The influence of a duckbilled platypus bow on ship motions

AUSTRALIAN

MARITIME

ENGINEERING

Australian Maritime Engineering CRC Ltd

Report

TECHNf3C

_W1VRSTEff

Laborato,ium voor

Sepshydromha,

ft.rchef Mekeiweg Z 2628 CD

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-18133

THE INFLUENCE OF A DUCKBILLED PLATYPUS

BOW ON SHIP MOTIONS

By: L J Doctors

FOR PRESENTATION AT:

Small Graft Marine Engiheering,

Resistance and Propulsion Symposium

The University of Michigan

Ann Arbor, Michigan

15-17 May, 1996

Abstract

B = Beam of vessel

= Hydrodynarnic damping coefficient The quest to develop an efficient and practical

cii

= Hydrostatic stiffness

computer-based shiphull generation technique has F3 = Complex heave force lasted at least three decades now. F5 Complex pitch moment

The method developed in the current research FN = Nominal Froude number

can be described as mode-based. That is, a library IS = Moment of inertia of craft of practical huilforms is first created. The program L = Length of vessel

then "merges" Or "blends" these hulls from the data LN = Nominal length of vessel

base. In a sense, the new hulls are formed by mixing LCG = Longitudinal center of gravity the "parent" or basic hulls in different proportions. M = Mass of vessel

This new method guarantees that reasonable hull- N = Number of parent hulls forms will always be generated. T = Draft of vessel

Examples of the created hulls are presented in TN

-

Nominal draft of vessel this paper. In addition, the influence of varying de- U = Speed of vessel

grees of typical features, such as a pronounced bul-bous bow, on the motions of high-speed vessels (de-signed in this manner) are demonstrated.

x

a33 =

Hull surface vector

Sectional added mass In previous work, the method has been used b33 = Sectional damping coefficent

to successfully create huilforms with a marked bul- ₉ = Acceleration due to gravity bous or "proboscidean" bow. That huilform, which 2 = Index for parent hull

could be describd as a semi-small-waterplane-area ₃ = Imaginary component twin-hull (semi-SWATH) ship, possesses unusual k = Directional scaling factor

frequency-response curves, with peak pitch acceler- k0 = Fundamental circular wave number

ations up to 85% less than those of a traditional

k5 = Pitch radius of gyration of vessel slender huilform. The reduction in heave response

= Time

was, however, somewhat less. _{= Longitudinal coordinate}

In the current work, the development of the

_y = Tra.nsverse coordinate

huilform has been taken a step further, by

ex-amining different forms of the bulbous bow. In

particular, a flattened bow form, sinilar to the

z

a

=

=

Longitudinal coordinate Scaling factor

shape of the bill of the platypus, is shown here

= Displacement of vessel

to reduce the heave motions by about one half - = Direction Of seas (0 degrees is stern seas)

although the reduction in pitch motions is not as C= Wave elevation

high as the figure quoted above. = Complex heave of vessel

75 = Complex pitch of vessel

Nomenclature

p = Density of water

w _{= Encounter angular frequency}

A0 _{= Amplitude of sea wave = Sea-wave angular frequency} A3 = Amplitude of heave motion

A5 = Amplitude of pitch motion _{Time-rate change of variable}

Introduction

Background

A fundamental approach to mathematically de-fine the surface to the hull is to use splines. There is a vast array of different splines suitable for this purpose. An early example is the work of Berger, Webster, Tapia, and Atkins (1966), in which two-dimensional splines were used to smooth a given hull surface. In the spline approach, mathematical patches are used to cover the surface. A well-known spline is that of Bézier (1972). Such a spline may be applied to different orders, thus permitting the user

to select the degree of continuity of the surface of the

hull. A number of papers on this subject was pub-lished in the conference proceedings of Banda and Kuo (1985), which was specially dedicated to this subject. The methods described therein are suffi-ciently sophisticated to handle surfaces with sharp edges that can, if desired, fade (or wash out). The case of B-splines was specifically described by Piegi and Tifier (1987). In the application of these splines, the control points, often referred to as knots, do not necessarily lie on the hull surface. This makes the approach more suitable to design - rather than just fitting an existing hull surface.

