certain definite value after its gradual growth, the vortex starts to be separated from the cylinder and is shedding away in the after-flow.

It is defined

T=period of vortices generated in succession,

V=mean speed tangential to the surface of a cylinder, rdensity of circulations distributed on the surface

of a cylinder.

Since ¿r- is determined by the form of the cylinder and its advance

speed as well as by the distributed vortices In the after-flow, lt

can be

expressed by

C 8)

)1=o

where

_¡;

depends only upon the

form and the

_{advance speed of the}

cylinder, ì;,r3.- upon the corresponding

vortex

_{in the}

after-flow. Then the

circulation

_fl

can be given by the following

equation.

(A

-L0W

---*----In a case as shown ---*----In sketch (a),

for

example,

the third vortex and

the following ones locate outside of

end plates for which

3X'--become smaller than

_and

_{2 ' and thereby it is clear from}

-, ¿J _s4 l I J I t ¡,P I1 j 1111Ff i

-'

16

C

Çrd

= C

₍₉₎

2,7 = Cn

Li d t =

_c:

Since the effect of a

vortex in the

after-flow upon

_{the cylinder}

is less pronounced with

an increase in the distance from

the

cylinder,

cli

becomes

smaller for a vortex far removed from the

cylinder.

Considering a cylinder

located

_{between end plates, vortices in}

the after-flow remaining

_between

_{the pletes do not represent any}

remarkable

changes, while

every one of those come out of the

plates

form a vortex string which is

cut

_{off at both ends and a tendency}

or growing into an infinite vortex. _{As the total circulation is}

constant, the circulation in an unit

length becomes

ì1/,

, _a

being the distance

between the end

_{plates, and 1,}

the length of a

Eq.(9) that T ahould increase (

_{namely, the frequency n should}

decrease

)

so as to keep

r'

constant.

Figure 3 illustrates

the results of tests conducted for the

purpose of

determining a critical length of plates _{for which the}

ef-fect of

vortices outside of the plates

_upon

_{the frequency n can be}

1gnored

( See the

test results

marked 2,5,6,7 and 8 in the

figure.)

From Fig.3 the results are reduced to a curve in Fìg.4 where it is

seen that the critical length

_{is approximately 6.5 times the}

_breadth

of the

cylinder.

It is

_{also noticed that this length is almost equal}

to a space between adjoining two vortices _{in line calculated from}

the test results, and thus the length of end plates necessary

for

Ignoring the influence of the redundant vortices upon the frequency

would be such that at least the first two vortices started from _one

side of a cylinder are included _{within an inside of the end}

plate.

( See sketch (b).)

From the results of the investigations _{as described in the fore-.}

going it i decided

that

only end

plates will

_{be attached to a square}

u1

cylinder foc a towing type speed meter, while both end,slde plates

be fitted to

that of a ship-equipped speed _meter.

It is simply

be-cause that a ship-equipped speed meter must be used through a

cali-bration ( speed vs. frequency ) _{in order to}

_eliminate

_{effects of hull,}

and therefore smaller

_one

_{becomes preferable as long es a linear}

re-lationship between

_speed

_{and frequency is maintained.}

General

discussion on

_{the fundamental problems}

_{concerning a}

speed

meter of this type has been made, and hereafter some considerations

into a detail of the

practical

_{problems such as type of pick-up,}

indicating and recording set-up and towing cable, will be

described.

V METhOD FOR PICKING UP

THE VORTEX FREQUENCY

At first sight it

seems quite simple to

_{pick up the}

_{frequency of}

vortices, however, there involved several conditions which have to

be considered

in the actual production of the _apparatus.

These would be;

high sensibility without causing

a mi8action,

constant out-put for one cycle

_{irrespective of}

the frequency,

simple construction,

durability, and

to be independent of

the water pressure

(

a pick-up of towing type sinks down when

ship stops ).

