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AUSTRALIAN
MAR ITI ME
ENGINEERING
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THE EFFECT OF HTJLLFORM ON SHIP MOTIONS
By: L J Doctors, D Holloway & M R Davis
PRESENTED AT:
The Twenty-Sixth Israel Conference on
Mechanical Engineering Technion City, Haifa, Israel
21-22 May 1996
The Effect of Huilform on Ship Motioiis
Lawrence J. Doctors, Damien Holloway, and Michael R. Davis
Australian Maritime Engineering Cooperative. Research Centre
Sydney, NSW 2052 and Hobart, TAS 7001, Australia
Conference Presenter
Abstract
In previous work on this subject, a computerized
technique for creating practical ship hulls was presented
This approach: is based on the utilization of a set of
parent hulls, which possess the desired characteristics. Such characteristics include the suggested longitudinal
variation of the transverse sections and the
longitudi-nal distribution of the volume. Additiolongitudi-nal typical
fea-tures which can be included in the definition of the
hulls are bulbous bows, transom sterns, and other sharpedges, which are manifested in the form of keels and chines. Blending the parents in different propoitions
creates new hulls, which often have rather exaggerated features and which can exhibit excellent hydrodynamic characteristics, such as vastly, reduced heave-and-pitch motions in waves. In the current research, the longitu-dinal location of the minimum vertical, acceleration is studied. Furthermore, comparisons of the. theory with experiments performed on hullforms waisted in the re-gion of the waterplane are seen to be very promising.
Introduction
Background
A new approach to ship-hull creation is described here. A set of parent hulls is first created. The com
puter program then "merges" or "blends" these hulls
from the data base. The hull is next analyzed by a
ship-motion program HYDROS, described by Doctors [1].
This program has the ability to automatically generate
the required computer panelling and mesh needed for
the subsequent hydrodynamic analysis.
Current Work
The research of Doctors [2 and 3] is carried a step
further by extending the calculations on ship hulls de-rived from the data bank of the parent hulls previously studied. These calculations include the local vertical
accelerations at different points along the length of the
vessel. In addition, a set of experiments on promising new huilforms is condñcted, in order to further verify
the theory and the associated computer programs.,
Methodology
Hull Definition
The surface of the hull is defined by a surface mesh which consists of a set of longitudinal lines and a set of
girthwise. lines.
1
Method of Hull Generation,
We assume that there is a set of N parent hulls,
whose surface coordinates are given by X1(z1,
y, z).
The coordinates z, y, and z are respectivelylongitu-dinal to bow, transverse to port, and vertically upward. The index i refers to the particular parent hull and, for the sake of brevity, we omit the index for the individual points on any one hull.
The hulls are combined in the following manner:
z
y =
y,iYi,2 =
Hete, ci2,1, an,,, and as,,, are the scaling factors which will, in principle, be different for each parent hull.
Hydrodynarnic Analysis of the Hull
We now wish to show computed results foE heave and pitch, based on the method of Salvesen, Tuck, and
Faltinsen [4] They demonstrated that the heave
(in-dex 3) and pitch (in(in-dex 5) equations of motion could be written as:
(4
+ M)3 + B33i3 + c33+ A3s5+
+B35is + G351?s = P3 expjwi), (4)A533 + B533 + C53i73 + (A55 + 15)715±
+B55i5 ± = P5exp(jwt), (5) where M is the vessel mass and I is the moment of iner-tia about the transverse axis (which is located at the lon-gitudinal centre Of gravity LCG). The coçfficients A1, B13, and C are the hydrodynamic added mass, damp-ing, and stiffness, respectively. The complex heave and
pitch are denoted by 713 and . The generalized forces,
that is, the complex heave force and pitch moment, are
denoted by F3 and F5. The hat is used to indicate the
relevant quantity without the phaser expjwt).
Next, t is the time and w is the encotsnter angular frequency given by
where w0 is the angular frequency of the sea wave, U is the speed of the vessel and y is the direction of the sea (00 being stern seas). The sea wavenumber is given by
k0
± w/g,
(7)in which g is the acceleration due to gravity.
Finally, the formula for the local elevation of the sea
wave itself is
C Aoexp[j(koxcos'-y+koysin-y+wot)], (8)
where it is understood that the real part is desired. Ad-ditionally, A0 is the sea wave amplitude.
Parametric Studies
Examples of Generated Hulls
At the time of writing, a total of five different par-ent hulls has been utilized in this research. Figures 1(a)
and (b) show the body view and a pictorial view,
re-spectively, for the three of these five parent hulls.
Parent 1 is a 20 m demihull suitable for a
catama-ran, which was drawn by Soars [5]. The design
water-line length is 18.5 m. This corresponds to a nominal draft TN of 1.500 m (relative to the baseline) and a
draft of 0.658 m. Parent 2 (not shown here) is identical
to Parent 1, except that the longitudinal fairing line in
the planing part of the hull surface below the chine has
been shifted outward and forward to create a bulbous
bow. Next, Parent 3 (also not shown here) is identical
to Parent 2, with the single ezception of the
forward-most point on the abovementioned shifted longitudinal fairing line, 'which is now somewhat lower, creating a deeper bulb. Parents 4 and' 5 are shown in Figure 1.
