• Nie Znaleziono Wyników

Some studies on the procedure of assessing the open character of a ship in steering with special reference to the closed loop behaviour

N/A
N/A
Protected

Academic year: 2021

Share "Some studies on the procedure of assessing the open character of a ship in steering with special reference to the closed loop behaviour"

Copied!
15
0
0

Pełen tekst

(1)

lak y. ScheepsbouwkunTTTC

-Technische Hogeschoot

RCHIEF

Some Studit!

'n tI'e Procedui-t of ssesing the open Cbaract*r of a

)1anoeuvrability Committee 1970, Zagreb

Ship in Steering with Speie ial Reference to the Closed locp Behaviour. K. Nomoto

Manaeuvrability nf ships should he treated in the aspect of

control engineering as well as of ship hydrodynamics. In th&s aspect,

the closedloop analysis and synthesis of the whole system composed

of a .ship, automatic steeri.n device and/or helmsman and steering

gear become important. In these studies the open character of a

ship in steering

is

one of the important components. This character

implies a relation between rudder movement applied and resulting ship motion, and it is desctibed analytically with a set of coupled. linear differential equation! for a small motion.

lt is true that manoeuvring motion is not always small, but so far as concerned the closed loop studies, emphasis should be reasonably laid on rather small motion for the time being.

The coupled e]uation of uotion aforrnentior.ed can be reduced

into the following euation which describes directly rudder to yaw

response:

7T

(T,i'T2)

where ' denotes yawrate and

â

rudder angle. K, T1,T2 and

being composed of t}'einertin! and bydrodyiinmic coefficients of the

aquation of rnption, 1efine the open choracter of a rhip in ste'ririr.

A sip ii ed equation based upon tb Eq. (1),

bas been found useful in u1alysing rather steady manoeuvres and this

iiving a rough figure of manoeuvrabilitv uf a ship. It sho1ld be,

however, no ted thnt thi s aJ)'r)ioati on is no more valid fer' closed

i i;.

hthaviour at which rather frequent rudder movement makes the

terms

,X7

/ and

77

to play .ri important role. KT analysis

of 7.i--za

test does thus lose its use in this aspect of study: sen'e

new ç.rocedijre should be devised.

In 1969, the present riter published a new procedure of defining

the characteristic coustan s K, i', T, and T3 using a radiocontr lied

mo'el or actua] s'i:p /1/. l

ri. iravnlea a parallel rhifting of ship's

path e:npioyirg a i upi e uutonnt le coursekeeping inst ruinent, and a

a seri es of periodic steerings with a few different frequencies.

(2)

-Iloth can be done at a conventional towing basin.

A series of harmonic analysis of the parallel shifting motion,

using the equation;

Y

=

L

_ta1Lu))Ldt

y-O

o

gives the values of the transfer function

e nuiber of

frequencies, ranging from zero to intermediate frequency band.

The neriodic steering is carried out at the frequencies ranging

the intermediate to high frequricies so that the arupiitude and

phase of ship motion give the transfer function at higher frequencies.

The tra osier function is written as

¿/,' «77R/7" 1w T2)

a

obtained by taking the laplace transform of the both sides of Eq.(l).

Figs. 2,3,4 and 5 indicate some of the results obtained.

Some corrections for a posnible small deviation from the null initial

'

conditions and also the effect of external disturbanc', that must

be small, but stili

e:yist to a small amount, are necessary to

obtain consistent result.

The det,ails will be found in ref./l/.

Recently Bech and Vtagner-Scnitt proposed another procedure of

assesing the operi character of a ship in steering /2/, which is quite

useful, for a course-unsiabe ship.

Analysis on such a ship is now

of grat importance in conjunction with the rapidly rirowing

super-tanker fleet.

a

This prodedure is based upon a non-linear equation made by

modifying Eqj]), cf. rel's. /3/,/4/,

and also upon the phase plane

trajectory analysis.

The now type of equation is wri.teii as

7T

'Hc) - Ici

(3)

(hoch type non-linearity)

or

KTJJ

(4)

(cubic type non-linearity)

where K, T1, T2 and T3

are those characteristic constants at zerO

motion.

The first. step of this procedure is t7Aefine lle

or K and «

'from r' -

J characteristics obtained through reversed spirai test.

