20160105204036_2
TRANSCRIPT
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High Performance Yacht Design Conference
Auckland, 4-6 December,2002
THE EFFECT OF PITCH RADIUS OF GYRATION ON SAILING YACHT
PERFORMANCE
Peter Ottosson1, [email protected]
Mats Brown2, [email protected] Larsson
Abstract. Traditionally a racing yacht is designed with as low radii of gyration as possible, especially regarding the pitch radius. Asmall radius normally provides less relative velocities between hull and water and thus less added resistance. Recent model tests atSSPA with a sailing yacht in head seas have indicated that a minimum of the added resistance can be found for a certain radius ofgyration. The relation between the radius of gyration and the added resistance is of course best investigated by extensive model tests.
However this is expensive and time consuming. A cost effective procedure is to combine model tests with computer based velocity
predictions.
There are a number of different Velocity Prediction Programs (VPP’s) available around the world today. Most of them are based onequations of equilibrium, one for each degree of freedom, that are explicitly solved. These programs work well as a basis for the
judgment of the calm water characteristics for a sailing yacht. Many of them also have algorithms for estimating the added resistancein waves, which is normally based on regression formulas, derived from frequency based strip theory calculations.
At SSPA a time domain dynamic prediction program has been developed , a DVPP (Dynamic VPP), that provides possibilities tostudy also the dynamic characteristics of a sailing yacht. The input data are the same as for a conventional VPP, however, also the
hull form is entered in the form of sectional coordinates. The principles for the program is that all the horizontal hydrodynamic forcesare expressed in the same way as in the conventional program, however the velocities in the different degrees of freedom arecorrected for the wave particle velocities. Additional wave induced forces are also obtained from wave particle accelerations and by pressure integration over the whole momentary wetted surface.
1 M.Sc. (Naval Arch.), Project Manager, SSPA Sweden AB
2 M.Sc. (Naval Arch.), Project Manager, SSPA Sweden AB
3 Professor, Naval Architecture and Ocean Engineering, Chalmers University of Technology
NOMENCLATURE
Symbol Description Dimension
a44 Added mass moment of inertia
in roll
kg m2
AR k Effective aspect ration of keel -B Beam m
bk Double total span of keel,including hull and bulb
m
br Double span of rudder
b33(x) Vertical sectional dampingcoefficient
N/(m/s)/m
c Wave propagation velocity m/s
cK Mean chord of keel mCLk Lift coefficient on keel -cr Mean chord of rudder
Cs Local sectional area coefficient
E Energy Nmh Effective draught of section m
K z Roll wave moment, pos to stbd Nmk Wave number 1/mk peak Wave number for peak
frequency
1/m
Mz Pitch wave moment, bow up pos
Nm
Nz Yaw wave moment, pos for bow to stbd
Nm
m(x) Sectional vertical added mass kg/m
Pz(x) Sectional generated power W/m
p Roll rate rad/s p(s) Dynamic pressure N/m2
q Pitch velocity, pos when bow isgoing upwards
rad/s
R aw Added resistance N
r Turning rate rad/sswlf Short wave length factor -T Time Sec
ts Local sectional draught MV Boat velocity m/sVz(x) Sectional vertical relative
velocity
m/s
w Heave velocity, posdownwards
m/s
xsec Sectional x coordinates, relLCG
M
xkr Axial distance between keel
CE and rudder CE
M
Yw Lateral wave force, pos to stbd NZw Vertical wave force, pos down N
z Vertical coordinate, pos down m
αik Downwash angle at keel due tokeel circulation
rad
εcr Downwash angle on rudder dueto keel circulation
rad
εr Downwash angle at rudder dueto free vortex from keel
η Wave elevation, pos upwards mλ Wave length mµ Wave direction, 0 when rad
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coming from north
θ Pitch angle, pos for bow up radρ Density of water kg(m3 ω Wave frequency rad/sωe Encountering wave frequency rad/sψ Heading angle rad
ζ Wave profile mζa Wave amplitude m
1. INTRODUCTION
During 2001 extensive model tests were carried out forVictory Challenge for the America’s Cup. Parallel to thedifferent model test studies, work was also carried out in
order to develop a Dynamic Velocity Prediction Program(DVPP). The purpose of the program is to be able tostudy phenomena which are highly related to the
dynamic behaviour of the yacht, such as wind gusts,
waves, tacking procedures, etc.
