Shipboard acoustics proceedings of the 2nd international symposium on shipboard acoustics ISSA ’86

SHIPBOARD
ACOUSTICS
Shipboard
Acoustics
Proceedings
of
the 2nd International Symposium on Shipboard Acoustics
ISSA
'
86,
The Hague, The Netherlands, October
7-9,
1986
Organized by the
Netherlands Organization
for
Applied Scientific Research (TNO)
TNO Institute
of
Applied Physics (TPD)
in
co-operation with
Maritime Research Institute Netherlands (MARIN)
National Foundation
for
the co-ordination
of
Maritime Research
in
the Netherlands
Royal Netherlands Navy

edited by
J.
BUITEN
TNO Institute
of
Applied Physics (TPD)
Delft, The Netherlands
1986
MARTINUS NIJHOFF PUBLISHERS
~.
a member
of
the KLUWER ACADEMIC PUBLISHERS GROUP lIiII
DORDRECHT / BOSTON / LANCASTER •
Distributors
for
the United States and
Canada:
Kluwer Academic Publishers,
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for
the
UK
and Ireland: Kluwer Academic Publishers, MTP Press Limited,
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UK

for
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P.O.
Box
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AH
Dordrecht, The Netherlands
ISBN -13:978-94-010-8070-5
e-ISBN
-13
:978-94-009-3515-0
DOl:
10.1007/978-94-009-3515-0
Copyright
©
1986
by Martinus Nijhoff Publishers, Dordrecht.
All rights reserved. No part
of
this publication may be reproduced, stored in a
retrieval system, or transmitted in any form or by any means, mechanical,
photocopying, recording, or otherwise, without the prior written permission
of
the publishers,
Martinus Nijhoff Publishers, P.O. Box
163,
3300
AD Dordrecht,
The Netherlands.
PREFACE

The
first
International
Symposium
on
Shipboard Acoustics, held
in
Noordwijkerhout
(The
Netherlands)
in
1976,
was
a meeting
of
invited
experts,
each having
considerable
expertise
in
ship
acoustics.
Many
of
the
participants
were
dealing
with

research
on
various
ship
acoustical
subjects,
and
it
proved
to
be
a
good
idea
to
discuss
future
investigations
and
new
techniques.
At
that
time
acousticians
learned
to
use
real-time
signal-processing

techniques
and
attempts
were
made
to
establish
sound
level
prediction
methods based
on
semi-fundamental
considerations
instead
of
the
methods using
empirically
obtained
data.
Time
was
pressing
as
it
was
assumed
that,
in

view
of
the
adoption
of
Recommendation
141
of
the
International
Labour Conference
in
1970,
authorities
would soon
make
appropriate
provisions
to
"protect
seafarers
from
the
ill
effects
of
noise".
This
resulted
in

several
national
recommendations followed
by
the
IMO
"Code
on
noise
levels
aboard
ships"
which
was
adopted
by
the
IMO
Assembly
in
1981. After
that,
pressure
on
the
authorities
was
increased
further
by

the
decision
of
the
European
Community
to
protect
labourers
against
harmful noise
at
their
workplaces,
including
ships.
Legally
enforceable
noise
limits
will
therefore
become
normal
in
the
future.
In
many
countries

recommendations with
respect
to
maximum
allowable sound
pressure
levels
in
the
crew accomodations
and
work
area
aboard
ships
were
already
taken
into
account
by
ship
owners, long
before
the
existence
of
the
Recommendations.
Shipyards

are
confronted with
the
problem
of
how
to
fulfil
the
requirements
at
the
lowest
possible
costs,
a
situation
which does not
essentially
differ
from
that
in
1976. In
addition
however,
modern
ships
tend
to

be
of
a
lighter
construction
and
as a consequence,
the
acoustic
countermeasures have
to
be
light.
Yards
are
constructing
ships
that
are
more
specialized
and
technically
more
complicated
than
in
the
past;
acoustical

standard
solutions
are
of
little
use
for
these
vessels.
The
yards
are
compelled
to
find
solutions
that
have'
flexibility
in
the
design
stage
and
standardization
in
the
production
stage.
The

consultant
is
confronted with
rapid
and
drastically
changing
demands
of
owners
and
yards,
which
require
fast
and highly
precise
answers.
He
should
have
perfect
knowledge
of
the
results
of
research
and
has

to
transform
these
into
practical
tools.
Much
more
often
than
before,
he
has
to
combine
disciplines,
which
makes
it
difficult
to
be
an
expert
in
one
of
them.
In
the

past
ten
years
research
workers have experienced a
rapidly
growing
demand
on
research,
followed
by
a sharp decrease
of
funds. Their
tools
changed
dramatically
compared with preceding decennia,
in
capabilities
as
well
as
in
the
necessary
investments,
especially
in

computer hardward and
in
software.
They
discovered
that
solutions
of
rapidly
increasing
quality
could
be
given, but
that
costs
increased
correspondingly.
Many
developments
VI
in
the
vJide
area
of
"noise"
and
"vibration"
force

the
scientist
to
extend
eXisting,
or
to
establish
new
data
bases.
Increasing
demands
on
research
cause
increasing
specialisation
and,
for
the
research
worker
an
increasing
need
for
open
discussions
with

colleagues.
Society
however,
requires
methods
that
are
simple
to
handle, and
industry
wants
to
protect
its
trade
secrets.
In
spite
of
the
conflicting
demands
of
the
different
parties
involved
in
design,

construction
and management
of
ships,
and
those
in
charge
of
the
crew and
passengers,
much
has been
attained
in
the
last
decennium.
At
a
symposium
on
shipboard
acoustics
and
vibrations
only
some
recent

highlights
and
experiences
can be emphasized
in
a
limited
number
of
papers.
The
discussions,
which
will
be
added
to
this
issue
later,
will
certainly
complete
the
papers
presented.
We
trust
that
the

contributions
to
this
book
will
give
rise
to
an
exchange
of
ideas
on
the
application
of
research
results,
on
subjects
for
future
research
and
on
the
necessary
standardization.
The
Organizing Committee

expresses
its
thanks
to
the
authors
who
shaped
this
symposium.
The
efforts
of
the
Netherlands
Organization
for
Applied
Scientific
Research
(TNO)
and
the
members
of
the
TNO
Corporate Communication Department
are
gratefully

acknowledged.
The
editor
would
like
to
thank
his
colleagues
of
the
TNO
Institute
of
Applied Physics
(TPD)
and Dr.
A.
de
Bruijn
of
SACLANT
ASW
Research Centre
for
their
assistance,
and
the
authors

who
made
this
task
a
pleasant
one.
August
1986
J.
Buiten
TABLE
OF
CONTENTS
PREFACE
1.
A.
de
Bruijn,
W.H.
Moelker,
and
F
.G.J.
Absil
Prediction
Method
for
the
Acoustic Source