They correspond to Parents 2 and 3, but with twice the lateral displacement of the abovementioned fairing line.
We now turn to Figures 2(a) and (b), which show
three linear combinations of Parents 1, 4 and 5, referred
to as the Eighth Set. For this purpose, the parameters
in Equations (1) to (3) have been selected as follows:
a1,1 =
= az,
= (1/18.5)a1 , (9) in which the overall scaling factor has been chosen to make the waterline length of' Parent 1 equal to unity.This is the nominal length LN, which, in addition to g
and the density of the water p, is used for
nondimen-sionalizing the results.
In general, a simple combination of hulls leads to
both the vessel length L and its displacement i varying as the scaling factors are changed. In order to make
subsequent comparisons of the motions more equitable,
overall scaling factors have been applied to both the
length and the cross section to keep these two quantities constant. This was described by Doctors [1].
Systematic Investigation ofHulI Variation
A typical set of results for heave and pitch is shown in Figures 3(a) and (b), respectively. The heave
ampli-tude A3 and the pitch ampliampli-tude A5 have been made
dimensionless in the usual way, as has the angular
fre-quency of the sea wave w0. Other parameters on the
graph include the nominal-draft-to-length ratio TN/Lt..',
the ratio of the longitudinal radius of gyration to the
nominal length ks/LN and the nominal Froude number
FN = U//77.
Regarding heave, in Figure 3(a), 'the effect of adding the bulbous bow by means of merging Parents 1 and 4 -corresponding to the geometries shown in Figure 2 -- is seen to decrease the peak acceleration response and to lower the frequency at which this occurs. On the other hand, the pitch response in Figure 3(b) is seen to drop substantially, on a 'percentage basis, in the neighborhood of a dimensionless frequency of 1.75.
It is important to note that the naval architect must
also be concerned with questions such as the. resistance of the vessel. In this regard, Hulls 83 and 85 are likely
to be problematic, because of vortex shedding off the
fiat bulb, creating an undesired drag penalty.
Further Measures of Ship-Motion Response
We now consider the vertical motion at some station z, which is given by
773, = A3 exp[j(wi + e3)]
-- (a -- LCG)A5 exp[j(wi + e5)] , (10)
where e3 and e5 are the phase angles of the heave and pitch responses. Next, Equation (10) can be
manipu-lated to give the magnitude of the response, which can
be differentiated with respect to a and set to zero, to
yield what might be referred to as the longitudinal cen-tre of pitch:
LCP = LCG + A3 cos(e3 - e5)/A5,
(11) as well as the corresponding amplitude of the minimum vertical motion:A3min = A3 sin(e3 - es)I .
(12)The outcome of such computations appears in the
four parts of Figure 4. The longitudinal centre of pitch is plotted in Figure 4(a) for three different hulls. For the
original, and traditional, hull it may be noted that the
LCP is relatively constant with respect to the frequency; it has a typical value of about 0.4, implying that the part
of the vessel with the lest vertical motion is just aft of
midships - a result which is known in practice. On
the other hand, the position of this point varies wildly for the prominent huilforms studied here. Figure 4(b)
shows the motion at this point on the vessel. Figure 4(c) gives the root-mean square vertical accelerationover the
middle 50% of the vessel; one can discern considerable
improvement in the ride for the hulls developed here.
