Report 977-P, Keuning, J.A

DYNAMIC
BEHAVIOUR
MONOHULLS
J.A. Keuning
F.H.H.A. Quadvüeg
Report No. 977-P
May 1993
RINA-Symposium
OF
FAST
RINA
INTERNATIONAL CONFERENCE
on
HIGH SPEED PASSENGER CRAFT FUTURE DEVELOPMENTS AND THE NORDIC INITIATIVE
LONDON
15 16 June 1993
© 1993 The Royal Institution of Naval Architects
The Institution is not, as a body, responsible for the opinions
expressed by the individual authors or speakers.
THE R O Y A L INSTITUTION O F NAVAL A R C H I T E C T S
10 Upper Belgrave Street,
London, S W 1 X 8 B Q
Telephone: 071-235-4622
Fax: 071-245-6959
INTERNATIONAL CONFERENCE
o n
HIGH SPEED PASSENGER CRAFT FUTURE DEVELOPMENTS AND T H E
NORDIC INITIATIVE
15 16 JUNE 1993 LONDON
PROCEEDINGS
THE ROYAL INSTITUTION OF NAVAL ARCHITECTS
10 UPPER BELGRAVE STREET, LONDON, SWIX 8BQ. Telephone 071-235-4622
DYNAMIC BEHAVIOUR OF FAST MONOHULLS
by:
J . A . Keuning
Delft University, Ship hydromechanics 1-aboratoty
F . H . H . A . Q u a d v ü e g Maritime R e s e a r c h Institute Netherlands
SUMMARY:
A non-linear computational model has been developed to calculate the heave and pitch motions of planing ships in
irregular head w a v e s .
The
computational model is based on the previous model as presented by Z a r n i c k [1] i n 1979. T h i s model has been
extended
significantly to be able to handle the behaviour of planing craft in irregular w a v e s . F o r this purpose a "wavemalcing" routine has been
added w h i c h malces it possible to calculate the w a v e elevation along the length of the ship any time corresponding to a predetermined
w a v e spectrum.
I n addition polynomial expressions for sinlcage and trim of fhe craft at speed have been developed based on a n extensive series o f
model experiments with a systematic series of planing hull forms. I n a new computational routine fhe resulting sinkage and trim are
being used to asses fhe pressure distribution over the length of the planing model at speed. T h i s determines fhe relative magnitude of
the hydrostatic and hydro dynamic part of the lift.
T h e formulations used for the determination of the added mass and the w a v e exciting forces h a v e been examined and extended fo
become dependent fo fhe geometry o f fhe craft in actual contact with fhe waves while performing large relative motions.
A computer code has been developed fo solve fhe non-linear equations in the time domain. T h e results have been extensively verified
with experimental resuits derived from tests in the Delft T o w i n g T a n k .
F i n a l l y it will be shown that a proper formulation of fhe limiting criteria with respect to workability o f a craft is o f great importance on
the final outcome of an optimisation and this determines whether a linear or a non-linear calculation method may be used.
the
1 - INTRODUCTION
bow
shape
and
flare,
more
particular
the
geometry o f the hull above fhe still waterline.
fhe d y n a m i c lift developed by the planing bottom,
the sinkage and trim o f the c r a f l at speed,
During the last decades a growing interest i n fast ships may be
noticed. I n particular the possible fulfilment o f existing needs
forces related fo fhe large relative motions,
in the field of fast transport of light and expensive cargo, fhe
the effects of high forward speeds.
transportation of passengers at high speeds and the possible use
for surveillance and patrol functions has drawn considerable
Most o f these parameters and phenomena are the cause of
interest o f both shipowner, designers and researchers to faster
important non-linearities in fhe equations describing the forces
ships. A l l kind o f so called "advanced" concepts h a v e been
and motions.