Strength
of
Propeller
Cavitation
v
2.
A.
Colombo,
P. Ausonio,
L.
Grossi,
and
L.
Accardo
21
Propeller
Induced Noise and
Vibration
Reduction: Acquired
Experience
in
Design and
Testing
Approach
3.
J.
van
del' Kooij
43
Experimental and

Analytical
Aspects
of
Propeller
Induced
Pressure
Fluctuations
4.
T.
Sasajima, N.Nakamura,
and
A.
Oshima
63
Model
and
Full
Scale Measurements
of
Propeller
Cavitation
Noise
on
an
Oceanographic Research Ship with
Two
Different
Types
of
Screw

Propeller
5.
Wei
Yi-mai
75
A Study
of
Simulation
and
Elimination
of
Propeller
Sinqing
6.
B.
Bajic,
J.
Tasic,
A.
Dzubur, and
I.
Jovanovic
91
Propeller
Noise:
Some
Topics
from
the
Activities

of
Brodarski
Institute
7. J.H.
Janssen,
and
W.H.
Moelker
103
Some
Experiments
on
the
Transmission
of
Propeller
Cavitation
Noise
into
the
Ship's
Structure
8.
J.I.
Smull
in
121
Quiet High-Speed Yachts
and
Water

Jet
Applications
9.
J.R.
Chapman
135
Model-Scale Measurements
of
the
Transmission
and
Radiation
of
Hull-Borne
Vibrational
Energy Using Frequency/Wavenumber Analysis
10.
M.
Purshouse
155
Underwater Noise Radiation
Due
to
Transmission through
the
Cooling Water System
of
a Marine
Diesel
Engine

11.
A.R.
Clark
and
P.S. Watkinson
Measurements
of
Underwater Acoustic
Intensity
in
the
Nearfield
of
a
Point
Excited
Periodically
Ribbed Cylinder
177
VIII
12.
Zhu
Xiqing
189
Sound
Generation from a
Moving
Shell
13.
E.

Bonetti
and P. Calcagno
201
Low
Noise Levels
as
the
First
Task
of
a
Vessel.
A
Description
and
Some
Remarks about Acoustic
Quieting
Design
Criteria
and
Features
of
Saclant
ASW
Centre
Oceanographic Research Vessel
14.
J.
0degaard

217
Ship Noise
Criteria.
Do
They
Reflect
the
Present
Level
of
Noise
Reduction Technology?
15. P.
Hynna
233
A
Literature
Survey Concerning
Propeller
as
a Noise Source and
Prediction
Methods
of
Structure-Borne
Noise
in
Ships
16. P. Calcagno,
R.

Maltese,
and F.
Pinazzi
245
Applications
o"f
Two
Mathematical Approaches
to
Predict
Airborne
Noise Levels
in
Ship
Superstructures
17.
R.
Kinns
265
Some
Observations
on
the
Achievable
Properties
of
Diesel
Isolation
Systems
18.

J.G.
van Bakel
Acoustic
Transfer
Functions
of
Flexible
Shaft
Couplings;
Measurement
Method
and
Results
279
19.
A.D.
Sykes
295
Random
Vibration
of
Multiterminal
Mechanical Systems
20.
P. Tilmann 317
The
Influence
of
the
Internal

Impedance
on
Vibration
Reduction
21.
G.
Mancuso
and F. Sacchi 335
Main
Propulsion
Diesel
Generator
Sets
with Acoustic Enclosure
and Double
Resilient
Mounting
for
Low
Noise
Application
22.
B.
E.
Douglas 353
Flexural
Wave
Damping
in
Ship

Hulls,
Decks and Bulkheads
23. S.
Weyna
,
365
Determination
of
Acoustic
Properties
of
Ship's
Sound
Reducing
Floors
24.
A.
Blanchet,
G.
Chatel,
and
A.
Paradis
Study
of
Structure-Borne
Noise Transmission
Inside
Cabins
by

Sound-Intensity
Measurements
377
25. M.J.A.M.
de
Regt
Experiments
on
Sound
Reducing
Floors
Including
Visco-Elastic-Damping
on
Board a Rhine Cruise Vessel
IX
393
PART
I
LECTURES
PRESENTED
AT
THE
SYMPOSIUM
PREDICTION
METHOD
FOR
THE
ACOUSTIC
SOURCE

STRENGTH
OF
PROPELLER
CAVITATION
A.
DE
BRUIJN*,
W.H.
MOELKER,
F.G.J.
ABSIL
TNO
INSTITUTE
OF
APPLIED
PHYSICS
(TPD)
,
DELFT,
THE
NETHERLANDS
1.
INTRODUCTION
Ship
propeller cavitation is considered to
be
one
of the
most
impor-

tant
sources
of
underwater
noi
se. Furthermore
it
often contri butes
con-
siderably to the noise level
aboard
the ship.
Much
research
has
been
carried
out
in
this
field
in
order to reduce the extent
of
cavitation
by
a
proper blade design.
Also
through the

use
of
model
simulation techniques
more
insight into the cavitation
performance
has
been
gained.
An
important
overview
about
this
subject
has
been
presented
by
ISAY
[1].
Modern
computer-based design techniques,(cf.
KERWIN
[2],
VAN
GENT
[3])
applying three-dimensional

lifting
surface theories,
have
improved
con-
siderably the insight into the
hydromechanical
aspects.
For
example,
the
pressure distribution
on
the blades gives the position
where
cavitation
probably will occur.
The
price to
be
paid to reduce the cavitation is mostly the decrease
of
propulsion efficiency.
This
is the reason that
in
the design
phase
the
con-

sequence
of noise reduction
has
to
be
known
at a very early stage.
Mostly
nothing
more
is
known
but the propulsion
power,
rotation speed, diameter
of the propeller
etc.,
so
the
noi
se
and
vi
br,ation
anal
i
st
is
1
eft

with
empi
ri
ca
1
methods
to predi
ct
the acoustic source strength
or
the hull-
induced
vibrations.
Prediction
of
the hull-pressures
induced
by
the cavitation
has
been
the
subject
of
considerable investigations.
NOORDZIJ
[4J
has
attempted to
deve-

lop
a calculation
scheme
for estimating the cavitation
volumes
at
any
blade
position.
By
calculating the
volume
variations
he
was
able to determine the
pressure amplitudes exerted
on
the hull.
The
agreement
with
experiments is
quite limited
but
useful
in
comparative studies.
Up
ti

