Catamaran Ingles

7/30/2019 Catamaran Ingles

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WAVE RESISTANCE FOR HIGH SPEED CATAMARAN

H.B.Moraes*

J.M.Vasconcellos**

R.G.Latorre ***

* Assistant Professor at Par University / Brazil

** Associate Professor at COPPE / UFRJ Brazil

*** Professor at University of New Orleans - USA

1. Abstract

The object of this work is investigate the wave resistance component for high speed catamarans.

Two methods were applied: the theory of the slender body proposed by Mitchel and a 3D method

used by ShipflowTM software.The results were used for different types of twin hulls and special attention was given for the

effects of the catamaran hulls approximation. The results comparison founded by Millward are

shown.

The investigation included also the effects of shallow water on the wave resistance component.Special attention is given to the waves height generated by the craft with the objective to find out

the consequences in the river margin.

2. Introduction

The demand for high-speed craft for passenger transportation, mainly the catamarans, isincreasing significantly in the past years. Looking for being capable to attend the increasingly

demand, the international market of high-speed crafts is passing for deep changes.

Different types of crafts are being used for passenger transportation. However, the catamaransand monohulls have been the main ship owners choice not only for passenger transportation but

also as a ferryboat. The investigation for more efficient hydrodynamic shapes, the engine

improvement, and lighter hulls with aluminum and composite materials application made

possible enlarge the speed.The improvement of the craft quality, high speed, larger deck area compared with monohull craft

justifies in certain way the demand for catamarans.

The market for high speed crafts is demanding a project of catamarans with different types anddimensions with the focus on lower resistance and power for high speed. Therefore, the

optimization of the hull resistance is fundamental for the success of a high speed catamaran hull.

The theoretical calculation of the hull resistance is complex, however its offer lower costs than

the model test evaluation. This reason justifies the effort to study many different theoreticalmethods capable to show an appropriated evaluation of the hull resistance.

This research focus on two methods for catamaran wave resistance calculation in differentpositions of hull separation and water depth. The 3D method based on the potential theory, used


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in the SHIPFLOWTM software and the method that uses the theory of the slender body, with an

easier application were applied.The SHIPFLOWTM program application allowed many analyses for catamarans hull wave

resistance. In special the interference effect between hulls and the effect of shallow water can be

investigated.

This work also look at the maximum waves height generated by the craft, in different waterdepth. The objective is to evaluate and minimize the possible effects against the river shore and/

or nearby small boats.

2.1 High Speed Craft

The high speed crafts have been always in the forefront naval engineering and the hydrodynamicresearching.

At the end of the 19th century and in the beginning of the 20 th, there were many solutions for

alternatives types of high speed crafts, with many concepts being patented.

The first hydrofoil were build by Forlanini in 1905, achiving 61 knots. However, it was the BaronSchertei between 1920 and 1930 that improved the hydrofoil which was created to work in calm

waters for a craft capable to operate in sea condition.

In 1716, appeared the first hovercraft, sailing at 40 knots. However, there were problems with theair cushion not solved until the work of Rockerill and Latimrer Needham during 1950. This work

leaded to the development of a vehicle of air cushion capable of being used in ocean waters.

The high speed crafts can be classified as shown in table I.

Table I Classification of the types of high speed crafts

Category Types of craft

Crafts supported by air Air Cushion Vehicles ACV and Surface Effect Ship

SES

Crafts supported by foils Surface Piercing Foil (Hydrofoil) and Jetfoil

Displacement, planing andcraft for semi-displacement

Standard monohull, catamaran, Small Waterline Area TwinHull SWATH, Air lubricated hulls and Wave Piercing

According to International Maritime Organization (IMO) rules and recommendations through itsspecial code called IMO-HSC Code (High Speed Craft) approved in the 63 rd section of May 94

trough MSC.36 (63), that specifies as a high speed craft the one that has its maximum speed is

equal or the same or superior as:

)/(7.3 1667.0 smVolV = ( 1 )

Where:

Vol is the displacement volume at design water line (m3).

Figure 1 shows the speed limit curve for a craft to be considered as a high speed craft.

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0 . 0 0 2 0 0 . 0 0 4 0 0 . 0 0 6 0 0 . 0 0 8 0 0 . 0 0 1 0 0 0 . 0 0

V o l - D i s p l a c e m e n t V o l u m e ( m 3 )

0 . 0 0

2 0 . 0 0

4 0 . 0 0

6 0 . 0 0

S

p

e

e

d

(

k

n

o

ts

)

H i g h S p e e d C r a f t

Figure 1 Speed Limit for High Speed Craft

Regarding catamarans, the hydrodynamic performance depends on the wetted geometrical forms,the hulls separation and the water depth where the craft is going to sail.

3. Comparative Results Between Hull Resistance Evaluation Methods

The SHIPFLOW TM results and the slender body theory application, were compared with the

Millward [11] works for the investigation of the catamarans hull separation effect as well as theshallow water effects in a wide Froude number range.

The Millward [11] results can be compared with catamarans hull in the following range:

Length / breadth (L/b) 6.00 12.00

Breadth/draught (b/T) 1.00 3.00

Block coefficient 0.33 0,45

Froude number 0 < Fn < 1

3.1- Hulls Geometry

Two hulls geometry were used to compare the wave resistance calculation methods. The first one

utilized the mathematical model proposed by Wigley (Figure 2) and the second geometry is achine hull as indicated in figure 3.