developed of w h i c h the planing craft, the catamaran, fhe air
T h i s makes the u s e o f fhe commonly used calculation routines
cushion vehicle, the surface effect ship, the small waterplane
for ships moving with forward speed in w a v e s ,
area twin hull ship and the hydrofoil should be mentioned. A l l
based on fhe so called linear strip theory method, less ap-
w h i c h are
these concepts were aimed af high speeds and possibly high
plicable.
sustained speeds in a seaway. C o m p a r e d fo the planing boat ail
So a computational model has been developing w h i c h takes
other concepts are more complicated and often in the need for
those effects info account. It w a s in fhe scope of this project to
a "ride control" system fo improve their seakeeping behaviour.
derive for ail phenomena involved an exact formulation for use
This
and
within the foreseen setup o f fhe present computational model,
therefore usually more expensive. I n particuiar the reliability of
but emphasis has been placed on a qualitative correct prediction
fhe ship seen from an operating point of view, makes these
o f the effect of fhe predominant parameters under consideration
more
on fhe performance of the pianing hull in w a v e s .
fends
fo
m a k e these concepts
complicated
concepts
more
economically
complicated
less
attractive.
T h e r e f o r e there remains a place for fhe relative "simple" and
well-proven concept o f fhe planing boat, i . e . , the fast monohull,
in fhe foreseeable future. Considerable effort however
2 - COMPUTATIONAL MODEL
should be put in opfimising the seakeeping capabilities of the
fast planing monohulls.
T h e basis of the presented non-linear computational model is
F r o m experience it is k n o w n that fhe heave and pitch motions
formed by the w o r k of Z a r n i c k ( R e f 1.) as pubiished in 1979.
and more in particular the vertical (bow) accelerations aboard
H e formulated the computational model for fhe heave and pitch
the ships in head seas are the limiting factors with respect fo
motions of a hard chine planing craft with constant deadrise
the seakeeping capabilities of planing boats. T h e r e f o r e fhe need
over the length of the ship in regular head waves.
for
ac-
A short summary o f this model will be presented here. F o r a
celerations o f these fast monohulls in irregular w a v e s is ob-
a
suitable
prediction
tool
for
these
motions
and
more detailed description of fhe computational model reference
vious to be able to optimise their seakeeping behaviour and
is made to ( R e f 2 . ) .
with that their operability.
T h e model is a non-linear strip theory approach, i n w h i c h fhe
T h i s prediction fool should properly incorporate the effect of
hull
fhe p r i m e parameters and phenomena
transverse strips with assumed constant cross sectional shape.
motions
so particular for the
in w a v e s o f these planing boats.
These were
con-
sidered fo be, amongst others:
is
in a number ( i . e . ,
20)
of
T h e coordinate used is presented in F i g u r e 1, representing the
ship in a steady state equilibrium position af constant forward
speed.
the deadrise distribution over the length of fhe hull.
divided over the length
where:
the orbital velocity of the water,
Z; the instantaneous position of strip i,
i the position o f the strip.
A c c o r d i n g to Wagner's formulation the dynamic lift is considered to originate from the change of momentum o f the incoming
fluid and a cross flow drag force on the section.
Elaboration o f the equations for the dynamic and static lift
forces and moments yields:
Figure I
Coordinate system used.
+ cos$ [-MJ(xcos$-zsme)+
m^—lcosBdi-
m^w^esinddi
Altliougli tlie mathematical justification for using a modified
striptheory is not very rigorous, both Z a r n i c k and IVIartin (Ref.
3 . ) obtained results for the motions in regular waves w h i c h
compared w e l l with measured values.
T h e equations of motion for heave, pitch and surge are written
as:
^^CG = Tcos(e+e)
MzcG
= -Tsm(e+e)
Id =
- Nsine
-
DcosB
- AfcosS -
+ Aft, + Bjx^ -
+ Dsinff + W
(1)
Dxj
in w h i c h : T represents the towing force,
D the drag force
N the hydrodynamic lifting force
the buoyancy force
M the mass o f the ship
B y assuming constant forward speed, the acceleration along the
in w h i c h :
X - a x i s may considered to be z e r o . I n the present formulation
-NCOSS-BL
this simplification w i l l be made, although its omittance is a
NX^-I-BLX|,
development foreseen in the near fiiture.
