Testing of Ships

8/6/2019 Testing of Ships

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TUMSTShip Manoeuvrability- Theory and Assessment- 1

Ship Manoeuvrability- Theory and Assessment -

Toshio Iseki

Tokyo University of Marine

Science and Technology


2/49

TUMST Ship Manoeuvrability- Theory and Assessment- 2

IMO (International Maritime Organization)

MSC (Maritime Safety Committee)

Interim Standards for Ship Manoeuvrability

(IMO Resolution A.751(18), 1993)

Standards for ship manoeuvrability

(IMO Resolution MSC.137(76), 2002)

Exclusion of the ships that were built with very

poor manoeuvring qualities.(causes of marine casualties & pollution)


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Contents

Basic theory of ship manoeuvrability

Manoeuvring equation of motion

Directional stability

Manoeuvrability indices

Assessment of ship manoeuvrability

Graphical analysis of Zig-zag test

Real-time identification of shipmanoeuvrability (IIR filter)


4/49


Co-ordinate systems

O Y

X

x

GUT

u

v

rT jviu

TTT!

torlocity vecAngulerve:

angleHeading:

dt

d

r

U

U

!

T

axesyandxthealongorsUnit vect:, ji

TT


5/49


Time derivative of a rotating co-ordinate system

productVector:

,

rotationfororUnit vect:

v

!v!v ijkjik

kTTTTTT

T

jdt

dik

dt

dir

dt

id TTTTTT

UU!v!v!

idtdjk

dtdjr

dtjd

TTTTTT

UU !v!v!

jdt

du

dt

dvi

dt

dv

dt

dudt

jdvj

dt

dv

dt

idui

dt

du

dt

Ud

TT

TT

TT

T

!

!

UU


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Equations of motion

!

!

!

NrI

Yurvm

Xvrum

zz

)(

)(

momentandforcesExternal:,,

inartiaofMoment:

shiptheofMass:

NYX

I

m

zz


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Definition of external forces

External forces

Acting on the upper part from the water line

Wind force, etc.

Acting on the lower part from the water line

Hydrodynamic forces based on manoeuvre,

Current force

Another forcesTowing force of tug boat


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Hydrodynamic forces

_ a)(),(),(),(),(),(),()( ttrtvtutrtvtuYtY H!

Manoeuvring hydrodynamic derivative

H

H

H

!

YrYvYuYrYvYuY

YrvurvuY

rvurvu

0,,,,,,

_ a0,0,0,0,0,0,0 UYY !

vv

vv

YY

!x

x!

Taylor expansion


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Manoeuvring equations of motion

!

!

!

H

H

H

H

NrNrNvNvNN

YrYrYvYvYY

uu

rrvv

rrvv

uu

!

!

!

NrI

YmUrvm

Xum

zz

uUu p)(,,

)1(

Iorvu

oU

!

!


10/49


Linear manoeuvring equations of motion

!

!

!

H

H

H

H

NrNvNvNrNI

YrYrmUYvYvYm

uXuXm

rvvrzz

rrvv

uu

)(

)()(

)(

!

!

!

rzz

vy

ux

Nj

Ym

Xm

!

!

!

H

H

H

H

NrNvNvNrjI

YrYrmUYvYvmm

uXumm

rvvzzzz

rrvy

ux

)(

)()(

)(

Added mass, Added inertia moment


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Non-dimensional expression

),(

speedshipofcomponentConstant:

draft:length,Ship:

salt waterofdensityMass:

vuUU

U

dL

!T

V

dL

mm

!2

2

1':ass

V 22

1':Force

UdL

XX

!

