Conceptual Study of a Fast Landing Craft Unit

Part 2 - Analysis

MIKAEL RAZOLA razola@kth.se 070-7104074

TORVALD HVISTENDAHL

torvald@kth.se 070-4856392

Master Thesis KTH Centre for Naval Architecture

Stockholm, Sweden, February 2010

KTH Centre for

Naval Architecture

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CONTENTS Contents..........................................................................................................................................................................2 Introduction ...................................................................................................................................................................4

1.1. Outline.............................................................................................................................................................4 2. Benchmarking ........................................................................................................................................................5

2.1. Conventional landing crafts .........................................................................................................................5 2.2. Hovercraft LCU.............................................................................................................................................5 2.3. Catamaran concept........................................................................................................................................6 2.4. SES PACSCAT concept...............................................................................................................................7

3. Concept evaluation................................................................................................................................................8 4. Material..................................................................................................................................................................11

4.1. Composite system........................................................................................................................................11 4.2. Aluminium & Steel ......................................................................................................................................14

5. Hull Structural Design ........................................................................................................................................15 5.1. Scantlings method .......................................................................................................................................15 5.2. Structural Arrangement Aluminium Craft...............................................................................................16 5.3. Scantlings Aluminium Craft.......................................................................................................................17 5.4. Structural arrangement Composite craft..................................................................................................19 5.5. Scantlings composite...................................................................................................................................22 5.6. Conclusions and discussion .......................................................................................................................32

6. Mass analysis ........................................................................................................................................................34 6.1. Method ..........................................................................................................................................................34 6.2. Results ...........................................................................................................................................................34

7. Hydrostatics..........................................................................................................................................................36 7.1. Method ..........................................................................................................................................................36 7.2. Flotation and Trim ......................................................................................................................................36 7.3. Large angle stability .....................................................................................................................................38 7.4. Discussion.....................................................................................................................................................40

8. Resistance .............................................................................................................................................................41 8.1. Methods ........................................................................................................................................................41 8.2. Results ...........................................................................................................................................................43

9. Manoeuvring ........................................................................................................................................................46 10. Seakeeping ..........................................................................................................................................................48

10.1. Fundamental hydrodynamics for body and wave interaction ............................................................48 10.2. Survey of methods.....................................................................................................................................51 10.3. Seakeeping analysis of the FLCU............................................................................................................55

11. Structural design cargo Platform ....................................................................................................................59 11.1. General & structural arrangment platform............................................................................................59 11.2. Material........................................................................................................................................................60 11.3. Scantlings method platform.....................................................................................................................60 11.4. Loads ...........................................................................................................................................................60 11.5. DNV Scantlings .........................................................................................................................................61 11.6. Direct calculations .....................................................................................................................................64 11.7. Results .........................................................................................................................................................67

12. Cargo Control System (CCS) Design.............................................................................................................70 12.1. CCS Design and Definitions ...................................................................................................................70 12.2. CCS coarse structural design and Global Stiffness ..............................................................................70 12.3. Detailed analysis of connection between platform tube beam and lever arm .................................77 12.4. System design .............................................................................................................................................83

13. References ..........................................................................................................................................................86

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1. Appendix, Semi-empirical method for estimation of resistance....................................................................1 2. Appendix, Weight estimation model..................................................................................................................2 3. Appendix, Mass distribution................................................................................................................................4

3.1. Carbon composite version ...........................................................................................................................4 3.2. Aluminum concept........................................................................................................................................7

4. Appendix, Large angle stability Calculations ..................................................................................................10

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INTRODUCTION Part one of this report presents the background and vision of initial design of the Fast Landing Craft Unit (FLCU). It contains descriptions of the general arrangement and the different systems used onboard as well as conclusions and suggestions for further work.

This second part of this report contains a more thorough review of the current landing craft operations and designs, and provides a section on the concept development of the Fast Landing Craft Unit. It also contains the full methods and results from the different analysis performed on the craft. The intention is that this part of the report is used as a reference report to part one.

1.1. OUTLINE

The outline of this second part of the report starts with a thorough benchmark study in section 2, followed by the concept evaluation in section 3.

Section 4 presents the proposed material concepts, which is followed by the structural arrangement and scantlings in section 5.

A detailed mass analysis is presented in section 6.

Section 7 deals with the hydrostatic analysis and section 8 with the resistance and powering analysis.

A short section on manoeuvring is then followed by section 10, which presents a survey of available methods for seakeeping analysis of semi-displacing, high-speed catamarans together with the seakeeping analysis of the FLCU.

Section 11 and 12 describes the direct calculations and scantlings of the cargo platform and the Cargo Control System (CSS).

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2. BENCHMARKING The following chapter presents some of the different types of landing crafts that are in use or being developed today. The purpose of this collocation is to provide an overall picture of the main particulars, performance and concepts of the landing crafts currently in use.

2.1. CONVENTIONAL LANDING CRAFTS The type of craft in this category typically has a box-like hull with little or no superstructure. It can often be disembarked in both the bow and stern and generally travels at speeds between 8 – 12.5 knots. The operable range of these crafts vary significantly between 130 – 2280 NM depending on craft size (Figure 1).

Figure 1. MK 10 Landing Craft Utility, commissioned by the Royal Navy in 2003.

The advantage is a robust and fairly simple construction that can be used in a great variety of environments. However the disadvantage is slow speed and sensitivity to high sea states. These types of crafts have a cargo to lightweight ratio between 0.41 – 1.32, probably depending on armament and ballistic protection etc. The draught at disembarkation i.e. full load is in the region between 1.17 – 1.7 m, this is likely due to the maximum wading depth for typical tanks. This type of landing craft is currently being used by USA, Russia, Australia and Great Britain to mention a few. Table 1 presents the main particulars of some of the crafts of the more conventional type for reference [1-6].

Table 1. Main particulars of a selected number of traditional Landing Craft Utilities.

