High Speed Catamaran Design

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Ocean Engineering Engineering

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Multiple criteria optimization applied to high speed catamaran preliminary design H.B. Moraesa, J.M. Vasconcellos b,Ã, P.M. Almeida c a

Federal University of Para´ , Bele´ m/Para m/Para´ , Brazil  COPPE, Federal University of Rio de Janeiro, Brazil  c COPPE, Rio de Janeiro, Brazil 

b

Received 6 June 2005; accepted 1 December 2005

Abstract

The demand for high-speed craft (mainly catamarans) used as passenger vessel has increased significantly in the recent years. Looking towards the future and trying to respond to the increasing requirement, high-speed crafts international market is passing through deep changes. Different types of high-speed crafts are being used for passenger transport. However, catamarans and monohulls have been the main choice not only for passenger vessel but also as ferryboat. Generally speaking, the efficient hydrodynamic hull shapes, engine improvements, and lighter hull structures using aluminum and composite materials make possible the increase in cruising speed. The high demand for catamarans are due to its proven performance in calm waters, large deck area compared to monohull crafts and higher higher speed efficiency efficiency using less power. Although Although the advantages advantages aforementio aforementioned, ned, the performan performance ce of catamaran catamaran vessels in wave conditions still needs to be improved. The high-speed crafts (HSC) market is demanding different HSC designs and a wide range of dimensions focusing on lower resistance and power for higher speed. Therefore, the hull resistance optimization is a key element for a high-speed hull success. In addition to that, trade-off high-speed catamaran (HSCat) design has been improved to achieve main characteristics and hull geometry. This paper presents a contribution to HSCat preliminary design phase. The HSCat preliminary design problem is raised and one solution is attained by multiple criteria optimization technique. The mathematical model was developed considering: hull arrangement (area and volume), lightweight material application (aluminum hull), hull resistance evaluation (using a slender body theory), as well as wave interference effect between hulls, calculated with 3D theory application. Goal programming optimization system was applied to solve the HSCat preliminary design. Finally Finally this paper paper includes includes an illustrat illustrative ive example example showing showing the mathematical mathematical model and the optimizatio optimization n solution. solution. An HSCat HSCat passenger inland transport in Amazon area preliminary design was used as case study. The problem is presented, the main constrains analyzed and the optimum solution shown. Trade off graphs was also included to highlight the mathematical model convergence process. r 2006 Elsevier Ltd. All rights reserved. Keywords: High speed craft; Ship design; Multiple criteria optimization

1. Introduction Introduction

The Amazon region is one of the poorest areas in Brazil, with with a low low popu popula latio tion n dens densit ity. y. Few Few rail railro road ads, s, road road precar precariou iousne sness ss and airpla airplane ne ticket ticket high high cost cost impos imposee the river river as an ava availa ilable ble alterna alternativ tivee to transp transport ort cargo cargo and passenger. The majority of the eight million habitants of  Ã

Corresponding Corresponding author. author. Tel.: +55 21 25628742; 25628742; fax: +55 21 25628715. 25628715. E-mail address: [email protected] (J.M. Vasconcellos).

0029-80 0029-8018/ 18/$ $ - see front matter matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.oceaneng.2005.12.009 doi:10.1016/j.oceaneng.2005.12.009

the states in the Brazilian Amazon region need a low-priced and reliable means of transport. The rivers in this area are, therefore, an attractive way to develop cargo and passenger transport. Desp Despit itee this this unde undesi sira rabl blee tran transpo sport rt situ situat atio ion n in the the Amazon area, some development can be seen. In Bele ´ ´ mMacapa ´ ´ river line, there is one SES (surface effect ships) and some moderate speed monohulls sailing and changing the old scenario of low speed wood or steel vessels. New techno technolog logy y is also also changi changing ng the way people people at Amazo Amazon n