A method of picking up the pressure

difference

between the right

and the left hand side on a back surface of cylinder'was first

re-garded as an ideal one, and

_{my efforts were directed to an}

investi-gation on the

application of the

_{surface phenomenon of}

_{mercury to the}

system. But the

results seemed unsatisfacto'ybecause

_{its rnisaction}

sometimes taken place in _{case of a high frequency could}

_{hardly be}

e-liininated and the pressure

difference

between

_{each side of}

_the

surface was not sufficiently large. After all it was concluded

_that

the

most simple and suitable way is to pick up an electromotive

force

produced by e vibration of a movable flag

attached

to the cylinder

behind.

_{The first pick-up of this}

_{type tested was of an}

electromag-netic one and its mechanism

_{is illustrated in Fig. 5 (a).}

_It

_as

found, however, that the

_{pick-up of this type was lacking in the}

-19

bility

due to a wear or a

break-down of the flag

_{shaft, i.e. the}

vi-brator, which was sometimes experienc

as a

consequence of the

ex-istence of stoppers necessary for its mechanism.

_Moreover

_the

out-put or the pick-up of this type is too sensibly _{inf1uened by a}

slight variation of the vortex frequency, and its restricted

movement of the vibretor

due to the

_{stoppers might change}

_the

origi-, ,

nal characteristics

of KABIVIAN Vortex Street in the

after-flow.

Further

improved pick-up

system of an

electromagnetic type was

devised as illustrated in Fig. 5 (b). This new type of the pick-up

has the following advantages; firstly, since no stopper is _attached,

the flag shaft is free from its break-down,

secondly the flag can

freely rotate to a wide range of angle so

that

_{it does not influence}

upon the flow, end thirdly a deviation in the out-put corresponding

to one

cycle of the vortex frequency is

_not

significant.

_{As the}

pick-up of this

type is of a simple

_{construction and}

_{furthermore lt}

has been found from the results of

_{actual applications that}

_its

function is satisfactorily reliable, _{the present use of the pick-up}

is limited to this

type only.

It should be pointed

out that there must exist

_{an optimum length}

of the

flag which responds most

correctly to the vortex

_frequency.

C

See Ref. 1 ).

From the

results of the

test on flags having a

length of 0.35 to 2.21 times breadth of a cylinder, it

_{can be said}

that a flag of 0.7 to 1.1 times

_{the cylinder breadth gives}

satis-factory

results,

and hence generally used is

_{a flag of which the}

length is equal to the breadth of a cylinder.

VI _{SPEED INDICATOR AND ThE} RiSC ORDING APPARATUS'

VI-1 Outline of the research work

The frequency of KABMAN Vortex Street as _{directly governed by the}

advance speed of flow can be detected by the _{above-explained}

e1ectro-magnetic pick-up which is connected to a cabtire _{cable leading to the}

inside of ship. _{Then, by means of a}

suitable appratus the frequency

of the vibrator may be converted into an _{exacty proportional}

amount of electricity which exerts a speed indicator of a direct-reading

type or its recording _system.

The apparatus should

satisfy the

following

_{requirements:}

The final out-put

_{corresponding}

_{to an unit cycle must always}

be constant irrespective of either the magnitude _{of electromotive}

force picked up or the wave pattern of each _cycle.

It should not be influenced

_{by a possible variation in voltage}

of power supply.

The mechanism should be as compact and simple _{as possible.}

In general,

_{the magnitude of the electromotive force picked}

up by

3 _{flag fluctuates}

_{with the}

variation of the advance _{speed of e}

cylinder, and besides,

the wave pattern of the

_{electromotive}

_force

corresponding to each

_{cycle of the vibration}

_{Is not necessarily}

the

sanie even at a _{constant speed.}

It might

be a method for solving

these difficulties _{to transform the}

weves into same

_{rectangular ones}

by means of

_{the ordinary procedure}

_{through cutting}

off and amplifying

the patterns,

_and

_{then amplify its}

power accurately by

using a

2o

tilt,

constant voltage regulator, finally

_{connecting to an ammeter}

_{or a}

recorder after

integration and

Çattenin

of the patterns.

_However

this method may involve unfavorable

_{points such as variations}

_in

characteristics of valves,

indefinite accuracy of a _{constant voltae}

regulator and

extraordinarily complicated

_{mechanism of the}

app-ratus.

In this situation,

_{use of a newly-devised transformer}

_of

which the core is made from

_{a special alloy of high degree}

_{of satu-.}

ration seemed to have solved all these problems.