11
now
a cheaper,
but
st
i
11
re 1 i
ab
1 e,
method
is
the
semi
-empi
ri
ca
1
approach.
The
method
is
based
on
the
compari
son
of
a great
number

of
experimental data taken
from
as
many
ships
as
possible.
By
statistical
regression
it
has
been
attempted to find the significant parameters
which
describe the
induced
hull-pressures. A successful evaluation
of
this
approach
for hull-induced pressures at the
two
lowest blade-rate frequen-
cies
is
given
by
HOLDEN

et
al
[10].
* Currently
employed
at:
SACLANT
ASW
Research
Centre,
La
Spezia, Italy
Buiten,
J.
(ed), Shipboard Acoustics.
ISBN
90-247-3402-7.
©
1986.'
Martinus
Nijho!!
Publishers, Dordrecht.
2
The
higher frequency
range
of
the cavitation noise
remains
a

difficult
problem
although
it
can
be
dealt
with
the concept that
it
consists
still
of
a 1 arge
number
of
hi
gher
harmon
i
cs
[5].
These
are,
however,
part of the
random
spectrum.
The
cavitation

volume
variations
can
be
hardly called
"harmonic".
The
sheet is
randomly
vibrating, giving
rise
to
random
noise
components.
Contrary to the general
opi
nion
these
random
components
are
very
significant.
They
are extremely
difficult
to predict since
no
suitable

mathematical
model
exists to calculate these
random
vibrations.
This
paper
presents a
method
which
is
very
much
related to
HOLDEN's
method,
but
with
the difference that
it
attempts to predict the source strength of
propeller cavitation noise
above
the lowest blade-rate frequencies, viz.
between
30
and
500
Hz.
It

makes
use
of
many
experimental data
on
propeller
noise
measured
aboard
a variety of
Dutch
ships.
By
means
of
a
statistical
regression analysis a semi-empirical prediction
formula
has
been
found.
2.
INVENTARISATION
OF
PROBLEMS
As
stated
many

times the noise
aboard
ships is a
difficult
problem
for
the
des
i
gner
as
well
as
for the acoust i ci
an.
The
propeller
des
i
gner
is
always
interested
in
reducing the cavitation, although
he
knows
that the
price to
be

paid
can
be
quite high:
reduced
efficiency, larger diameters,
adaption of the
wake.
He
ends
up
with a
compromise;
acceptable cavitation
performance
(mostly
in
view
of erosion)
with
acceptable
hydromechanical
properties.
Required
acceptable noise levels
in
the
accommodation
are
well

established
and
give guidelines
how
far cavitation should
be
avoided.
Still
he
is
left
with
an
unresolved question:
what
is
acceptable for cavi-
tation
in
view
of
noise
and
vibrations
or
what
is the relation
between
ca-vitation picture
or

performance
and
the perceived noise level
in
the
accommodation.
From
the point
of
erosion the solution
is,
however,
not
so
difficult:
avoid
bubble
cavitation,
cloud
cavitation
or
pressure-side cavi-
tation.
With
the present
st~te
of the design techniques
this
is feasible.
Mostly

it
is
quite
difficult
to
avoid
both
sheet-cavitation
and
tip-vortex
cavitation.
These
types are
mainly
responsible for the noise generated
aboard
the ship
or
underwater.
The
main
question is
now
what
is
the relation
between
the cavitation pic-
ture
and

the noise generated.
An
a-priori
answer
cannot
be
given, since
there is
no
suitable mathematical sol ution
on
the relation
between
the
noise
and
the picture.
Model
experiments
can
give
reliable
solutions. Cavitation
has
been
investi-
gated
traditionally
in
cavitation tunnels

in
which
the
static
pressure
in
the fluid
and
the
flow
speed
can
be
varied.
To
improve
the simulation of
full-scale
conditions,
and
thus the prediction
of
cavitation
and
its
detri-
mental
effects (like propeller erosion, pressure fluctuations, noise)
several special
facilities

have
been
built
during the
last
two
decades.
Among
these the
NSMB
Depressurized
Towing
Tank
occupies a special place.
This
large
tank
is
in
operation since 1972.
The
original
purpose
was
to
perform
propulsion
tests
with
models

of
the (at the time)
even
increasing
size of tankers,
bulk
carriers
and
container ships at a reasonable scale,
say
1:30.
By
adding
the possibility of controlling the
air
pressure
in
the
tank, a
unique
facility
was
obtained for testing cavitation
and
its
asso-
ciated
phenomena.
In
the depressurized

towing
tank
it
is feasible to
measure
the radiated noise
in
an
appropriate
way,
since the reflections to
3
the walls
can
be
kept quite
reduced
in
contrast
with
the cavitation tunnel.
The
acoustic
results
taken
from
experiments
in
this
tank converted to the

full-scale
have
proven
to
be
quite
reliable,
cf.
VAN
DER
KOOIJ
&
DE
BRUIJN
[8].
Sti
11
there is another factor
that
comp
1 i cates the matter
cons
i derab ly.
The
noi
se
generated
by
the propeller is transmitted through the shi p' s
structure.

This
means
that the noise levels
do
not
yield
unambiguous
infor-
mation
.on
the source strength
of
the propeller cavitation proper.
Comparison
of
levels either
in
different spaces
or
in
different ships is
meaningless without a correction for the transmission loss. Transfer
of
sound
through the steel structure is a
most
comp
1 i cated affai
r,
not

very
much
understood
or
predictable, although the progress
in
this
field
is
quite impressive.
It
is
of
prime
importance to eliminate the transfer func-
tion before judging the source strength
of
various propellers.
This
paper
concentrates
on
the determination
and
evaluation
of
the cavita-
tion source strength.
This
is a

first
step
in
the prediction
scheme
for the
noise
aboard
the ship. Transmission
of
the propeller noise should
be
dealt
with separately.
We
refer
to another
paper
in
this
proceedings
[9].
The
source strength
can
be
obtained
by
model
experiments,

as
explained
above.
This
is a lengthy procedure
and
in
fact not suitable
in
early design
stage.
Another
successful
quick
method
is
based
on
the evaluation
of
empirical data obtained
from
ships
of
the
same
kind.
HOLDEN
[10]
has

been
rather successful
in
predicting the hull-induced pressures.
His
approach
was
in
fact simple:
measure
the hull-pressures
on
a variety
of
ships
and
apply a
statistical
regression analysis
so
that
the
induced
pressures
can
be
related to a
number
of
hydrodynamical

parameters: the
wake
field,
geometry
of
the propeller, loading
of
the propeller
etc.
By
calculating or
estimating
this
kind
of
parameters for all his ships
and
applying a
sta-
tistical
regression
method
he
was
able to formulate
an
empirical rule for
the amplitude
of
the hull-pressures at the blade-rate frequencies.

