PMM tests with two full-form models, and a comparison with results from static drift angle test

REPORT NO. 322

AUGUST 1971

LABORATORIUM VO'OR

SCHEEPSBOUWKUNDE

TECHNISCHE HOGESCHOOL DELFI

SYSTEMATIC HORIZONTAL OSCILLATION TESTS WITH

M:OD;ELS OF SERIES 60, BLOCKCOEFFICIENT 70

WITH VARYING LENGTH-BREADTH RATIOS

BY

IR. C. C. GLANSDORP

'AND

2"

- .'-

'-,415 ,> f?.f I, _/ /i

13th INTERNATIONAL TOWING TANK CONFERENCE 1972

SUBJECT : MANOEUVIABILITY

A note on results of PMM-tests with two models of low LîB_rat:io

with emphasis on frequency effects and a comparison with straight

line oblique towing.

by : Ir. C.C. Glansdorp and J.G.L. Pjjfers

Abstract :

The results of PÌ4M tests with two models with low L/B t are

given. Special emphasis is given on frequency effects and a comparison

is made with the results of straight line oblique towing.

Introduction

During the last decade several attempts have been made to calculate

the hydrodynainic derivatives in a horizontal plane for low frequencies.

To this end generally simple flow concepts are used for the calculation together with the results of low aspect ratio theory. It is important to have some experimental information with respect to the effect of

frequency upon the derivatives. On the other hand it is important to provide experimental data with respect to the straight line oblique towing derivatives; these data can be compared with the corresponding

swaying derivt ives.

A series 60, CB .70 model was adopted with two L/B_ratios and 5.5.

In the near future the same experiments will be performed with models with

higher L/B_ratios, and higher model speeds.

In this note the results of PMM-tests for swaying and yawing are given

Auguat 1971 Report No. 322

111

LABORATORIUM VOOR

SCH EEPSBOUWKUNDE

TECHNISCHE HOGESCHOOL DELFT

r

SYSTEMATIC HORIZONTAL OSCILLATION TESTS WITH

MODELS OF SERIES 6o, BLOCKCOEFFICIENT .70 WITH VARYING LENGTH-BREADTH RATIOS

by

Ir.C.C.

Glarisdorp

arid

Ab3traott

Pie1imenaxy reaulta of aytematic horizontal oscillation teats are

presented. The ultimate purpose of these teste is to provide

experimen-tal. data about the influence of L/jo on the linear hydrodynamio

derivatives.

The theory of Jacobs with some emperieal allowances has been applied

to the models in order to compare the theoretical values with the

1. Introduotion

During the last decade aevera]. attoinpts have been made to

calcu-late the hydrodynamic derivatives in a borizonial plane for low

frequencies. To this end generally, simple flow conoepte are used for

the ealoulation together with the resulte of 1cv aspect ratio theory.

In this oase especially the distribution of this thickness aver the

lateral plane is important for merica1 allowances on the the

oreti-os]. calculated derivatives. Therefore, it was decided to provide

experimental values about the influence of the L/B-ratio

A series 60, L/B _{- 7,} Cj

a

_{.70 was adopted sa a}

_{parent model.} The whole range of L/B_rattoe is covered by 6 modela, L/B 4, 5.5,

7, 10, 20,00.

In this note the results of oac.tflator _{tSBLB for svaying and yawing}

are given for the

LID_ratio 'a 4 and 55

In order to oheok the validity of the theoretical resulta at the higher wave

mkthg

_{speeds the tests were performed not only wt Pr}

l5 but also at

Pr

_{.20 and .30 The resulta of the higher oude} numbers will be given in a later report.

-1-2 DesariDtion of modela and test

oea.

The polyester models wer, testad in the bare hull condition The

mL4vi _{are given in bbl. L}

Table 1. Main particulars of modele.

lmngth

_{36048 m}

1sut

0.1742 m

3looic coefficient

700

Priseette coefficient

_.710

Length center of

yranciJ

+ 0.0152 *

11/3

4, 5.5, 7, 10, 20,0O.

Thiring the testa the models were tree to hevo and. pitch. and

reatrsiz*d for ro1

tubs

,ti.a1Mcx* were fitted. The

testing teo]mipi. and apperatue uaed have been. described in (i).