Williams (1964) investigated a variety of math-ematical forms, including fourth- fifth and tenth-order polynomials. He referred to the awkward fea-tures of typical ships, which suggests that it might be necessary to divide the length of the hull into its en-trance, parallel middle-body, and run, and consider them separately in the hull-definition computation.

In a similar manner, Durand, Meinhold, Younger, and Parsons (1984) also researched the

rep-resentation of ships by means of polynomials. In

their case, they subdivided the length of the vessel into a total of six regions, using a separate math-ematical function over each region. Similarly, the cross sections were also subdivided, to allow for an accurate modeling of a flat floor, deadrise angle, round bilge, and ship side.

The question of the mathematical construction and approximation of a ship hull was addressed by Buczkowski (1969), who used the "strain energy" in the equivalent draftperson's batten fitted through the surface as a measure of smoothness of the re-sult. He presented techniques for minimization of the energy. He also referred to the problem of dis-continuities that occur in many common hullforms. The desire of many naval architects to utilize series hulls, which can vary in a systematic fashion, was

researched by Hally (1988). He used three

piecewise-cubic splines over the length of the vessel in order to handle the three relatively distinct parts of the hull. The first derivatives were smooth at the break points, while the second derivatives (representing the curvature) were not.

Keane (1987) reported a computer-based

method for producing simple huilforms. The

method permitted the user to specify such

geo-metric quantities as the rise-offloor angle at the keel, the flare angle at the waterline, half-angle of entrance, transom beam, and so on. Such an

approach is a very practical one, but is limited

to the family of forms for which it was initially

designed.

A radically different

idea was proposed by

Letcher (1984). His so-called Fairline

hull-definition method comprises a family of mathemat-ical schemes, simple enough to implement on small computers. The system represents the three

coor-dinates of any point on the hull surface by funo-

-tions of two surface parametric variables. The re-sulting hull surface is remarkably well behaved. An interesting characteristic of the surface is that it can

possess negative offsets near the two ends of the

ves-sel. These two "negative parts" are trimmed (or removed) by the program, thus producing a hull in which the stem and the stern have a rake or sweep, characteristic of practical hulls, such as yachts. Fur-ther developments of this popular method were de-scribed by Letcher, Brown, and Stanley (1988). There, the matter of modeling chines was solved by using multiple surfaces. Additionally, the

practi-cal advantage of employing developable surfaces was

also discussed. This practical Fairline system is in everyday use by a number of naval-architecture de-sign companies around the world.

During the process of the design of a ship

-

par-ticularly referring to the huilformn itself it is vital to evaluate the hydrodynamic and other qualities of the shape. This question, plus that of the de-tails of the variation of the hullform, were addressed by Nowacki (1993) and Nowacki, Bloor, and

Olek-siewicz (1995).

Since many huilforms might have to be nu-merically tested, this secondary process is almost certain to be the main stumbling block in the auto-

-mated design of ships by computers, unless efficient iteration procedures, such as the genetic algorithm described by Goldberg (1989), are employed. More traditional approaches, including hill-climbing

optimizers, while considerably faster in a theoretical sense, suffer from the fact that they find only local optimums and can almost certainly be ruled out as impractical for general-design purposes.

Current Work

The aim of the current work is to continue the development of a practical technique for producing "shipshape" hulls which will have immediate appli-cation. While, no doubt, these sentiments would also be expressed. by the researchers whose works have been cited above, there is very little to guar-antee that those. methods (mainly computer-based) will, indeed, produce viable huilforms. It would seem that only the Fairline technique has inherent properties that will almost certainly generate a prac-tical hull.

Of course, the approaches listed in the previ-ous section can describe many complicated shapes, but the basic difficulty with them is that the hull is

described by a large data base - usually a list of

three-dimensional coordinates of points on the hull surface or, otherwise, control points. In any case, there is little to prevent the program from generat-.ing impractical shapes. The other basic approach of using conformal mapping or algebraic functions involves the use of a smaller data set, but has the distinct disadvantage of not being general enough and, frequently, incapable of producing typical fea-tures of hulls, such as bulbous bows, transom sterns, and chines.