This
method
has
been
proven
to
be
extremely
fruitful
in
the selection of a pro-
peller
geometry
in
the design stage. Additions
or
alternatives
have
been
proposed
(such
as
the influence
of
skew-back),
but
essentially
this
approach
has

been
maintained.
We
refer also to the
work
of
HOLTROP
[11]
and
LEENAARS
&
FORBES
[12]
on
the prediction
of
hUll-vibrations.
As
stated
above
this
method
applies to the amplitudes
of
the blade-rate
frequencies.
For
the higher
harmonics
it

seems
not too accurate
any
more.
This
means
that the audible noise cannot
be
predicted
by
this
method.
Also
the concept
of
hull-pressures is
not
relevant to transfer
of
sound
in
the
accommodat
ion.
For
thi s
purpose
we
have
developed

the idea
of
the
equi
va-
lent
monopole.
This
is
based
on
the observation that the noise generated
in
the water
is
mainly
C:ue
to
vol
ume
variations.
With
respect to
sound
generation
we
could
say
that a
monopole

representation
can
be
assumed.
On
vessels
with
a sharp
wake
non-uniformity
this
dominant
volume
variation
component
of
the pressure
may
be
approximated
by
an
oscillating
monopole
source fixed
in
a position
below
the
ship's

hull, radiating the free
field
pressure
p = p f U / 2r
where:
U =
volume
velocity, f = frequency
r
= distance
from
monopole
to observation point
4
The
source strength either expressed
in
terms
of a
monopole
strength or
by
the
sound
pressure at a
fictitious
distance
of
1 m
has

been
the subject
of
various prediction
methods.
The
best
known
are
given
by
ROSS
[6J
and
BROWN
[7J.
Both
methods
are
very
much
inaccurate at frequencies
below
100
Hz
as
has
been
pointed out
by

measurements
by
THIELE/0DEGAARD
[14J.
3.
DETERMINATION
OF
VOLUME
VELOCITY
The
source strength
of
propeller cavitation
can
be
determined
in
either
two
ways.
Directly
in
the water or
by
means
of
the
method
based
on

the principle of reciprocity applied
onboard
the ship.
The
first
method
is
becoming
more
popular.
We
refer to the
work
of
SASAJIMA
et
al.
[13]
and
THIELEl0DEGAARD
[14
J.
By
measuri
ng
the
noi
se
radi ated
underwater

at
dif-
ferent distances
from
the ship, the source level
being
the pressure at a
distance of 1 m
from
a
fictitious
monopole
source placed at the cavitation
centre
was
obtained.
This
source level is
found
by
adding
the estimated
transmission loss to the
measured
sound
pressure levels.
The
transmission
loss
depends

on
the distance
between
the
measuring
hydrophone
and
the ship.
Mostly
the
underwater
noise level
was
measured
with
the aid
of
an
array
of
hydrophones,
whi
ch
was
suspended
into the water
from
a pil ot boat.
The
underwater noise recordings

were
performed
continuously
from
the
pilot,
while the ship approached,
passed
and
left
the recording position. A
dif-
ficulty
in
these
measurements
is
the correct determination
of
the distance.
One
investigator
used
a pistol
sound
as
a distance indicator.
THIELE/
0DEGAARD
measured

the transmission loss
by
means
of
small
explosive charges
and
two
hydrophones,
one
close to the explosion ("source
hydrophone")
and
one
placed at different distances
from
it
("receiver hydrophone").
Other
investigators
assumed
a simple square distance
law
in
the transmission
loss,
neglecting the reflections
from
the sea
bottom

and
surface.
These
methods
are
very
expensive
and
time-consuming.
Morever,
these experiments
are to
be
performed
in
deep
water.
Thi
s
makes
thi s
method
unwi
e 1
dy
for
routine
measurements.
For
the determination of the source level

onboard
another
method
can
be
adopted. Place a large
sound
source
in
the propeller region
and
measure
the
response
in
the
accommodation.
Since the acoustic source strength is
known
for
such
a transducer, the levels
due
to the propeller cavitation
can
be
di
rect ly
compared
with

those obtained
from
the auxil i ary source. Sti
11
this
method
is only feasible
when
a transducer
can
be
mounted
in
the pro-
peller region. A strong electro-dynamical
underwater
sound
source is
heavy
and
difficult
to
handle
in
the propeller region
by
divers.
To
avoid
these

kinds of experiments
we
have
proposed
another variant
of
this
method.
At
low
frequencies,
say
below
1
kHz,
the
sound
source is
much
smaller
than
an
acoustic
wavelengt~.
As
has
been
observed
during
viewing

trials
the cavita-
Hon
is mostly concentrated
on
the blade
in
the
upper-most
position.
This
means
that the
dimension
and
duration is quite limited
so
it
is
safe to consider the cavitation
as
a point source.
The
measuring
technique
is
based
in
the reci procity pri
nci

p 1 e.
Each
measurement
cons
i
sts
of
two
different experiments (Fig. 1).
First
experiment
Propeller
not
in operation
Measure
i
and
p
~J:jkx
~
Second
experiment
Propeller
in
operation
fleasure e
~ ~, ,~~
"';];Xlectro-
~
acoustical

U transducer
Fig.
1:
Test
p;POcedure
for
determining
the
voZ·ume
velocity
of
propeUer
cavitation.
5
In
the
first
("silent")
experiment the transfer function
is
measured
and
it
is determined
by
a reciprocal technique for practical reas'ons.
In
the
second
("sailing")

one
the noise
or
vibrations
due
to the propeller cavita-
tion at
an
arbitrary point
in
the
accommodation
are
measured.
These
results
represent the
combining
effect
of
the source strength
of
the
operating propeller
and
the transfer function describing the relation bet-
ween
the source strength
and
the

vi
brat ions
in
the selected
poi
nt
in
the
accommodation.
In
practice the procedure is
as
follows. A reversible
linear ,mechanical- or electrical-acoustical transducer is installed
in
the
accommodation.
In
principle the transducer
can
be
placed
anywhere
in
the
accommodat
i
on
above
the propeller,

but
inmost
cases a 1 ocat
ion
close
to the propeller is
chosen
in
order to obtain the highest signal-to-noise
ratio.
In
the
first
experiment the ship propeller is idle thus
not
rotat
i
ng.
A
number
of
hydrophones
is
mounted
onto
the the blade
in
the
upper
pos

it
ion.
The
transducer
is
used
now
as
an
exc
iter,
dri
ven
by
an
electric
current
i,
while the average resulting pressure p is
measured
by
means
of
the
hydrophones.
In
the
second
experiment the propeller is
in

operation
and
the output
open
voltage e
of
the transducer is
measured.
According
to the reciprocity principle the
volume
velocity
of
the cavita-
tion U is
given
by:
U = e • i
Ip
(m
3
/s)
This
equation holds for
pure
tones
but
can
be
easily extended to 1/3-octave