Finally, in Figure 4(d), the motion at the bow is plotted
and the vast reduction in this motion for the
30
'20
: 15 5 10-Curve 0 2 0 -2 -6 0 0 2 4 8 Ship = IriCat Fixed L & = 0.0625 FN = 0.5 z Parent 1 AFigure 2: Sections for the Eighth Set
of Mergers (a) Front Elevation
Parent 4
A
3
Figure 2: Sections for the Eighth Set
of Mergers (b) Pictorial View
Figure 1: Input Mesh for the Parent Hulls
Figure 1: Input Mesh for the Parent Hulls
(a) Front Elevation
(b) Pictorial View
Figure 3: Response Curves for the Eighth Set
Figure 3: Response Curves for the Eighth
Set01 iviergers
a) tleave Acceleration
of Mergers (b) Pitch Acceleration
0 0.5 1.5 2 2.5 3
0 -0.5 -1 0 28 -24 20 0 16-:. 12 8 0 2.5
2- 1.5-- 10.5 -Cui-ve FHo2!osFo4 05ii
0 0 -1 -6I8 0 I. 0I p -6 0 0 8 0Figure 4: Other Response Curves
forVariousMergers (a) Longitudinal Centre of Pitch
0 8 o4 a5 0 0 -6 0 8 0.5
Figure 4: Other Response Curves for Various
Mergers (c) RMS Vertical Acceleration
1.5 2 7-5 3
16
3:
Figure 4: Other Response Curves fOr Vai1ious
Mergers (b) Minimum Vertical Acceleration
70 50 :- 30 20 10 0 0 0 Curve 01 02 0 8 03 05 0 0 -6 0 0 8 Curve 0 -6 0 8 0 cc' 0 -6 0 8 0.5 SWATH 1 I 1.5 2 25
Figure 4 Other Response Curves for Various
Mergers (d) Bow Vertical Acceleration
SWATH 3 Ship =,InCát Fixed = L & k25/L 0.0625 = 0.5 4 0 0.5 1.5 2 25 3 3 0.5 1.5 2 2.5 03 Curve - Cr2
a) rront rdevatlon
Figure 5: Sections for the Semi-SWATH
ModelsFigure- 5: Sections for the Semi-SWATH
Models
(b) Pictorial View
- TN
4-05 Ship - SWATH 1 = 0.025 m = (FJYlA =12I'
a a / o'O ,',0 0D O urve F DaCL
0 a 0 LG e 2 25 o 0.202 Exp. a 0.414 Exp. O 0.626 Exp. 0.202 Theory 0.414 Theory 0626 Theory = 25m 0.03661 mFigure 6: Theory and Experiments for the
Semi-SWATH Models (a) SWATH 1
Experimental Investigation
In order to add weight to the validity of these
theoretical investigations, we will now present some results for two sem-smail-waterplane-area twin-hull (semi-SWATH) ships. One demihufl of each of these two
vessels appears in Figures 5(a) and (b). Both hulls are
very slender, particularly so in the case of SWATH 1, which exhibits a very waisted geometry in way of the waterplane. The interested reader should refer to the
experimental work reported by Schack [6], *hich also
applied to semi-SWATH designs of the typeconsidered
here;
The heave motions for SWATH. I and SWATH2 are
presented in Figures 6(a) and (b), where comparisons between theory and experiments are made. It is
gratifying to observe how the theory predicts the shift of peak frequencies with the Froude number F, which
is based on the submerged length L of thevessel. The
very high peak responses are not always experienced in
practice - probably due to
severe nonlinear hydrody-namic behavior at the resonance.Conclusions
The research in this paper has shown the great
ease with which practical huilforms can be generated using the. extremely simple concept of adding linear combinations of parent hulls The viability of such designs is indicated by the considerable reduction in
motions that can be obtained. Additionally, it has been
demonstrated how the theory provides an excellent
prediction of these motions, making the
describedprocedure very applicable to the evaluation of new and unusual hull designs.
Acknowledgments
The authors would like to express their gratitude to
Mr S. Phillips for his accurateconstruction of the test
35 5 [3] [5] 0 0 I 0.202 0.404 0.606 0.202 0.4.04 0.606 Data Exp. Exp. Exp. Theory Theory Theory 0 2 23 c0v'Z7
Figure 6: Theory and Experiments for the
Semi-SWATH Models (b) SWATH 2
models and to Mr G. Macfarlane, Mr R. Home, and the other staff of the Towing Tank at the.Australian Maritime College in Launceston, for their invaluable
assistance with the conduct of the ship-motion
experi-ments.
References
[1] DOCTORS, LJ.: "A Versatile Hull-Generator
Program", Proc. Twenty-First GenturyShIpping
Symposium, University of New South Wales,
Syd-ney, New South Wales, pp 140-158, Discussion
158-159 (November 1995)
[2] DOCTORS, L.J.:
"The Influence of
a.Pro-boscidean Bow on Ship Motions", Proc. Twelfth
A ustralasiaii Fluid Mechanics Conference
(12 AFMG,), University of Sydney, Sydney, New South Wales, pp 263-266 (December 1995)
DOCTORS, L.J:
"The Influence of a
Duck-billed Platypus Bow on Ship Motions", Proc.
Small Craft Marine Engineering, Resistance and Propulsion Symposium, University of Michigan, Ann Arbor, Michigan, 19+i pp (May 1996)
[4] SALVESEN, N., Tuoic, E.O., AND FALTINSEN, 0.: "Ship Motions and Sea Loads", Trans.
So-ciety of Naval Architects and Marine Engineers,
Vol. 78, pp 250-279, Discussion: 279-287 (De-cember 1970)
SOARS, A.J.: "Twenty-Metre T.D. Catamaran Lines Plan", Drawing 899/1-2, Incat
Pty Ltd,
Chatswood, New South Wales (February 1987)
[6] SCHACK, C.: "Research on Semi-SWATH Hull Form", Proc.
Third International
Confer-ence on Fast Sea Transpoitation (FAST '95),
Traverniinde, Germany, VoL 1, pp 527-538
(September 1995)
Ship =.SWATH 2 Curve
a -TN 0.025 m