The method described in this paper is based on a very simple idea. It requires the user to establish a small data bank of huilforms which are known to be practical fom the point of view of, for example, re. sistance, motions, and stability. The computer pro-gram simply interpolates between selected members of the parent hulls. Naturally, it is then necessary to analyze the new huilform in order to determine its usefulness.

Previous work on this subject has been pub-lished by Doctors (1995a and 1995b). The method

proposed here has been effective in generating real-istic hulls, while preserving the important geometric features inherent in most model designs, as noted above. In this paper, the question of the bow form is studied in further detail and the influence of the.

width of the bulb on the motion of the vessel in

waves is computed.

Methodology

Hull Definition

The development work to be detailed here is based on the suite of computer programs Hydros, which has already been described by Doctors (1993a and 1993b). Briefly, in its current form, Hydros

has the capabilities to perform hydrostatic, ship-resistance, and ship-motion-and-load calculations of marine vehicles, including monohulls, catamarans, and multihulls.

The primary input information consists of the 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 girt.hwise lines. The points lie on the surface of the hull. It is claimed here that such a set of lines can be used to describe any reasonable hull shape. For further generality, the lines can be run together; that is, some or all of the points on any particular set of two or more adjacent longitudinal (or girthwise) lines can be identical. In this man-ner, the number of physical girthwise (for example) points can be altered from one station to the next.

The girthwise lines, which can be thought of as stations, do not have to be either equally spaced, vertical, or planar They can possess any shape. Thus, curved or sloping transom sterns can be ac-commodated and any desired bow, including tradi-tional vertical stems, as well as pointed, bulbous, and wavepiercing types can be accommodated. The important requirement of sharp edges used to rep-resent chines associated with planing surfaces and also for the definition of transoms is handled by em-ploying a pair of continuity codes, which allows the surface to be continuous or discontinuous in slope, in either or both of the longitudinal and girthwise directions, at any desired surface point of the mesh.

The refinement of the mesh and the

naval-architectural analysis is described below. It is

sufficient at this point to summarize this subsection

by stating that a two-dimensional grid of points

used in the computer to define each body.

Examples of three parent hullforms are shown in

Figures 1(a) and (b).

These are so-called split views, in which the port half of the forward part

of the hull plus the starboard half of the stern

part of the vessel are shown, according to common convention. These hulls illustrate chines, a transom stern, and the merging of lines, as detailed in the above paragraphs.

Method of Hull Generation

We assume that there is a set of N parent hulls, whose surface coordinates are given by X(x1,y, zn).

The x, y, and z are respectively longitudinal 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.

Figure 1: Input Mesh for the Parent Hulls

Front Elevation

Figure 1: Input Mesh for the Parent Hulls

Pictorial View

would be the combination:

=

y =

ay,iyi,

z

Here a,j,

_,,, and are the three scaling factors which can, in principle, be different in the three co-ordinate directions and will, almost certainly, vary from one parent hull to the next.

In Equations (1) to (3), it is implicit that the scaling factors are constant over the surface of the hull. However, an obvious generalization for future research would permit the scaling factors to vary in a user-prescribed manner.

Hydrodynamie Analysis

The purpose of this paper is to demonstrate a simple and effective hull-generation technique. A powerful application is to the study of the influence

of the hull shape on ship motion. To this end, we will

show computed results for heave and pitch, based on the methods of Korvin-Kroukovsky and Jacobs (1957) and Salvesen, Tuck, and Faltinsen (1970).

In both of these methods, one firstly establishes the linear heave and pitch motions (indices 3 and 5), which may be considered separately from the sway, roll, and yaw motions (indices 2, 4, and 6). These two equations of motion can be written as:

(A33 + M)3 + B33i3 + C3373 + A3ss+ +B355 + c35?75 = F3 expjwt), (4)

A533 + B533 + c53m + (A55 + I5)'5+

+B55r)5 + Cr = P5 expjt),

(5)

where M is the vessel mass and 15 is the moment of inertia.about the transverse axis (which is located at the longitudinal center of gravity LCG). The

coeffi-cients A11, B11, and C1 are the hydrodynamic added

mass, damping, and stiffness, respectively. The com plex heave and pitch are denoted by

and i. 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 with-out the phaser exp(jwt). The absolute value and argument of' these quantities give their magnitude and the phase.