frequency bands, although there are
some
pitfalls.
The
noise
from
the pro-
peller cavitation (represented
by
the
measured
quantity
e)
is mostly
broadband,
but
the
ratio
ilp
is mostly
made
up
by
the generation
of
sweep
tones to obtain the best signal-to-noise
ratio.
The
result

of
the
measure-
ment
depends
heavily
on
the location
of
the
hydrophone
in
the
first
experi-
ment.
From
extensive investigations
it
has
been
found
that the best
location
is
the centre
of
the sheet cavitation
when
the sheet

has
started
its
collapse stage.
To
obtain a reasonably
unique
transfer function
from
the cavitation region to a point inside the ship
or
model
it
is absolutely
necessary to take
more
measuring
positions
in
order to average these
transfer functions
with
respect to position.
It
has
become
standard prac-
6
tice
to place three

hydrophones
at the 0.8-0.9 R position
of
the blade near
the centre
and
take
moreover
3 blade
pos
it
ions near the hull
by
sl i
ght
rotation.
We
obtain then 9 transfer functions,
which
can
be
easily
averaged.
It
has
turned out that the pressure
sometimes
shows
very sharp
dips,

so
it
is
recommended
to average p instead
of
i/p.
Frequency-
averaging
is
also essential to obtain reasonably
unique
transfer functions.
We
prefer to take 1/3-octave frequency bands,
narrow
enough
to observe the
i nfl
uence
of
the
bl
ade-rate
harmoni
cs
separately
and
wi
de

enough
to get
reasonably stable averages.
4.
SHIPS
Seven
single-screw ships
have
been
investigated.
The
size of these
ships
and
their
trial
speeds
covered
a
fairly
wide
range.
The
ships
were
investigated mostly
in
the harbour, especially
with
respect to the "silent"

experiments.
The
"sail i
ng
" experiments
were,
of course,
performed
at sea,
preferably
in
deep
water.
ype
Length
Dead
Propeller
a.o.
Weight
Diameter(D
p
)
Blades(Z
RPM(N)
Speed(V
s
)
(m)
tonnes
(m)

(during
trials)
knots
1.
container
225,83
•
32825
7,0 5
110
22,9
~.
cargo 82,0
3500
3,1
4
143/195
10/13
~.
cargo 82,50
3650
3,2 4
183
l3,4
~.
coaster
65.82
1567
1,75 4
387

9.5
~.
coaster
65.82
1567
2,10
(cp)
3
296
10,6
~.
oceanogr.
84,00·
2800
3,4 6
120/160
12,3
vessel /15,6
7
. ro/ro .
196.53
40000
6,5
4 87/99/108 15/17/19
container
/117
20,5
2
frigates
(twin-screw)

TABLE
1:
Characteristics of ships
which
have
been
investigated
Not
in
all cases the data
of
the ships could
be
obtained, especially
con-
cerning the propulsion.
Mostly
the size
of
the ship is
known
and
something
about the
geometry.
but
little
about
the propulsion configuration.
The

res i stance
and
the
propul
s i
on
power
were
cal
cul
ated accordi
ng
the
method
of
HOLTROP
[15J.
From
these data the optimum blade area
and
pitch
can
be
calculated.
It
has
assumed
that
for
normal

propellers a
Wageningen
B-design
could
be
adopted
and
the
MCR-power
could
be
calculated.
These
parameters
were
necessary to obtai n the relevant parameters,
on
whi
ch
the source
strength depends.
7
5.
HYDRODYNAMICAL
PARAMETERS
It
is
expected
that
a 1 arge

number
of
hydrodynami
ca 1 parameters
wi
11
playa
role
in
the generation of
cavitation
noise.
With
the
aid of a
sta-
tistical
regression the relevance of these parameters
has
been
analysed.
Geometrical
variables,
whose
influence
has
been
analysed
are:
prismatic

coefficient,
number
of
propeller
blades
Z,
thrust
coefficient
KT,
torque
coefficient
KQ,
thrust
coefficient
KT/J2
(where
J =
ratio
of advance
VA/nD
p
,
VA
=
effective
flow
velo~ity~,
torque
coefficient
(KQ/J5)0.25,

Froude
number,
Reynolds
number,
cavltatlon
number
0,
etc.
ThlS
klnd
of parameters has
been
studied
and
from
this
statistical
analysis
it
can
be
concluded
that
only
two
parameters are important
[19]:
The
logarithm of
the

dimensionless
power:
K'Q
=
19
(KQ/J5)0,25
0,25
19
(2
'IT
P
s
.n
2
/
P.
VA
5
)
VA
=
(1
- w).V
s
(effective
flow
velocity)
Vs
= ship speed
w =

effective
wake
field
value
and
a parameter about
the
blade geometry: cf.
HOLDEN
[10]
F =
(AE/AO)N
(AE/AO)A
where:
(AE/AO)N
reference blade area
ratio
according to
HOLDEN
[10J
1,9.(0,235.0+
0,063) * (1,067 -
0,23.(P/D
p
)0,7)
(AE/AO)A
= actual blade area
ratio
(P/D
p

)0,7 = pitch/diameter
at
0,7 of the radius
o =
cavitation
number
(Po
- P
v
) /
{!
P
(V
2
A + (0,7
'IT
.n.D
p
)2}
The
factor
F i
ndi
cates
how
far
a
cav
i
tat

ion
criteri
urn
has
exceeded.
The
ref
erence blade area appears
to
be
a funct i
on
of
the
thrust
coeffi c i
ent,
cavitation
number,
the
effective
wakefield
and
the
pitch.
The
larger
the
value of F the
stronger

the
propeller
cavitates.
The
most
significant
parameter K'a gives
an
indication
about the
quality
of the propulsion con-
figuration.
It
is
a measure
for
the
propeller
load.
The
larger
the value
the
more
the
propeller
is
loaded.
In

the various speed conditions of the
sh
i p K I Q does not vary very
much.
The
quantity
(KQ/
J5) 0.25
is
related
to
8
the parameter B
p
,
well-known
in
1
iterature.
We
should consider
it
a
variable
which
indicates the
difficulty
in
the design.
It

is
not
so
understandable that only these
two
parameters describe the noise generated.
We
would
expect that the wakefield
and
the
Reynolds
number
to
be
more
significant parameters.
6.
VOLUME
VELOCITIES
The
values
of
the
volume
variations determined
forthe
various ships are
frequency-dependent,
but

an
average value
with
respect to a
wide
frequency
band
could
be
a
meaningful
quantity to
compare
various designs [18J.
It
is
evident
that
the smaller the propeller, the smaller the cavitation
volumes
to
be
generated
become.
Therefore
it
is necessary to
make
it
dimensionless

by
dividing the
volume
velocities
by
the factor
n.D
p
3
(n
= rotation
speed
(s-I);
Dp
= propeller diameter.
This
removes
in
the
volume
velocities,
in
any
case factors
wh
i
ch
are related to the size
of
the