MK10 Sabre c las s LCU 1600

Class LCM

8 LCM

6 Bal ikpapan

Class Length [m] 29.8 60 41.1 22.5 17.1 44.5 Beam [m] 7.4 11.9 8.8 6.4 4.3 10.1 Draught (disembark) [m] 1.7 1.6 2.3 1.6 1.17 0 Displacement (light) [tons] 170 500 203 58.7 30.5 136 Cargo capacity [tons] 70 210 170 54.4 34.5 180 Speed [knots] 8.5 12,5 8 9 9 9 Range [NM] 600 2280 1200 190 130 1300

2.2. HOVERCRAFT LCU The hovercraft can travel equally well on land and water and since they ride on a cushion of air the resistance is down to a minimum. However, they are very versatile since they do not require any minimum water depth. The models studied here is the Russian Zubr Air Cushion Landing Craft and the U.S. Landing Craft Air Cushion, LCAC (Figure 2).

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Figure 2. The LCAC landing craft in operation.

The LCAC has a top speed of 40 knots and the larger Zubr 60 knots. Both these concepts have their limitations. The LCAC requires 458 meters for a full stop and 1829 meters turning radius at full speed. This is a crucial disadvantage in confined spaces or in an archipelago environment. The cargo capacity of these crafts is 130 tons for the Zubr and 75 tons for the LCAC, which gives cargo to lightweight ratios between 0.3 – 0.6. The Zubr can land at shores with gradients up to 5° and clear vertical obstacles of up to 1.6 m. The main particulars of these crafts are presented in Table 2 [1-6].

Table 2. Main particulars of the hovercraft type landing utilities.

LCAC The Zubr ALC Lenght [m] 29.3 57 Beam [m] 15.7 22.3 Draught (disembark) [m] 0 0 Displacement (light) [tons] 125 425 Cargo capacity [tons] 75 130 Speed [knots] 40 55 Range [NM] 200 300

2.3. CATAMARAN CONCEPT In the end of 2008, the French company CNIM presented a prototype of a completely new LCU, which the French navy are expected to order. The concept goes under the name L-cat and is an innovative and completely new type of concept. The craft is a combination of a catamaran and a classic LCU. It consists of a multihull with an abatable loading platform in the middle. When docking in or approaching the landing area the platform is lowered down, changing the submerged hull so that the craft operates more like a traditional LCU. During transportation the platform is raised and the craft operates as a catamaran. The advantage of this is combining the low draught characteristics of the traditional LCUs with the low resistance slender hull shape of the catamaran for increased speed performance (Figure 3).

Figure 3. The prototype L-cat.

The existing prototype has been tested at the Mistral class LPD with good results. It measures 30 m overall and has a beam of 12.8 m. The draught in debarking mode is 0.6 m and in transit mode 2.5 m. It is powered by 4 MTU diesel engines, each at 1220 kW giving a maximum speed of 30 knots. At 15 knots the

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range is 1000 NM. The L-cat can carry two Leclerc 4 battle tank with the total weight of 130 tonnes at the same time. Table 3 presents the main particulars of the L-cat prototype [1-6].

Table 3. Main particulars of the L-cat

L-ca t Lenght [m] 30 Beam [m] 12,8 Draught (disembark) [m] 0,6 Displacement (light) [tons] 190 Cargo capacity [tons] 112 Speed [knots] 30 Range [NM] 1000

2.4. SES PACSCAT CONCEPT At the end of 2006 the British Royal Marine started a project to build a fast landing craft. The craft is a SES (Surface Effect Ship), which is a catamaran hull running on an air cushion built up by large fans beneath. A prototype was built during 2009 and commissioned for sea trials in October. The craft is based on the design of LCU mk10 and shares the same footprint. It is claimed to make up to 34 knots unloaded and 18 knots loaded with one 55-ton battle tank. In order to allow for efficient cargo handling operation it is designed with so called roll-on, roll-off design. A picture of PACSCAT can be seen in Figure 4

Figure 4. CAD drawing of British PACSCAT [29]

Main data of PACSCAT are presented in Table 4.

Table 4. Main particulars PACSCAT

PACSCAT Lenght [m] 30 Beam [m] 7.7 Draught (disembark) [m] 0.6 Displacement (loaded) [tons] 175 Cargo capacity [tons] 55 Speed [knots] 18-34 Range [NM] >300

According to a Youtube animation [30] showing a possible scenario, PACSCAT should be able to make two transportations from the LPD in the same time as a traditional LCU mk10 makes one. In this scenario the distance between the shore and the LPD is 30 NM and the approximate time for the comparison 3.5 hours.

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3. CONCEPT EVALUATION This section describes briefly the general procedure behind the development of the FLCU concept.

At a very early stage of the development a brainstorming was carried out. It was done with the purpose of identifying new ideas and openings on how to solve the transportation work. The following list shows a summary of the results from the brainstorming and classification of different solutions:

• Improved conventional LCU The idea of this concept is to improve the conventional LCU so that it fits the specification of requirements i.e. higher speed, better seakeeping properties and compatibility with different shorelines.

• Improved Hovercraft The idea is to try to make the hovercraft lighter and thus reduce the required power and weight from the machinery. The manoeuvrability is also critical to improve if this concept is chosen.

• Multihull solutions: o Using lower able box/platform

Similar to the concept used by French L-Cat with a box/platform which can be lowered and elevated in order to change the draft of the craft for embarkation and disembarkation.

o Mud-crawler An idea of using caterpillar bands on the hull to give it the possibility of moving in shallow water without having to worry about draft.

o Wire-concept A lightweight solution using two hulls and crossbeams fitted with lifting wires able to connect to the hooking points on the tank. The craft would then be manoeuvred over the tank, and the tank lifted out of the water being placed on supports from the hulls.

o Trim-concept An idea of that the cargo should be movable in order to trim the craft and thus make it possible to go closer to disembarking area.

o Hydrofoil Get higher speed for less power

o Surface Effect Ship (SES) Combination of a twin hull and a hovercraft with a flexible skirt in the bow and the aft used to enclose the air cushion between the hull and water surface. This concept would then combine the low resistance characteristics of the hovercraft with the manoeuvrability of a conventional craft.

• Submerged solution The idea is that the LCU transports the tank submerged to the shore at moderate speed and then leaves back to the LPD in a surface mode at high speed. This would allow for a surprise attack.

The list above shows four main directions. Each direction was judged on a five-grade scale to different criteria, where 1 corresponds to a disadvantage and 5 correspond to an advantage. Each criterion was then weighted with the importance for the system and finally summarized. It is important to observe the different criterion as properties i.e. simplicity means by judgement 1, a disadvantage to the concept, since it will require a larger effort to realize.