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Figure 2: Wigley catamaran hull

Figure 3: Catamarans chine hull

The parabolic hull proposed by Wigley has been already submitted to exhaustive theoretical testsand experiments, being so well known and tested. The hull geometry in a no- dimensionalform of

the Wigley hull is given by the equation:

)]1)(41(2

1[Y

2

22

d

zxb = ( 2 )

,2

1

2

1 x 0zd-

Where b and d are constants, being b=0, 1 e d=0,0625.

4

B

S


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L

b=b ( 3 )

L

Td = ( 4 )

Where,

L = lengthB = breadth

T = draught

The chine hull catamaran form is defined by straight water lines forming a triangle in the forebody, a parallel central part forming a rectangle and a after body with triangular or rectangular

form, when considered a transom. The hull section has a V shape geometry (Figure 3).

An algorithmic was developed in the FORTRANTM for the chine hull generation. The hull iscreated following the range constraints:

- S/L => 0,2 S/L 1,0

- b/T => 10 b/T 16- Deadrise angle (degrees) 25

- Entrance bodys length 0,3 L

- Exit bodys length 0,3 L

Where:S= the distance between hulls (m)

L= crafts length (m)

B= breadth (m)T= crafts draught(m)

The catamaran hull geometry generated by the Fortran program output the hull data in a standard

format for the SHIPFLOWTM

program and the slender body program were the wave resistancecalculation are done.

Figure 4 Flow chart of the algorithmic form generator

5

Input Data

Standard OutputSlender Body

SLENDER

Standard Output

SHIPFLOWTM

Geometry


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3.2- Wigleys Hull Results

The wave coefficient (Cw) were used to compare the catamaran wave resistance results given by

the programs SHIPFLOWTM and SLENDER (slender body theory). The Wigley hull was tested,

in deep waters, for three different hulls separations (S/L=0,2, 0,4 e 1,0), were S is the distance

between the hulls center and L is the hull length.The results for a fixed hull (related to water surface) is presented in figures 7, 8 and 9.

0 . 2 0 0 . 4 0 0 . 6 0 0 . 8 0 1 . 0 0

F n

0 . 0 0

2 . 0 0

4 . 0 0

6 . 0 0

8 . 0 0

C

w

x

1

0

^

3

M i l l w a r d

S l e n d e r b o d y

S h i p f l o w

W i g l e y h u l lS / L = 0 . 2

Figure 7: Wave coefficient (Cw) Wigley case Catamaran (S/L=0.2)

0 . 2 0 0 . 4 0 0 . 6 0 0 . 8 0 1 . 0 0

F n

0 . 0 0

2 . 0 0

4 . 0 0

6 . 0 0

8 . 0 0

C

w

x

1

0

^

3

W i g l e y h u l lS / L = 0 . 4

M i ll w a r d


S h i p f l o w


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0 . 2 0 0 . 4 0 0 . 6 0 0 . 8 0 1 . 0 0

F n

0 . 0 0

2 . 0 0

4 . 0 0

6 . 0 0

8 . 0 0

C

w

x

1

0

^

3

W i g l e y h u l lS / L = 1 . 0

M i ll w a r d


S h i p f l o w


The methods shows similar tread off results. The 3D method used by SHIPFLOW TH program and

slender body theory presented different results in Froude numbers between 0.5 and 0.7. Thedifference can be explained once the SHIPFLOWTH program applied a 3D method and can taking

into account the hull interference more strong in this Froude range while Millward and Slender

program use a similar methodology (2D).The results highlight a substantial increase in the wave resistance coefficient when the hulls

distance is small showing the interference hull effect.

Figures 7, 8 and 9 indicate the following conclusions:

- small S/L indicates increase in the difference between the results given by the SHIPFLOW TM

program and the Slender program

- for 0.2 Fn 0.4 and Fn > 0.8 the results given by the SHIPFLOWTM program and the

ones given by the Slender program, compared with the Millward [11] work are very close,

what confirms the precision of all that methods for this Fround range.

- It can be seen for the Froudes number higher than 0,8 in all observed relations of S/L (0.2 ,

0.4 and 1.0) exists a converging value of Cw around 0,0002.

- It also can be percept as smaller the space between the twin hulls, higher is the Cw curveselevation for Froudes number around 0,5.

Regarding the previous results been taken with fixed hull related to the water surface, research

was done with the utilization of SHIPFLOWTM program in a free condition to find out the Cw

curve trade off, the hull under water volumes variation and the wetted surface for differentFroude numbers.

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Figures 10 and 11 show and compare the given results for the Wigley monohull in fixed and free

conditions, and in shallow and deep water (L/h=5, L = length, h = depth)

0 . 2 0 0 . 4 0 0 . 6 0 0 . 8 0 1 . 0 0

F n

0 . 0 0

2 . 0 0

4 . 0 0

6 . 0 0

8 . 0 0

1 0 . 0 0

1 2 . 0 0

1 4 . 0 0

C

w

x

1

0

^

3

W i g l e y m o n o h u l l - f r e e

S h a l o w w a t e r ( L / h = 5 )D e e p w a t e r

Figure 10: Cw values for monohull in a free condition

0 . 2 0 0 . 4 0 0 . 6 0 0 . 8 0 1 . 0 0

F n

0 . 0 0

2 . 0 0

4 . 0 0

6 . 0 0

8 . 0 0

1 0 . 0 0

1 2 . 0 0

1 4 . 0 0

C

w

x

1

0

^

3

W i g l e y m o n o h u l l - f ix e d

S h a l lo w w a t e r ( L / h = 5 )

D e e p w a t e r

Figure 11: Cw values for monohull in a fixed condition

Results indicate relevant difference in the Cw values for Froudes number between 0.3 and 0.6

for the free and fixed monohull condition related to the water surface. Those differences are even

higher when the depth effect is included. When the sea or river bottom is close to the hull thecraft draft is increased and as a consequence displacement and wetted area is increased.