V

tL

Ut !d:Time

dt

d

U

L

td

d!

d:derivativeTime


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TUMSTShip Manoeuvrability

- Theory and Assessment- 12

Non-dimensional manoeuvring equations

ddddddd!ddd

dddddddd!ddd

dd!ddd

H

H

H

H

NrNvNvNrjI

YrYrmYvYvmm

uXumm

rvvzzzz

rrvy

ux

)(

)()(

)(


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Mathematical models

Hydrodynamic force model

Abkowitz

MMG model (SNAJ, JTTC)

Response model

Nomoto model

System

(Ship)

Input output

Rudder Yaw rate


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Response model

dddddd!dddd

dddddd!ddddd

H

H

H

H

NrjIrNvNvN

YrYrmYvYvmm

zzzzrvv

rrvy

)(

)()(

0ssuming !du

vv dd andliminate

HH d!ddd 54321 qqrqrqrq

ddddd!

dddd!

ddddd!

ddddddddddd!

dddddd!

HH

HH

YNNmmq

YNYNq

mYNNYq

mYNmmNjIYYNq

YNjImmq

vy

vv

rvrv

rvyrzzzzvrv

rvzzzzy

)(

)(

)()()(

))((

5

4

3

2

1


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Nomoto model (2nd-order & 1storder)

HH dddd!ddddddd 32121 )( TKKrrTTrTT

4

5

3

3

4

3

2

21

3

121 ,,,

q

qT

q

qK

q

qTT

q

qTT !d!d!dd!dd

Manoeuvrability indices

KT model

HKrrT d!ddd 321 TTTT ddd!d


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Directional stability analysis

0)( 2121 !ddddddd rrTTrTT

Course stability without any steering function

Characteristic equation

terr P0ubstitute !d

01)( 21

2

21!dddd

PP TTTTVite's formulas (relation between the roots of a quadratic equation )


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Directional stability criterion

01

0

2121

21

2121

"dd

!

dd

dd!

TT

TT

TT

PP

PP

Vite's formulas (relation between the roots of a quadratic equation )

v

v

r

r

YN

mYN

dd"

ddd

Neutral point:

The center of pressure in

pure sway.

The center of pressure in pure yaw.


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Solution of KT model

Turning test

HKrrT d!ddd

u!

)0()

0(

0)(

0ttt

HH

0H

T

K

T

r

dt

rd

d

d!

d

d

d)(

10

HKrTdt

rddd

d!

d

T

dt

Kr

rd

d!

dd

d

0H

CT

tKr

d!dd )log(

0H T

t

CeKtr d

d!d0

)( H


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Solution of KT model

Initial condition: 00 !d! rt .

0HKd!

)1()( 0T

t

eKtrd

d!d H)(trd

t

0HKd

063.0 HKd

Td0

0

10

63.0)1( HH KeKrTt !d!dd! .


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TUMST

Ship Manoeuvrability- Theory and Assessment- 20

Assessment of

manoeuvring performance

Standards for ship manoeuvrability(IMO Resolution MSC.137(76), 2002)

Turning tests

Zig-zag testsStopping tests


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10r/10rZig-zag manoeuvre (stb.)

1. The ship is brought to a steady course and speedaccording to the specific approach condition.

2. The rudder is ordered to 10rto starboard.

3. When the heading has changed by 10roff the basecourse, the rudder is shifted to 10rto port. The shipsyaw will be checked and a turn in the oppositedirection will begin.

4. When the heading is 10r port off the base course, the

rudder is reversed as before.5. The procedure is repeated until the ship heading has

passed the base course no less than two times.


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Requirements of the standards for

ship manoeuvrability

The 10r/10rand 20r/20rzig-zag tests

(Essential information)

The overshoot angles

Initial turning time to second execute

The time to check yaw


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-20

-10

0

10

20

0 20 40 60 80 100 120

Graphical estimation of T, K indices

te

te

te

!eee ttt

dttKdtdt

tddt

dt

tdT

0002

2

)()()(

HUU

)0()()0()()0()(

0

!

brt

mee tKdttKt

dt

d

dt

tdT

e

HHUUUU

er

t

me tKdttKte

HHU !0

)()(

Ae

(te)


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eree tKKA HU !

''' eree tKKA HU !

'''''' eree tKKA HU !

rK H,23

2

123 KKK

!