Mj,
B
actual pitch angle
T h e total lift force on a strip of the ship is determined by:
w^
vertical component orbital velocity
dF =
- C o , , pbV''
)cosff
(2)
-at^pgA
total vertical force
total pitching moment
total added mass
I
length coordinate body fixed axis
k,
added mass correction factor
I n the formulations the instantaneous wetted beam and submerin w h i c h : d F
ma
v
the force per strip
ged cross sectional areas o f the sections are being used resul-
the added mass of the strip
ting firom the actual momentaneous relative motion o f each
the vertical velocity in the plane of the
section as a combined result of heave, pitch and w a v e elevati-
cross section
on. T h i s implies that the w a v e elevation at each time along the
length of the forward moving craft must be k n o w n i n irregular
cross flow drag coefficient
instantaneous
half
beam
of
the
strip,
submerged
cross
sectional
wave
generator
is
being
build
into
the
M o s k o w i t z or a measured spectrum. T h e irregular w a v e train
is being simulated using a random phase model according to;
area
g
a
frequency domain according to the formulations of Pierson-
buoyancy correction coefficient
instantaneous
Hereto
program, using either the w e l l - k n o w n energy distribution i n the
including "pile up"
A
waves.
w
acceleration due to gravity
i{x,t)
=
« , sin(co,./ + V
+ <i>i>
^"^
T h e buoyancy correction coefficient accounts for the difference
between the actual pressure distribution over the
submerged
part of the h u l l , composed of hydrodynamic and hydrostatic
pressure, when compared with the "lift" force arising from an
I n addition also the vertical and horizontal orbital velocities are
assumed hydrostatic pressure distribution over the submerged
being calculated as a function of time (t) and place (x) along
volume.
the length o f the model using
T h e velocity components U and V of the relative motion of the
^
coshfc,(/i+z)
water along the hull resulting f r o m the forward velocity of the
craft, the heave and pitch motions and the orbital velocity i n
the w a v e s may be written as:
V = HcG
- w ^ c o s f l +xsm9
U = i c o s f f - ( Z c G - W j ) sine
(8)
v(«,0 =
£^
(3)
sinhfc,.(/i+z)
— . . • , cos(co,.f+/:^+0;)
SlDnK^l
(4)
in w h i c h :
N
number of components
amplitude of i"" component
frequency o f i"" component
w a v e number i * component
h
water depth
91
phase
empirical formulations for the pressure distribution over the
length
of
the planing bottom
as
derived
from
model
ex-
periments with planing wedges. T h e s e expressions h a v e been
Using
the
water
formulated among others by Sottorf ( R e f . 5 . ) , Sedov ( R e f . 6 . ) ,
generated
Shufold ( R e f . 7 . ) . Savitsky ( R e f . 8 . ) used these formulations for
using a random phase generator for the phase of the different
the determination o f the running trim of a planing craft at
waves,
well-Itnown
dispersion
relation
for
deep
the time history of the w a v e elevation is
components.
speed. Z a r n i c k derived the u n k n o w n coefficients a.^[,
I n the simulation program the vessel is moving with a constant
C q „ using these formulations and used those values in the
and
equations of motion describing the c a l m water condition, i.e.,
speed against these w a v e s .
by omitting any w a v e induced term. B y doing so a steady state
equilibrium position is obtained, w h i c h is used as the reference
2.1
position for the motions of the craft in w a v e s . T h e validity of
Steady State Planing Condition
the values o f the coefficients obtained from planing wedges
In the case o f ships advancing at relative high forward speeds,
with mostly constant deadrise remains uncertain and the results
it is Icnown that the sinkage and trim of the crafl may become
of sinkage and trim obtained by this method are often in no
quite substantial. T h e radical change in reference position, i.e.,
good agreement with measured values.