Fcr each model a teat program e'nizad in tubi. 2 bas been or will

be performed for three d.iffereth speeds, _{.].5,.20 and .30.}

Table 2. Teat program.

Lght lina

teMs

Swaying and yawing

_{oscillatoreaplitude}

_(y0)

teøte

o.05(o.0)Q.25 m

oseil1atoxfreusnoy

(cJ)

3

Remilla.

M thu aent the reeulta of the first two

ode1a are available.

In thie not. the re.ulte of Px

15 viii be pr.sented In fig. U the

remite of dl

ion].eee 1pim:fetøea in the swaylng aod. per imit

¿zenaiclems aap1i4s have been plotted Ørais

dimengiciileas

fre-qeicy

for both L/3ratiosd It can be meen. tr

theem plotE

that in a flikited frequeno-rmnge a linear r.latic,imhip between

nor-mfle.d force end frequency orLate independent et amplitud., thus

i-plying a constant value of the derivative.

rtb.r acre the value of

thie derivative tenda to the valua derived frc

the atreight line

test, see table 3; thim fact can be considered

an expertmental

verification of the fact that

(;')

(s')

iw«

ø

The deviation of the ]i.near relatiomehip in the higher frepieney

rengo (4'"1.5) impliem non linear effeota, Le. frequency-,

ampli-tu&e- eM the effects of cross flew.

With respect to the daanpingeacesnt

' in. the swaying mede it can be

observed that na eiiîicant amplitude dependence exista and that only

small departures of the linear relatiounhip between noiized

moment and dimensiorleas frequency are present, mee fig. IB. Aein

comparing the atraight Une derivative with the swayIng derivative

no appreciable difference has been fennd, mee table 3. In. fig. 2 the

nprmlized rotary faroei aM -moments have been plotted versus

di-nensionleas frequency.

t i

owjou.e from the plots that a

rameau-able linear relation exists between no'e

ed force or moment and

dimensioulesa frequency in the range of O

)

1.5; no amplitude

dependence In present.

In the higher frequency range eapeciafly for the rotary damping

moment amplitude dependence existe. Thi. to the effect

of mama in

the

ratary damping foro. no øignficant non linearity can be detected.

Mama derivatives show a. perfect linear relationship with the square

of the dtmenionleas frequencr op to c

1

_{3 end. no noticeable}

ampli-tude d.pendence can be found.

The significance of maas coupling In reduced due to relative smell

values of the mass coupling derivatives.

I

-4-.

It is, however, to be noted that severe departures of linearity exist. Amplitude effects are not present.

Zn table 3 the values of the linear derivatives are sIÑvized.

4. Etiasticsi cf derivativas

In table

3 the d,rivativea are compared.

with the resulta of a

method of estimation, given by Jacobe(2) In appendix I the formula's are given. Bowevar, saine emperical allowances are g*vn euch that the damping derivatives are as close as possible

to the measurements. This

uzlta in an euaperioal factor K, as a aultiplicator in the low aspect

ratio lift equation. Inane (3) presented

a paper in which he suggested

the same factor which has nearLy the ease magnitude.

With respect to the center of lift force Xp/L which is assumed by Jacobø

at the center of the lateral plane and

therefore differs obly slightly

with the center of gravity generally, it io asatmied that this center

of lift force is acting yoU behind the center of gravity. This

coin-cides to a certain extent with measurements of Martin on slender bodies

of revelution. It is probable that the same reasoning as given by 3acoba

holds here, bu.t it is possible that the extent of eddy ganeratien along

the forward part of the keel is not so

high as assumed, so that the

center of lift force is not located torward of the center of gravity.

5. pi

remarks.

In this stage of the investigation it is difficult to draw final

conclusions clue to the fact that only a emafl part of the whole progrem

flef eren9.e i

() Zund.rdorp, H.X. and ttenhek, L:

"Oøcillat cry teolmiquas at the Shipbuilding laboratory".

Report 113. of the Shipbuilding laboratory

of the Technological

University - Deif t, 196.

Jacobs, V.Ra

Htition of stability derivativas and indices of various ship

foras and coaparison with arperisental reaulta".

Journal of Ship Research, septeaber 1966.

¡noue, S.*

"The determinAtion of transversa hrod&najnio non

lineai' forces

by mn.e of steady turning".