The same test were done for twin hull craft. Figures 12, 13 and 14 are shown the results given forthe Wigley catamaran hull for different twin hull space (S/L) and depths in a free condition.

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0 . 2 0 0 . 4 0 0 . 6 0 0 . 8 0 1 . 0 0

F n

0 . 0 0

2 . 0 0

4 . 0 0

6 . 0 0

8 . 0 0

1 0 . 0 0

1 2 . 0 0

1 4 . 0 0

C

w

x

1

0

^

3

S h a l l o w w a t e r ( L / h = 5 )

D e e p w a t e r

W i g l e y c a t a m a r a n - f r e eS / L = 0 , 2

Figure 12: Cw values for Wigley Catamaran in a free condition and S/L = 0.2

0 . 2 0 0 . 4 0 0 . 6 0 0 . 8 0 1 . 0 0

F n

0 . 0 0

2 . 0 0

4 . 0 0

6 . 0 0

8 . 0 0

1 0 . 0 0

1 2 . 0 0

1 4 . 0 0

C

w

x

1

0

^

3

S h a l l o w w a t e r ( L / h = 5 )

D e e p w a t e r



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0 . 2 0 0 . 4 0 0 . 6 0 0 . 8 0 1 . 0 0

F n

0 . 0 0

2 . 0 0

4 . 0 0

6 . 0 0

8 . 0 0

1 0 . 0 0

1 2 . 0 0

1 4 . 0 0

C

w

x

1

0

^

3

S h a l l o w w a t e r ( L / h = 5 )

D e e p w a t e r



It can be understood from the Figure 12, 13 and 14, when compared to the Figures 7, 8 e 9 thatthere is a tendency to higher values of Cw for the free condition for Froude numbers between 0.3

and 0.6 for monohulls. Regarding the Catamaran, this effect is even higher when the hulls

distance is small, being that effect increased when the shallow water effect occurs. For Froudenumbers greater than 0.7 results shown that the Cw values are basically the same for monohull as

well as catamaran it does no matter the hulls distance, what leads us to conclude. For Froude

numbers greater than 0,7 the hull interference practically does not exist and the catamaran wave

resistance can be calculated by two times the monohull resistance.In the previous Figures, Cw values for Froude numbers between 0.3 and 0.6 are greater in the

free case. That happens because of the sinking of the hull.

Figures 15, 16, 17 and 18 show an increased percentage of the under water volume as well as the

wetted hull surface. The monohull volume increases approximately 12% related to the fixed hull

condition in deep water and approximately 20% in shallow waters (L/h = 5).

In the Catamarans case this effect is powered, as a consequence of the hulls interference, as can

be seen in the graphics of figure 16, 17 and 18. Figure 17 shows an increasing of 33% in thevolume when the twin hull distance is 0.2 (S/L) in shallow waters and Froude numbers between

0.3 and 0.5. It is also shown that the Cw curve reaches a pick, for deep water around 0.5, and

shift the peak for Froude number around 0.4 when the shallow water effect occur.

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0 . 0 0 0 . 2 0 0 . 4 0 0 . 6 0 0 . 8 0 1 . 0 0

F n

0 . 0 0

5 . 0 0

1 0 . 0 0

1 5 . 0 0

2 0 . 0 0

2 5 . 0 0

3 0 . 0 0

3 5 . 0 0

V

a

ria

to

in

o

f

th

e

su

b

m

e

rge

d

vo

lu

m

e

(

%

)

S h a l l o w w a t e r ( L / h = 5 )

D e e p w a t e r


Figure 15: Volume variation for monohull in a free condition

0 . 0 0 0 . 2 0 0 . 4 0 0 . 6 0 0 . 8 0 1 . 0 0

F n

0 . 0 0

5 . 0 0

1 0 . 0 0

1 5 . 0 0

2 0 . 0 0

2 5 . 0 0

3 0 . 0 0

3 5 . 0 0

V

a

ria

tio

n

o

f

th

e

s

u

b

m

e

rg

e

d

vo

lu

m

e

(

%

)

S h a l l o w w a t e r ( L / h = 5 )

D e e p w a t e r


Figure 16: Volume variation for Catamaran in a free condition and S/L = 0.2

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0 . 0 0 0 . 2 0 0 . 4 0 0 . 6 0 0 . 8 0 1 . 0 0

F n

0 . 0 0

5 . 0 0

1 0 . 0 0

1 5 . 0 0

2 0 . 0 0

2 5 . 0 0

3 0 . 0 0

3 5 . 0 0

V

a

ria

tio

n

o

f

th

e

su

b

m

e

rge

d

vo

lu

m

e

(

%

)

S h a l lo w w a t e r ( L / h = 5 )

D e e p w a t e r



0 . 0 0 0 . 2 0 0 . 4 0 0 . 6 0 0 . 8 0 1 . 0 0

F n

0 . 0 0

5 . 0 0

1 0 . 0 0

1 5 . 0 0

2 0 . 0 0

2 5 . 0 0

3 0 . 0 0

3 5 . 0 0

V

a

ria

tio

n

o

f

th

e

su

b

m

e

rg

e

d

vo

lu

m

e

(

%

)