the position around w h i c h the craft is supposed to perform its
the
I n the present computational model the procedure is reversed:
following modifications with respect to the equations o f motion
instead of determining a^f, C p , and k^ f r o m experiments with
wave
induced
motions,
implies
among
other
things
describing the dynamic behaviour of the craft in waves:
planing wedges, the value o f these coefficients is determined
the existence of dynamic lift resulting from the high
using a calculated value for the sinkage and trim o f the particu-
relative water velocity over the inclined bottom
lar planing craft under consideration at a given speed. T h e
a change of the submerged geometry
sinkage and trim are obtained from polynomial
of the craft
w h e n compared to the zero trim, zero sinkage and
expressions
derived from an extensive series of model tests with a large
systematic series o f planing hull forms. T h e parent model of
zero speed situation.
Both effects account for part o f the non-linear behaviour of the
this series w a s the 12.5 degrees deadrise model used by C l e -
craft at speed in w a v e s and are not accounted for in the usually
ment and Blount ( R e f . 9 . ) w h o tested this model in 1963 with 5
T h e introduction of these non-linearities
different length to beam ratio's, 4 different displacements and 4
into the computational model may be performed in different
different longitudinal positions of the centre o f gravity. T h i s
used linear theory.
systematic series has been extended by K e u n i n g and Gerritsma
ways:
in 1982 with a similar series with 25 degrees deadrise (Ref. 10.)
First,
one
could account only for the change
in reference
and in 1992 with 30 degrees deadrise ( R e f . l 1.).
position (sinkage and trim) and u s e the changed geometry as an
T h e bodyplans o f the three parent models of these series are
input in the otherwise linear calculations. T h i s has been done
presented in F i g u r e 3 .
among others by Beukelman ( R e f 4) and it yields improved
correlation with model experiments in comparison with calculations using the zero speed reference position. It is obvious that
the introduction of the reference position i n this manner only
accounts for the change in geometry o f the submerged hull and
not for the change in pressure distribution. S e e F i g u r e 2 .
20 k n
,
Trim /,/t8
with rtUfenct
posiVion
i^^tA
Pitch
20
L
10
THtn-o.si
1
w l l h z e r o sfieed
r « ( e r - e n c e position
>.
F i g u r e 2 . Influence o f reference position on the pitch motion of
planing craft, using linear strip theory.
Figures
Bodyplans
of
the
12.5,
25.0
and
3 0 . 0 degrees
deadrise systematic planing hull form series.
T h e reference position of the craft at speed is obtained in this
particular case from results of a model experiment.
T h e parameters used in the polynomial expressions are:
the length to beam ratio over the chine
the weight of displacement related to the projected
Another method w a s followed by Z a r n i c k . H e made u s e of the
area of the planing bottom
the deadrise angle at midship
the longitudinal position of the centre o f gravity.
Force (N/m)
T h e polynomial expressions have been derived using a least
square fitting routine through the data for a number of specific
500
volumetric F r o u d e numbers and have the following form:
0
Ig
2Vg^
3Vg^
4^2/3
5^y2/3^
«^y2/3^
V'/3
A n interpolation routine is being used for intermediate values
of the deadrise angle between 12.5, 2 5 and 30 degrees.
A typical example o f the goodness o f fit of the polynomial
approximation compared with measured daUi o f a model not
belonging to the systematic series is shown in F i g u r e 4.
Figure 5
L i f t force distribution over the length of the model.