Normally a VPP considers axial and lateral forces as wellas the heeling and restoring moments. The fullydeveloped DVPP comprise all six degrees of freedom, i.
e. surge, sway, heave, roll, pitch and yaw. When theVPP explicitly solves the forces of equilibrium, theDVPP solves the motions in a time stepping procedure.
The paper describes the model tests, on which parts ofthe DVPP development relies, as well as the
mathematical model in more or less detail. A limitedsystematic simulation study is carried out in order to
show the influence of different pitch radii of gyration onthe upwind performance. Another feature of the programis also demonstrated, the possibility to study the tacking performance of a yacht. The results from the simulations
are presented and discussed.
2. MODEL TESTS
The tests were performed in SSPA’s towing tank with thedimensions: length 260m, breath 10m and depth 5m.The test program comprised both calm water tests and
head wave tests. The former covered tests with ninedifferent models and the latter, which this paper will
focus on, two different models. The reason for performing the wave tests was mainly to get an answer totwo questions:
1. Are the relative characteristics for individual
models identified in calm water tests the sameas those obtained from wave tests, i.e. is adesign that is effective in calm water also
effective in waves?2. What is the influence of the pitch radius of
gyration?
Although the yacht will hardly ever experience headseas, this can serve as a good basis for validation of a
mathematical model of the added resistance.
1:4 scale model tests were performed in irregular headseas with two different mean periods:Wave 1: H1/3=70cm, T=3.5 s (full scale)
Wave 2: H1/3=70cm, T=4.2 s (full scale)Model A was tested with a radius of gyration of 21.8% ofLbg (length between girths) at both wave spectra and at
speeds corresponding to 6, 8 and 10 knots at full-scale.The test series was repeated with a heel angle of 25°.Model A was also tested with an increased radius ofgyration of 25.86% at wave 1, upright at 8 knots.
Model B was tested in two wave spectra, three speeds (6,8 and 10 knots) upright and heeled conditions and with
three radii of gyration: 19.1%, 20.1% and 26.2% of Lbg.
A semi-captive, three-post system developed by the
Wolfson Unit was used for the model tests. In thisarrangement the measurement of side force is throughforce blocks on the fore and aft posts, and resistance is
measured on the centre post. The model is free to heave, by means of the towing posts running on roller bearings,and free to pitch through a gimbal mechanism on the 3 posts. Through the arrangement of the gimbals restraint
is provided in surge, sway and yaw while isolating theresistance force block from side force and vice-versa.
The roll and yaw angles are set fixed. During the wave-tests no yaw angles were set. Accelerometers werearranged fore and aft on the models.
During the tests measurement were taken of speed, trim,resistance, vertical acceleration fore and aft, wave-height
and period.
2.2 Results from model tests
The tests results for model B are presented in Figure 1 toFigure 4, where the added resistance is plotted versus theradius of gyration for various speeds both for upright andheeled conditions. As is seen in the plots the added
resistance was lower for wave 2 (with longer period) both in upright and heeled conditions. The addedresistance was slightly lower in the heeled condition in
both waves though the figures are not consistent.
One unexpected phenomenon was that the curves for
added resistance seem to have a minimum regarding the
radius of gyration at the speed of 10 knots.
The differences between the two models tested wererather small. Although the added resistance in 0.7 msignificant wave height was between 20 and 50% of the
calm water resistance, the test programme was notextensive enough to make the results conclusive. Moretests have to be made, and may have to cover a larger
number of wave encounters, than was the case this time.Due to the limited time available, only one run was madefor each condition. Often each condition may require
several runs to get a sufficient basis for a statisticalanalysis.