'oxt contribution to the

11th Xnternatiônal Towing

Tank

Appendix I

Foxu1q's uaod tor oompariaon according to Jacobo' theory.

The aWOy damping damping force is given by, the resistance coefficient

baa been neglected in thie caee:

TV'

-K

L2

(i)

and the awar damping moment io composed by adding Think'ø destabilizing

moment to the away damping force adding at X (po*nt of application of

vincoue preaaure).

r

The rotary force derivative is found by

and the rotary innment by

(2

_T2

Nr' 'T

_{2 /}

L2

L2

In (4) C is ha1t thepriwnatic cOefficient, iod.d by Aibrng1

2

The acceleration derivatives are calculated according to the tolloving

forjmz].a

bow

-7TK2

(5)

-1f L;

- ¿ - A

L4

_rr.KI

A

r

_L'

at.ru

bow

J

gt.rn

7

ateril

bGw

item

C*T(z)zzIx

IC2

In the.. feul'

aM K1 indicat, the coefficiente of acoeesiou

to inertia, lateral and rotatioi*l, fox an equivalent ellipsoid.

indfeat.s th. lateral added aiea ooeífioierit determined at each

itation, following Prohaaka

T(x) lndioeLes the local draft; T indicates deaign draft.

K is the eaperioal all.wenoe vn the Jones' lift equation.

LU other symbole are according SNAM-ncaienolature.

OaT2(z)xdx

-

_L

(6)

Table 3.

Compariaon between meaewed and eetiaated I

rodynaic derivativefi

X

l0

LV

line

(Ç)atrjght

_line

-I

Tl

-L',

't

,

t,

I B; -

5.5

expeti-nient

theory

experi-ment

theory

.1723

-1796

_-1723

_-1878

612

_{- 676}

- 668

- 693

786

_-1781

-600

- 690

-98

-1756

-1186

-1160

- 260

.. 244

- 294

- 25

-1048

-1020

-1120

-1086

126

-

18

-

,i.

- 20

-56

-

59

- 31

100

-

- 112

-

18

1.75

1.65

-o169

0.172

1999

1413

342

103

0.2665

0.2700

Qe u)

I

o o -250 N(r)

S

sinp o. -500 -750 w, 3 4

N

o o 4 o o L/B=4

Fig. 2 A

FIg. 2 B

NormaLized yawing damping forces and moments versus dimensionLess frequency

Y(r,) 2

LÏB=55

I

1isin'p -

r

L/B=55

N)5

A O

4inç

-1000--1 --

-o L--s o --

-Fig. lA

Fig. lB

Norrvatized swaying damping forces and moments

_{versus dimensionLess. freqúency}

-a-

W' 00 1.. -- 2 3 4 L/8= 5.5 2000 Yo a A 4000 S _a

-9 _E S o -6000 D 00 WI 2 .3

4-WI 3 -4 L/B= 5.5 1000 1000 1o5

_I

,,10-N(v) y';

t

y; a - 2000 A _-2000 I

I

A £ -3000 ₃₀₀₀ R

82425

TECHNISCHE HOGESCHOOL DELFT

AFDELING DER MARITIEME TECHNIEK

LABORATORIUM VOOR SCHEEPSHYDROMECHANICA

PMM TESTS WITH TWO FULL-FORM MODELS,

AND A COMPARISON WITH RESULTS FROM

STATIC DRIFT ANGLE TESTS

by

C.C.. Glansdorp and

J.G.L. Pijfers

Rapport 322-P

1971

Delft University of Technology

Ship Hydromechanics Laboratory MekeIweg2

2628 CD DELFT

The Netherlands Phone 015 -786882

SUBJECT MAÑOEUVRAB.ILITy

PMM TESTS WITH TWO

_FULL-FORM

_{MODELS, AND A}

_COMPARISON

WITH

RESULTS FROM

STATIC DRIFT ANGLE TESTS

by C.C. Glansdorp' and .J.G.L.. Pijfers

Abstract

L

The results of ,Pt'24: tests with two models _{with low lB-ratios are}

given. Special emphasis is given. on frequency .èffects and a comparison

is made with the iesults of straight line oblique towing.