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Nomenclature

L B  b T  D S  N  N trip N pass P tp P ot SPF Dist V  C ad P est M  LWork

total length (m) catamaran beam (m) twin hull beam (m) draught (m) vessel height (including superstructure) (m) space between hulls (m) rpm crew number passenger number average passenger weight (135 kg for long trips and 80 kg for short trips) cruising power (HP) specific fuel consumption (0.19 kg/HP h ) at 1900 rpm in average distance (km) cruising speed (knots) consumption—water (l/passenger x day) structure weight (ton) material cost/ton (aluminum ¼ US$ 5250) hours/ton (600 for simple structures and 900 for complex structures)

travel by boat. Comfortable armchairs are replacing the hammocks (very common in Amazon area) providing more safety to passengers. Air conditioning, audio and video services are also bringing leisure to passengers. Major changes are necessary to transform the existing boat transport in a reasonable and reliable way to transport people in Amazon area. The creation of private passenger ports is urgent in almost all the Amazon area. It is unbelievable, but many times passengers can spend up to three days for boat departure. In these cases many passengers end up using the boat as temporary hostels. Currently, investments in updating equipments and technologies have been the main concern for ship owners in Amazon region. Competition in Amazon passenger transport market is remarkable. Traditional companies are trying to improve their management procedures and relationship with their clients. Nevertheless, technological advancements in Amazon region are insignificant if  compared to the real needs (see Figs. 1 and 2), some changes can be noticed. Comfort, safety and speed are the main challenges to achieve. Fig. 3 presents the increasing in speed considering boats used in Amazon region since 1950. The graph shows an average speed of 13 knots. In 1998 the Arapari III craft  ´ line with cruising started to operate in Belem-Macapa speed of 28 knots. In 2000 the craft named Atlantico I serving the same line started to sail at cruising speed of 30 knots. These new aluminum vessels reduced the trip BelemMacapa ´ from 24 to 11 h in average. This paper focuses the HSCat preliminary design with the objective of helping designers, ship owners and

H  P equi C est C equi C ma N va T n T p C TA sm enc Alim Prcomb Prlub T s C f  Rn V  L Am P  m

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man–hour cost (US$ 30) equipment weight (ton) structure cost (US$) equipment cost (US$) engine cost (US$) number of trip/year sailing time (h) stop time at schedule (h) building cost (US$) crew average salary (US$ 710,00) social taxes ( 0.87) crew average expenses (food)—US$ 4.00 oil cost (US$/t) lub cost (US$/t) cruising time (s) frictional resistance coefficient Reynolds number speed (m/s) length (m) wetted area (m2) density (kg/m3) viscosity (m2/s)

government investment analysts to assess the potential of  passenger transport in many Amazon routes. Although the focus is the Amazon area, the mathematical model has a broad-spectrum and can be applied in many places. The mathematical model presented herein is for catamaran craft. Monohull vessel mathematical model should also be assessed and compared to determine the best choice. 2. Design methodology

The mathematical model developed herein for HSCat river transport preliminary design was organized as per the flowchart presented in Fig. 4. This paper includes module II (HSCat Preliminary Design) and IV (HSCat Cost Analysis) for HSCat preliminary design. 3. HSCat preliminary design

3.1. Power evaluation Hull hydrodynamic resistance and power assessment is one of the most important aspect to evaluate in HSC design during preliminary phase. The method applied herein to build the mathematical model is based on slender body theory for wave resistance and flat plate theory to frictional resistance. Moraes et al. (2004) researched and compared the slender body theory and the 3D theory results. A broadspectrum analysis was carried out to compare wave

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Fig. 1. A poor ‘‘terminal’’ in Rondonia.

Fig. 2. A typical terminal in Macapa  ´ .

35 30 25

   )   s    t   o 20   n    k    (    d 15   e   e   p    S 10

5 0 1940

1960

1980

2000

Year Fig. 3. Passenger boat speed in Amazon region.

2020

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Requirements (Module I ) -

-

Distance Time Physics and Operational Constraints Number of Passengers, etc...

HSCat Preliminary Design (ModuleII) Volume and Weights Areas Hydrostatic Parameters Power Preliminary Evaluation

Terminal Preliminary Design

-

(Module III) Area Equipment Number of Docks

Cost Analysis (Module IV) Fig. 4. HSCat river transportation preliminary design diagram.

resistance for different models. Monohull and catamaran models were tested to determine the interference phenomenon. Even though research is in place, the slender body application theory was applied in preliminary design phase to select a suitable model. The 3D theory models are more complex and time consuming. They use a CFD approach and in the author’s point of view should be reserved to advanced design phases. 3.1.1. Slender body theory (wave resistance) The wave resistance (Rw) evaluation using the slender body theory is based on the wave energy behavior. The method was developed by Michell (1889). The interaction effect between the twin catamaran hulls is considered by using the image method that is equivalent to assess a monohull resistance when displacing along the channel center line. An algorithm was implemented in SLENDER Fortran program by Williams (1994). 3.1.2. Flat plate theory (frictional resistance) Frictional resistance is important when the hull is operating at low speed. In some cases the frictional resistance can achieve 80% of total resistance. Following Froude (1872) flat plate hypothesis, many formulations were proposed establishing that the ship frictional resistance is approximately the same as a flat plate with the same wetted area. The ITTC— International Towing Tank Conference (1957) proposed the line to be used in the HSCat mathematical model. Eqs. (1)–(3) present the frictional resistance coefficient proposed by ITTC. C f  ¼