_{Because of its}

ex-cessively high saturation of

flux, the current induced in the

secondary coil becomes always

_{constant regardless of any variation}

in form and magnitude of

_{the current in the primary coil when it}

ex-ceeds saturation current of the core.

Accordingly, if the

prirnry

current picked up is amplified beyond its saturation

_{value then the}

Induced current in

the secondary coil will

_{not be influenced by}

the

variation in the amplitude _{of the}

_{vibration or voltage of}

power

sup-ply, indicating a value _proportional

_{to the}

frequency of the

vibra-tor.

At that time such

_{a special alloy was first}

manufactured by the

Tôhoku-Kinzoku CO.

, _{and the test results}

verified its

suitable

characteristics for the

desired use. Even

with a variation in

_the

voltage of power supply _{of 60 to}

_{120 V, for instance,}

nothing was

found to be wrong in

the test results _{on the transformer of}

_{this type}

(loo V standard).

_{This special alloy}

_{was soon put on the}

market

under the name of _"cen-delta".

The first set-up manufactured for trial is of

a _{rectangular-wave}

converting type with a constant-voltage regulator, and the second _one

is of the _{special transformer}

one was also manufactured ror trial, _{so a detailed explanation}

about the first two set-ups will be omitted in this

article,

VI-2 Details of the indicator and the

_{recording apparatus}

As has been discussed in the _{previous article}

_{the fundamental}

problems are ali

settled, but still

_remains

_{the following defects}

in the second set-up

None of the ammeter of a _{simple and compact}

_{construction and}

yet of a high _{accuracy is available.}

It is impossible to _{measure the}

_{characteristics of sea}

waves

because of its large time _constant.

) The calibration

system is imperfect

due to its mechanical

function.

As the set-up contains many valves, a reduction of the weight

and

electric

_power

_consumption

_cn

_{hardly be}

expected.

It sometimes gets

out of order.

At the time when

the second set-up

_{was designed the main object}

was to measure only a

_{ship speed, and therefore}

_{the time}

constant in

the circuit of the _{set-up was taken as}

large as possible in order

to

avoid unnecessary

movement of a needle in _{the ammeter due to}

an

instantaneous effect of

sea waves.

_{However, as will be seen from}

VIII-3, it has become clear _{that the speed meter}

is also useful for

8n

observation aI' the _{characteristics of sea}

waves, e.g. wave height

and its length.

From this view point the

_{recording apparatus would preferably be}

operated at either the _{same speed as that of the original vibration}

or a reduced speed,

_{the tormer}

method being

_{used in the}

_{cese of}

mile-post test

_{or observation}

_{of the}

sea wave

_{characteristics}

and

wind effects,

_{etc., and the}

_{latter for}

a measurement

_{of the ship}

speed and

_{travel distance.}

Taking all

_{these into}

consíder*tion the

third set-up

_{was manufactured}

for trial and

_{its mechanism is shown}

by a block diagram in Fig.

6.

_{This may be}

interpreted in the

followings:

In-put to the set-up Is

_{fully amplified}

at firat and

_then

led to the

_{primary coil}

_{of the}

special

_transformer,

_induc1n

_a

current in the

_{secondary coil exactly}

proportional to

_{the frequency}

of vortices.

_{The induced}

_{current is}

then carried

_{to en}

_ammeter

after being

_{integrated and}

also made

_{flat through an integrating}

e-quipìnent.

_{The ammeter}

_{;ives a direct}

reading of the

_{ship speed.}

This part of the

_{second set-up}

_{is also the}

same.

The ammeter

_{should include}

a calibration

_system.

_{It is con}

sisted of

_{a standard}

_{wave of 50}

cycles per

_{second that hes been}

di

tulnished

_successively

_{from a 400}

cycle wave

_{caused by}

_{an electric}

oscillator.

_Calibration

_{can be done,}

if

_{necessary, by operating a}

8WitOh

_{introducing the}

standard wave into the

_{amplifier in}

place of

the in-put.