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Model B, upright, wave 1
18.00 20.00 22.00 24.00 26.00 28.00
Kyy (% of Lbg)
A d d e d r e s i s t a n c e
6 knots
8 knots
10 knots
Figure 1 Model B, upright, wave 1
Model B, heel 25°, wave 1
18.00 20.00 22.00 24.00 26.00 28.00
Kyy (% of Lbg)
A d d e d r e s i s t a n c e
6 knots
8 knots
10 knots
Figure 2 Model B, heel 25°, wave 1
Model B, upright, wave 2
18.00 20.00 22.00 24.00 26.00 28.00
Kyy (% of Lbg)
A d d e d r e s i s t
a n c e
6 knots
8 knots
10 knots
Figure 3 Model B, upright, waves 2
Model B, heel 25°, wave 2
18.00 20.00 22.00 24.00 26.00 28.00
Kyy (% of Lbg)
A d d e d
r e s i s
t a n c e
6 knots
8 knots
10 knots
Figure 4 Model B, heel 25°, wave 2
The diagrams clearly show that the pitch radius of
gyration has a great influence on the added resistance.The range of the radius variation in the tests was ratherwide. At this stage it is difficult to fully evaluate theimportance of the magnitude of the radius of gyration,since the authors are not updated with information ofhow much the pitch radius of gyration may vary in reallife.
3. MATHEMATICAL MODEL
The mathematical model of the boat dynamics is based
on the rigid body dynamics and on the hydro- andaerodynamic forces and moments that represent the boat
motions: _ _
Fam =
The model consists of six main equations of motions inthree sets of equations:
surgesway, roll and yawheave and pitch
In each set of equations, the different degrees of freedomare coupled. The left hand side of the equationscomprise accelerations and total masses, the latter
including added masses, while the right hand sideincludes all the forces (moments) acting on the yacht.
The total forces, on the right hand side of the mainequations, are principally expressed by:
F = FCB + FR + FK + FSAIL
The indices represent forces (moments) from:CB = canoe bodyR = rudder
K = keel, including bulb and wingletsSAIL = sail
All contributions comprise both linear and non-linear parts. The models for calculating lift and drag on the
canoe body and on the different appendages are well
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documented in other presentations, and will not bespecifically commented upon here. The model used inthe SSPA DVPP is mainly based on principles described
in van Ossanen [3] and in Larsson & Eliasson [4].However, those parts in the model that have beenmodified in the DVPP are described in the following.
3.1 Total masses and mass moments of inertia
The left hand side of each equation is expressed as the product of mass and acceleration, the former including
body mass as well as added mass. The roll inertia is, forinstance, written as
( )dt
dpamk xx 44
2 +
where a44 is divided into three different parts
shk hh aaaa 44444444 ++=
wherea44hh = Hydrodynamic mass moment of inertia fromhull, taken from strip theory
a44hk = Hydrodynamic mass moment of inertia from keela44 = Aerodynamic mass moment of inertia from sails
3.2 Canoe body forces
The canoe body forces comprise both “maneuvering”forces and wave forces, the former being damping forces based on velocities in the different degrees of freedom.
The latter are based on strip theory.
The procedure of combining maneuvering andseakeeping theory into one time domain simulation program is based on a program for ship motions: theSSPA general simulation program for manoeuvring and
seakeeping, called SEAMAN, which has been describedin Ottosson [6].
3.3 Resistance
The total resistance is divided into five parts: viscous,wave, induced, heel and added resistance. All thesecontributions are based on standard theory and have been
described in detail elsewhere, see for instance vanOssanen [3] and Larsson & Eliasson [4].. Somecomments will, however, be given here.