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Table 5. Evaluation matrix

(1-5 1=disadvantage, 5 = advantage)

Improved conventional

LCU

Improved Hovercraft Multihull Submerged

Weighting (1-5, 1= not important,5=

important)

Energy consumption 2 1 3 3 3

Simplicity 5 1 4 1 5 Cargo flexibility 5 3 5 1 4

Compatibility with different shorelines 4 2 4 2 4

Compatibility with different well decks 5 2 5 2 4

Sea keeping properties 2 2 5 5 5

Return-trip time 3 5 5 2 4

Weighted sum 109 66 130 67

Table 5 shows that the multihull solution and the improved conventional LCU seem to be the most attractive concept. However, one should be careful in drawing to fast conclusions from these results since they are much dependent on the subjective judgement made by the evaluator. Thus the result from this was only used as an indicator. More reliable results would be obtained if these directions were investigated more thoroughly before judging which one is the most attractive. However this study will only focus on one direction and thus a choice was made in corporation with SSPA. It fell on the twin hull direction based on the assumptions that:

• The concept has good potential to reach higher speed • High speed can be maintained even in difficult sea state • Good seakeeping properties • The cargo handling can be solved in several ways • Can easily stand on a flat well deck without the extra support, necessary for v-shaped hulls

The first idea of solution was to develop the French L-CAT concept and design a craft on the same principal but with a beam small enough to fit in the LPD loading lanes. This would mean that the craft must be nearly half as wide as the L-CAT, which is 12.8 m. Judging the geometry of the necessary parts could quite fast dismiss this option. The platform must be at least 4.6 m wide with a manoeuvring clearance of 40 cm at each side of the tank. Adding two suitable engines around 1 m wide would leave in total a margin of 80 cm for hull, platform elevation system, stiffening, clearance to engine, outfitting etc. It might be possible to solve but the margins are too small and thus another solution was needed.

If the platform carrying the tank could be placed on top of the hulls before entering the LPD it would be possible to use wider hulls and still have enough space on the platform. During transportation the platform is kept in an elevated position between the hulls and then lowered down in to the water upon approach of the beach landing area. The system would then have the benefit of a lower draught in beach landing mode but still fit in to the existing LPD. The principal modes of this solution are shown in Figure 5 together with the questions, validating the possibility to realize this concept.

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Figure 5. Principal modes and questions to answer in their inter order, (note that the difference in draught is slightly

exaggerated) It is quite obvious that this concept have certain challenges. The solution of the movement between the different modes is by no means trivial. In the beginning, the platform handling system was kept in a virtual way as it is shown in Figure 5 with three representative modes. The reason was to focus on the question; “Would the craft have a potential to fulfil the specification of requirements during the different modes? This question can be divided in some sub questions, which has to be answered before treating the question of how to solve the translation between the modes. The questions and their intern difference of level are also shown in Figure 5.

The methods used to answer the questions where basically the same as described further on under each section of this report. Neither methods nor explicit results will thus be treated here. The results from these calculations did however show that the concept has a potential to fulfil the requirements.

Substantial effort was spent to find a functional system for the translation between the modes. The movement can be divided in one transverse part and one vertical part. A system that handles each isolated movement is fairly easy to design. The challenge is to manage the transfer from vertical to transverse movement and vice versa. One should also remember that this system will be used in an extreme environment and also be subjected to very high loads due to wave-induced motions. Thus the system must be robust, strong and stiff. Another challenge is to make the platform compatible with different cargos and provide roll-on roll-off capacity.

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4. MATERIAL This section gives a detailed account of the different material systems used in the design of the FLCU. There are several important aspects, such as weight, robustness, price and stealth, to consider when selecting the proper material system for a high-speed craft.

In this study two material concepts are evaluated against each other: aluminium with some elements of steel and carbon sandwich. This allows for an evaluation of the possible pros and cons of the respective material system. This section describes the different materials and laminates used in the design of the fast landing craft utility. DNV §X:Y:Z is the notation used to refer to the DNV High Speed Light Craft & Naval Surface Craft rules [33].

4.1. COMPOSITE SYSTEM A sandwich composite structure has several benefits compared to other common material systems such as metal or single skin. The lower weight, but high strength and stiffness that the sandwich structure provides is the strongest argument in most applications, although in this case the low magnetic profile that the composite provides compared to metal is a strong argument as well. The sandwich plate as a structural member is in itself a stiffened plate that is in less need of additional stiffeners compared to metal or single skin panels. The major setback with the sandwich structure is the complicated and expensive manufacturing and the difficulties of predicting the properties of the material. In steel or aluminium marine constructions, the classification societies certify the material before the manufacturing. However, when using composites, the material is created during the manufacturing of the craft, which might imply much more uncertainty about the mechanical properties of the material. The classification societies hence require laminate samples for testing to approve the material system. Also, the fact that a sandwich plate consists of three parts, one core and two laminates, and that the composite laminates are anisotropic, makes the engineering and manufacturing of the material complicated compared to metals. On the other hand, the anisotropic properties permit the engineer to specifically design the laminate for its intended use.

There are several composite material systems to choose from, some more accepted than others. The most common composite reinforcement in marine applications is standard glass fibres due to its low price, but in sandwich high-performance applications, carbon fibre reinforcements is more commonly used due to its superior mechanical properties. In this study a carbon sandwich composite will be used as structural material. This choice is made due to the superior strength and stiffness to weight that carbon provides. A standard modulus fibre T700 (E<265 GPa) is chosen to provide a good balance between strength and stiffness [15]. The use of this quality of carbon fibre is also well documented in project such as the Visby class corvette and the Combat boat 90E. In a more detailed analysis using different fibres at different locations where either strength or stiffness sets the limits could optimize the weight of the structure. The mechanical properties for the fibre are presented in

Table 6 [15].

Table 6. Mechanical properties of T-700 carbon fibre. Density 1760 [kg/m3] Modulus of elasticity 230 [GPa] Tensile strength 3530 [MPa] Compressive strength 2118 [MPa] Elongation at break 1.5 [%] Poisson’s ratio 0.22 [-]

In the DNV regulations §3:4:5, a robustness criterion of the laminates is expressed as a minimum weight of the reinforcements in the laminates. The type of reinforcement used determines this criterion and the limits for carbon is presented in Table 8.