Next is

'to define T1 and T0

ori the phase pinne trajectory of the

O

o

(D

im

w

'i

(D c+ (D (D CD t-'. co '-b

'i

o E 'D

(3)

1i1' motion during the conventional 7igzar

manoeuvre, taking the

phanes

at which the rudder retnains a

cons tant angle.

Final step

is the determination nf T3 on the same trajectory but taking the

phases

at which the rudder is moving.

Pigs.

,7,8,9nd Table 1,2 and 3 irdicate some of the results.

Table 4 shows the particulars nf the ships tested.

In order to draw the 7phase pLine trajectory from the

yawrate

record obtained with a rategyro instrument,

a numerical smoothing

arid differentiation by fi.ttin

cubic polinomials upon every seven

cnn$ecutive values of yawrate read up aL

an eival time intervnl.

incidentally a careful application of this method

can yield a fairly

consistent phase prtrait even frort

a conventional heading deviation

record.

The results look reasonable and promising in general.

The

Meak poin

of the Firstorder syster

approxiaatit-in,

as a1

ready mentioned,

is clearly seen on t}'e phase plane trajectory,

e.g-g. Fig..

This

can not be improved by introducioff the nonlinear term as also

seen

'n the figure.

te f e re nc es

/1 /

L. .ornoto

l.K.trarno,

.. nc

procedure of ¡Danneuvring model

experiment.

Soc. Nay. arch. Japan, lcfW.

/2/

M.

[lech & l..\VagnerSmitt,

Analogue simulation of ship manoeuvres

based on fullscale trials or freesailing

model tests, J!yn Report No.14, Sept.

1q69.

/3/ N.

TI. Norrbin, Zigzag provets tekuik och analys

Alimän Rapport

fran S.S.F.L

I 965.

/4/

.

Nomoto,

Àpporxirnat' nonlinear analysis on steoring motion,

12th ITTC contribution, lP6P.

(4)

-,-rev.rs.e the rudr and turn on automatic steer. system. towed free by r,$w, cart,- L -09e.,

TI

r

mode' ships trojectory

au tomo tic steering

transient stage carriage L'(t)ships heading ¡(t) rudder angle mod,! ship

I

enlarged

illustration of a Parallel Shift

Manoeuvre Test 02 MiJe ¡52 Tana Tes f Fr.qiierey Respcv'se Anolys's for Sir, Steer,

05

f,,w

o //T;.3.12o N

ijy1

o -02 -0.4 o -0.6 - 0.8 i.2 I.' -. - £zperiment

Linear Analysis with no regard te ca-deperrderrCr

Fig. 4 Steering Transfer Funtion of M. No.152 as obtained

by Frequency Response Experiment

FreQten7 Resoonse Ar.afysS for Porote.' Sh,f MIJo ¡55 Tar,.k Test Response Anaiys,S for Sm Steer:r,g T2.579 T.023l /

T0.7l/

o o steady state / Response ArayS,S

for Pra!tp/ Shift

f-la,oeu ver -05

'Is

.*'d 2.17 O-7

'/I-7

60' --. - EoOerrne.f

L,necr Anc(yss -fh no regcrC to w-depence

Fig. 5 Steering Transfer Function of Nl. No. 158 as obtained

(5)

I

.

;/Y5íw)f

S.'J. ¡

000 ¡

o.,

L=3'io

B= 7:

d=2,

V11.'

d4=i.o

3.2O

/

O :1- -i-+

F/i. 2

Tfr-*-: 7''P

/4f#td7Uífl

a

fr4 ín.Jtq

1rn'er

I' o.ic

11.02 2+AO.S2

T'J.Ù22-A0.S.

T31 O.

6

(6)

-I. o

i

i'

O 2.3

V 2.1

I.q4

1A3

-F

5-1e 7

QI'333

L\

o,o47

o, o 32

O.

0,7

-ûS

¡o

-f. o

m. 3

7fra,s74,

e/It S a supr- tanA'eK

F-s'

2.0q4

i' r-.q2

T' o.71-

T3' 1.73

T' î-f°

T' 2.O

S.W./0002

-.

-o.