prope
11
er
and
the
rotation speed.
L ' U (
i)
L U (
i)
-
20
1 g
(n.
D
p
3 ) ,
frequency
band
number
L'U(i) propeller size corrected
volume
velocity level
The
volume
velocity
depends
heavily
on
the blade-rate frequency

of
the pro-
peller.
Since for every propeller
this
blade-rate frequency
lies
in
a
dif-
ferent 113-octave
band,
it
appears necessary to
shift
all the frequency
scales to
one
reference I/3-octave
band
in
which
all the blade-rate
fre-
qiencies coincide.The transformation is
such
that the I/3-octave
band
with
the lowest blade-rate frequency is assigned the

number
1.
L'UBF(j)
L'u(i)
where
j i -
BF'
+1
BF'=
Ent(lO
19
fo
+ 0,5)
L'UBF
= frequency shifted
volume
velocity level
j =
band
number
of
shifted 1/3-octave-band
i =
band
number
of actual 1/3-octave-band
BF'=
band
number
of

1/3 octave
band
of
blade-rate
fo
= blade-rate frequency
(=
NZ/60)
It
is
an
interesting question
whether
the
volume
velocity
or
the radiated
acoustical
power
is the
fundamental
physical quantity
which
describes the
acoustical process. Acoustical
power
can
be
related to the

mechanical
power.
In
thi s
way
a proper
compari
son
between
shi
ps
wi
th different pro-
pulsion
powers
can
be
justified.
Since the acoustical
power
contains a fac-
tor
f2
when
related to tne
volume
velocity
we
have
to include a frequency

correction, since
Wac
=
TI
.p.U2.f
2
/c.
Because
we
have
made
a
transfor-
9
mation
with
respect to the lowest blade frequency
it
is essential to
include
now
a correction
on
the levels
by
the frequency
shift.
L"UBF(j)
L'UBF(j)
+

20
19
fo
where
L"UBF(j) = frequency-corrected
volume
velocity level
So
the
val
ues
of
the
vol
ume
velocities are transformed
by
three opera-
tions.
cf. Fig.
2:
*
make
the
volume
velocities dimensionless;
* a frequency transformation to e 1
imi
nate the infl
uence

of
the blade
rate frequency;
* corrections
of
the levels
in
view
of
similarity
of
radiated
power.
7.
STATISTICAL
METHOD
The
linear regression
has
been
carried
out
with
the aid
of
the for-
mula:
L"UBF
= Clj·
K'Q

+
C2j·F
+
C3j
The
values Clj.
C2j
and
C3j
have
been
determined
in
two
steps,
which
were
repeated a
number
of
times.
Firstly:
L"UBF
-
C2j·F
with
K'Q
as
the parameter
with

the application
of
weighting.
From
this
we
find the value
of
Clj;
Secondly:
L"UBF
- Clj.
K'Q
with
F
as
the parameter without the application
of
weighting.
This
leads to
the coefficient
C2j
and
C3j.
The
weighting
was
necessary
because

some
ships
were
investigated at
more
than
one
speed.
The
parameter
K'Q
is a typical parameter
dependent
on
the
quality
of
the propeller design while F is a typical parameter concerning
the rotation
speed
of
the propeller
and
its
cavitation behaviour. F is
characteristic for the observation proper
and
not
for the ship. while
K'Q

is
very
much
ship dependent. Therefore
we
have
to include a weighting fac-
tor
which
corrects for the fact that
sometimes
more
than
one
measurement
has
been
obtained
aboard
one
specific ship.
The
weighting factor
has
been
calculated
so
that every ship counts equally. independent
of
the

number
of
the observations
of
a particular ship.
10
The
weighting factor is defined
as
follows:
weighting factor
(j,k)
N (obs.,
total)
N
(ships,total)
=
N (obs.,ships)
N (obs.,
tot
a 1 )
N(ships,
total)
x N(obs.,ships)
weighting factor
of
the observations
of
ship k
in

frequency
band
j
total
number
of
observations
in
the
frequency
band
j
total
number
of
ships
in
band
j
total
number
of
observations
on
ship k
and
frequency
band
j
For

the determination
of
F the weighting factor is
always
one.
Every
obser-
vation
is
equally
dependent
on
this
factor.
For
the factor
K'a
is
this
dif-
ferent since
this
factor
is
very
much
dependent
of
the type of ship.
8.

PREDICTION
FORMULA
The
volume
velocity
in
third-octave frequency
bands
of a
fictitious
equivalent
monopole
in
the position
of
the
upper
part of the blade
in
the
upper
position
can
be
approximated
by
the following equation:
LU
(i)
= Clj . (K'a) +

C2j
. F +
C3j
+
20
19(n. D
p
3)
-
20
19(n~Z)
i = j +
BF
I - 1
in
which
the coefficients CIj,
C2j
and
C3j
depend.
on
the frequency
bands
relative
to the blade-rate frequency
band
(for
which
j = 1)

as
follows:
j
CIj
C2j
C3j
(band
number)
5 30,83
16
52,79
6
31,71
20
51,92
7 36,20
10
63,28
8
44,67
5
68,40
9 48,22 0 68,04
10
39,29 0 63,12
11
26,93 0
60,67
12
38,40 0 56,91

13
47,26 0
54,97
14
59,41 0
56,25
15
50,05
0
51,20
16
25,45 0 45,07
TABLE
2:
The
values
of
the various regression coefficients
11
The
table presents
results
for frequency
bands
larger
than
the
second
har-
monic

of
the blade
rate
frequency (j=4).
It
was
possible to
go
lower, but
we
did
not
have
enough
data to support the
statistical
results.
9.
COMPARISON
OF
MEASURED
AND
PREDICTED
SOURCE
STRENGTH
Taking
the
above
mentioned
formula

it
is
possible to calculate again
the
volume
velocities for a ship
which
has
been
part
of
the collection.
We
can
compare
in
this
way
whether
the
statistical
regresssion analysis leads
to acceptable "prediction" (Figs. 3).
The
agreement
of
the calculated data
with the
measured
ones

is
satisfactory
for
most
ships.
Of
course
we
must
realize
that
this
kind
of
calculation
has
limited
validity
and
proves
nothing
about
the regression analysis
itself.
The
ro-ro container ship
(No.7) is a typical
example
where
the

peak
of
31,5
Hz
is
very outspoken.
It
is
quite
unusual
for the fourth
harmonic
to
be
so
strong.
In
this
way
the
model
appears
not
to
be
so
adequate.
Also
the
results

for the
oceanographic vessel (No.6) are disappointing.
The
propeller
was
fairly
large, 6-bladed with
relatively
thick blades.
Only
a tip-vortex
was
visible,
no
sheet cavitation.
The
noise levels are
much
lower
than the
calculated ones, especially for the
low
frequencies.
An
interesting question
remains
the
sensitivity
of
the predictions.