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Table 8. Minimum requirements for amount of reinforcement. Hull bottom, transom & outside of hull

1600 [g/m2]

Hull side above deepest WL 1100 [g/m2] Hull bottom & side, inside of hull

1100 [g/m2]

Stem & keel 4000 [g/m2] Weather deck, not for cargo 1100 [g/m2] Wet deck 1100 [g/m2] Cargo deck 2000 [g/m2] Decks underside skin 500 [g/m2] Tank bulkheads 1100 [g/m2] Watertight bulkheads 1100 [g/m2] Superstructure 800 [g/m2]

The compressive strength of the material is based on rule requirements from DNV 3:4:3, which stipulates design compression strength not greater than 60 % of the tensile strength.

Vinylester resin is chosen as matrix for the carbon fibres due to its excellent physical properties as impact and fatigue resistance as well as providing a good permeation barrier for the laminate [16]. The mechanical properties of the vinylester resin are presented in Table 9.

Table 9. Physical properties of Vinylester. Density 1120 [kg/m3] Modulus of elasticity 3.85 [GPa] Tensile strength 62.5 [MPa] Elongation at break 6 [%]

Now using these two materials and their respective mechanical properties the following mechanical properties can be calculated for a unidirectional sample of the composite (Table 10) [17,18]. A fibre volume fraction of 0.55 is assumed which gives a conservative value and this is largely dependent on method of manufacturing, which will be discussed.

Table 10. Mechanical properties for UD lamina with carbon-vinylester at a fibre volume fraction of 0.55. Density 1440 [kg/m3] Ex 128.2 [GPa] Ey 8.4 [GPa] Gxy 5.07 [GPa]

4.1.1. PANELS

Together these materials make up the laminate for the plates. If the plates are assumed to be quasi-isotropic this gives, according to laminate theory (Zenkert & Battley, 1996), the following properties for the finished laminate (Table 12). The allowed stress according to DNV is denoted σb,plate.

Table 12. Properties of quasi-isotropic plate laminate. Density 1440 [kg/m3] Ex 49.8 [GPa] Ey 49.8 [GPa] Gxy 19.3 [MPa] σb,plate 187.5 [MPa]

Further a proper core material for the panels needs to be selected, according to the DNV rules a minimum density of 130 kg/m3 is to be used in hull bottoms exposed to slamming. This is according to research done at KTH and FMV a non-conservative value so a slightly heavier, but stronger core will be used in these panels (Table 13).

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Table 13. Core properties for divinycell H160. Density 160 [kg/m3] Shear modulus 73 [MPa] Modulus of elasticity 205 [MPa] Shear strength 2.6 [MPa]

There have been indications that a stronger and thinner core allows for a better absorption of slamming loads. The design could also benefit from different core densities in different areas of the structure, e.g. high density in slamming exposed areas and lower densities in side and deck structures. This would allow a better weight optimization of the craft.

4.1.2. Beams The same material is used in the beams as in the plates, however the lay-up of the fibres can be done differently to get a better efficiency. For the beam flange, which will be subjected to normal stresses, it’s preferable to have as much fibres in the longitudinal direction as possible. Hence it is assumed that 80 % of the fibres run in the 0° direction and 20 % in the 90° direction. The webs primarily deal with shear stresses and thus the fibre orientation is [+45° -45°] for these. Using laminate theory and the data for the UD fibre lay-up in the previous section the following mechanical properties can be determined (Table 14). The stress limits displayed in Table 14 are the allowable stress according to DNV, with safety factors applied.

Table 14. Material properties for flanges and webs. Flange Ex 104.8 [GPa] σb, flange 473.2 [MPa] Web Ex 17.7 [GPa] Gxy 33.4 [GPa] σb, web 57.7 [MPa]

τb,web 264.5 [MPa]

The strength of the laminates is determined using the 10 % rule and the modulus of shear and elasticity using laminate theory.

4.1.3. Factors of safety The factors of safety are outlined in DNV 3:4 B500 and gives safety factors on stresses and deflections on panels. The stress factors are applied on both panels and beams, but there are no deflection criteria for beams. From [19] it’s however determined to use wmax<0.05l for beams in general and wmax<0.02l for beam supporting engines, where l is the length of the beam. The following factors apply for plates regarding stress and deflection (Table 15). The σ and τ values in Table 15 and Table 16 is the estimated strength of the laminates calculated in the previous section.

Table 15. Safety factors according to DNV. σallow τallow w/b Panels 0.3σb, calc 0.4τb, calc 0.02

Here b is the shortest side of the panel and σallow and τallow are allowable stresses in the laminate and core. For the beams the following factors are applied (Table 16).

Table 16. Safety factors for beams according to DNV. σallow τallow

Stiffener 0.3σb, calc 0.25τb, calc

Web frame 0.3σb, calc 0.25τb, calc

Girder 0.3σb, calc 0.25τb, calc

It’s important to take into account the reduction in allowable stresses when analysing compression, this is the case in some parts for both panels and beams.

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4.2. ALUMINIUM & STEEL For the aluminium and steel design the material system is a little simpler since the constituents are isotropic. It is however a big difference in mechanical properties between different grades of these two metals. In this study the DNV system for classification is used and the mechanical properties for aluminium are presented in

Table 17.

Table 17. Mechanical properties for aluminium. Grade V-5086-H34 E 70 [GPa] G 26.9 [GPa] ν 0.3 [-] Density 2800 [kg/m3] Minimum Yield strength 220 [MPa] Minimum elongation 7 [%]

The mechanical properties for the chosen steel are presented in Table 18. This is a high-strength steel, according to the DNV material classification, with a minimum yield strength of 500 MPa.

Table 18. Mechanical properties for steel. Grade NV-500 E 206 [GPa] G 79.2 [GPa] ν 0.3 [-] Density 7800 [kg/m3] Minimum Yield strength 500 [MPa]

4.2.1. Factors of safety Using the DNV system for materials and factors of safety gives the maximum allowed stress as a factor f1 times a nominal strength of 160 MPa. In fact this nominal value differs depending on the structural member considered, but it is here chosen as 160 since this is a conservative value. For a complete list refer to DNV §3:5:5 and §3:2:5. The factors and resulting stress limits are given in Table 19.