Introduction :

During the last decade several attempts _{have been. made to calculate}

the hydrodynamic derivatives in _{a horizontal piane f.Ör lòw frequencies.}

To this end generally simple flow _{concepts are used for the calculation} together with the results of low aspect ratio theory. It is important to have some experimental information with _{respect t the effect of,}

frequency upon .the derivatives. On the other hand it. is important to

provide experimental data with respect to the straight line oblique

towing derivatives; thes.e data _{can be compared with the corresponding}

swaying derivatives.

A series 60,, C.... .70 model was adopted with two L/.B_ratios, le

and '5.:5.

In. the nèar future the same experiments wiI., _{be performed with models with}

higher L/B_ratios _{and higher model speeds.}

In this note the results of PMM-tests for swaying and yawing are given

for the /B-rat:ios le and _{5,. 5 at a Froude number of}

. 15. .

14ó

2. Description of nodols and terst program.

The polyester modèle vere tested in the bare hull condition. 'Iba

in particulars are &.ven in table., 1.

Thble 1. M.in particulars of nodale.

LegUi

_3.048m

Draught

_{0.1742 *}

Block coefficient _.700

Prismatic coefficient _.710

Length center of buoyancy + 0.0152 .m

LiB

_4,

_{5.5, 7, 10, 20,00.}

Thiring the tests the models wére free to heave and pitch, and reatrainod for rolling. No turbi _{ne iula tors vere fitted. Thé}

testing technique and apparatus used have been described in (i).

Por each model a test prograia

8thrn-'ized

in table 2 has been or will be performed for three differenò speeda, Fr

5

_.20

_{and .30.}

Table 2. Teat program.

l.'Streight

liño

tenta ,

2. Swaying and yawing _{osctilntoramplitud'e}

_(y0)

teata _{0.05(0.05)0.25 rn}

oacillatorfrequency (c.i)

14.1

3.

ROsults.

At this InninAnt the results

of the fi,at two

odeia are aai1abie.

In, thiá note

the

resulta of Pr - .15 will be presented. in fig. iL the

resulta of d.tmensionlesa da pin Lotees In the swayiflg mode per amit.

dlzensionless amplitude bave been plotted versus a dimensionless

fre-quency c)' .- for both s It can be seen from these plots

that in a 11ml ted frequency'-rnn«e a linear relationship between nor-. tiwl Ized force and frequency exists independent of az:iplitude, thais jim.-plyiiig a constant valuo of the derivative. \irther moro the value of

this derivativo tends to the value derived from the straight line test, see table

_3;

this fact can be considered as an experimental verification of the fact that

(',)

Ctraight line

(r')

The

deviation of

the

linear relationship in the higher frequency. range (&''i.5) inipliea non linear effècta, i.e. frequency'-,

ampli-tude-

and the effects of cross flow. .

-With respect to the dampingsmomeut ,' in thé swaying mode it can be

observed that. no significant amplitude dependence exists and that. only!

1l departures of the linear relationship between norrtil Ied moment azd dimensionless frequency are present, see fig. lB. Again

comparing the straight lina derivative with the swaying derivative

no

appreciable difference baa been found, see

table 3, in,

fig. 2 the

norms%l zed rotary forceB

and

-moments have been

plotted

versus di-Mensioniess frequency. It is obvious from the plots that a reason-able linear relation. exists between norrulized force or moment and dimensionless frequency in the range of O CY 1.5i no amplitude dependence is present.

In the higher frequency rangO especially for the rotary damping mo'nt amplitude dependence exista. Due. to the effect of masa in the 'rotary damping force no significant non linearity can be detected.

Xaaa derivatives chow a perfect linear relationAhip with the square

of the dimensionless frequency op to (j 'i.

₃

and no noticeable ampli-tude dependence can be found.

The significance of mass coupling is reduced due to relative nmAt1 values of the masa coupling derivatives.

142

It is, however, to be noted that nevero departures of linearity exist. Amplitude effects axe not present.

In table _{3 the values of the linear derivatives are ann'mrized,}

4.

timation of dérivatives.