3.4 Added resistance
The added resistance is here considered as a result ofradiated waves created by vertical relative motion of the
ship. The momentary vertical damping force can bewritten as [2]:
( ) ( )
( )xVdx
xdmVx b)x(dF z33z
−−=
and the generated power as:
( ) ( ) ( )xVxdFxdP zzz =
The relative velocity is obtained by:
( ) ssCktz eVqxwxV −
•++−= ηθ
The radiated energy over a certain time T is written as:
( ) ( ) ( )
( ) dtdxxV
dx
xdmVx bdtdxxdPE
T
0
L
0
2z33
T
0
L
0
z
∫ ∫ ∫ ∫
−=
=
The energy can also be obtained by:
( )( ) awR TcoscVE µψ −+=
W a v e p r o p a g a t i o n d i r e c t i o n - V e l o c i t y c V
ψ
µ
ψ−µc cos( )ψ−µ
W av e c r e s t
Figure 5 Definition of wave direction
which provides:
( )( )
( ) ( ) ( ) dtdxxVdx
xdmVx b
Tµ?ccosV
1R
T
0
L
0
2z33
aw
∫ ∫
−
−+=
When running a new boat in the DVPP, a matrix ofadded resistance RAO is generated by simulating regular
waves in a number of combinations of speeds, directionsand wave frequencies. When running simulations inirregular waves, the mean added resistance is then
obtained from:
( )∫ ∞
=
0
eeawaw
_
dSC2R ωωζ
where Caw is the added resistance RAO (ResponseAmplitude Operator)
The procedure outlined here requires, of course, asufficiently long simulation time for each regular wave
component, in order to obtain an appropriate mean value.
3.5 Lift forces
The lift force on the hull is, as is the case also with the
turning moment, based on regression formulas derivedfrom model tests with slender merchant vessels. Theseforces or moments are based on the transverse velocity
and turning rate, both corrected for the local wave particle velocities.
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3.6 Wave forces
The sectional vertical wave induced forces are, for heaveand pitch respectively, written as:
_
peak hk 'z
w e)x(mdx
)x(dmV N
dx
dZ −•••
+
−−= ηη
dx
dZx
dx
dM wsec
W −=
Corresponding lateral forces are, for sway, roll and yaw
respectively, written as:
( ) swlf vMk v)x(Mdx
dYws peak ws
w
−+=
••
φ
OGdx
dYswlf vM
dx
dK wws
w −
−=
•
φ
dx
dYx
dx
dN wsec
W =
( )
( )µsin?
pB
µsin?
pBsin
swlf
=
Superimposed on these forces are the integrated pressure
forces. The local pressure is obtained by:
( )kz
?g?e?gzs p −
+= The pressure is then integrated over the whole
momentary wetted part of the section, see Figure 6, withcomponents in the different degrees of freedom (sway,heave, roll, pitch and yaw).
s ds
p(s) z
ζStill water line
W a v e p r o f i l e
Figure 6 Pressure definition figure
3.7 Keel and rudder forces
Both keel and rudder forces are modelled as described byvan Ossanen [3], however with angles of attack correctedfor the wave induced particle velocities.
The interaction between rudder and keel due todownwash is also modified compared as described by
van Ossanen [3]. The effect of the keel on the rudderconsists of two parts, one due to the bound vortex on thekeel and the other due to the free vortex sheet trailing
behind the keel [7]. The first is written as:
kr x
k b
0.25
ik a
cr e =
k AR
Lk C
ik πα =
k c
k b
k AR =
The second part is expressed as:
0.2ik
r =α
ε
The total downwash angle on the rudder is thusexpressed as:
r rk rtot εεε +=
In the same way as the keel has an effect on the rudder,the rudder has an effect on the keel, an upwash due to the
bound vortex on the rudder.
kr
r
ir
ck
x
b25.0=
α
ε
There is, however, no trailing vortex effect from therudder on the keel.
4. COMPARISONS WITH MODEL TESTS
In order to demonstrate the accuracy of the program,some comparisons have been made with model tests
carried out for Victory Challenge during spring andautumn 2001. Due to confidentiality the yacht particulars cannot be presented. The tests comprised
calm water tests as well as tests in an irregular head sea.
The predicted upright resistance agrees very well with
the measured one, see Figure 7. As for the totalresistance in a typical sailing condition, i.e. 9.5 knot
speed and 25° heel, the agreement is acceptable, seeFigure 8.
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Figure 7 Upright resistance – Comparison with model
tests
Figure 8 Total resistance for 9.5 knots speed, 25° heeland different leeways
The lift forces for different leeway angles are shown inFigure 9. In all the cases shown in the diagram, the
trimtab angle is 7.5° and the rudder angle is 3.0°.