Table 19. Allowable stresses. Aluminium Steel f1 0.8 2.08 [-] σallow 128 332.8 [MPa]

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5. HULL STRUCTURAL DESIGN This section outlines the design philosophy of the two different material concepts and presents the method from determining the scantlings and the results from the scantling calculations. The scantlings which are determined here are to be considered as minimum requirements and the purpose of these calculations is to obtain approximate masses for the different material concepts. The main particulars of the craft can be found in part I of this report and the structural design of the cargo platform and crossbeams are treated in chapter 11 & 11. The scantlings are determined according to the DNV High Speed, Light Craft and Naval Surface Craft (2006) [33], here referred to as DNV §X:Y:Z.

5.1. SCANTLINGS METHOD

The general rules for the classification of the craft are given in DNV §1:1:2. The service area restriction which applies to the LCU is coastal, R3, which means that the ship is not allowed to go any further away from the nearest harbour or safe anchorage area than 16 NM under winter conditions, 45 NM under summer condition and 80 NM under tropical conditions (reduction factor for light craft included). The class notation given to the LCU will be 1A1 HSLC R3 Naval Landing Craft.

For the LCU there are no particular requirements for the subdivision of the hulls with bulkheads except the general rules defined in DNV §3:1. This means that at least two bulkheads must be fitted forward and aft of the engine compartment and a collision bulkhead at the bow. The craft is divided into 5 sections by the bulkheads (Figure 6).

The structural arrangement of the landing catamaran requires some special considerations. There are two main issues to deal with: the craft should be able to stand both on the well deck and on the beach fully loaded and the introduction of the crossbeam loads.

One of the most important parameters to determine when analysing the forces acting on the craft’s hull is the vertical design acceleration. The design loads given in DNV §3:1:2 are derived from full-scale measurements and statistical analysis of high speed and light craft designs. It does however state that new design concepts, such as this craft, could require tank tests, theoretical studies, or full-scale measurements to accurately determine the magnitude of the design acceleration. The magnitude of this acceleration is very difficult to assess, especially due to the unconventional nature of this particular craft. This should be kept in mind when evaluating the results of the analysis.

The general scheme of calculation starts with determining the vertical acceleration at the centre of gravity of the craft, acg. This is done using the speed and length of the craft together with an acceleration factor, fg, determined by service and service area notation. For this particular craft the vertical design acceleration is determined to be 10.1 m/s2. This is an extreme value with a 1% probability of being exceeded, in the worst intended condition of operation. The vertical acceleration at an arbitrary position along the hull, av, is determined using a longitudinal distribution factor, kv. This factor is 1 from the stern to midship, increasing linearly to 2 at the forward perpendicular. This design acceleration could be crosschecked with the vertical acceleration obtained from the seakeeping analysis.

Using the design acceleration, the various design pressures can be determined. The design pressures suggested by DNV are simplified and categorised from the actual and very complex loading situation occurring when a craft is travelling at high speed in seaway. There are four different design pressures to consider according to DNV; bottom slamming pressure, forebody side and bow impact pressure, slamming pressure on flat cross structures and sea pressure. In addition to these pressures special consideration must be taken for a landing craft. There are then two additional pressures; beaching pressure and LPD contact pressure. For the latter pressure there is no explicit rule formulation, however DNV stipulates that the craft should have a flat footprint for low nominal contact pressure. The beaching pressure is not considered for the hulls since the cargo platform is designed to take this impact.

The pressures naturally vary depending on the considered location, so the maximum pressure for each structural member must be determined.

Since the displacement and speed of the craft changes dramatically when unloading the cargo, the acceleration and resulting design pressures for the unloaded condition must also be considered. For this particular craft the governing design pressures where those obtained in the fully loaded condition.

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The method of determining the scantlings of the craft’s structure is taken from DNV HSLC §3:3 Hull structural design, Aluminium Alloy and §3:4 Hull Structural Design, Fibre Composites and Sandwich Construction. These sections describe the structural principles, materials, safety factors and calculation methods for plating, panels, stiffeners and beams. The formulas are implemented in an optimization scheme, to obtain minimum weight, that provides the geometries of the different structural members for a given load case. Typical constraints are minimum thicknesses of plating, fibre weight, sectional modulus of beams and deflection. A detailed account of the optimization method used for the composite structure may be found in [34].

The hull is defined according to section 5.2 and 0, where panel sizes and limiting girder heights etc. can be found together with of the longitudinal, vertical and transverse position of the considered structural member. The geometry of the plating are simplified and they are assumed to be rectangular, triangular sections are considered as rectangular with the width taken as half the width if the triangle. No account is taken to the curvature of the hull, which is conservative. There is no account taken for the fact that some beams are not perpendicular to the hull surface, in reality this means that the effective height of the considered beam is reduced.

The method and results of the scantling calculation is presented for both the aluminium and the composite version of the craft to allow for a proper evaluation of structural weight of the different material concepts.

5.2. STRUCTURAL ARRANGEMENT ALUMINIUM CRAFT This section describes the aluminium structural arrangement and presents the results of the scantling calculations. The aluminium version was done at a preliminary deign phase and is thus not as thoroughly evaluated as the carbon composite version.

5.2.1. Bottom The aft compartment contains the water-jet machinery and the bottom is cut out to accommodate this. The longitudinal girders, G1, are placed at this cut to transfer the loads from the propulsion system to the structure. As progressing towards the bow the engine girders, G2, are raised to allow the MTU engine and gearbox enough clearance to the bottom of the craft. This also determines the spacing of the supporting girders. These girders continue into the tank compartment separated by bulkhead 3 and 4. Girders G3 & G4 are continuous as progressing forward until terminating at bulkhead 5 (Figure 6).

Figure 6. Structural arrangement for the bottom

To allow the craft to stand on the bottom a set of centre girders, G5-G8 is installed that starts at bulkhead 2 and terminates at the bow. The height of these girders is limited by the presence of the engine and the height of the engine support girders. This gives a separation of 0.5 m between the girders and to make the structure well balanced and the plates equally sized a third set of girders, G9-G10, is placed outside girders G1-G4. The web frames are equally spaced between the supporting bulkheads with a separation of 1 m. Longitudinal stiffeners are placed with a spacing of 250 mm throughout the bottom of the craft according to the recommendation of DNV.