0:075 ðlog10 Rn À 2Þ2

,

(1)

Rn ¼

Rf  ¼

VLr

,

(2)

1 2 rAm V  C f . 2

(3)

m

3.2. Weight Model  Weight evaluation is a fundamental part of preliminary ship design. In special for HSCraft the weight estimates are important and can make a difference in performance assessment. There is few data available to develop a statistical model for high-speed catamaran hull weight evaluation although the importance of establishing a reliable weight approaches. The HSCat weight is divided in lightweight (structure, equipment, engine propulsion), operational (oil, lube, water, crew and food) and cargo weight (passenger, luggage and vehicles). 3.2.1. Lightweight—structure weight The structure weight is evaluated by mathematical model of  Karayannis et al. (1999). It includes the hull structure and superstructure weights. Karayannis et al. (1999) works present a mathematical model based on catamarans with 100, 75 and 50 m long, twin hull separation ratio (S /L) with range varying from 0.20 to 0.26 and limited to aluminum HSCat. The model is also based on Lloyds Register of Shipping Classification Society—Rules for the classification of special service craft (1997). The model uses equipment numeral ‘‘E ’’ developed by Watson and Gilfillan (1977) for displacement ships. This method has been investigated to HS crafts with relative success. Eq. (4) shows the ‘‘E ’’ numeral formula: E  ¼ 2Lðb þ T Þ þ 0:85LðD À T Þ þ 1:6LðB À 2bÞ,

(4)

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where

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The equipment weight (P equip) is

B ¼ S þ b,

(5)

D ¼ 4 þ 0:44B .

(6)

Eqs. (7) and (8) present the structural weight as function of ‘‘E ’’ number. P structðtÞ ¼ 0:00064E 1:7 for ðE o3025Þ,

(7)

P structðtÞ ¼ 0:39E 0:9 for ðE X3025Þ.

(8)

3.2.2. Lightweight—equipment weight According to Karayannis et al. (1999), the equipment weight is a function of HSCat length and breadth. Service area weight (P serv) is estimated between 80 and 100 kg/m2. The following equations are to calculate the equipment weight. Ap ¼

]

ðL Â B Þ À 138 2 ðm Þ, 0:91

(9)

As ¼ Ap =1:3ðm2 Þ,

(10)

N pass ¼ As =0:75.

(11)

Adopting 90 kg/m2, service area weight (P serv) is estimated as per Eq. (12) and remaining weight (P rest) calculated as per Eq. (13).

(14)

P equip ¼ P serv þ P rest ðtÞ.

3.2.3. Lightweight—propulsion weight Karayannis et al. (1999) propulsion weight model considers main engine, gearbox and waterjet. Main engine: Fig. 5 shows power and associated weight for Karayannis et al. (1999) model and several mainengines weight (MTU, Carterpilar, Zvezda, and Wartsila) were plotted for comparison purposes. Generic gas turbine was also included in Fig. 5. Data was selected from highspeed marine transportation, Jane’s Book (1996–1997) and engine catalog. Fig. 5 shows that up to 5000 hp, results are very similar and Karayannis et al. (1999) model presents good correlation. Eq. (15) shows the diesel engine mathematical model. Eq. (16) shows the gas turbine model and Eq. (17) the gear box weight mathematical model. Diesel engine (Powerp14000 kW or 18800hp),



0:85



P ot ðkWÞ P dieselengineðtÞ ¼ 6:82 nðrpmÞ

ðtÞ.

(15)

P serv ¼ Ap  90  10À3 ðtÞ,

(12)

Gas turbine (Power between 6000 kW (8000hp) and 25000 kW (33 500 hp))

P rest ¼ 0:03 Â L Â B Â 10À3 ðtÞ.

(13)

P gasturbine ðtÞ ¼ 3 þ 0:00056P ot ðkWÞðtÞ.