Also, t is the time and w is the encounter angular

frequency given by

= woUkocos-y,

(6)

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 (0° being stern seas). The sea wavenumber

is given by

k0

=

(7)

in which g is theacceleration due to gravity. Finally, the formula for the local elevation of the

sea wave itself is

= Ao exp[j(koz coS + koysin-y + wot)], (8)

where it is understood that the real part is desired, and A0 is the sea wave amplitude.

It is mathematically possible to consider sepa-rately the sway, roll, and yaw motions (indices 2, 4, and 6). Further information on this subJect can be found in Salvesen, Tuck, and Faltinsen (1970) and Doctors (1993a and 1993b).

The method of computing the two-dimensional added-mass and damping coefficients, a33 and b, has been detailed by Doctors (1988). The boundary-element method was used for this purpose. In partic-ular, the Galerkin approach was employed, in which the usual condition of no relative normal velocity on the Surface of the body is satisfied in an aver-age sense on each panel; this gives somewhat more converged results for the same number of panels.

As is well known, these two-dimensional coefficients

are integrated longitudinally to produce the three-dimensional coefficients A1, and B1, which appear in Equations (4) and (5).

Regarding the question of ir:regular frequencies, these have been eliminated by making use of an

"ar-tificial lid" on the internal free surface of each ship section, where this exists. _{(Of course, in the} re-gion of some of the prominent bows, a typical sec-tion is totally immersed and there is no irregular-frequency effect.)

The reader is referred to the

work of Haraguchi and Ohmatsu (1983) and Lee and

Sclavounos (1989), for more informationon the mat-ter of the irregular frequencies.

A number of tests

for convergence of the numerical procedure was run on the more extreme hull shapes. In the worse case, it was found that the use of 20 panels on each section (on both the ex-ternal wetted surface and the inex-ternal free surface),

together with 20 ship sections, gave results that

had converged within one or two percent. For this purpose, it was a great advantage that the computer

program could compute this surface paneling au-tomatically from the given three-.dimensional mesh defining the ship surface, without any intervention from the user.

Results and Discussion

Examples of Generated Hulls

Figures 1(a) and (b) show the body view and a pictorial view, respectively, for the three parent hulls used in the current investigations. The views are those Of the original input mesh, as represented by the girth lines (which happen to be vertical sec-tions in all cases, except for the girth line forming the raked stem). There are 15 girth lines and, 13 longitudinal lines; although, advantage was taken

of the fact that Hydros permits half the latter to

be supplied because of the lateral symmetry of the

demihuib

Parent 1 is a 20 m demihull suitable for a cata-maran, which was drawn by Soars (1987). The de-sign waterline length is 18.5 m. This corresponds to a nominal draft TN of 1.500 m (relative to the base-line) and a draft T of 0.658 m. Other symbols used in the figures are the wetted length of the vessel L and the wetted beam B. The demihull has a vertical transom stern and a well-defined chine on each side. One can also discern a small flat of keel that would play little hydrodynamic role.

In previous work, two additional parents, called

Parent 2 and Parent 3, were used. The reader is

encouraged to examine the two relevant public3tions by Doctors (1995a and 1995b) and to observe the subtle differences between the total of the five parent hulls, which have now been utilized. We introduce two new parent hulls in the current work.

Parent 4 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. For the record, it should be noted that this shift used to create Parent 4 is precisely twice the shift used to create Parent 2. The bulb appears crude in Fig-ure 1, but it should be noted that this is an input hull before the mesh-refinement process. Secondly, Parent 5 is identical to Parent 4, with the sin.gle ez-ception. of the forward-most point on the abovemen-tioned shifted longitudinal fairing line, which isnow

somewhat lower, creating a deeper bulb. Again, it is important to note the fact that the shift required to create Parent 5 is exactly twice the shift used in creating Parent 3.

We now turn to Figures 2(a) and (b), which show

three out of the five linear combinations of Parents 1 and 4, whose motions are to be considered. For this purpose, the parameters in Equations (1) to (3) have

been chosen as follows:

= a,,1 = a

=

(1/18.5)a,

(9)

in which the ovetall scaling factor has been selected to make the wetted 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 nondimensionalizing the results. (In this example, the three scaling parameters are identical for each

hull.)