5.2.2. Side

The web frames continue onto the craft’s sides and are thus spaced at 1 m. There are no longitudinal girders in the craft sides. Figure 7 also shows the centre girders and the raised engine supports. The loads from the cross beams are assumed to be introduced into the deck structure. Additional beams might be fitted around the water-jet machinery to transfer loads from the stern bulkhead to the bottom and sides.

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Figure 7. Structural arrangement for the sides.

5.2.3. Deck The deck is supported by a set of centre girders together with additional side girders; this provides a strong base on which to attach the crossbeams connecting the two hulls. The web frames are also continual from side to side of the craft. The longitudinal stiffeners are placed at 250 mm apart, these are not depicted in the figure below.

Figure 8. Structural arrangement for the deck.

5.3. SCANTLINGS ALUMINIUM CRAFT The method of calculation starts with determining the plating thickness. This is done using three different cases; minimum thickness in general, minimum thickness due to bending and minimum thickness due to slamming pressure. Then the minimum stiffener sectional modulus due to bending and slamming is determined. Finally the girder and web frame system is evaluated using minimum shear areas, bending stiffness and minimum plating thicknesses for each structural member.

Since the optimization scheme naturally puts more material in the flange than in the web the minimum plating thickness is the governing constraint for the webs. In some cases even the flange thickness approaches the minimum thickness, due to the low design pressures. These scantlings give the total structural weight of the aluminium craft to 13.7 ton.

5.3.1. Bottom

The bottom of the craft is partitioned according to Figure 6. For the sake of simplicity and to reduce calculation time, the plating in the bottom is divided into two sections, P1-P12, between the transom and bulkhead 3 and P13-P19, between bulkhead 3 and the bow. Each of these sections has different thickness instead of having individual thickness on each plate. The design pressures for the bottom plating vary from 59 kPa to 219 kPa depending on plate location and size. The largest pressure is the slamming pressure at the bow. The resulting thicknesses are 6 mm for plates P1-P12 and 9 mm for P13-P19.

The stiffeners are treated in a similar manner and are assumed to be of constant cross-section throughout the bottom structure.

It can be observed that girders 3, 5 and 9 stretching between bulkhead 3 and 4 are subjected to very large design pressures due to the beaching load and corresponding small load area. In reality the interaction between these girders and the transverse web frames would make the situation look a little bit different since the load would be transferred from the girders via the web frames to the side structure, maybe reducing the size and thus weight of the girders. The scantlings for the floors are obtain in the same manner as for the girders. The input and results of the bottom scantling calculations are displayed in table 18-20.

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Table 18. Scantlings for bottom stiffeners of the aluminium craft. Bottom st i f f ene rs Web height, hw 80 [mm] Web thickness, tw 8 [mm] Flange breadth, bf 80 [mm] Flange thickness, tfl 8 [mm]

Table 19. Bottom girder scantlings for the aluminium craft.

Girde r 1 2 3 4 5 6 7 8 9 Load point [m], x 1.7 5.2 9.5 14 17.4 1.7 5.2 9.5 14 Span [m], l 3.3 3.7 5 4 2.8 3.3 3.7 5 4 Pressure [kPa], p 32 41 49 256 256 32 41 49 256 Web height [mm], hw 160 160 180 290 200 160 160 180 290 Web thickness [mm], tw 3.6 4.8 30 30.1 30 3.6 4.8 31 31 Flange breadth [mm], bf 100 100 170 280 190 100 100 170 280 Flange thickness [mm], tf 11.9 22.8 30 30.1 30 11.9 2.8 31 31

Table 20. floor scantlings for aluminium craft.

Floor 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Load point [m], x 1.1 2.2 4 5 6 8 9 10 11 13 14 15 17 18 Span [m], l 1 1.1 2.4 2.6 2.7 2.8 2.8 2.6 2.2 1.8 1.5 1.2 1 0.5 Pressure [kPa], p 35 37 35 37 39 44 46 51 59 74 256 256 256 256 Web height [mm], hw 110 130 150 150 150 150 150 150 150 150 170 150 150 150 Web thickness [mm], tw 3.6 3.6 5.7 6.5 7.1 8.3 8.7 9 8.8 9.1 20 20 17.3 8.6 Flange breadth [mm], bf 100 100 100 100 100 130 140 130 100 100 170 150 100 100 Flange thickness [mm], tf 3.6 3.6 13 17 20 20 20 20 20 14 20 20 16 3.6

5.3.2. Side scantlings

The loads on the side plating vary between 10-20 kPa depending in the vertical load point. The plating for the side structure is determined by the minimum thickness criteria and is thus set to 6 mm. The stiffeners are assumed to be of the same cross-section throughout the side and the dimensions are presented in There are no girders in the side structure. The design pressures are in the region of 20kPa. With the web height constraint set to 150 mm the web thickness ends up at between 3.7 – 5 mm depending on location and length of the web frame. The constraint on flange breadth of 100 mm results in flange thicknesses between 6 – 13 mm. The input and the results for the side are displayed in table 21-22.

Table 21. There are no girders in the side structure. The design pressures are in the region of 20kPa. With the web height constraint set to 150 mm the web thickness ends up at between 3.7 – 5 mm depending on location and length of the web frame. The constraint on flange breadth of 100 mm results in flange thicknesses between 6 – 13 mm. The input and the results for the side are displayed in table 21-22.

Table 21. Scantlings for side stiffeners. Side s t i f f ene rs Web height, hw 40 [mm] Web thickness, tw 4 [mm] Flange breadth, bf 40 [mm] Flange thickness, tfl 4 [mm]

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Table 22. Side frame scantlings for the aluminium craft. Side f rame 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Load point [m], x 1.1 2.2 4 5 6 8 9 10 11 13 14 15 17 18 Span [m], l 1 1.1 2.4 2.6 2.7 2.8 2.8 2.6 2.2 1.8 1.5 1.2 1 0.5 Pressure [kPa], p 20 20 20 20 20 20 20 20 20 20 20 20 20 20 Web height [mm], hw 150 150 150 150 150 150 150 150 150 150 150 150 150 150 Web thickness [mm], tw 4.6 4.7 4.9 4.9 4.9 4.9 4.9 4.9 4.9 4.8 4.6 4.5 4 3.7 Flange breadth [mm], bf 100 100 100 100 100 100 100 100 100 100 100 100 100 100 Flange thickness [mm], tf 11 12 13 13 13 13 13 13 13 12 11 10 8 6

5.3.3. Deck scantlings The dimensioning pressure for the deck plating is the sea pressure at deck level and is determined to be 16 kPa, thus rather low compared to the bottom structure. This yields a minimum plating thickness of 5 mm, which is used throughout the deck structure. Note that this doesn’t account for the extreme local loads imposed by the crossbeams. The stiffeners are of same cross-section throughout the deck.