L3o o. o

c1ci.l

Cb= o,S'3

v=

/.0

(7)

-40

Ship

o

Turning

Reversed Spirsi

-30

-20

-10

I

.1

I I I I i

10

20

30

40

deg.

\

(8)

Ship

A

Exp. No. 1

Port

200 Z

0.01-Observed

¿ A JW/

"'

2

-Non-linear Simulatin

( Second Order )

Non-linear Simulation

( First Order )

Linear Simulation

( First Order )

5P

(deg/sec)

(9)

cb d eg.

-40

10 20 30

40

-/

=--Ship* A

-Exp. L\o. i /

/_

\_.

'N

Fort 20°Z

I/I

7' /'

\

II

\

/

/

/

/

-Fig. '3

/

- - - 'SS S-\\ \

Observed

800

Sec.

Linear Simulation

K68=0. 0303,

T68128.

3

Non-linear Simulation

(

First Order )

Ko=-O.043, V=-7.65, To=-214.O

Non-linear Simuletjon

( Second Order )

T 1T2/K=79800, (T1T2)/K556o.

T3=39.Q

(10)

-40

T urning

Reversed Spirai

Loop

resdth

8.5 deg.

Iviodel

220

(

O Model- )

R4 1/56 Rudder

--LO

I I

10

20

30

40 deg.

1.0

-r'

0.5

(11)

L

-5.0

v!oie]

No. 220

Fxo.

No. 103

stab.

10 Z

Fig.

o

Observed

'on-1inear Simulation

(

Second Order

)

e g/ sec)

(12)

32

£rp.tvb. 7t

X0'

7;'

J'

Ka L-'

JO4

/

-20 °Z -/26

27 -/2.96 -0

adJ

-247.0 -765

a. a303 728.3

2

+20

OZ '

'

-a

0417 -2/75 -727

a

035? ¡6'!

/

3

i/ O

'

-ao432 -2/0.0 -732

698 3o2

3

4

-/0

°Z

'

'?

'

-a

o426 -2725

-753

455 ¡ã52 O

/

+5°Z

-

27 -1635 -9253 -0256 -56e 0 -33.6

a

/5

472 /

2

-/0Z

// 1

-0.235

-6/3.0 -39.6

aa95'

27'

3

"/5°Z

"

"

"

-02/3 -67/0 -472

o.0428 ¡29.9

iÌfo.No.

220

73

í-20°Z

-/799 -3.45

-/7 7 -03o3

-2023

-o.123 02762 /5328

,,-0g

,, // .

.yìg -/9.2

-.//66 o6'9

3622

¡aS 1/Z

// " ,,

-3/

-/927 -//22 3254 20776

L

239

234

#5°!

7/46

23.0

40.0

2.3(9

117.0

02823 /306

i753

/9/

-/o°g

.

2.d2 ¡û2.9 0.263

3/4 279.?

236

/5°Z

2.317 /14.0 0.2984 &384

,'75

229

*20°!

2.2

/1

9

0.332 0.246

¡o.77

.7!

-'/0°Z /055' /4'5'

63(92 aJo2J './3

a0229 0232

3.737

237

/0

20°Z -/724 -255 -/2.

-v.32/

-/3.7

-a/6/

22'3 77

L

(13)

'-)1 V'

i

TaJ-e I

JJ'

5hÌp

,9 i:

4ppac14

S,nrd'

1

-7t

.--a'

4

EpNO. 73 /7

17 -7O

T

r

(a?cn

7 t-foNo,

3 /

Ño

¡o

'77-',

33

-1.1

Ta hA 2

Coarc'gûìi /d Yg,/ì7 2u'e/

,997C4

T,., T

Inir

¿/

#e, ,,

-&p. A/o.

Test

/<O 2)

7o

7

() (7

7

-2o°g -003 -765

-2/2.0

/4.5

296

-3c0. -1975

7w74

2

20°g

-a0!/7 -Z 7

-2/6

ì

7

30.0

-3/0.

-20/3

3

+/°g -ooJ2 -732 -2o0 /4.2

29.0

-2960.

-y932

4

-707

-00426 -753

-2/7.0 /4.4

2.4 -30Û

-i96.6

p

J

5°Z -0256 -33.6 -93 5./p -3.4v

-3!1

-94

7o./o1

2

¡«Z -a235 -39'6

-657.4

63

3.