Rotation of

_{a pulse}

_{motor driven}

by an

_{amplified power of the}

in-put (

_{the frequency}

_{of which has been}

gradually

_decreased

)

can

be transmitted

_{to the}

recorder after

_{being reduced}

_{to a suitable}

ratio by

_{assorted gears. This recoider}

cn be used for obt8ining

mean speed

_{or a travelling}

distance of

_{a ship during a long}

period0

The recorder

_{is also}

_{useful for}

recording the frequency of

en in-put through its direct amplification.

_{This enables us to}

see a speed variation within

_{short time, end thereby}

_{this re}

cording system can be utilized In

_{ship tr11s or in a case of}

ob-taming the characteristics of

sea waves.

_{The two sets ot}

empli-fier illustrated in the lower

_{part of Fig.6 are to be used}

_{when a}

ship-equiped type speed meter is calibrated by a towing-type

_one.

The detailed circuit diagrams

_{are illustrated in Figs. 7 and}

_8,

and Photos, 2,3 and 4

_{show the apparatus of}

_{a test product.}

24

5)

_{In expectation of an accuracy}

_{for the time signal the above}

mentioned electric oscillator is also used to send 400 cycle

waves

which are recuced to 1/8 of the original frequency and then led to a

pulse motor after being amplified In

_power.

_{The rotation of the}

motor is again reducth to

_{a suitable ratio sending the time}

_signal

to the recorder.

_{Providing against its}

_{emergency a changeover}

switch is readily attached for

_{the time signal of outside}

_{or an}

1 ¿ -' _a:4I_j .IIl!: I I1 I t I

The cable used for the first time was of a four circuit cabtire

cable having tin-coated steel wire (as tension member) in its core.

Currently used is a single circuit type cabtire cable which is

corn-posed of insulated wires of tin-coated steel.

The details of the

cable are given In Table 2.

VIII TEST RESULTS OF THE

SPEED METER

During a stage of the investigation on the trial manufacturing

of the speed. meter many tests have been conducted on the actual

ships at sea, and. Borne of the Interesting results will be described

in the following.

VIII-1

Distaflce of the preliminary run at a mile post speed trial

On the occasion of the mile-post speed trials, the speed variation

at the preliminary run, which takes place after a completion of

turning and settling the rudder amidships until she reaches a mile-post course, has been measured and recorded on not less than

ten cases by means of the newly-designed speed meter. The principal

particulars of these ships and the data necessary for the analysis

are shown in Tables 3 and Li

respectively.

Relationship between the speed recovery and the time elapsed are illustrated in Figs.9 to 15. From these resulte it can be observed, in general, that the distance of the preliminary run before entering

the mile post course is not sufficient enough to reach a constant

speed,

and. this is especially pronounced in the case of

large sized

tankers To find out the distanee of the preliminary run required

for a speed trial, the following theoretical some analysis is made on the basis of the test results.

The equation of motion and its solution are given by,

(1)

= T

V; z

s =

'

-w-

/

0e I T?

"

26

-where

Vo

ship Bpeed when therudder le eettled. amidships

after a completion of turning,

VI =

terminal speed of ship,

Tj

thrust of a propeller corresponding to the

terminal speed,

w i::::

displacement of a ship,

si

distance of the preliminary nm

from V,to V,

k =

coefficient of the added mass,

T

thrust of a propeller to maintain the speed y.

According to the test results on the Greyhound, the value. of k

was found to be 0.2, however, Lamb and other latest exerimental

results give between 0.02 to 0.07 for ships of block coefficient

virying fro'm O4 to 0.9, and therefore it was taken as 0.05 for each

ship.

At the instance when a ship enters into a straight nm

after n

completion of turning, revolutions of the propeller within an unit

time are still lower than its terminal one but on the other hand its

slip ratio is higher than usual, and therefore the thnst

can be

assumed to remain constant T

As can be seen from Equation (11), S

_{becomes infinity when V is}

taken as equal to V1

,

and thus the value of 5. corresponding to

V = o.q7vj

was assumed to be the neces8ary distance for the

pre-liminary nin.

When computing s,

, it becomes necessary to know the value of T,

and therefore the thrust constant

Kt= T/ çncfr

the advance constant of the propeller

3 = V1 'n[)

corresponding to

28

Assuming that J is equal to 0.45 for any kind of propellers, the

Kt values were determined from the Design Chart of A4-40 Type of

T.T.R.I. for propellers with four blades and

from that of ATJ5-65

Type for five-bladed propellers.