The scantlings of the girders are governed by the restrictions set on the web height and flange breadth.

Since the optimization scheme naturally puts more material in the flange than in the web the minimum plating thickness is the governing constraint for the webs. In some cases even the flange thickness approaches the minimum thickness, due to the low design pressures. These scantlings give the total structural weight of the aluminium craft to 13.7 ton. The input and results for the deck are presented in table 23-25.

Table 23. Scantlings for deck stiffeners of the aluminium craft. Deck s t i f f e ne rs Web height, hw 40 [mm] Web thickness, tw 2 [mm] Flange breadth, bf 40 [mm] Flange thickness, tfl 2 [mm]

Table 26. Scantlings for deck girders.

Girde r 1 2 3 4 5 6 7 8 9 Load point [m], x 1.7 5.2 9.5 14 17.4 1.7 5.2 9.5 14 Span [m], l 3.3 3.7 5 4 2.8 3.3 3.7 5 4 Pressure [kPa], p 13 13 13 13 13 13 13 13 13 Web height [mm], hw 200 200 200 200 110 200 200 200 200 Web thickness [mm], tw 3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.6 Flange breadth [mm], bf 100 100 100 100 100 100 100 100 100 Flange thickness [mm], tf 5.2 7.4 17.4 9.4 3.6 5.2 7.4 17.4 9.4

Table 27. Scantlings for deck beams.

Deck web f rame 1 2 3 4 5 6 7 8 9 10 11 12 13 Load point [m], x 1.1 2.2 4 5 6 8 9 10 11 13 14 15 17 Span [m], l 2.3 2.4 2.6 2.7 2.8 2.8 2.9 2.9 2.8 2.7 2.5 2.2 1 Pressure [kPa], p 13 13 13 13 13 13 13 13 13 13 13 13 13 Web height [mm], hw 150 150 150 150 150 150 150 150 150 150 150 150 150 Web thickness [mm], tw 3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.6 Flange breadth [mm], bf 100 100 100 100 100 100 100 100 100 100 100 100 100 Flange thickness [mm], tf 4.1 4.6 5.8 6.4 7.1 7.1 7.8 7.8 7.1 6.5 5.3 3.6 3.6

5.4. STRUCTURAL ARRANGEMENT COMPOSITE CRAFT Due to the inherent stiffness of the sandwich panels the composite structure is somewhat less cluttered than the aluminium structure. The basic bulkhead placement is determined by DNV regulations and

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crossbeam placement as well as providing a well-balanced structure. Engine and water-jet dimensions are also key parameters when determining bulkhead separation.

5.4.1. Bottom structure In the same way as for the aluminium option, the engine and the water-jet provides the basic girder spacing in the bottom of the craft. However the outer girders in the central part of the bottom are here determined to be excessive and are thus removed. A benefit of using a composite structure is the ability to use more complex geometries of the different structural members. This is used in the forward part of the craft where the girder are double curved, this partition the panels into equal sizes as well as providing continuity in girder height (Figure 9). The girders supporting the engine are widened to match the mounting width on the engine and also provide continuity from the aft girder placed at the mounting width of the water-jet. The girder supporting the engine is raised to provide enough clearance from the engine to the bottom of the craft. This is done with continuity in mind and the raised section is tapered in both ends. The chine running along the side of the craft is assumed to be stiff separating the bottom and side structure dividing the bottom into panels according to Figure 9.

Figure 9. Structural arrangement of bottom.

Between bulkhead 3 and 4 a web frame is placed to partition the otherwise long girders and partitioning the panels into more proportional sizes. It is assumed that the cargo platform will take most of the beaching pressure and thus there is no need for additional web frames in the forward part of the bottom structure. The outer girders between bulkhead 3 and the web frame provide excellent support for the fuel tanks as well as any additional required equipment.

A centre girder is used to cope with the possibly high local loads due to the craft standing on the shore or in the LPD fully loaded. In an area 200 mm wide below the centre girder the sandwich panel turns into a single skin laminate and there are two reasons for this (Figure 10). The primary reason is to handle to possibly extreme local contact pressures when mowing the cargo on the craft and the second reason is to allow for some unavoidable shave of the laminate due to beaching and docking at the LPD.

Figure 10. Schematic illustration of keel structural arrangement.

5.4.2. Side structure The side structure of the craft is perhaps more critical in this application than usual since the large loads introduced by the cross-beams must be distributed from the attachment in deck 1 and the sides to the rest of the structure in an efficient manner. The height of the deck is determined by the crossbeam attachments and the equipment required running the platform system. The deck is assumed to be stiff and thus partitions the panels above and below. To reduce panel size obtaining a more efficient structure a set of longitudinal beams, G1-G5, are placed below deck 1 (Figure 11).

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Figure 11. Structural arrangement sides.

The crossbeams are attached at bulkheads 3 and 5 and strong knees must be fitted between the deck and these bulkheads to distribute the loads from these attachments to the bulkheads.

5.4.3. Deck structures The craft has two decks; one primary deck where hydraulic and brake installations are made and one weather deck to provide protection for the equipment as well as reducing the wind resistance of the craft. This deck may also support the cargo platform when the craft is in docking mode and when the cargo is transferred from one craft to another. The deck for installations is referred to as deck 1 and the structural arrangement is displayed in Figure 12.

Figure 12. Structural arrangement of deck 1.