F r o m the formulations used for the dynamic lift it is obvious
that the change of sectional added mass over the length plays a
predominant role. Since in this calculation procedure the added
mass is being related to the wetted beam of the sections and the
beam is generally reducing i n the aft body of a planing hull, a
"negative" dynamic lift may occur in the aft body. T h i s trend
is not confirmed by data from literature. A s stated by P a y n e
(Ref. 12.) by using a different formulation for the added mass
0.,
h
of the sections with a wetted chine this phenomenon may b e
eliminated. I n the present formulation the negative slope of the
added mass is neglected i f it occurs and the hydrodynamic lift
set to zero for these sections.
-0.2
0.<
0
0.3
1.2
I.C
J
1.*
2.2 Added Mass
2.3
Fn
A s may be seen from the equations derived for the lift forces
on the planing hull, the added mass of the sections plays a n
Figure 4
Measured and approximated sinkage and trim for an
arbitrary planing hull.
important role, since the derivative of the added mass over the
length of the hull determines the magnitude of the dynamic lift
to a large extend. I n the presented computational model
the
A c c o r d i n g to Shufold [7], the cross flow drag coefficient of a
added mass is considered to be a function of the momentaneous
section with deadrise jS may be approximated by:
wetted
= 1.33cos(3
(10)
I f the steady state still water equilibrium position is k n o w n as
beam of the
section
using
the Wagner formulation
corrected for the pile up o f the water according to:
m„ - K\pb^
(11)
is assumed now by making use of the derived polynomials, the
remaining u n k n o w n coefficients a^f and k,, may be determined
by solving the two equations of motions simultaneously.
i n w h i c h k j is a constant for all sections.
T h i s procedure has been used on a variety o f planing boat
designs of w h i c h model test data were available to yield values
Other methods to calculate the added mass and damping distri-
of a(,f and k j . T h e results for the parent models o f the sys-
bution over the length of a hull moving at high forward speed
tematic series are presented in the T a b l e 1.
are not available yet. S o for the calculation of these hydrodynamic reaction forces in those conditions use is generally
being made of a strip theory approach.
T a b l e 1.
T o check on the validity o f this approach a series of oscillation
Co.c = 1-33
30°
"bf
0.8526
0.6395
Model 277
25°
K
"w
0.8473
0.7206
Model 276
12,5°
K
1.2658
0.6239
Model 251
experiments with a segmented model of the parent of the H i g h
Speed Displacement H u l l F o r m series has been carried out by
K e u n i n g ( R e f . l 3 . ) at the Delft Ship Hydromechanics Laboratory. T h i s H S D H F series has been tested extensively at M A R I N
on resistance and motions in head w a v e s in a research project
CO-
sponsored
by the R o y a l
Netherlands N a v y , the
Royal
Australian N a v y and the D a v i d T a y l o r R e s e a r c h Centre ( U S A ) .
U s i n g these results B l o k and B e u k e l m a n (Ref. 14.) found quite
T h e resulting lift force distribution over Ihe length o f the model
is shown in F i g u r e 5 for one particular situation. It is obvious
that the dynamic lift prevails in the forepart o f the
wetted
length of the planing ship and the hydrostatic part aft. T h e lift
force due to the cross flow drag is of minor importance.
good correlation between measured and calculated heave and
pitch response operators of these models even at high forward
speeds (i.e. F n =
1.14) using a linear strip theory calculation
method.
F r o m the
presented
study
in
Reference
13.,
it
may
be
concluded that the introduction of the actual reference position
of the model at speed into both the experiment and the calculations was important for improving the agreement between
acceleiation/g
the measured and calculated data for the added mass.
Beyond this, the measured lift force distribution over the length
of the fast moving model in its proper reference position with
Bow acc (lims dep.)
respect to sinkage and trim has been brought into the procedure
used
for
the
determination
of
the
added
mass
from
' Bow acc (fixed)
tlie
•
•
•
•
• / ' ^ •/
i f / ^
• ^ C G acc (tiine dep.)
measured in-phase forces on the segments o f the model. T h e
CG acc (fixed)
lift force distribution over the length of the model due to the
•
forward speed and the change herein due to the change of
submergence of each section during the oscillatory motion has
been measured i n a quasi steady w a y . T h e time histories of the
force transducers of each section h a v e been elaborated using
-
r^^^"""!^
;
Model 276
these data to yield the added mass of each section. T h e derived
results show that the added mass of the sections, using this
d
method, becomes almost independent of the forward speed and
d
d
=
d
d
d
.d
d
W a v e f r e q u e n c y (rad/s)
the frequency of oscillation, ranging in that experiment from M
4 to (0 = 15 for a two meter long model.