Main Engine Weight x Power

40

30 CATERPILLAR Engine    )    t    (    t    h   g    i   e 20    W   e   n    i   g   n    E

DIESEL Engine Karayannis Model MTU Engine

10

WARTSILA Engine

Gas Turbine Karayannis Model

0 0

5000

10000

15000

20000

Power (HP) Fig. 5. Power between 1000 and 30,000hp.

25000

30000

(16)

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P gearbox ðtÞ ¼ 0:00348P ot ðkWÞ

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 Fuel weight (P  fuel )

Gear box (Power46000 kW or 8000 hp), 0:75

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P fuel ¼ P ower  SPF  T n  1:10=1000ðtÞ.

ðtÞ.

(17)

3.2.4. Waterjet weight Fig. 6 presents the waterjet weight as a function of  delivered power. Kamewa, Nigata and MJP waterjet where compared with Karayannis et al. (1999) model (power between 500 kW (670 hp) and 12 000kW (16 000 hp)). The graph proves a good correlation between mathematical model and the waterjet data. Eq. (18) presents the waterjet weight formula. P waterjetðtÞ ¼ 0:00018P ot ðkWÞ1:18 ðtÞ.

(21)

Fuel to auxiliary engine can be evaluated by 10%, as shown in Eq. (21). Time between ports (T v) can be evaluated by T v ¼ Dist=ð1:852 Â V Þ.

(22)

 Lub weight (P lub) P lub ¼ 0:05 Â P fuel ðtÞ.

(23)

 Fresh water weight (P  fw) P fw ¼ C fw  ðN pass þ N trip Þ Â ðT n =24Þ=1000,

(18)

C fw ¼ 30 l =person=day.

Other propulsion weights Karayannis et al. (1999) proposed 55% of engine, gear and waterjet weights to consider other related propulsion weights (Eq. (19)).

ð24Þ

 Food weight (P  food ) P food ¼ C food  ðN trip þ N pass Þ Â ðT n =24Þ=1000ðtÞ,

P other ¼ 0:55 Â ðP dieselengineðor P gasturbineÞ þ P gearbox þ P waterjet Þ.

C food ¼ 6 kg =person=day.

(19)

ð25Þ

The total operational weight (P oper) by trip is

3.3. Operational weight P oper ¼ P trip þ P fuel þ P lub þ P fw þ P food . The operational weight is a function of distance and time. It consist of the sum of crew, luggage, fuel, lube oil, fresh water and food. All operational weights are presented in Eqs. (20)–(25).

3.4. Cost assessment High speed, smooth hull lines and passenger appreciation are some of the major challenges for catamaran designers. It is common to see high costs in most of  high-speed vessel design. New technology is always more

 Crew and luggage weight (P trip) P crew ¼ P tp  N trip ðtÞ.

(20)

Waterjet Weight x Power

16

12    )    t    (    t    h   g    i   e 8    W    t   e    j   r   e    t   a    W

WATERJET NIIGATA

KARAYANNIS Model

4

WATERJET MJP WATERJET KAMEWA

0 0

5000

(26)

10000

15000

20000

Power (HP) Fig. 6. Waterjet weight Karayannis et al. (1999) model and waterjet data.

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expensive and high speed is always associated with higher oil consumption. In HSCat preliminary phase is necessary to assess some costs, such as: investment, operational and infrastructure.

3.4.1. Building cost Karayannis et al. (1999) proposed to split the investment costs in the following items: structure, equipment and engine. Structure cost (C est) The structure cost is the sum of the structure material costs and man/hour fee required for HS craft building. The mathematical model also considers additional 10% for material losses. The proposed equation is the following (US$): C est ¼ ½P est  M   1:10 þ ½P est  L  H .

(27)

Equipment cost (C equi ) Karayannis et al. (1999) proposed that equipment costs can be assessed based on equipment weight (P equi ) (US$): C equi ¼ 22:000 Â P equi .

(28)

 Main engine cost (C maq)



Total main engine cost comprehends main engine, gearbox and waterjet units. Eqs. (29)–(32) present the mathematical model based on equipment catalog. Diesel engine cost (C md ) (US$): C md ¼ ð0:262 Â P ot Þ Â 103 .

(29)

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The number of trips per year is modeled as per Eq. (36). N va ¼ 330=ðT n þ 2T p Þ.

(36)

3.4.2. Operational cost Operational cost comprehends the following items: repairing and maintenance, crew salary and taxes, food, vessel insurance and administration costs.