The dernihulls have been remeshed here, using 5 longitudinal lines for each original 2 longitudinal lines and 5 girthwise lines for each original 2

girth-wise lines.

It is remarkable to note that one can

extrapolate (as opposed to interpolate) the hulls, by selecting scaling factors greater than one, so that (for example) the generated bulb is more p±orninent than in Parent 4.

The demihull is displayed by means of 21 equally

spaced vertical stations. These comments in this paragraph also apply to Figure 2 through Figure 4. In some examples, the width-to-depth ratio of the bulb reaches about 34.

The two parts of Figure 3 may be compared to the corresponding two parts of Figure 2. In this case, however, Parents 1 and 3 have been combined

-rather than Parents 1 and 2.

Next, we examine Figure 4, in which all three

parents have been combined in the proportions

noted by the values of the scaling factors a,. An important design point in this work is the fact that the (wetted) length L and the displacement vary as the scaling parameters change. This makes the

comparison of seakeeping performance and other

by-drodynamic criteria somewhat unfair, as it is well known that more slender hulls usually behave bet-ter.

It was therefore decided to run this set of tests in which the two constraints of constant length and displacement were applied. This was easily achieved by employing additional overaliscaling factors to all

the hulls, as follows:

Essentially, these two constraints can be met by a

Set-Fixed=

z

11u1151

B&T

a1=1

a4 = 0

Figure 2: Sections for Fifth Set of Mergers

Front Elevation

z

Hu1153

a1 = 0

a4 = 1

Figure 2: Sections for Fifth Set of Mergers

Pictorial View

z

Hu1155

a1 = 1

Hull 61

a1 = 1

a5 = 0

Figure 3: Sections for Sixth Set of Mergers

Front Elevation

Fixed =

z

_B&T

_a1

Hull 65

₌

1

a5=

2

HuM 63

a1 = 0

x

a5=1

Figure 3: Sections for Sixth Set of Mergers

Figure 4: Sections for Eighth Set of Mergers

Front Elevation

z

11u1183

z

Hu1185

a1 = -1

a1 = -1

a42

a5=

4 1IIr

a5=

8

Figure 4: Sections for Eighth Set of Mergers

ting k equal to k ensures that the sections them-selves are not distorted.

Thus, the beam-to-draft ratios for the dernihulls

in Figure 4 are the same as those that would be

generated without this additional manipulation. At the same time, a careful visual study of the three parts of Figure 4(a) will reveal that the dimensions of the sections are marginally reduced as the more radical bow 'forms are generated and which would otherwise increase the length and displacement of

the vessel.

In summary, we can see the possibility of creat-ing very prominent shapes by the simple expediency of using suitable scaling factors, which can certainly 'exceed a value of unity.

Numerical Convergence Tests

As noted above, a vital part of any hydrody-narnic computational work is whether the mesh has been refined sufficiently for convergent results to be obtained. For the sake of brevity, the convergence

tests are not shown here.

For all of the results

presented, it was decided to use 20 sections and 20 girth points on each section provided, as these choices provided converged results for the responses for all of the cases to be discussed in this paper. It should be noted that the sections, used for the hydrodynamic analysis relate to the wetted volume, are created automatically by Hydros; these depend

on the, set draft and trim, and are generally not

the same as those seen in the geometric displays in Figure 2 through Figure 4.

Investigation of Hull Variation

The first set of results for heave and pitch are

shown in Figures 5(a) and (b), respectively. The

heave amplitude A3 has' been made dimensionless using the sea wave amplitude, while the pitch ampli-tude A5 has been nondimensionalized using the sea wave slope k0A0. The dimensionless (or reduced)

an-gular frequency of the sea wave is wo/T7. Other parameters on the graph include the nominal-draft-to-length ratio TN/LN, the ratio of the longitudinal radius of gyration to the nominal length ks/LN and the nominal Froude number FN

U//jL.