(

See Table 5 ).

The calculated values of S based upon

the foregoing assumptions

together

with the measured S

are shown in Table

6; furthermore a

comparison of their results in terms of a non-dimensional form,

1/7Y3

_{is shown in Fig. 16.}

From

these

results it can be easily

seen that the calculated values are generally

in good accordance

with the

actually measured ones In spite of the assumptions made for

the computation.

It is also found that the variation in

the re-.

quired preliminary run due to the

difference In the

out-put of main

engine is relatively small, being less than about 13%. Thus using

the results for the 4/4 out-put of the

main engine

the

required

distance

of the preliminary run can be determined from Equation (11)

or

from the following analytical relations,

--

₁₆₀

ç7Y3

for an ordinary cargo ship,

JyZ70

for a large sized oil tanker.

It should be emphasized that.a comparison of

tank test results

with

those of speed trials

of an

insufficient preliminary run is not

only useless but also liable to lead to misunderstanding for the

sh11ow water effects. This is especially

important

in the case of

large sized oil tankers for which a very long preliminary _{run is}

required before entering a mile post course.

VIII-2 Error in the milepost distance and the shallow water

effects

It Was reported that the propulsive performances under service

condition of the ships built at a certain ship yard were _always

significantly better compared with their trial results, and the reason of this phenomena has been believed as the effect of the

shallow water in the

mile-post

course.

The depth of the water in the nille post of 19 to 22 meters as

given by a chart is shallow indeed, but since there is _{some doubt}

oÍ a possibleerror in the mile-post distance, tests were conducted in both a mile-post course and the open sea by using the newly

de-signed speed meter.

The test results are shown in Fig. 1? where the speed variation

against time is illustrated ( _{the data marked i to 8 are for the}

mile-post results, whereas 9 to 12 at open sea ). The mean speed of

each return trip as compared with the results of

ordinary

mile-post

tests

(

measured by the

shipyard ) are shown in Table 7 and in Flg.18.

As can be seen from Fig. 18, it has _{become clear that the method}

of the mile-post _{course speed trial may involve not}

_{only the}

shallow

water effect but also an

unexpected error in

_{the mile post distance.}

VIII-3 easurement of sea waves

Since there would be no possibility of existing a time lag effect in the mechanism of our speed meter, the indicated speed should

in-dude the effects of both the ship ïnaking weves and sea waves.

Ac-cordinly it will be possible to obtain also the chaxacteristj.cs of the sea waves, 1f necessary, by analyzing speed curves recorded by

the speed meter.

With this object in view,

the following

several tests were

carried out on the LI.S. "Argentina iiaru" on the occasion of her

re-turn voyage

from Yokohama to Osaka.

VIII-3-1 Waves made by the ship

A) Wavelength

The cable of the speed meter was drawn behind the ship with

a length of 50 meters, and then at every

5 meter

interval it

held for 30 to 50 seconds to take readings for

the

measurement until

its

length

reached 400 meters. The recording of the results was done by a method of penwritlng of the originel vibration.

Since

the frequency of the sea waves, in

_{general, is considerably}

lower than the above-mentioned period,

the effects of sea waves will

never appear in the

mean

speed of the

recorded

results which include

only the

effects of the wave made by the ship caused by its

molecu-lar motion.

The recorded speed along

the distance from the aft

perpendicular of a ship are

shown in

Fig. 19. The heavy solid

line

in the figure indicates

the ships speed which is varied with a

change

of such conditions as the course direction, wind force, etc. ( For

the

detail, see

Ref. 16 "Notes on the TJse Of

a Towing Type Speed

Meter and its

Application

to the easurement

of Sea Waves" ).

