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 characterimplies 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 andbeing 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 theterms
,X7
/ and
77
to play .ri important role. KT analysisof 7.i--za
test does thus lose its use in this aspect of study: sen'enew 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.
-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
(Dim
w'i
(D c+ (D (D CD t-'. co '-b'i
o E 'D1i1' 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$ecutive values of yawrate read up aL
an eival time intervnl.
incidentally a careful application of this method
can yield a fairly
consistent phase prtrait even frort
a conventional heading deviation
record.
The results look reasonable and promising in general.
TheMeak poin
of the Firstorder syster
approxiaatit-in,
as a1
ready mentioned,
is clearly seen on t}'e phase plane trajectory,
e.g-g. Fig..
This
can not be improved by introducioff the nonlinear term as also
seen
'n the figure.
te f e re nc es
/1 /
L. .ornoto
l.K.trarno,
.. nc
procedure of ¡Danneuvring model
experiment.
Soc. Nay. arch. Japan, lcfW.
/2/
M.[lech & l..\VagnerSmitt,
Analogue simulation of ship manoeuvres
based on fullscale trials or freesailing
model tests, J!yn Report No.14, Sept.
1q69.
/3/ N.
TI. Norrbin, Zigzag provets tekuik och analys
Alimän Rapport
fran S.S.F.L
I 965.
/4/
.Nomoto,
Àpporxirnat' nonlinear analysis on steoring motion,
12th ITTC contribution, lP6P.
-,-rev.rs.e the rudr and turn on automatic steer. system. towed free by r,$w, cart,- L -09e.,
TI
rmode' ships trojectory
au tomo tic steering
transient stage carriage L'(t)ships heading ¡(t) rudder angle mod,! ship
I
enlargedillustration 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 Nijy1
o -02 -0.4 o -0.6 - 0.8 i.2 I.' -. - £zperimentLinear 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,Sfor Pra!tp/ Shift
f-la,oeu ver -05
'Is
.*'d 2.17 O-7'/I-7
60' --. - EoOerrne.fL,necr Anc(yss -fh no regcrC to w-depence
Fig. 5 Steering Transfer Function of Nl. No. 158 as obtained
I
.;/Y5íw)f
S.'J. ¡
000 ¡
o.,
L=3'io
B= 7:
d=2,
V11.'
d4=i.o
3.2O
/
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Tfr-*-: 7''P
/4f#td7Uífl
a
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1rn'er
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11.02 2+AO.S2
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Cb= o,S'3v=
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Ship
o
Turning
Reversed Spirsi
-30
-20
-10
I.1
I I I I i10
20
30
40
deg.
\
Ship
AExp. No. 1
Port
200 Z0.01-Observed
¿ A JW/"'
2-Non-linear Simulatin
( Second Order )
Non-linear Simulation
( First Order )
Linear Simulation
( First Order )
5P(deg/sec)
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10 20 3040
-/
=--Ship* A
-Exp. L\o. i //_
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-Fig. '3/
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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
-40
T urning
Reversed Spirai
Loop
resdth
8.5 deg.
Iviodel
220
(O Model- )
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--LO
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30
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No. 220
Fxo.
No. 103
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Fig.
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Tab 3
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'lodeL'
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