S h a l lo w w a t e r ( L / h = 5 )

D e e p w a t e r



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0 . 0 0 0 . 2 0 0 . 4 0 0 . 6 0 0 . 8 0 1 . 0 0

F n

0 . 0 0

5 . 0 0

1 0 . 0 0

1 5 . 0 0

2 0 . 0 0

V

a

ria

tio

n

o

f

th

e

w

e

tte

d

su

rfa

c

e

a

re

a

(

%

)

S h a l lo w w a t e r ( L / h = 5 )

D e e p w a t e r


Figure 19: Wetted surface variation for monohull in a free condition

0 . 0 0 0 . 2 0 0 . 4 0 0 . 6 0 0 . 8 0 1 . 0 0

F n

0 . 0 0

5 . 0 0

1 0 . 0 0

1 5 . 0 0

2 0 . 0 0

V

a

ria

tio

n

o

f

th

e

w

e

tte

d

s

u

rfa

c

e

a

re

a

(

%

)

S h a l lo w w a t e r ( L / h = 5 )

D e e p w a t e r


Figure 20: Wetted surface variation for Catamaran in a free condition and S/L = 0.2

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0 . 0 0 0 . 2 0 0 . 4 0 0 . 6 0 0 . 8 0 1 . 0 0

F n

0 . 0 0

5 . 0 0

1 0 . 0 0

1 5 . 0 0

2 0 . 0 0

V

a

ria

tio

n

o

f

th

e

w

e

tte

d

sur

fa

c

e

a

re

a

(

%

)

S h a l lo w w a t e r ( L / h = 5 )

d e e p w a t e r



0 . 0 0 0 . 2 0 0 . 4 0 0 . 6 0 0 . 8 0 1 . 0 0

F n

0 . 0 0

5 . 0 0

1 0 . 0 0

1 5 . 0 0

2 0 . 0 0

V

a

ria

tio

n

o

f

th

e

w

e

tte

d

s

u

rfa

c

e

a

re

a

(

%

)

S h a l lo w w a t e r ( L / h = 5 )

D e e p w a t e r



The same effect that happens in the volume also happens in the wetted surface, however with anincreased percentage smaller, around 19% in the most critical condition (shallow waters and

relationship S/L = 0.2).

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3.3 - CATAMARAN CHINE HULL RESULTS

Chengyi [12] work shows that the hull shape of symmetrical catamaran hull has little influence in

the results of catamaran wave resistance. To investigate a different catamaran chine hull

geometry (hull separation and water deep effect) with SHIPFLOWTM program an algorithm was

used that quickly modifies the geometric forms of the hull without a lot of effort.

The hull generated for analysis has the following characteristics:

Length (L): 40 m

Breadth (b): 3,5 m

Draught (T): 1.5 mDeadrise Angle (A): 25

The results of wave resistance were obtained using the program SHIPFLOWTM using the same

twin hull separation and water depths analyzed in the Millward [11] work.s.

The nomenclature used in the variables it was defined according to outlines below:

Figure 23: 40 meter catamaran hull section

Figure 24: Waterline shape

The results are analyzed accordingly to Froudes numbers (Fn) and speeds (V) presented in tableII.

15

b=breadthh=depth

S = space between hulls

L = length


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Table II - Froude number and speed for a 40 m chine hull catamaran

Fn V ( m/s ) V ( knots )

0,2 3,96 7,70

0,3 5,94 11,54

0,4 7,92 15,390,5 9,90 19,24

0,6 11,90 23,12

0,7 13,86 26,93

0,8 15,84 30,78

0,9 17,82 34,62

1,0 19,80 38,48

Figures 25, 26 and 27 show the main results obtained by the program SHIPFLOWTM for chine

hull catamaran in the free condition.

0 . 2 0 0 . 4 0 0 . 6 0 0 . 8 0 1 . 0 0

F n

0 . 0 0

2 . 0 0

4 . 0 0

6 . 0 0

8 . 0 0

1 0 . 0 0

1 2 . 0 0

1 4 . 0 0

1 6 . 0 0

C

w

x

1

0

^

3

C a t a m a r 4 0 m - l i v r e

S / L = 0 , 2

g u a s r a s a s ( L / h = 6 )

g u a s r a s a s ( L / h = 5 )

g u a s r a s a s ( L / h = 4 )

g u a s p r o f u n d a s

Figure 25: Comparison of CW for S/L = 0,2 in several water depths.

16

Catamaran 40m - free

Shallow water (L/h=6)Shallow water (L/h=5)Shallow water (L/h=4)

Deep water


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0 . 2 0 0 . 4 0 0 . 6 0 0 . 8 0 1 . 0 0

F n

0 . 0 0

2 . 0 0

4 . 0 0

6 . 0 0

8 . 0 0

1 0 . 0 0

1 2 . 0 0

1 4 . 0 0

1 6 . 0 0

C

w

x

1

0

^

3


S / L = 0 , 4

g u a s r a s a s ( L / h = 6 )

g u a s r a s a s ( L / h = 5 )

g u a s r a s a s ( L / h = 4 )


Figure 26: Comparison of CW for S/L = 0,4 in several water depths.