Four
variables are important:
20
19
(n.Dp'
3
),
20
19
(n.Z),
K'Q,
and
F.
These
variables
show
some
spread,
expressea
in
the standard deviation. If
this
value for
each
variable
is
multiplied
by
the coefficient averaged for
a

11
frequency
bands
we
obtai n the average
devi
at i
on
of
the cal
cu
1 ated
volume
velocities
in
dB
as
the
results
of
the standard deviations
of
the
various variables.
variable
SD
coefficient
SD
x coefficient
20

19
n.D
p
3
5,9
1 5,9
(dB)
20
19
n.Z
3,4
1
3,4
F 0,21 ca.
10
2,1
K'Q
0,22
ca.
40
8,8
TABLE
3:
Mean
deviation
of
the calculated
volume
velocities
in

dB
as
the
results
of
the standard deviation
of
the variables
of
the
prediction
method
The
interpretation
of
the data gives
some
information
on
the importance
of
each
vari
ab
1 e.
The
size
of
the propeller appears important.
Thi

sis
quite understandable, since
it
is the
major
factor for scaling.
The
factor
K'Q
appears also to
be
significant.
This
is
less understandable.
Especially at the
high
frequencies
this
variable predicts the values
of
the
volume
velocities apparently
very
well.
There
are
no
specific

arguments
to
support
this
fact.
Maybe
the physical
background
of
the high-frequency
noise generation
has
not
been
explained
sufficiently
yet.
The
factor F is
only important for the
low
frequencies.
This
is
most
probably
due
to the
fact
that

a
high
value
of
F agrees with
an
outspoken
sheet cavitation with
strong low-frequency deterministic
components.
12
Another
way
of
checking
the accuracy
of
the prediction
method
is
to calcu-
1 ate the infl
uence
of a rather
diffi
cult
parameter 1
i.
ke
the

wake-
field
w.
Assume
that the quantity takes values
between
0,4
and
0,9
(mean
value 0,6).
As
given
above
this
factor is included
in
the effective velo-
city
VA
and
this
quantity
is
also included
in
both
the factors
K'Q
and

F.
Calculations learn that the variation
in
volume
velocity level
is
about
3
to 4
dB
around
the
mean
value
in
all frequency bands.
In
view
of the uncer-
tainty
of the value of the wakefield
we
may
conclude that
it
still
leads to
an
acceptable spread
in

the
volume
velocities.
The
best'way to
check
the validity
of
the
method
is
to
measure
the
volume
velocities
aboard
a
number
of
other ships outside the collection
and
to
compare
the calculated data
with
the experimental ones.
We
have
chosen

three dredging ships,
which
were
measured
after
the period
in
which
the
present
method
was
developed
by
J.A.
Wind.
The
following table gives the characteristics of the three ships.
Ship
Length
Prope
11
ers
Speed
P
s
a.o.
(2x)
(knots)
(kW)

(m)
Blades
Diameter(D
p
)
RPM
Vs
(z)
(m)
N
10
112,5
4 3,4
180
15
2x3400
slight
skew-back
11
79,0
4
2,4
1230
11,6
2x838
moderate
skew-back
12
113,6
4 3,4

1175
13,7
2x4265
heavy
skew-back
TABLE
4:
Characteristics
of
three dredging ships
All
three ships
have
a twin-propeller propulsion configuration.
The
volume
velocities
have
not
been
determined
by
the above-described reciprocal
method,
but
with the aid of the hull-plate response.
This
method
is
experi-

mentally simpler
and
has
recently
been
developed
by
TPD
.
The
results are
in
good
agreement
with
those obtained
by
the reciprocal
method
as
has
been
checked
with a
number
of
ships.
The
results for the dredging ships are presented
in

the Figs. 4.
The
ship
with
the rather conventional propeller design gives the
most
satisfactory
results.
The
agreement
with
the "predicted" values is encouraging.
The
next
ship
had
a propeller design
with
some
skeW-back.
The
results
are already
somewhat
disappointing
in
the
low
frequency region.
The

last
dredging ship
gave
experimental results
much
lower
than the predicted ones.
It
is
evident
that the
skew-back
propeller
has
a
geometry
which
falls
outside the collec-
tion of propellers
in
the semi-empirical
method.
The
difference
can
be
apparently
more
than

10
dB
in
a
broad
frequency-range.
13
This
was
also observed
on
two
sister
ships:
PASADENA
and
PATAGONIA
[17J.
The
first
ship
had
a conventional 4-bladed propeller, while the other
one
had
an
advanced
skew-back
des
i

gn.
For
both
sh
ips the pressure vari at ions
on
the hull-plating
up
to the 6th
harmonic
have
been
measured.
Also
in
this
case a remarkable difference
in
the pressures
was
been
observed.
10.
DISCUSSION
AND
CONCLUSIONS
Although
the
number
of

ships
in
the
statistical
collection
was
quite
limited
we
believe
it
was
sufficient to
develop
a.
reasonably
reliable
pre-
diction
method.
A strong point
in
the analysis
was
that a
wide
range
of
ship types
was

taken into account.
This
makes
the
method
applicable to
dif-
ferent types
of
vessels.
The
disadvantage is that
it
makes
the prediction
less
reliable.
The
interpretation
of
the data is
still
difficult.
The
best
manner
to
start
a regression analysis is to take clear physical quantities
which

describes
the process adequately.
This
was
not possible
in
the present investigation.
The
noise generation
by
cavitation is
such
a complicated process
with
so
many
different,
sometimes
dependent, variables, that
an
a-priori
selection
of
important parameters is useless.
By
a careful
appl
ication
of
the

statistical
regression
method
with
many
meaningful
parameters
we
could
select
2 significant quantities.
It
is surprising that only a limited
number
of
parameters
appear
to
be
significant.
Fortunately
we
could reduce
the significant parameters to dimensionless
numbers,
which
seem
to
have
some

physical significance.
One
quantity is related to the propulsion
con-
figuration (K'Q), while the other
one
is related to the loading
of
the pro-
peller.
Skew-back
of
the propeller blade
was
not
included
in
the present
model
and
the
first
results
on
this
point
were
quite disappointing.
Maybe
it

is
possible
in
the future to correct
it
by
reducing the factor
Cj3
by
about
10
dB.
An
attractive
point
of
the present
method
is that
it
can
also
be
used
in
model
experiments.
All
quantities involved
can

be
made
dimensionless,
so
the experimental
results
of
this
kind
of
tests
can
be
used
to
update
the
present prediction technique.
The
following conclusions
can
be
put
forward:
*
*
*
It
appears possible to predict the acoustic source strength for pro-
peller cavitation reasonably accurately