 Repairing and maintenance (C rm) Repairing and maintenance costs are estimated as 6% of  craft total acquisition cost (CTA). C rm ¼ 0:06 Â C TA

(37)

 Crew salary and taxes (C sal ) Salary and taxes vary from country to country. An average value was adopted (sm) and 14 workers were considered. C sal ¼ 12  sm  N trip  ð1 þ encÞ.

(38)

 Food cost–crew (C alim) C alim ¼ N trip  Alim  365.

(39)

 Hull insurance (C seg) The mathematical model considers the insurance cost in Brazil as 3% of craft total acquisition cost (C TA). C seg ¼ 0:03 Â C TA .

(40)

 Administration cost (C adm) Administration cost is considered as 15% of the following cost:

 Gas turbine cost (C tg) (US$): C tg ¼ ð0:35 Â ðP ot Þ À 3 Â 10À6 Â ðP ot Þ2 Þ Â 103 .

]

(30) C adm ¼ 0:15 Â ðC sal þ C alim þ C rm þ C seg Þ.

(41)

 Gear box cost (C rv) (US$): C rv ¼ ð57 þ 0:0214 Â ðP ot Þ À 3 Â 10À7 Â ðP ot Þ2 Þ Â 103 . (31)

 Waterjet cost (C wj ): C wj ¼ ð0:468 Â ðP ot Þ0:82 Þ Â 103 US$.

 Oil cost (C comb) (32)

The total cost considers an additional 40% to other equipments associated with main engine and man/hour costs to install all main engine equipment. C ma ¼ ½C md ðor C tg Þ þ C rv þ C wj  Â 1:40.

(33)

The craft total acquisition cost (C TA) is modeled as per Eq. (34). C TA ¼ C est þ C equi þ C ma .

C comb ¼ Prcomb  P c

(42)

 LUB cost (C lub) C lub ¼ Prlub  P lub .

(43)

Using all the formulae above, the total cost per trip (C TOT) is determined by Eq. (44). C TOT ¼ ðC TA Â F RC Þ þ C rm þ C sal þ C alim þ C seg þ C adm þ C comb þ C lub .

(34)

(44)

(35)

The mathematical model for a preliminary HSCat design can be solved by an optimization procedure. Goal programming was used as an optimization technique.

The total cost per trip is modeled as per Eq. (35). C TAV ¼ C TA =N va .

3.4.3. Trip cost Trip cost comprehends the following items: oil and lubricant costs.

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In the next section a goal programming method overview is pointed out. 4. Optimization model goal programming

The multi-objective goal programming method is based on the simplex linear programming that was developed during World War II. The method was developed to solve military strategic problems. The simplex method provides a procedure to optimize linear mathematics problems with one objective function. Ignizio (1976) presents a linear and non-linear goal programming as an extension of the simplex method. In the multi-objective goal programming approach it is necessary to follow three steps: Step1: Identify the decision variables (x j ). Step 2: Formulate mathematical model objectives (G i).   Step 3: Formulate achievement function (ak ). All the mathematical model constraints are converted into goals in the goal programming procedure with multiple objectives. The following criteria define the objectives: (1) Designer criteria Example: Minimize construction costs, maximize tank volume, minimize forces and tensions, minimize motion, etc. (2) Resource limitation Example: Material, cost, etc. (3) All remaining constraints that could affect the decision variables. Example: Physic constraints (decision variable nonnegative, size constraints in the shipyard, etc.) (4) The mathematical formulas of the goals (G i)  are function of the decision variables ( f i(x)):   (45)

G i  ¼ f i ðxÞ.

All objectives are associated to a value (bi ) in the right hand side of the equation:  f i ðxÞ ¼ ðbi Þ,

(46)

where b is the value the objective needs to fulfill. Finally, we can write the goals as G i  ) f i ðx j Þ þ ni  À pi  ¼ bi ; i  ¼ 1; 2; 3; . . . ; m ðm objectivesÞ,  j  ¼ 1; 2; 3; . . . ; k ðk variablesÞ, ð47Þ where ni  and pi  are the negative and positive deviation variables , respectively, from the objective. Table 1 shows formulation procedure for the achievement function.