Figure 9 Total lift for 9.5 knots speed, 25° heel anddifferent leeways
The predicted lift force differs somewhat from the
measured one, especially for smaller drift angles. Thereason for this is an underestimation of the additional liftfrom the trimtab in the simulation model.
The model test program comprised some tests in anirregular head sea for different pitch radii of gyration.The agreement between simulations and model tests are
shown in Figure 10 and Figure 11.
Figure 10 Added resistance in head sea. H1/3=0.7 m
and Tz=3.5 sec
Figure 11 Added resistance in head sea. H1/3=0.7 m
and Tz=4.2 sec
Two different theories have been compared with the
model tests, Theory 1 and Theory 2. The first representthe conventional strip theory where the restoring forcesin heave and pitch are based on an assumption of vertical
sides above the still water line.
In theory 2, which is the one which has been
implemented in the DVPP, the wave forces as well as therestoring forces and moments are based on an integration
over the whole momentary wetted surface, see above.
The diagrams indicate that Theory 2, with pressure
integration, provides better agreement with the modeltests. As a whole the agreement is very good.
5. TEST BOAT DATA
An America’s Cup yacht was designed in order to serveas a basis for some comparative simulations. The
intention was primarily to give dimensions that fairly
well represent the boats as they are designed today. Itmay not be optimal with regard to speed performance.
0
510
15
20
25
0 4 8 12 16
Speed (knots)
T o t a l
r e s i s t a n c e Model tests
VPP
0
1
2
3
4
5
0 1 2 3 4
Leeway angle (deg)
T o t a l r e s i s t a n c e
ModeltestsVPP
0
5
10
15
20
25
30
0 1 2 3 4Leeway angle (deg)
T o t a l l i f t
Model tests
VPP
0
0.2
0.4
0.6
0.8
1
3 4 5 6Pitch radius of gyration (m)
A d d e d r e s i s t a n c e
Model tests
Theory 1
Theory 2
0
0.2
0.4
0.6
0.8
1
3 4 5 6Pitch radius of gyration (m)
L i f t
Model tests
Theory 1
Theory 2
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The yacht data were as provided in Table 1, Table 2,Table 3, Table 4, and Table 5.
Canoe body particular Symbol Dimension Magnitude
Length over all Loa m 25.00
Max beam B m 3.80
Max water line beam Bwl m 3.20
Length between girths Lbg m 20.10Design water line length
(without sails and crew)
Lwld m 18.40
Water line length (including
sails and crew)
Lwl m 19.10
Canoe body displacement ∇cb m3 25.0Draught of canoe body Tcb m 0.90
Prismatic coefficient Cp - 0.58
Table 1 Canoe body particulars
Keel particulars Symbol Dimension MagnitudeSpan of keel fin sk m 2.40
Upper chord of keel cku m 1.00
Lower chord of keel ckl m 0.85
Thickness ratio of keel ttck - 0.10
Volume of keel fin ∇k m3
0.15Sweep angle of keel fin sak deg 0.00
Length of bulb Lb m 4.40
Height of bulb hb m 0.75
Volume of bulb ∇ b m3 1.70Chord of trimtab, rel total
keel chord
ctt % 20
Long position of fore end of
keel, Lwl/2
xk m -0.96
Table 2 Keel particulars
Rudder particulars Symbol Dimension Magnitude
Span of rudder sk m 2.6
Upper chord of rudder cku m 0.50
Lower chord of rudder ckl m 0.40
Thickness ratio of rudder ttck - 0.12Volume of rudder ∇k m3 0.044Sweep angle of rudder sak deg 10
Long position of fore end of
rudder, relative Lwl/2
xr m -9.6
Table 3 Rudder particulars
Weight data Symbol Dimension MagnitudeTotal mass incl crew and rig mass kg 2 700
Long center of gravity,
relative lwl/2
lcg m -1.5
Vertical distance BL to CG KG m -0.78
Roll radius of gyration kxx m 4.30
Yaw radius of gyration kzz m 2.20
Pitch radius of gyration kyy m 4.80
Table 4 Weight particulars
Sail data Symbol Dimension MagnitudeBase of main E m 12.0
Height of main P m 32.00
Base of fore triangle J m 8.00
Height of fore triangle I m 26.50
Mainsail upper girth mgu m 4.8
Mainsail lower girth mgl m 7.6
Spinnaker leech sl m 26.5
Spinnaker width smw m 17.9
Spinnaker pole length spl m 10.26
Long position of mast
relative Lwl/2
xmast m -0.10
Table 5 Sail particulars
Loa
tcb
hb
sk ckl
cku
Alcb
sr
clr
clu
abulb
lbulb
Lwl/2
xk
s a k sar
ctt
-xr
cku
lwl
Figure 12 Definition figure
The program provides, based on the boat data given
above, a calm water resistance as shown in Figure 13.