As

30

J

-f-

-

e2Tr

f

2 ₂

( Z)

can be seen from Fig. 19, the speed Indicated by

the speed meter

shows a periodical change with a variation

In

the cable

length,

while the relative speed of the ship against water (

the heavy

solid line

)

indicates a

monotonous variation. The maximum or the

minimum speed as appeared periodically in the figure means a

rela-tive speed when the speed meter is

located

at

the trough

or the

crest of the wave made by the ship, and therefore the

distance

be-tween

the two

adjacent

troughs

( or

crests

) in the

figure

indi-cates

nothing but

the wave

length made by the. ship. This

fact

can

be clearly

understood

from the results shown in Table 8, indicatIng

a close

agreement between the theoretically obtained wave speed and

the

mean

value measured by the speed

meter.

Thus

it

becomes

possi-ble to

determine

the wave length by

using the newly designed

speed

meter of towing

type.

B)' Vave height

As the speed meter of

towing

type works underneath

_{the free}

surface of water, the

indicated velue corresponds

to a

speed at its

depth ( d meter

) Instead of showing

the true

speed on

the free

surface.

The correction should be made by

_{the following forfllula,}

where Vmax. end Vmin. are the maximum and the

_{minimum speed as}

given by the speed

variation curve in Fig.19,

_{wave length, and}

the suffixes o and d of the

brackets denote for

_{values at the free}

surface and at depth d, respectively.

_{Then the wave height at the}

free surface can be given by

H0 = Z

± (V1 - Vmin)o

₂

-

(f3)

The wave height at

a position of 2.3L behind the aft

perpendicu-lar of the ship running at speed

of 18 knots is calculated

_{as shown}

In Table 9,

where d is assumed to be 5

_{meters, no actual data}

_beine

available.

A theoretical value of the

wave

height

for a

_{two-dimensional}

model with similar principal

particulars to the M.S. _"Argentina

)eru"

C

see

the later explanations

) is also given In the saine

table, and it coincides fairly

_{we1l with that calculated from the}

actual data.

_It

can therefore be

estimated that the height of

_the

wave made by the _{"Argentina Maru" at speed of 18 knots was}

approxi-mately equal

to 50 cm.

VIII-3-2 Sea waves

The above-described

_{Investigations have fullyverified that our}

newly designed

speed meter is of

a quite satisfactory sensibility

end

accuracy for detecting the

_{effect of waves.}

When the speed meter

is used in sea waves it _{should be able}

_to

_record

_their

effects

in-elusively, and thereby to determine

_{their characteristics from}

_an

a-nalysis or the records

_{With the object to check}

_{up on the matter,}

the following theoretical

_{study will be made.}

_{Using the notations}

2

-T

¡g

'b

₄ I27Í . ₂

\_T

9

t0L+v'

H =

I 21t9 y' ,k

4fcosQe ]

wave òhead

Ö<<oD)

The value of ( Vrnax-Vmin )d is the difference between the

maxi-mum and the minimaxi-mum

speeds

indicated by the

speed

meter

when a sea

wave passes over it and is obtainable from the records.

Since the

time required for a sea wave to pass

over

the speed meter is

gener-ally very short, lt is necessary to get a detailed aspect of

speed

variations

due

to sea waves when the length of the cable is kept

constant.

. ,II'tIIl ¡ ti

1

L

₍₁₊₎

4/i

:i::

_{VÖiow:nwdVe (Ç6<8;)}

¿ _cogo(

X

(Is)

T

period of encounter,

oK entrance an1e of sea

waves with the advance

direction of a ship,

V :;:

sh1p

speed,

41J:

:::

wave length of

sea

waves,

4.

Ho

wave height of sea

waves,

vo ::::

advance speed of sea

waves,

the length and height of

sea waves can be

expressed as follows;

Three examples of speed

variations

for O to 50 seconds were chosen from the records of test results on the "Argentina Maru" as

shown in Fig. 20. Each plotted speed in the figure is the mean

speed corresponding to ten cycles of vortices. The aspect of the

speed variation due to the sea waves can certainly be perceived in

Fig. 20 except for No. 3. s the condition for No. 2 is

a following

sea, the variation in the mean curve shown by a solid line should be

considered es the one due to the see waves. The calculated values

of H and ?LØ are given in Table lO

As can be seen from Table 10, the length and height of sea waves

obtained analytically seem to be reasonable. It is therefore

con-cluded that our speed meter used as a towing type can be utilized for both the measurement of ships speed and the observation of the

characteristics of sea waves.