In table '3 the dorivativee axe. compared with the' resulta of a

method of entimation given by Jacobs (2.). in appenil 4

r

the forriula15:

are given. However1 nonio emperical allowances are given such that the damping derivatives are aa close as posible to the inéasurementa, Thin resulta in an emperical factor K, _{aa a ¡nultiplicator in the low aspect}

ratio lirt equation. inane (3) presented a paper in which e suggested

'the naine factor

which has

_{nearly the same}

With respect to the center of' litt force Xp/L which is assumed by Jacobs at the center of the lateral plane and _{therefore differs oÌU.y slightly}

with the center of gravity generally, it is assumed 'that this center of lift force is acting well behind 'the center of gravity. This cáin-cides to a certain extent with measurements of Mar.tin on slender bodies of revolution, it in probable that the same reasoning an given by Jacobs holds here, but it is possible that the extent of eddy generation along the forward part of the keel is not so high as assumed, so that the center of' lift force is not located forward of the center of gravity.

5.

'inal rerarks.

In this stage of the investigation it is difficult to draw

_f1'nl-1

conclusions due to the fact that only

_a

_{anvi-li part of the 'whole program}

143

Ref erencen &

(i)

Zm1erdorp, H.J. and Buitmihek, M0 s

"Oscillatory teolmiques at the Shipbuilding laboratory".

Report 111 of the Shipbuil&ing Laboratory of the Technological

University - Deift:,

1963.

Jacobs, W.R.s

Estimation of stability derivatives and. Indices of various ship

foruis and comparison with experimAntal

results"

ournal of Ship Research, september

1966.

moue, S.s

"The detelminAtion of

.transvOrse hydrodynainio non linear forces by

means of steady turning".

Porcal contribution to the 11th

internationAl Towing Tuk

-

,-.-.,1_- ' )__ '.

''

'

Appendix i.

FoEnula's used for oonparison according to Jacobs' theory.

The sway damping, dßmping fOrce is given by, the' reatetance coefficient

has been neglected in th.ts casez

and the sway danping moment ja composed by adding Hunk's destabiliziflg moment to the sway damping force adding at .X (point cf application or

viscous pressure). '

r

L2

(v')

The rotary force derivative is Íomd by

...('

-

e)

KTP

_'(3)

ant the rotary moment by

Nr' Y;' liT2

₍₄₎

In (4) C, is half the: prismatic cóefflòient, introduced

_by

_Aibring.

2'

The acceleration derivatives are calcu,lated _{acoordiné to tite following}

bow

-01T?(x)dx

irE:2

î

(5)

stern 144

ov .-08T2(x)xdx - Y;'

Btor,1

X-atom

_17

C8?(x)xd

-atem

(6)

Xn theae formui'e E2 and X' ivMcate _{the coefficients of accession}

to inertia, lateral and rotational, for an equivalent ellipsoid.

f _{41eate3 the lateral added, as}

_000fficiet.

doterm(ned at 'each

station, following Prohaáka.

T(x) indicates the, local

_{draft; T n4catea, design draft.}

K is the. ainperical allowanoo _{on the Jònea' lift equation.}

All other symbols ar, according

_{'A11E-iomeno]aturo.}

,

i 46

Table 3

Comparison between measured and estimated hyd.rodynamic derivatives

10 -1798 -1736 -1186 -1160 N ' r - 260 - 244 - 294 - 256 Y,' _-1048 -1020 -1120 -1086 - 126 - 18 - 51 - 20 - 36 - 59 - 31 - 63 Y!,' 100 - 16 - Ï12 - 18 K i

_{. I.,}

.7 1 83 -0.169 _{-0 172} X expe,i-ment theorr experi-ment theory

yVI

-1723 -1796 -Ì723 -1878 N ' V

-612

- 676 - 668 - 693

(Y')

y

straight line,

-1786 -1781

(N')

y

straight line

-

oOO - 690

I!'.X

lO5

_{1999 1413}

I' X 142 103

IC.

X 0.2665 0.2700

Fig. lA

Fig. lB

NormaLized swaying damping forces and moments versus dimensionLess frequency

w, w, 2

'L/8S.5

2>

D a

L/B=55

«io-5 s s y; 2000 -2flO. -A L.

i

-2S0 airS _N1r) ii simp o. sao -750

Fig. 2 A

Fig.29

NormaLized yawing damping forces and moments versus dimensionLess frequency

I

,10-'f(r)

a z

V(r)

L.

I

-J.tsinp -4000

-6000-I

g

Nir)

4 . o a--1000

---.,

o _a o o £ a o

I

o

I