_


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-20

-10

0

10

20

0 20 40 60 80 100 120


to to to

!ooo ttt

dttKdtdt

tddt

dt

tdT

0002

2

)()()(

HUU

)0()()0()()0()(

0

!

ort

moo tKdttKt

dt

d

dt

tdT

o

HHUUUU

or

t

m tKdttKTo

HHE !0

)(tan

Ao

Ao or

t

mo tKdttK

dt

tdT

o

HHU

!0

)()(


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oro tKKAT HE !tan

'''tanorotKKAT H!

''''''tan oro tKKAT H!

2

2/)( 876 TTTT !


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TUMST

Ship Manoeuvrability- Theory and Assessment- 27

On-line Identification of Ship Manoeuvrability

Indices by Using IIR Filters( IIR: Infinite Impulse Response)

HKrrT !


28/49



Real-time identification

RLS: RecursiveLeast Square

Direct method: IIR filter

Indirect method: Pulse response function


29/49



Response function

)/1(

/

)(

)()( Tss

TK

s

s

sG !! HU

Laplace transform

)(/)()/1(

)()()(

)}({)}()({

2

sTKsTss

sKssTs

tKLttTL

HU

HU

HUU

!

!

!


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TUMST

Ship Manoeuvrability


G zb z b

z a z a( ) !

1 2

2

1 2

a p a p p e

b KTh

T p b KT p

h

T

h

T1 2

1 2

1

1 1 1

! ! !

!

!

( ), ,

,

Pulse response function

Z-Transformation

)1()(

timesam lin

1

1

!

!

kkz

hezhs

UU

! )(

1)1()( 11 sG

s

LZzzG


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TUMST



ARX model

)()2()1(

)2()1()(

21

21

kekbkb

kakak

!

HH

UUU

)(

)()(

212

21

k

k

azaz

bzbzG

H

U!

!

( )t kh!

e k white noise( ) :


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TUMST



RLS (Recursive Least Square) Method

J k e k we k

w e w ek k

( ) ( ) ( )

( ) ( )

!

2 2

4 2 3 2

1

4 3

.

.IH v! ck)(

wkkkDT

/)1()()1(1 ! H

wDkkkG /)1()()1( ! H

)()1()1( kkk T !U

_ a)1()1()1()()1( ! kkkGkk UU

_ a wkkkGk T /)()1()1()1( HIH !


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TUMST



Integrated Form ofthe Linear Response Model

)()()( 210 kkk FHEUU !

E F! !1T

KT

,

!

!

!

kh

hk

kh

hk

kh

hk

ddkk

dkk

khk

)1( )1(1122

)1(

11

0

)()1()(

,)()1()(

)()(

XXXHHH

XXUUU

UU

! dtdttKdtdtttT )())()(( HUU


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TUMST



Impulse response of

FIR filter and IIR filter

1

t0(! Lt

)(tg

1

t0(! Lt

)(tg

s

esH

sL(!

1)( P

!s

sH1

)(

)()()( (! Ltututgtetg P!)(


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TUMST



IIR Filter

G ss

( ) !

1

P

n

z

z

hs

n

n

z

z

hssGzP

!

!

!!

P

P 11

1

12 1

12

)(

1)()(

1

1


37/49

TUMST



_ a

_ a

_ a)2()(2)(2

)2()(2)(

)2()(2

)2()(2)(

)2()(2)(

)2()(2)(

2

22

22

2

02

00

!

!

!

kkkBh

kAkAk

kkBh

kAkAk

kkkB

kAkAk

HHH

HHH

UU

UUU

UUU

UUU

IIR Filter

A

h

hB

h!

!

12

12

12

2P

PP,


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TUMST



Measurement conditions and T-K value

Table 1 Measurement conditions and T-K valueNO. S eed Wave T(sec) K(1/sec)

11.5kt Head 7.57 0.138 9.9kt Head 7.83 0.116

7.6kt Head 9.63 0.094

12.3kt Follow 7.74 0.153

9.5kt Follow 8.55 0.132

7.4kt Follow 12.41 0.089


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TUMST



Measured time histories

7 LP HVH F

Documents

Testing of Ships