Figure 13 Calm water resistance
6. SIMULATIONS
A number of simulations have been carried out in upwindconditions, with the pitch radius of gyration varied from
3.8 m up to 5.8 m, which corresponds to 18.9% of theLbg up to 28.9%.
6.1 Added resistance in regular waves
Figure 14 and Figure 15 show the added resistance in
regular waves, head seas for 8 and 10 knots respectively.For the three different radii of gyrations tested the peak
varies from 3.3 sec up to 3.8 sec, i. e. wave lengths from17 m up to 23 m.
The wave height was for all periods 1.0 m.
0
1
2
3
4
5
0 2 4 6 8 10
Boat speed (knots)
R e s i s t a n c e ( k N )
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Figure 14 Added resistance in regular waves. 8
knots speed
Figure 15 Added resistance in regular waves. 10
knots speed
As is shown in Figure 14 and Figure 15 above, there isonly a small difference added in resistance between the
two speeds tested, the higher speed proves a slightlyhigher resistance. The model tests were not conclusivein this respect.
6.2 Variation of radius of gyration
Figure 16 shows how the added resistance in a realseaway varies with the pitch radius of gyration. The set
point course over ground was in each case optimized
with regards to the vmg. This meant 37° for 10 knots,35° for 15 knots and 34° for 20 knots wind respectively.In calm water the corresponding figures were 34°, 32° and 31° respectively
Figure 16 Added resistance. H1/3=0.75 m Tz=3.5 sec
In Figure 17 the corresponding VMG values are
provided.
Figure 17 Velocity made good. H1/3=0.75 m Tz=3.5 sec
The phenomenon found in the model tests, see above,
that a minimum added resistance was obtained for aradius of gyration, which was not the smallest one, wasnot identified in the simulations.
6.3 Variation of mean wave period
Figure 18 and Figure 19 show how added resistance andVMG vary with the mean zero crossing period.
Figure 18 Added resistance. H1/3=0.75 m k yy=4.8 m
0
2
4
6
8
10
0 2 4 6 8 10
Period (sec)
A d d e d r e s
i s t a n c e ( k N )
kyy=3.8
kyy=4.8
kyy=5.8
0
2
4
6
8
10
0 2 4 6 8 10
Period (sec)
A d d e d r e s i s t a n c e ( k N )
kyy=3.8
kyy=4.8
kyy=5.8
0
0.2
0.4
0.6
0.8
1
1.2
3 4 5 6
Pitch radius of gyration (m)
A d d e d r e s i s t a n c e ( k N )
10 kn wind
15 kn wind
20 kn wind
6
6,5
7
7,5
8
8,5
3 4 5 6Pitch radius of gyration (m)
V e l o c i t y M a d e G o o d ( k n )
10 kn wind
15 kn wind
20 kn wind
0
0.2
0.4
0.6
0.8
1
1.2
3 3.5 4 4.5
Mean period (sec)
A d d e d r e s i s t a n c e ( k N )
10 kn wind
15 kn wind
20 kn wind
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Figure 19Velocity made good. H1/3=0.75 m k yy=4.8 m
6.4 Variation of wind speed and wave height
Figure 20 shows how the added resistance varies withdifferent weather conditions. The cases tested are as
follows:
Sign wave height
(m)
Mean period
(sec)
Wind speed
(kn)0.3 2.5 100.6 3.0 150.9 3.5 201.2 4.0 25
Table 6 Wave spectra tested
Figure 20 Added resistance
The VMG values for the different weather conditions aregiven in Figure 21
For the wind speeds tested, the boat speed varies between9.2 and 9.9 knots. According to Figure 13, the calmwater resistance is for 9.5 knots approximately 3.5 kN.