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Table 1 Formulation procedure for the achievement function Objective

Procedure

G i Xbi  G i pbi  G i  ¼ bi 

minimize ni  minimize pi  minimize (ni  þ pi )

For the achievement function is necessary to assign the priority level (P 1, P 2,y) for each objective. We can write the mathematical model as minimize a ¼ fP 1½g1 ðn; pÞ; P 2½g2 ðn; pÞ; . . . ; Pk ½gk ðn; pÞg,

(48)

where gk (n, p) is the linear function of the deviation variables, Pk  is the function gk (n, p) priority k pm (number of objectives). Finally, the mathematical model can be written in a short form, as follows: Find x0 ¼ ðx1 ; x2 ; . . . ; xj Þ to minimize a ¼ ða1 ; a2 ; . . . ; ak Þ

(49)

where a1 ¼ g1 ðn; pÞ a2 ¼ g2 ðn; pÞ ak  ¼ gk ðn; pÞ for,  f i ðx j Þ þ ni  À pi  ¼ bi ; i  ¼ 1; 2; . . . m ðobjectivesÞ,  j  ¼ 1; 2; . . . k ðvariablesÞ

ð50Þ

and x0 ; ni ; pi p0. 4.1. Non-linear goal programming Griffith and Stewart (1961), presented a procedure for non-linear models using Taylor series expansion. The goal programming they used takes the two first terms of the Taylor expansion to approximate the goal functions near the test point. Smith et al. (1987) incorporated the third term of Taylor expansion in their goal optimization procedure. We can write the nonlinear goal function using the mathematical model presented in Eq. (51) and in linearization procedure (52): G i  ) f i ðx j Þ þ ni  À pi  ¼ bi ;

i  ¼ 1; 2; 3; . . . ; m ðm objectivesÞ,

 j  ¼ 1; 2; 3; . . . ; k ðk variablesÞ. ð51Þ Considering the function f i(x    j ) continuously differentiable and assuming xs one solution for the objectives, the

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function approximation is giving by J 

 f i ðxÞ ¼ bi  À ni  þ pi  ¼ f i ðxs Þ þ

X  j ¼1

q f ðxs Þ qðx j Þ

i  ¼ 1; 2; 3; . . . ; m.

ðx j  À xs; j Þ, ð52Þ

The non-linear goal programming optimization technique was developed and implemented in a FORTRAN code. HScat preliminary design mathematical model and goal programming optimization technique are added to study two passenger transport cases in Amazon area. The first is a Belem-Macapa ´ route and the second case a very long route Belem-Manaus. Following case studies are presented and results shown. 5. Case studies

The Amazon area in Brazil (Fig. 7) was selected to  ´ line, presented in present two case studies. Bele ´m-Macapa Table 2, correspond to a short line (574 km–300miles) no stop. Bele ´m-Manaus line, presented in Table 3, represents a long line (1646 km–890 miles) with many intermediate scales.

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around 30 knots. Many aspects should be considered before speed set up. Experience with existing high speed vessel  ´ route indicates speed limit at operating in Belem-Macapa around 35 knots. Brazilian Navy determines the speed limit to operate in shallow channels around Marajo Island. The presence of small fishing and passenger boats in the same route requires a reduced speed. Another aspect that should be considered to establish reduced operation speed is the presence of objects in the river as tree-trunks and small sand islands. Many accidents involving large floating objects with commercial boats have often been described.

Table 2 Bele ´m-Macapa ´ (route data) Distance Fleet Fleet age Time Ticket price (average) Passenger capacity (average)

309 miles/574 km 6 5 Yrs Conventional boat—22 h High speed vessel—12 h US$ 27 396

Table 3 Bele ´m-Manaus (route data)

5.1. Case study 1: Bele´ m-acapa´  route Bele ´m-Macapa ´ is a line where high-speed vessels have been used for passenger transportation since 2001. The operation generally is made no stop and through rivers and  ´ Island natural channels that surround the south of Marajo in Para ´ state (see Fig. 7). The total number of passengers using this line is around 180,000 on an annual basis. Preliminary design requirements establish a 400 passenger vessel to achieve the current demand. Speed was defined

Distance Fleet Fleet age Time Ticket price (average) Passenger capacity (average) Stops: Breves, Gurupa´, Almerim, Prainha, Monte Alegre, Santare ´ m,  ´ bidos, Parintins and Itacoatiara O

Fig. 7. Amazon area.