with
the aid
of
the
above-
ment
i
oned
semi
-empi
ri
ca
1
method
in
a frequency range
from
30
Hz
and
500
Hz.
Below
that
lower
frequency
and
especially for the amplitudes
of
the blade-rate frequencies

we
refer to
HOLDEN's
method.
The
present
method
holds
for conventional propeller designs.
Skew-back
designs
need
more
attention
and
it
is
most
necessary to collect
more
information
about
the cavitation noise
performance
of
this
kind
of
propellers.
More

measurements
about
the source strength
of
propeller
cav
i
tat
i
on
both
on
full-scale
and
model
scale are
recommended
to refine the pre-
sent semi-empirical approach.
14
11.
ACKNOWLEDGEMENT
This
study
is
the
result
of extensive
programme
aboard

sea-going ship
concerning propeller noise,
which
started
already
in
1973.
Much
of
this
research
has
been
funded
by
the
TNO
Nati
ona
1
Defence
Research
Council
and
by
the Netherlands
Maritime
Institute/Netherlands Foundation
on
the

Coordination for
Maritime
Research.
Most
of
the
statistical
work
has
been
carried out
by
J.A.
Wind
as
a graduate research study for the
Department
of
Marine
Technology
of
the Delft University
of
Technology
in
cooperation
with
the
Institute
of Applied Physics

TNO,
Ship
Acoustics Section.
12.
REFERENCES
[1
J W •
H.
Is
ay
,
Kavitation
Schiffahrtverlag "Hanser",
C.
Schroeter &
Co,
1981,
Hamburg
[2J J.E.
Kerwin,
Marine
Propellers,
Annual
Review
of
Fluid
Mechanics
1986,
pp
367

-
403
[3J
W.
van
Gent,
On
the
use
of
lifting
surface theory for moderately
and
heavily
loaded
ship propellers,
NSMB
Publication
No.
536,
1977,
MARIN,
Wageningen
[4J
L.
Noordzij,
[5]
Pressure
field
induced

by
a cavitating propeller,
Int.
Shipbuilding Progress
~
(1976),
pp.
93
-
105
N.P.Tyvand,
Theoretical
model
for propeller
Paper
Gin
No
i
se
Sources
Milj0vardserien
1981:2
noise prediction,
in
Ships; I: Propellers,
Nordforsk,
[6J
D.
Ross,
Mechanics

of
Underwater
Noise,
Pergamon
Press,
New
York
etc.,1976,
p.276
[7]
N.
Brown,
Cavitation noise
problems
and
solutions,
Proceedings International
Symposium
in
Shipboard Acoustics,
1976,
Ed.
J.H. Janssen, Elseviers
Scientific
Publishing
Company,
Amsterdam,
1977,
pp.
21

-
38
[8J J.
van
der Kooij,
A.
de
Bruijn,
Acoustic
measurements
in
the
NSMB
depressurized
towing
tank,
Int.
Shipbuilding Progress
II
(1984),
pp.
13
-
25
[9J J.H. Janssen,
W.H.
Moelker,
Some
experiments
on

the transmission
of
propeller cavitation noise
into
ship's
structure,
Present proceedings
15
[10J
K.O.
Holden
,
O.
Fagerjord,
R.
Frostad,
Early
design-stage
approach
to reducing hull surface forces
due
to
propeller cavitation,
Transactions
of
the Society
of
Naval
Architects
and

Marine
Engineers
(SNAME),
Vol.
88
(1980),
pp.
403
-
442
[l1J J. Holtrop,
Estimation
of
propeller
induced
vibratory hull forces at the
design
stage
of
a ship,
RINA
Sympos
i
urn
on
Propeller
Induced
Shi
p
Vi

brati
on,
December
1979,
London,
Paper
no.
11
[12] C.E.J. Leenaars,
P.E.
Forbes,
An
approach
to vibrations
problems
at the
design
stage,
RINA
Symposium
on
Propeller
Induced
Ship
Vibration,
December
1979,
London,
Paper
no.

17
[13]
T.
Sasajima,
M.
Nakamura,
A.
Oshima,
Model
and
full-sca)e
measurements
on
propeller cavitation
of
an
oceanographic research ship
with
two
different propeller designs,
Present proceedings
[14J
L.
Thiele, J.
~degaard,
Underwater
noise
from
the propellers
of

a
triple
screw
container ship,
Report
82.54,
0degaard
&
Dannesk
i
~l
d-Sams
~e
K/
S,
Copenhagen,
November
1983
[15J
J. Holtrop,
G.G.J.
Mennen,
A
statistical
power
prediction
method,
Int. Shipbuilding Progress
25
(1978),

pp
253
-
256
[16]
N.R.
Draper,
H.
Smith,
Applied
regression analysis,
John
Wiley
&
Sons,
New
York,
1981,
2e
edition
[17J
G.
Bar.k,
C A.
Johnsson,
Prediction
of
cavitation noise
from
model

experiments
in
a large cavi-
tation tunnel,
Paper
F
in
Noise
Sources
in
Ships;I: Propellers, Nordforsk,
Miljovardserien,
1981:2
[18J
A.
de
Bruijn,
Acoustic
source strength
of
propeller cavitation,
Proceedings
INTER-NOISE
79,
Warzawa,
Paper
115
-
C,
pp

659-664,
1979
[19]
J.A.
Wind
Investigation into the empirical relation
between
the acoustical
source strength
of
cavitating ship propellers
and
ship
hydrodynamical
parameters (in
Dutch)
Delft University
of
Technology,
Department
of
Marine
Technology,
Laboratory of
Ship
Constructions,
Report
No.
265,
November

1983.
16
,
LU
in
dB
rf
10-
6
LU
in
dB
rf
10-
6
.3/
s
(1/3
oct
. )
f
t
60
1
00
SO
'
~
\
rv

~
2
III
I
\
\ !
(I)
90
40
\
'1\
1
r'
80
30
70
20
\
~
60 10
16
63
250
16
63
250

Freque n
cy
in

Hz

F reque
nc
y
"
- 6
LUBF
i n dB re 10
in dS re 10-
6
,
j"
SO
~
___
~
~
______
+-
____
~
;
t
90
BO
70
60
3'0
1 +-

~ \ 1
j
50
20
~
+-
-
r-~-4 ;
40
10
L-
___
~
____
~
__
~~
1.
'0
2.
3.
+
+
+
30
-c-
o
10 15
0

5
10
___
Transformed f r
equency
band
nu.bfr
________
Fig, 2: Trans ormation
of
the
vo~ume
ve~oeitie
in
dimensionZess, frequen y-
shi
ted
and
orreeted
quantities
(2
hips)
.
-b-
in
Hz
15