A typical result o f these measurements is shown in F i g u r e 6.
The
results
of
these
measurements justify the
use
of
the
frequency independent formulation of Wagner for the added
Figure 7
mass.
By
Response operator bow vertical accelerations with
and without time dependent added mass.
using this frequency independent formulation for the added
mass, w h i c h is only based on the waterline beam of the section, it becomes easily possible to make the added mass time
dependent.
In
the
formulation the
momentaneous
2.3 Wave Forces.
waterline
beam o f the section based on the relative motion is taken into
A
the calculations.
forces, another source o f non-linear behaviour of a planing
Hereto use
is being
made
of
a
complete
geometry description of the ship from baseline to deckline.
similar approach has been followed with the w a v e exciting
boat in waves. I n assessing the limits of the operability of a
fast craft in w a v e s , one is more interested i n extreme motions
Trim
Based
- 1.62°
on a c t u a l
restoring
force
and
peak values of accelerations than in the extrapolation of
behaviour derived
from
otherwise
linear
calculations
with
infinite small amplitudes. T h i s implies that the large relative
Fn.
motions o f the craft with respect to the waves should be taken
=• L . 14
into account.
= 0, 01:
With the same segmented model of the H S D H F parent w a v e
force measurements h a v e been performed at high speeds,
1
1
Fn
= 0.57 and F n =
i.e.
1.14. T h e results of these measurements
showed that the w a v e forces w e r e dominated by the F r o u d e
K r i l o f f component. T h i s enables the introduction of the non•
linear parts o f these forces into the calculation procedure by
using the actual momentaneous submerged volume o f the craft,
due to heave, pitch and w a v e elevation, for the determination
of
the
Froude Kriloff
force.
In
this
procedure
also
the
geometry of the craft f r o m baseline to decldine is being used.
Z a r n i c k in his method turned to vertical sidewalls above the
chine. T h e influence of this on the calculated results for the
2 5 . 0 degrees deadrise model is shown in F i g u r e 8. It should be
noted that this influence extends in both the w a v e forces and
the added mass calculation ( and therefore the lift ) .
1
*.
Figure 6
Aco./g
1
torsion 2
•loasLiromont
Added mass distribution along the length of a model
at high forward speed.
To
illustrate the relative importance of the time dependency of
the added mass, figure 7 shows the response operator for the
vertical bow accelerations on the 2 5 degrees deadrise parent
model calculated with and without the time dependency of the
added mass.
2
3
4
5
Wave Frequency (rad/s)
Figure 8
Bow
accelerations
with
sidewalls above the chine.
and
without
vertical
It is important to note tliat tlie buoyancy correction coefficient
%l
4
OPERABILITY ANALYSIS
is also used in the determination o f the F r o u d e K r i l o f f
forces on the ship in waves. T h i s is an arbitrary method but
based on the assumption that the character of the flow around
the hull, i.e.
flow
separation at the chine and transom and a
stagnation line with spray area, on w h i c h the correction factor
is based, remains roughly unchanged. F r o m correlation with
experimental results this appeared to yield quite satisfactory
results.
O n e particular aspect of F i g u r e 10 should be emphasised a
little more.