-366'O. -6464

3

/5°Z -0.215 -472 -7/22 6.15

4.15

-4370. -7ú5.

o. No.

220

73

20°Z -a306

-0123

-22.0

2 4

4.23 -3 9

-/946

7;»-375

T'o132

7=.72/

77

-js°Z -osi4 -i/66 -2/5

2.4k

/4

-33.

-7902

¡aS

/OcZ -0.3/2 -0//2 -21.

24

/5

-p3.6

-/9/2

$. No.

7/

-ì-/0°Z

0022?

J!

o3/

o.5

,S?

2

¡45

7.o7

1.No

/0

t 2 °Z -0.321 -o./6/

-/6'.

/. ?

7

-900

-/.5 O

¿i'- a.555

(14)

ft

I

5%',b,4/

Z-7T?s-'

?

C),eracP

239

4

c r

rt-d'

3T

*)VL

Tab 3

Cnpatson cf r17e Stnq

,/c3

I-'-

i

/ Ic

34

Ep No s ; C?2O- 7

7'

.

(77

7 S/i/pA

/

20°Z 0.554

2.02

0.745

79û0. 5560.

3 = o. ?56

(77 t7''

= 242 ° 6 7 2

"27Z

//

3

/ûg

'

4270.

2

4

/ûZ

i'

'

47/Oc. 3920. 32. Ho. A/o.

239

234

t5Z

2. 0

26

7ä4

4

t 30

/9/

-70 Z

F 7 3

/. 27

236

t5Z

" "

.4 O

/. .13

229

-t2oZ

'

4

95 542

1. 4

(15)

7a/e

9

§2

R0

13. j

S i:

-

er

7E

Ru dc/e

(/IoUt

Z'DA'

Ica)

cf Zz-,dai

I

,

-;

fl

O)

t

j

C)

ti,T' }Ç

4'

R2

Tz5 i

Ç) 6?.?%

D6

ii

7o)(

It 'í'd

R0 T

k t

-i'a? 7

i\Q

7,( ¿

2.O

/

¿

Riz

Rtbt

,%j442dfi6 ,%/Vo.

220

N0.N0./97(,q,)

-«'-/Y11o.2Z0

J

t_

//O9/40C)f

*

2

ShtpA Sh8

f1od/No. 220

'lodeL'

(Vo. 239

R0. R2 R4 A - S C

3/0 26' 27a.

'45

" "

8

. o?2 a. 72 f " o. 72/ d,,7

/6 46'

o 247

' "

ô.2'

7 C5

o. 35

o .?35 " ' " a.

L/8

c.47

o'44

"

C/5)

0.129

a'S

" « '

8/d

292

2.q2

,' ', ,.

2.72

'4íd

'/62

'46

/55

'/g?

o

5

/6

qo

SFeed ¡7

" '

o7

¡o7

/

o

o

.

o

o_

spect

206

206

206

¡40

¡40

¡/

¡4/

/4/

-

Cytaty

Powiązane dokumenty

Teksty odwołują się do mistyki męki, polegającej na łączności z cierpiącym Jezusem, szczególnie powstałej w kręgu zakonnym: Mechtyldy z Magdeburga, kon- templującej

rozdział II, zatytułowany Harmonia w człowieku, dotyczy kategorii musica humana, a rozdział III, zatytułowany Dzieła ludzkie jako uczestnictwo w harmonii Bożego.. dzieła

In the first 10 diameters, the mean velocity profile of a standard (Woo = 0) jet approaches so-called similarity. Similarity for a jet or wake means, that variables such as the

[r]

Podwójne widzenie rzeczywistości, choć nie do końca spójne, ale przecież analogiczne, tworzyło swoisty rodzaj wizualnego dialogu między różnymi osobami i przestrzeniami

by MARIN) was extended to simulate the flow around ships sailing at non zero drift angle Promising results withirespect to quality of bothfieldand integrated

kilku chwilach rozmowy, zacząłem z podziwieniem przytomnych śpie­ wać w głos odwieczną jakąś piosneczkę. Zaledwie z tej strasznej omyłki wyszedłem, nim jeszcze

Из за- полненных после игры анкет следует, что, по мнению студентов, объединение в группы людей, ранее не знакомых друг с другом