889 miles/1646 km 11 15 years Conventional boat—100 h US$ 40 316 8

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Table 4 Four hundred passenger catamaran Variable

V ¼ 25 knots

V ¼ 30 knots

V ¼ 35 knots

Length (m) Twin hull breadth (m) Draft (m) S/L ratio

35.41 3.91 1.31 0.28

36.13 3.99 1.35 0.27

37.52 3.88 1.33 0.25

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The preliminary design mathematical model was applied and goal programming was used to find out a compromising solution. Table 4 presents the main catamaran dimensions for three different speeds. Figs. 8–11 indicate the convergence process during the optimization phase. Fig. 8 shows the twin hull breadth convergence for speed equals to 30 knots. The starting point was selected and the convergence reaches the value of  3.99 m for the twin hull breadth after 250 cycles.

7.00

6.00

5.00

   )   m    (    h    t    d   a   e   r 4.00    B

3.00

2.00 0.00

100.00

200.00

300.00

400.00

300.00

400.00

Cycles Fig. 8. Breadth convergence.

120.00

100.00

   )    $ 80.00    S    U    (   x   a   p    /    t 60.00   s   o    C

40.00

20.00 0.00

100.00

200.00 Cycles

Fig. 9. Cost/pax convergence.

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25000.00

20000.00

   )   p 15000.00    h    (   r   e   w   o    P 10000.00

5000.00

0.00 0.00

100.00

200.00 Cycles

300.00

400.00

Fig. 10. Power convergence.

Fig. 11. Design and average speed.

Fig. 9 presents the convergence process for cost/ passenger design characteristic. After 250 steps the optimization procedure reached a minimal cost/passenger (cost/pax) value of US$ 29.25 considering a 30 knots boat speed. Fig. 10 highlights the convergence process for vessel power design characteristic. Table 5 shows a power study for all three speeds. Considering 25 knots as a base speed, table 5 indicates the increasing power and cost per passenger to 30 and 35 knots. It is important to emphasize that the model capacity of allowing a power versus cost analysis. Table 5 makes clear the necessity to input high power and spend much more to achieve a speed higher than 25 knots. In this example, the cost increase is almost linear with speed, although power has a higher relationship. Fig. 11 shows design and average speed correlation. Average speed considers the reduction of cruising speed during the trip, due to: traffic near the cities, small boats (fishing and passenger) in the area for high speed craft navigation, maneuvering, night navigation and very big floating objects as tree-trunks and sand islands, specially in the Amazon River. In Belem-Macapa  ´ route 28% of the total trip is sailing under reduced speed because safety

Table 5 Power and cost analysis Speed (knots)

25

30

35

Power (hp) Speed gain Power increased (%) Cost increased (%)

3235 0 0 0

4780 20 48 20

6905 40 113 49

reasons pointed out above. Fig. 12 presents the time necessary to accomplish the total trip at different speeds. We see from the results the small gain in time when large speed (over 20 knots) is applied in this particular case studied Bele ´m-Macapa ´ route. 5.2. Case study 2: Bele´ m-Manaus route Case study two selected the largest Amazon route (1646 km). It is along the Amazon River. Passenger and cargo transport is performed at a very low speed with many stops (nine in the case study presented herein). Another important route aspect is the current effect (2 knots

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upstream). Because the restricted area (at southeast of  Marajo ´ Island in Breves) the cruising speed has also to be reduced to 16 knots in 167 km.Preliminary design requirements establish a 300 passenger vessel to achieve the current demand. Speed was established around 30 knots. The presence of small fishing and passenger boats in the same route requires speed reduction. As indicated in Belem-Macapa ´ route, reduced operation speed is necessary due the presence of objects in the river as tree-

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trunks and small sand islands. The preliminary design mathematical model was applied and goal programming was used to find out a compromise solution. Table 6 presents the main catamaran dimensions for three different speeds. Fig. 13 shows the twin hull breadth convergence for speed equals to 30 knots. The starting point was selected and the convergence process reaches the value of 3.56 m for the twin hull breadth.

Fig. 12. Time speed.

Table 6 Three hundred passenger catamaran Variable

V ¼ 25 knots

V ¼ 30 knots

V ¼ 35 knots

Length (m) Twin hull breadth (m) Draft (m) S /L ratio

34.25 3.49 1.18 0.25

35.77 3.56 1.19 0.23

37.00 3.55 1.18 0.21

3.70

3.65    )   m    (    h    t    d 3.60   a   e   r    B    l    l   u    H 3.55   n    i   w    T

3.50

3.45 0.00

50.00

100.00

150.00

200.00

Cycles Fig. 13. Twin hull breadth convergence.

250.00

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100.00

90.00

   )    $    S    U    (   x   a   p    /    t   s   o    C 80.00

70.00 0.00

50.00

100.00

150.00

200.00

250.00

200.00

250.00

Cycles Fig. 14. Cost/pax convergence.