0 . 2 0 0 . 4 0 0 . 6 0 0 . 8 0 1 . 0 0

F n

0 . 0 0

2 . 0 0

4 . 0 0

6 . 0 0

8 . 0 0

1 0 . 0 0

1 2 . 0 0

1 4 . 0 0

1 6 . 0 0

C

w

x

1

0

^

3


S / L = 1 , 0

g u a s r a s a s ( L / h = 6 )

g u a s r a s a s ( L / h = 5 )

g u a s r a s a s ( L / h = 4 )


Figure 27: Comparison of Cw for S/L = 1,0 in several water depths

Figures 25, 26 and 27 allowed the following conclusions:

- Figure 25 shows that critical Cw (the peak of Cw curve) tends to increase when the water

depth decreases. It is also observed that the hulls interference is practically the same for

Froude numbers higher than 0,7 in any water deep.

- For shallow water, the peak of Cw curve is close to 0,4 Froud number.

- Between 0,6 and 0,7 Froud number the wave resistance decrease when the water deep

decrease for all S/L range.

17

Shallow water (L/h=6)



Deep water



Shallow water (L/h=4)Deep water




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- For Froude numbers lower than 0,3 the results are practically the same for all S/L and L/h

range.

- Figures 26 and 27 show that when increasing the separation between twin hulls, Cw

coefficient achieves the lower value. However, Cw coefficient maintain the critical value for

Froude number 0,4 considering L/h 0,5).

For different S/b, Froude number where begins the negative interference - Fro (reduction in theresistance) can be calculated by the following expressions:

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2

3)1,0(057.055.0)6,1(

+==

Lb

SFro (A)

2

3)1,0(

050.055.0)0,2(

+==

Lb

SFro (B)

2

3)1,0(046.055.0)6,2(

+==

Lb

SFro (C) (6)

2

3)1,0(044.055.0)2,3(

+==

Lb

SFro (D)

2

3)1,0(042.055.0)0,6(

+=

Lb

SFro (E)

- Using the equations proposed by Chengyi [12], for blockage Froude (Frb) and the Froudenumber where the null interference (Fro) begins, the following values were calculated for the

catamaran analyzed in Figures 25, 26 and 27 respectively.

For Figure 25 (S/L=0,2 - k/b = 2,66) => Fro = 0,640 and Frb = 1,00

For Figure 26 (S/L=0,4 - k/b = 5,33) => Fro = 0,634 and Frb = 1,59

For Figure 27 (S/L=1,0 - k/b =13,33) = >Fro = 0,632 and Frb = 2,67

- It is observed that smaller distance between hulls, larger the value of Fro and the beginning of

the negative interference. In the catamaran case (chine hull), the negative interference begins,

according to the equation of Chengyi [10], in numbers of Froude higher than 0,63.

The submerged volume and wetted area variation had the following results:

0 . 0 0 0 . 2 0 0 . 4 0 0 . 6 0 0 . 8 0 1 . 0 0

F n

0 . 0 0

5 . 0 0

1 0 . 0 0

1 5 . 0 0

2 0 . 0 0

2 5 . 0 0

3 0 . 0 0

3 5 . 0 0

Va

ria

tio

n

o

f

th

e

su

b

m

erge

d

vo

lu

m

e

(%

)

C a t a m a r a n 4 0 m - f r e eS / L = 0 . 2

S h a l l o w w a t e r ( L / h = 5 )

D e e p w a t e r

Figure 28: 40 m catamaran submerged volume variation in the free condition and S/L = 0,2

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0 . 0 0 0 . 2 0 0 . 4 0 0 . 6 0 0 . 8 0 1 . 0 0F n

0 . 0 0

5 . 0 0

1 0 . 0 0

1 5 . 0 0

2 0 . 0 0

2 5 . 0 0

3 0 . 0 0

3 5 . 0 0

V

a

ria

tio

n

o

f

th

e

s

u

b

m

e

rg

e

d

vo

lu

m

e

(%

)

C a t a m a r a n 4 0 m - fr e eS / L = 1 . 0

S h a l l o w w a t e r ( L / h = 5 )

D e e p w a t e r

Figure 29 - 40 m catamaran submerged volume variation in the free condition and S/L = 1,0

The 40 m catamaran submerged volume suffers significant increase in shallow water and when

the interference effect is present. The percentage of sinking is 33%. The results show that when

both effects are present the resistance increases to very high value.In deep waters, the effects that take to an abrupt increase of the submerged volume increase to

13% (Fr = 0.5) and than low down to 11% for Fr > 0.6.

For 0,6 < Fn < 0,8 the submerged volume decrease in shallow waters compared with deep waters.

Following, the variation of the wetted surface will be shown for catamaran separation hull (S/L)

of 0,2 and 1,0 in shallow waters (L/h=5) and deep water.

0 . 0 0 0 . 2 0 0 . 4 0 0 . 6 0 0 . 8 0 1 . 0 0

F n

0 . 0 0

4 . 0 0

8 . 0 0

1 2 . 0 0

1 6 . 0 0

2 0 . 0 0

V

ariatio

n

o

f

th

e

w

etted

su

rfa

ce

area

(%

)


S h a l l o w w a t e r (L / h = 5 )

D e e p w a t e r

Figure 30 - 40 m catamaran wetted surface variation in the free condition and S/L = 0,2

20


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0 . 0 0 0 . 2 0 0 . 4 0 0 . 6 0 0 . 8 0 1 . 0 0

F n

0 . 0 0

5 . 0 0

1 0 . 0 0

1 5 . 0 0

2 0 . 0 0

V

a

ria

tio

n

o

f

th

e

w

e

tte

d

s

ur

fa

c

e

a

re

a

(%

)


S h a l l o w w a t e r ( L / h = 5 )

D e e p w a t e r

Figure 31 - 40 m catamaran wetted surface variation in the free condition and S/L = 1,0

The wetted surface variation for low Froude number (to approximately 0,3) is similar in all the

cases, however when Froude number reaches 0,4 a substantial increase in the wetted surface is

verified, mainly when the interference between hulls and the shallow water effects happen.