This means an increase of the total resistance, due to thewaves, of 20-50%.
Figure 21 Velocity made good
The diagram above clearly shows that the influence ofthe magnitude of radius of gyration on the sailing
properties is significant. A realistic variation of radius of
gyration of say 0.5m may mean a difference in VMG of0.1- 0.2 knots.
7. CONCLUSIONS
The purpose of the paper was partly to present a new
approach for making velocity predictions and partly tostudy the effect of different pitch radii of gyration inupwind conditions. The following comments can bemade.
Model tests results:The indications from the model tests that there might be
an optimum for the pitch radius of gyration is interesting but needs to be supported with more extensive modeltests to be reliable. Tests with larger variations of the pitch radius and a larger variation in wave spectra cangive an answer if this is a significant effect. The effect
was not identified in the simulations.
DVPP simulation tool:A time domain DVPP simulation program has beendeveloped. Comparisons with model tests have shown
that the program well represents the yacht speed indifferent arbitrary weather conditions. In particular, theadded resistance in waves is represented in the DVPP in
a satisfactory way, especially using the pressureintegration method introduced here.
Effect of different radii of gyration:The simulations show, as could be expected, a significantinfluence of the pitch radius of gyration magnitude on the boat performance for the higher waves tested. At 20knots wind speed and 0.9 m significant wave height, theVMG value varies from 7.45 to 7.70 knots when
changing the radius from 5.8 m down to 3.8 m; i.e. a3.3% reduction. However at the lower wind speeds andwave heights the difference is not so significant. For 15
knot wind and 0.6 m wave height, there is almost no
effect at all.
6
6.5
7
7.5
8
8.5
3 3.5 4 4.5
Mean period (sec)
V e l o c i t y M a
d e G o o d ( k n )
10 kn wind
15 kn wind
20 kn wind
0
0,5
1
1,5
2
0 5 10 15 20 25Wind speed (m)
A d d e d r e s i s t a n c e ( k N )
kyy=3.8kyy=4.3kyy=4.8kyy=5.3kyy=5.8
6
6.5
7
7.5
8
8.5
0 5 10 15 20 25
Wind speed (m)
V e l o c i t y M a d e
G o o d ( k n )
kyy=3.8kyy=4.3kyy=4.8kyy=5.3kyy=5.8No waves
-
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The mean added resistance obtained in some of themodel tests for a pitch radius of gyration which was notthe smallest one, has not been experienced in the
simulations.
The added resistance is according to both the model tests
and the simulations rather unaffected by the boat speed.
References
1. Lloyd A R J M: “Seakeeping Ship Behaviour in Rough Weather” Ellis Horwood Ltd, 1989
2. Gerritsma J & Beukelman W: “Analysis of theResistance Increase in Waves of a Fast Cargo
Ship”, Laboratorium voor Scheepsboukunde Report No 334, 1971
3. van Ossanen P: “Predicting the Speed of SailingYachts”, Paper No 12 , SNAME 1993
4. Larsson L & Eliasson R: “Principles of Yacht Design”, Adlard Coles Nautical, London 1994
5. Ottosson P: “Mathematical models inPORTSIM”, 3
rd International conference on
manoeuvring and control of marine craft
(MCMC 94), Southampton, UK 7-9 September1994. Papers, pp 177-196.
6. Ottosson P and Byström L: “Simulation of thedynamics of a ship manoeuvring in waves”.SNAME Transactions, Vol. 99, 1991, pp. 281-
298.
7. Hoerner S: “Fluid Dynamic Lift”, 1965