Four different sets of mergers have already been studied in the previous two papers on this subject. In the present work, we will consider a further five sets. The ones discussed here will be the fifth, sixth, eighth, and the ninth sets of mergers

Regarding heave, in Figure 5(a), the effect of adding the bulbous bow by means of merging Par

ents 1 and 4 - corresponding to the geometries

shown in Figure 2 - is seen to have a most favor-able effect. We see that there is a decrease in the

peak heave acceleration response of 58% far the most

extreme bulbous-bow form. In the same way, the maximum pitch acceleration response for the most extreme hull in Figure 5(b) is seen to drop by 65%, in the neighborhood of a dimensionless frequency

of'2.0.

Similarly, we see the heave and pitch acceler-ation responses in Figure 6 for merging Parents 1 and 5 - corresponding to the geometries shown 'in Figure 3. The relative reductions in the two peak re-sponses are 54% and 65%, respectively. Therefore,

in this case, the deeper bulb is apparently less

benefi-cial. This result is in contrast to that obtained in the previous work for a narrower bulb, where the deeper bulb demonstrated much better seakindliness.

Next, in Figure 7, are shown the responses for merging all three new parents, corresponding to the geometries seen in Figure 4; this is now effected on the basis of.constant length and volume, as already described above in some detail. It is probably more important to minimize pitch accelerations than to minimize heave accelerations, because 'this leads to generally lower local vertical accelerations along the length of the vessel. Hence, we see that the most

ge-ometrically extreme vessel is best from the viewpoint

of seakeeping alone. The maximum pitch accelera-tions are reduced by almost exactly 57%, according to the theory.

Finally, an attempt is made in the two parts

of Figure 8 to design a vessel by producing what is essentially a simply arithmetic mean of the best two vessels in Figures 5 and 6. . In each of these two figures, those two vessels are indicated by the last two plotted curves in each case. The respec-tive arithmetically-mean ships appear as the second

and the third curve in the two parts

Figure 8, where the heave and pitch acceleration responses are shown. The base vessel is shown by the first curve for the purpose of comparison. We notice that we

have achieved a substantial reduction in both the heave and pitch responses of the ship.

It is also

important to record the fact that while the above-mentioned, best two vessels exhibit generally simi-lar excellent improved seakindliness, there _{are still} relatively large differences in the pitch responses in the region of a reduced wave frequency between 0.8 and 1.8. Should the ambient sea spectrum be in this neighborhood, then it is clear that one or other of these two vessels will behave considerably better than the other.

30

10

5

0

25

20

0

1,15

-a5

=

0

- TN/LN = 0.08 108

= 0.Ô625

=

0.5

'

1,i

_\

\\\\

\

3

Fixed= B&T

/

/

1'

J-.''

/

_-

\

FN

=

0.5

a5

=

0

\\

-5

TN/LN = 0.08 108

= 0.0625

_'I

/

\'\

. N

-

v

0

I I

Curve

a1

cx4 1

0

11?

0.5

0

0.5

1

/

\x\

I

0.5

1.5

I

'\

1

2

/

,/

\

I

//\

/

_I,

I,

/

Ship

=

InCat

/

I,'

/

,

Fixed

B&T

Curve

a1

a4

1

0

0.5

0.5

0

1

0.5

1.5

1

2

0

0.5

1 1.5

2

2.5

w0-v'L/g

Figure 5: Response Curves for Fifth Set of Mergers

(a) Heave Acceleration

0

Ô.5 1 1.5

2

2.5

Figure 5: Response Curves for Fifth Set of Mergers

(b) Pitch Acceleration

Ship

=

InCat

25

0

20

15

25

20

15

:.

10

5

0

T

0

0.5

1 1.5

2

2.5

3

oJ0VL/g

Figure 6: Response Curves for Sixth Set of Mergers

(a) Heave Acceleration

Ship

=

InCat

Fixed = B& T

a4

0

-

TN/LN = 0.08 108

k/L = 0.0625

/

/

/

FN

0.5

/

I,

-I,

I,

_/ I, I" I'

I'

I'

\'

\\

\'

\\

-'S.-

\\

5'

3

30

20

15

10

-5

Curve

a1

a5

_FN

/

/

/

_/

/

/

,-/

_I,'

I,'

/

_I,

_\

\

=

I

'I

"