4800.00

4400.00

   ) 4000.00   p    h    (   r   e   w   o    P 3600.00

3200.00

2800.00 0.00

50.00

100.00 150.00 Cycles

Fig. 15. Power convergence.

Fig. 14 presents the convergence process for cost/ passenger design characteristic. After 200 steps the optimization procedure reached a minimal cost/passenger (cost/pax) value of US$ 84.56 considering a 30 knots boat speed. Fig. 15 highlights the convergence process for vessel power design characteristic. Table 7 presents a power study for all three speeds. Considering 25 knots as base speed, Table 7 shows the increasing of power and cost per passenger for 30 and 35 knots. Table 7 makes clear the increase in power and cost to achieve a speed higher than 25 knots.

Table 7 Power study Speed (knots)

25

30

35

Power (hp) Speed gain Power increase (%) Cost increase (%)

1965 0 0 0

4017 20 104 47

5523 40 180 70

Fig. 16 shows design and average speed correlation. Average speed considers the reduction of the cruising speed during the trip, due to the same reason as pointed out in

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Fig. 16. Design and average speed.

100 80    )    h    (   e 60   m    i    t   p 40    i   r    T

20 0 10

15

20

25

30

35

40

Speed (knots) Fig. 17. Time speed.

Belem-Macapa ´ route: traffic near the cities, small boats (fishing and passenger) in the area of high speed craft navigation, maneuvering, night navigation and, very big floating objects as tree-trunks and sand islands, specially in the Amazon River. Fig. 17 presents the time necessary to accomplish the total trip at different speeds. We see from the results the important gain in time when large speed (over 20 knots) is applied in this particular case studied Belem-Manaus route. 6. Conclusion

The preliminary design model presented was developed as a design tool. The goal is to assist in HSCatamaran design applied for passenger transport. The mathematical model was initially developed for river transport but ocean vessels can also be considered. Mathematical model applications were presented for both case studies. The routes chosen for this research were in the Amazon area. The Bele ´ m-Macapa ´ case study showed a cost/passenger price similar to that obtained for low speed vessels. This indicates a real possibility of changing the low speed vessel (22 h trip) for a HSCat (13 h trip at 30 knots). Bele ´m-Manaus case study, a long route example, presented many problems usual for inland navigation: speed constraints in many areas, strong current, many

stops and very long trip. As was indicated in the example, the average speed is lower than the cruising speed. The cost/passenger and time reduced should be investigated in more detail before an HSCat application is carried out. A large utilization of HSCatamaran is not feasible because a useful preliminary design evaluation was not applied.

Acknowledgements

The authors would like to thank the Brazilian National Scientific and Technical Development Board (Conselho   Nacional de Desenvolvimento Cientı´ fico e Tecnolo´ gico, CNPq), Federal University of Rio de Janeiro and Federal University of Para ´ to supporting this study. References Froude, W., 1872. Experiments on surface friction. Bristish Association Reports. Griffith, R.E., Stewart, R.A., 1961. A nonlinear programming techniques for the optimization of continuous processing systems. Management Science 7, 379–392. High-speed marine transportation. Jane 0 s Book, 291 edica˜o, 1996–1997. Ignizio, J.P., 1976. Goal programming and extensions. Lexington Books, Lexington, MA. ITTC, 1957. International Towing Tank Conference. -

ARTICLE IN PRESS H.B. Moraes et al. / Ocean Engineering Karayannis, T., Molland, A.F., Williams, Y.S., 1999. Design data for high-speed vessels. FAST-99. Michell, J.H., 1889. The wave resistance of a ship. Philosophical Magazine 45 (Series 5), 106–123. Moraes, H.B., Vasconcellos, J.M., Latorre, R.G., 2004. Wave resistance for high-speed catamarans. Ocean Engineering 31 (17–18), 2253–2282. Smith, W.F., Kamal, S., Mistree, F., 1987. The influence of hierarchical decisions on ship design. Marine Technology 24 (2), 131–142. Watson, D.G.M., Gilfillan, A.W., 1977. Some ship design methods. Transactions of the Royal Institution of Naval Architects 119.

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Williams, M.A., 1994. Hull form optimization of SWATH ships. M.Sc., Thesis, COPPE/UFRJ, Rio de Janeiro.

Further reading Lloyds Register of Shipping, 1997. Rules for Classification of Special Service Craft. Classification Society.