Millward [11] works was used to compare the results generated by the program SHIPFLOWTM

although his works did not contemplate the free craft condition.

The results were expressed in the form of non-dimensional (C *) wave resistance coefficient,

adopted Millward [11] works.

L

Tbg

R22

8R*

=

(7)

2

*C*

Fn

R= (8)

Where,

R = wave resistanceL = catamaran length (m)

b = breadth (m)

T = draft (m)

= Fluid density (kg/m3)

g = acceleration of gravity (m/s2)

Fn = Froude number

21


22/31

Figure 32: Catamaran C* coefficient for S/L = 0,2 in shallow and deep waters (Millward[11])

0 . 2 0 0 . 4 0 0 . 6 0 0 . 8 0 1 . 0 0

F n

0

2

4

6

8

1 0

1 2

1 4

1 6

1 8

C

*

C a t a m a r a n 4 0 m - f i x e dS / L = 0 , 2

S h a l l o w w a t e r ( L / h = 5 )

D e e p w a t e r

Figure 33: Catamaran C* coefficient for S/L = 0,2 in shallow and deep waters (SHIPFLOWTM)

Figures 32 and 37 show that the water depth as well as the distance between catamaran hulls has

low influence in the C* values for Froude numbers smaller than 0,3 and larger than 0,7. For

Froude numbers higher than 0,7 there is a convergence of C* values.

22


23/31

Figure 34: Catamaran C* coefficient for S/L = 0,4 in shallow and deep water (Millward[11]).

0 . 2 0 0 . 4 0 0 . 6 0 0 . 8 0 1 . 0 0

F n

0

2

4

6

8

1 0

1 2

1 4

C

*

C a t a m a r a n 4 0 m - f i x e d

S / L = 0 , 4

S h a l l o w w a t e r ( L / h = 5 )

D e e p w a t e r

Figure 35: Catamaran C* coefficient for S/L = 0,4 in shallow and deep water (SHIPFLOWTM).

23


24/31

Figure 36: Catamaran C* coefficient for S/L = 1,0 in shallow and deep water (Millward[11]).

0 . 2 0 0 . 4 0 0 . 6 0 0 . 8 0 1 . 0 0

F n

0

2

4

6

8

1 0

C

*

C a t a m a r a n 4 0 m - f i x e dS / L = 1 , 0

S h a l l o w w a t e r ( L / h = 5 )

D e e p w a t e r

Figure 37: Catamaran C* for S/L = 1,0 in shallow and deep water (SHIPFLOWTM)

The C* results obtained by SHIPFLOWTM program for the 40 m catamaran when compared withMillward [11] results, shown that the C* curve has the same aspect and it presents very close

results.

2.4 - CATAMARAN TRIMINVESTIGATION

Study for trim verification in high speed was conduct. Computational tests were conducted for

hull separation (S/L) 0,2 and 1,0. Shallow water (L/h=5) and deep waters were investigated.Figures 38 and 39 present the results in a graphic form.

24


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0 . 0 0 1 0 . 0 0 2 0 . 0 0 3 0 . 0 0 4 0 . 0 0

L e n g t h ( m )

0 . 0 00 . 1 00 . 2 00 . 3 00 . 4 00 . 5 00 . 6 00 . 7 00 . 8 00 . 9 01 . 0 01 . 1 01 . 2 01 . 3 01 . 4 01 . 5 01 . 6 01 . 7 01 . 8 01 . 9 02 . 0 0

2 . 1 02 . 2 02 . 3 02 . 4 02 . 5 02 . 6 02 . 7 02 . 8 02 . 9 03 . 0 0

D

ra

u

g

h

t

(

m

)

C a t a m a r a n 4 0 m - f r e eS / L = 0 , 2

D e e p w a t e r

F n = 0 , 2 F n = 0 , 3

F n = 0 , 4 F n = 0 , 5 F n = 0 , 6 F n = 0 , 7

F n = 0 , 8 F n = 0 , 9

F n = 0

Figure 38: Trim variation for different Froud numbers (S/L=0.2 and deep water).

It could be observed that for Froude numbers up to 0,3 dynamic trim is significant and the craft

sinks parallel.

When the catamaran achieve Froude number around 0,4 the catamaran acquires trim by stern

with significant draught variation. Above Froude number 0,5 the sinking happens practically withthe same trim angle with small variations.

Figure 39 presents the same test but in shallow water (L/h=5).

Figure 39: Trim variation for different Foude numbers (S/L = 0,2 L/h=5).

The bottom effect increases the dynamic trim as show in figure 39. Comparing with the sinking

in deep waters is observed that this sinking is larger in 29%.

Above Froude number 0,6 the stern reduces the sinking reaching draught of approximately 2,3m,

that is practically equal the value achieve in deep waters (2,4m). Therefore it can be concludedthat the effect of shallow waters only provokes significant sinking variation for the Froude range

between 0,4 and 0,6.