N

0.5

25

1

0.5

0

0.5

1

0

D.5 1 1.5

2

Ship

=

Fixed

a4

=

TN/LN =

k/L =

InCat

B&T

0

0.08108

0.0625

Curve

a1

a5

1

0

0.5

0.5

0

1

0.5

1.5

1

2

0

0.5

1 1.5

2

2.5

Figure 6: Response Curves for Sixth Set of Mergers

(b) Pitch Acceleration

30

25

0

20

:

15

10

5

0

25

20

0

15

10

5

0

Curve

0

2

0

2

6

0

0

2

4

8

Ship

= InCat

Fixed =L&

0.0625

FN

=

0.5

T

Curve

a1

a4

0

2

0

2

6

0

0

2

4

8

/ / / I

-

Ship

= InCat

-

-;:'

-'s

F

0

Ô.5 1.5

₂

2.5

Figure 7: Response Curves for Eighth Set of Mergers

(b) Pitch Acceleration

0

0.5

1 1.5

2

2.5

Figure 7: Response Curves for Eighth Set of Mergers

5 0 25 20

0

15 : 10 5 0 = 0.0625

_FN

=

0.5 _// \

-

Ship

= InCat

Fixed =L&

k/Lj, = 0.0625

FN

=

0.5 / / / / / .1 / / / / /

3

Curve

c5

1 0 0

0.75

1.75 0 0.75 0 1.75 // \ ' 30 20

-10

Curve

cx4

c5

/

/

/

/

/

,

/ 25 1

0.75

0.75 0 1.75 0 0 0 1.75

Ship

= InCat

Fixed =L&

0 0.5 1 1.5

2

2.5

w0VL/g

Figure 8: Response Curves for Ninth Set of Mergers

(a) Heave Acceleration

0 0.5 1 1.5 2 2.5

Figure 8: Response Curves for Ninth Set of Mergers

for the motions apply to a nominal Froude number of 0.5. Without doubt,

the responses will be

different at other Froude numbers.

Conclusions

The work described here. has again demonstrated that one can generate huilforms with greatly im-proved seakeeping characteristics in a passive

man-ner that is, without active ride-control devices,

such as fins and flaps.

The improvements are achieved by suitable distortions of a basic huilform

and, in particular, bulbous bows are seen to be

very effective. Furthermore, a comparison between the graphs of ship response in this publication with those of the previous two publications shows that a widened bulb has the distinct advantage of halving the heave response; however, this gain is accompa-nied by a lesser reduction in the pitch response over most of the frequency range.

One of the reviewers of this paper raised the question of the practicability of the extended bow forms, keeping in mind that there would be some similarity between the hydrodynamics of such bows and the hydrodynamics of anti-pitching fins. Such fins create the required damping in computer simula-tions but have been known to generate unwanted vi-brations when installed on ships. It is believed that the bow forms studied here constitute much more "compact" structural elements and would therefore be stiffer and less prone to such undesirable effects. Nevertheless, it is an important point that should be studied, experimentally, for example, at both model and full scale.

Secondly, it is important to note that the heave has been calculated at the center of gravity and that the center of gravity is at a different location for each of the vessels. This does influence the validity of the comparisons to some extent, although some numerical experiments have shown that the effect of choosing a slightly different reference point is not strong. One could argue that a fixed point should be selected for computing the heave, in order to make the comparisons more valid. An even more reason-able approach is to compute the vertical motions over a portion of the length of the vessel where the passengers are to be located, and to consider the root-mean-square amplitude of these motions. This approach is already under investigation and will be reported on in the future.

It is also planned to build upon the knowledge gained here and to utilize an efficient optimizer,

based on the genetic algorithm, as already

men-tioned previously, with the intention of searching

for the best vessel, from either a seakeeping or

resistance point of view, or both of these together.

Acknowledgments

The author would particularly like to express his appreciation to Mr N.A. Armstrong, previously of InCat Pty Ltd, Lane Cove, New South Wales, for providing him with the lines plans of a suitable

catamaran dernihull, as well as for a number of

valuable discussions. He is also grateful to Prof. M.

Davis of The University of Tasmania, Hobart,

Tasmania, Mr D. Fry of NQEA Australia Pty Ltd, Cairns, Queensland, and Mr C. Norman, of Austal Ships Pty Ltd, Henderson, Western Australia, for their interest and input into this research topic.

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