Vhen our speed meter is used hereafter for this purpose it must therefore be necessary to find out a method of knowing the actual

depth of the speed meter under the free surface of water..

34

VIII-3-3 Informations

1) As can be seen from Eq. (12) , the smaller the depth of a

speed meter under the free surface is the closer to unit the

coef-cL

ficient 2lT becomes, and thereby the errors accompanied by the

correction becomes smaller. However, the minimum depth should not

be taken smaller than a limiting value for which a cavitation takes

place behind the cylinder. The limiting depth at 20 kt, for

example, is approximately equal to 2 m.

The vertical component of the speed induced by the wave

motion Is neglected. This does not influence on the results of the

calculation of wave height, because the verical component of the

velocity vanishes at both the trough and the crest of the wave.

As have been already mentioned, rate of the speed variations

must be known when calculating the wave height. Since this rate is

influenced by various ship motions, degree of an error due to the

ship motions should be investigated0

If we take the effects of pitching and heaving into consideration,

setting aside those of surging, yawing and rolling, the maximum error will, at worst, be less than that given by the following

formula, where tiV V-

i 1 ( j

j'7r 4 -F-&5iflU),t ,

0'

xocrì.

L=length of the ship between perpendiculars in meter, k=1/L ( i is the length of the cable exposed above

the free surface. )

=h/L ( h is the height of the supporting point of

the cable from the free surface. ),

=pitchlng amplitude,

w,=angular velocity -xr. _fj ( L in meter ).

(I 6) 35

This relation indicates that their effects become large with the

Increase in L, ì'. , and kand with the decrease in k,,

ç = .:

-I -i

36

"Argentina Mani", AV/y

becomes 5 to 6%.

AccordIngly, when an

exact wave height is

to be obtained,

it should be calculated arter

rf p

these,due to ship motions are analytically excluded from the

records.

However, these effects

are comparatively small and become

neglegible if k, 18 taken very small.

VIII-4 Length of the towing cable

As the local disturbances in the vicinity of ship hull caused by

her movement diminish rather soon,,their effects on the speed

measurement may be

avoidable if

a suitably long cable is used, while

the waves made by

the ship will

never damp so quickly (see Fig. 19)

In order to see the whole picture of this problem, a theoretical

a-nalysis will

be made on

the distribution of the

induced velocity,

u, in the running direction of a two-dimensional ship model

( at

uniform velocity V ) _{of which principal particulars are similar to}

those of the "Argentina Maru". _{In this analysis, the verical}

in-duced velocity will

not be considered because of its insignificant

influence upon the final results, the maximum error due to

its

Ignorance

being given by

cg

--

- . ç- ) - C

7)

It can be seen fr _{the results of the calculation of the errors}

in the

case of

the "Argentina Meru"

that

this assumption is

quite

satisfactory. ( See Table 11)

Thus neglecting

the vertical induced velocity and the effect of

the local disturbances, u is expressed as follows,

:C) ' 2

LI - ! (°f°

dd5

L _xSeC

cos[(Xsecd

_{( 18 )}

, _{.L2 X,sec}

IC

j;

whe re

L =: length of ship,

B

breadth of ship,

D

draft,

?L

is a function indicating the ship

form, and can be given by

the following expanded formula In case of a two-dimensional model

symmetrical with respect to its midship;

2. 4

11=_ a0-t- a2i-O4

+ --

(q)

Then Eq. (18) leads to the following approximate tormula;

LL - :

8

lit. L

t-e

L

)

jp%(*I)

.

CO5?(1) -

---.. .

A'2)

(*i)

_(-t)

ççsX('s I)

sin(Ç I)

I- ---

[4I)

--- - J

hç-:)

:2X/L,

: g/2V

B

7 ---.?/$,

(20)

IÍJ, 7 - '::"A1 I ': ILT II

where

(;) = C()+ D(),

Ç 7 (271ff) - t, (2)))

C ( )

,

f(?) = C(') DP(),

The following relations fori are used depending upon each value of

theblock coefficient of ship;

() =

j

_

2 _4,

for Cb=

()

=

-

46

Çor _Cb 0.7 21