25


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2.5 - INVESTIGATION OF THE WAVES GENERATED BY THE HULL

The objective of the analysis of waves generated by the passage of the craft is the verification of

the waves heights spread starting from the catamaran hull to a certain distance. Here the distance

was considered as 60% of the hull length.

Figure 40 shows the positioning of a catamaran hull in x-y plane. The points in the graph

represent the center of each panel used to represent the free surface.

- 2 0 . 0 0 0 . 0 0 2 0 . 0 0 4 0 . 0 0 6 0 . 0 0 8 0 . 0 0

E i x o X - E x t e n s o l o n g i t u d i n a l

- 2 8 . 0 0

- 2 6 . 0 0

- 2 4 . 0 0

- 2 2 . 0 0

- 2 0 . 0 0

- 1 8 . 0 0

- 1 6 . 0 0

- 1 4 . 0 0

- 1 2 . 0 0

- 1 0 . 0 0

- 8 . 0 0

- 6 . 0 0

- 4 . 0 0

- 2 . 0 0

0 . 0 0

E

ixo

X

-

E

xte

n

s

o

tr

a

n

s

ve

rsa

l

C a t a m a r 4 0 m S / L = 0 , 2P o s i o d o s c e n t r i d e s d o s p a i n i s

Figure 40: Position of a 40 m catamaran hull and the free surface.

Figures 41 to 44 present a traverse cut plane showing the elevation of the points of the freesurface that define the wave height or elevation of each panel centerof the free surface. These

points are defined starting from the lateral of the hull of the catamaran in deep water and shallow

waters (L/h=5) condition and hull spacing S/L = 0,2, that is considered to be the most restrictive.

26

Catamaran 40 m S/L = 0.2Position of the Centers of the panels


27/31

- 3 0 . 0 0 - 2 0 . 0 0 - 1 0 . 0 0 0 . 0 0

E i x o Y - d i s t n c i a t r a n s v e r s a l d o c a s c o ( m )

- 1 . 5 0

- 1 . 4 0

- 1 . 3 0- 1 . 2 0

- 1 . 1 0

- 1 . 0 0

- 0 . 9 0- 0 . 8 0

- 0 . 7 0- 0 . 6 0

- 0 . 5 0

- 0 . 4 0

- 0 . 3 0- 0 . 2 0

- 0 . 1 0

0 . 0 0

0 . 1 0

0 . 2 00 . 3 00 . 4 0

0 . 5 0

0 . 6 0

0 . 7 00 . 8 0

0 . 9 0

1 . 0 0

1 . 1 0

1 . 2 01 . 3 0

1 . 4 0

1 . 5 0

A

ltu

ra

d

as

o

n

d

as

gerada

s

(

m

)

C a t a m a r 4 0 m - li v r eS / L = 0 , 2 - g u a s r a s a s ( L / h = 5 )

F n = 0 , 3

Figure 41: Wave height generated in shallow waters (L/h = 5) for Fn = 0,3

- 3 0 . 0 0 - 2 0 . 0 0 - 1 0 . 0 0 0 . 0 0

E i x o Y - d i s t n c i a t r a n s v e r s a l a o c a s c o ( m )

- 1 . 5 0- 1 . 4 0- 1 . 3 0- 1 . 2 0- 1 . 1 0- 1 . 0 0- 0 . 9 0- 0 . 8 0- 0 . 7 0- 0 . 6 0- 0 . 5 0

- 0 . 4 0- 0 . 3 0- 0 . 2 0- 0 . 1 0

0 . 0 00 . 1 00 . 2 00 . 3 00 . 4 00 . 5 00 . 6 00 . 7 00 . 8 00 . 9 01 . 0 01 . 1 01 . 2 01 . 3 01 . 4 01 . 5 0

A

ltu

ra

d

a

s

o

n

d

a

s

g

e

ra

d

a

s

(

m

)

C a t a m a r 4 0 m - li v r eS / L = 0 , 2 - g u a s p r o f u n d a s

F n = 0 , 3

Figure 42: Wave height in deep water for Fn=0,3

27

Catamar 40 m - free

S/L = 0.2 shallow water

Fn = 0.3

Height of the waves (m)


Catamar 40 m - free

S/L = 0.2 deep water

Fn = 0.3


28/31

- 3 0 . 0 0 - 2 0 . 0 0 - 1 0 . 0 0 0 . 0 0

E i x o Y - d i s t a 6 n c i a t r a n s v e r s a l a o c a s c o ( m )

- 1 . 5 0- 1 . 4 0- 1 . 3 0- 1 . 2 0- 1 . 1 0- 1 . 0 0- 0 . 9 0- 0 . 8 0- 0 . 7 0- 0 . 6 0- 0 . 5 0- 0 . 4 0- 0 . 3 0- 0 . 2 0- 0 . 1 0

0 . 0 00 . 1 00 . 2 00 . 3 00 . 4 0

0 . 5 00 . 6 00 . 7 00 . 8 00 . 9 01 . 0 01 . 1 01 . 2 01 . 3 01 . 4 01 . 5 0

A

ltu

ra

d

a

s

o

n

d

a

s

g

e

ra

da

s

(

m

)

C a t a m a r 4 0 m - l i v r eS / L = 0 , 2 - g u a s r a s a s ( L / h = 5 )

F n = 0 , 4

Figure 43: Wave height in shallow water (L/h = 5) for Fn = 0,4

- 3 0 . 0 0 - 2 0 . 0 0 - 1 0 . 0 0 0 . 0 0

E i x o Y - d i s t n c i a t r a n s v e r s a l a o c a s c o ( m )