A s may be seen from this
figure
the relation between the
significant and the m a x i m u m value o f the vertical bow acceleration is strongly dependent on tlie deadrise angle at ordinate
10 (midship) but rather on the deadrise of the whole planing
bottom,
since all three models used were derived from the
same parent and the distribution o f the deadrise over the length
of the ship is similar in a non-dimensional w a y . T h i s implies
3
VALIDATION
that there is a considerable discrepancy between the predicted
m a x i m u m value o f the vertical acceleration in an irregular sea
T h e computational model has been validated extensively using
using a non-linear or a linear theory. F o r the high deadrise
the data of model experiments carried out at the large towing
craft the relation between significant and peak value is roughly
tank
of
the
Delfl
Ship
Hydromechanics
Laboratory.
The
a factor of 2 , while for the low deadrise hull it may increase to
models used in the experiments were the three parent models
4 or 5.
o f the systematic series of planing hull forms, as depicted i n
U s i n g linear theory and assuming the w a v e heights to be R a y l -
F i g u r e 3 . T h e models have been tested in three different w a v e
eigh distributed, w h i c h is generally accepted
spectra of w h i c h the particulars are presented in table 3
ocean w a v e
statistics,
assumption i n
the m a x i m u m (or rather the
1/1000
wave) is approximately 2 times the significant value, both for
Table 3
the w a v e and the vertical acceleration. F r o m calculations it
appears that a linear strip theory motion calculation program is
Spectrum 1
H[/3 = 0.55 m
T p = 5.9 sec
capable to predict the significant values of heave and pitch o f a
Spectrum2
H,/3 =
1.10 m
T p = 6.7 sec
plamng craft i n a moderate w a v e condition quite reasonable.
Spectrum 3
Hy^
= 1.60 m
T p = 9.0 sec
T h e extrapolation to m a x i m u m values however may lead to
seriously underprediction of the peak accelerations.
T h e ship length is 15 meters.
A non-linear theory like the one here presented is capable o f
predicting the peak values quite reasonable using the
T h e speeds used
during the experiments
corresponded to
a
same
w a v e spectrum as an input.
volumetric F r o u d e number of 1.65 and 2.70 respectively.
T h e heave, pitch and vertical accelerations at the centre o f
S o , i f the operability of a planing craft is under consideration,
gravity and the bow have been measured and elaborated in the
it depends largely on the kind of limiting criteria that are being
usual w a y to yield significant values and maximum values.
used, what the outcome will be:
T h e results o f the calculated and measured vertical bow acce-
Most commonly the limiting criteria are based on significant
lerations are presented in F i g u r e 9 on a basis o f deadrise angle
values o f for instance vertical accelerations, because these are
at midship section.
rather easy to measure and to
calculate. I n particular say a
decade ago, no non-linear computational models were available
SpccCL-um I
to
designers
irregular
for assessing
waves.
The
the
motions
underlying
o f planing craft in
assumption
was
that
the
m a x i m u m values would be twice the significant ones (for all
craft similar) and these would
therefore not exceed
certain
values. F r o m full scale experiments on coastal patrol boats at
the Dutch North Sea coastal waters however, it was concluded
that rather the occurrence o f one peak value was the limiting
criterium for the voluntary speed reduction by the crew and not
signtficanc
the significant value.
T h i s may lead to a different outcome of an optimisation as is
Spcccrun
ÏII
shown by the results presented in F i g u r e 10, i n w h i c h the
results o f an operability analysis on a fast patrol boat are
shown. F o r the optimisation, the beam of the craft has been
increased and decreased by 10% and the effect on the operability is calculated using a scatter diagram from the North Sea
and the same limiting criteria. It should be noted that through
the change in beam while maintaining the depth a considerable
change in deadrise does occur.
0
S
10
IS
20
25
JO
3S
DoatJfise
Figure 9
Measured and calculated significant and m a x i m u m
vertical bow accelerations as fiinction o f deadrise.
Generally it was concluded from this validation study that the
agreement
between the measured and calculated values
heave pitch and vertical accelerations was in
although discrepancies still do occur.
for
good agreement,