- 1 . 5 0- 1 . 4 0- 1 . 3 0- 1 . 2 0- 1 . 1 0- 1 . 0 0- 0 . 9 0- 0 . 8 0- 0 . 7 0- 0 . 6 0- 0 . 5 0- 0 . 4 0- 0 . 3 0

- 0 . 2 0- 0 . 1 0

0 . 0 00 . 1 00 . 2 00 . 3 00 . 4 00 . 5 00 . 6 00 . 7 00 . 8 00 . 9 01 . 0 01 . 1 01 . 2 01 . 3 01 . 4 01 . 5 0

A

ltu

ra

d

as

o

n

d

a

s

g

era

d

a

s

(

m

)

C a t a m a r 4 0 m - l i v r eS / L = 0 , 2 - g u a s p r o f u n d a s

F n = 0 , 4

Figure 44: Wave height in deep water for Fn = 0,4

Figures 41 to 44 indicate:

- The SHIPFLOWTM program allowed to calculate the wave high generates by the catamaran

hull and also investigate this effect in the river shore.

- The effect of shallow water is very important when consider the wave high generate by the

catamaran hull.

28



Height of the waves (m)Height of the waves (m)Height of the waves (m)


Catamar 40 m - free

S/L = 0.2 shallow water Fn = 0.4

Catamar 40 m - free

S/L = 0.2 deep water Fn = 0.4


29/31

4 CONCLUSION

The SHIPFLOWTM and SLENDER computer software present good results to analyze the

catamaran in a preliminary design phase.

Some conclusions were extracted from catamaran simulation:

- For S / L > 0,6 are not verified significant effects of interference between the hulls and the

wave resistance can be calculated as a twin hulls infinitely separated.

- The type of the hull section is not a factor that modifies the wave resistance significantly.

- The maximum positive interference happens around Froude number = 0,5 for deep waters and

0,4 for shallow waters.

- Difference between SHIPFLOWTM and SLENDER program is high for smaller ration S / L

- For 0.2 Fn 0.4 and Fn > 0.8, the results obtained by SHIPFLOWTM and SLENDER

program, compared with Millward [11] works are very close.

- It is observed that for Froude numbers above than 0,8, in all S/L range (0.2, 0.4 and 1.0) a

convergence exists for values of Cw around 0,0002.

- It is also observed that as smaller the spacing between hulls greater is the elevation of the

curve of Cw, for Froude number around 0,5.

- When the effect of shallow waters is present, the interference is negative for Froude number

starting from 0,7.

- The effect of the hull separation added to the shallow water effect cause a significant increase

in critical Cw value.

- The wave high generate by the hull can be studied by SHIPFLOWTM. The results can be used

to study and minimize the effect in river shore.

29


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5 REFERENCES

1. Harward, SV. AA. "Resistance and Propulsion of Ships" , New York

2. J.L. Hess & A.M.O. Smith,1964, "Calculation Of Non-lifting Potential Flow About

Arbitrary Three- Dimensional Bodies".

3. Nishimoto, K., 1998, "Semi-deslocamento Aplicando Mecnica dos Fluidos Computacional".

4. Dawson, C.W., 1977, "A practical Computer Method for Solving Ship Wave Problems"2

International Conf. On Numerical Ship Hydrodynamics, Berkeley.

5. Picano, Hamilton P.,1999, "Resistncia ao Avano: Uma Aplicao de Dinmica dos

Fluidos Computacional" MSc, Thesis, COPPE/UFRJ, Rio de Janeiro.

6. Williams, M. A., "Otimizao da Forma do Casco de Embarcaes Tipo Swath", MSc,Thesis, COPPE/UFRJ, 1994, Rio de Janeiro.

7. Havelock, T. H., "The Calculation of Wave Resistance". Proc. Of the RS, series A, vol. 144,1934.

8. Newman, J. N. , Marine Hydrodynamics. The MIT press, Cambridge, Massachusetts andLondon, England, 1977.

9. Lunde, J. K. "On the Linearized Theory of Wave Resistance for Displacement Ship in Steadyand Accelerated Motions". Trans SNAME, vol. 59, pp. 25-85

10. FLOWTECH, 1998, "SHIPFLOWTM 2.4, User manual".

11. Millward, A., 1992, "The Effect of Hull Separation and Restricted Water Depth on

Catamaran Resistance" The Royal Institution of Naval Architects, 1992

12. Chengyi, Wang "Resistance Characteristic of High-Speed Catamaran and its Application"

Marine Design and Research Institute of China, 1994.

13. Everest J. T. "Some research and hydrodynamics of catamarans and multi-hulled vessels in

calm water" Trans. N.E.C.I.E.S., vol. 84, pp. 129-148, 1968.

14. Kostjukov A. "Wave resistance of a ship near walls", J. Gydromech, vol. 35, p 9-13, 1977

15. Insel M. and Molland A. F. "An investigation into the resistance components of high speed

displacement catamaran" Royal Institution of Naval Architects, Spring Meeting, paper no.11,1991.

16. Jane's "High-Speed Marine Transportation, 1996-97 Edition

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17. Fry ED & Graul T. "Design and application of modern high-speed catamarans, MarineTechnology, 1972.

18. Michell, J. H., "The Wave Resistance of a Ship". Phil. Mag., Series 5, vol. 45, pp.106-123,

1898.

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