The outer girders, G1 – G3, are placed in line with the hydraulics installed on the deck to absorb the forces from these and distributing them to the adjacent structure. In the aft section at bulkhead 1 these girders meet the two beams stiffening the stern bulkhead around the water-jet installation. In the forward part of the craft a centre girder is placed between bulkhead 4 and 5 to support the hydraulics operating the forward arm, the load from this girder is transferred to the outer girders by the means of two diagonal girders aft of bulkhead 4.

The weather deck is not as highly loaded as deck 1, and a single centre girder is assumed to suffice. This reduces the panel size and results in an efficient structure (Figure 13).

Figure 13. Structural arrangement of the weather deck.

For the scantling calculations the structure surrounding the raised sections at the platform arm is assumed to be stiff and the deck is divided into panels and girders according Figure 13. In reality this part of the structure could be subjected to extreme local loads, but these are of a more complex character and are thus dealt with separately.

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5.4.4. Bulkheads The bulkheads are divided by deck 1 into two parts; the lower part is stiffened with two vertical beams connecting to the bottom outer girders and the outer girders at deck 1 (Figure 14). This provides continuity in the structure and the large loads from the platform arm can be distributed in an efficient manner. Bulkheads 4 and 5 only have one vertical beam due to the size of these panels.

Figure 14. Structural arrangement for bulkheads.

5.5. SCANTLINGS COMPOSITE The scheme of calculation is to first determine the panel scantlings, i.e. face thickness and core thickness. The scantlings for the girders and web frame are then determined. The material data used in these calculations may be found in section 4.1. The girders and beams are of the type top-hat and web thicknesses refer to one of the web faces. The total weight for the composite structure of the entire craft is 7313 kg.

5.5.1. Bottom The bottom structure is subjected to extreme loads, not only from the slamming or pitching slamming pressure, but also from the fact that the craft will stand on the well deck fully loaded. This load case requires some special considerations. By observing the shape of the hull bottom it can be concluded that at rest, with the cargo secured, the total length of bottom in contact with the well deck is 10.5 meters. Now assuming that the contact width is 200 mm the contact pressure can be calculated to 271 kPa. The core material has a compressive strength of 3.4 MPa, hence it is able to handle this pressure, but only at this very moment when the cargo is at rest in its intended position. When embarking the pressure on the forward part of the bottom could locally be many times larger depending on the position of the cargo. The exact magnitude of this pressure is not determined, but this must be kept in mind.

This gives a total panel weight for one hull of 126.1 kg. It can also be observed that it is the minimum fibre weight together with the core shear strength that determines the thicknesses. This should mean that the panels would be even lighter with a core of lower density. In reality a couple of standard core thicknesses would be chosen when building the hull, hence the total weight might increase somewhat. One also has to consider the robustness of the skins; it might not be practical out of a manufacturing or user perspective to have only 1.7 mm of laminate.

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When determining the scantlings for the girders the LPD contact pressure must be taken into account, for the panels this was neglected. The load breadth for the centre girder is assumed to be 200 mm in consensus to the earlier discussion. The longitudinal extent of the load area is taken as the length between bulkheads and/or web frame. Girder G2, G4, G6 and G8 are all subjected to this pressure, which is of a greater magnitude than the slamming pressure. Calculations must however be done for both of these load cases sine the load area differs. For the slamming case the load area is larger, but the pressure smaller and the opposite for the contact pressure. For all of these girders it is the contact pressure that provides the final scantlings.

The results obtained in this analysis are largely dependent on the geometric limitations of the girders. It is important to limit e.g. the girder height so that stability problems can be avoided. The web and flange limitations also affect the results significantly and a great deal of engineering judgement must be used to obtain reasonable results. The total weight of the girders for one hull is 846.4 kg. A large contribution to this is the heavily loaded centre girders. It’s also interesting to see the difference in active constraints between the centre girders and the others. In most cases it is the minimum fibre weight that is the governing constraint, but not for the centre girders, which are subjected to much larger pressures.

The floor calculations are performed in a similar manner and the input and results for these as well as for the panels and the girders are presented in table 26-31.

The final weight of the bottom structure for one hull amounts to 2047.4 kg.

Table 26. In-data for bottom panel scantlings. Bottom panel 1 2 3 4 5 6 7 8 9 10 Indata Load point [m], x 1.65 5.15 5.15 8.40 8.40 10.80 10.80 14.00 14.00 17.30 Load point [m], z 0 0 0 0 0.27 0 0.27 0 0.27 0.27 Deadrise [deg], β 10 10 10 10 10 15 10 20 20 20 Panel length [m] 3.30 3.70 3.70 2.50 2.50 2.40 2.40 3.90 3.90 2.50 Panel breadth [m] 0.50 0.60 0.60 0.60 0.70 0.60 0.65 0.35 0.45 0.30 Pressure Type Slam Slam Slam Slam Slam Pitch Pitch Pitch Pitch Pitch Magnitude [kN/m2] 43.1 50.7 50.7 62.0 56.5 107.2 162.9 78.9 78.9 78.9

Table 27. Minimum scantling requirements for hull bottom panels.

Bottom panel 1 2 3 4 5 6 7 8 9 10 Geometry Face thickness [mm], tf 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 Core thickness [mm], tc 9 13 16 17 17 29 48 12 15 10 Constraints (% of allowable) Panel deflection 47.6 48.2 48.2 43.1 50.7 32.4 28.3 28.9 32.2 27.3 Core shear 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 Face stress 39.9 48.1 48.1 48.8 57.4 48.9 53.2 27.5 35.6 23.8 Local buckling 9.9 11.9 11.9 12.1 14.2 12.1 13.2 6.8 8.8 5.9 Min. fibre weight 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 Weight [kg] 10.4 15.5 15.5 11.2 13.3 13.7 19.7 9.2 12.9 4.8

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Table 28. In-data for bottom girders. Bottom gi rde rs 1 2 3 4 5 6 7 8 9 10 In-data Load point [m], x 1.65 5.15 5.15 8.40 8.40 10.80 10.80 14.00 14.00 17.30 Load point [m], z 0 0 0 0 0.27 0 0.27 0.00 0.27 0.27 Deadrise [deg], β 10 10 10 10 10 15 10 20 20 20 Beam length [m] 3.30 3.70 3.70 2.55 2.55 2.50 2.50 4.00 4.00 2.60 Load breadth [m] 0.25 0.20 0.60 0.20 0.70 0.20 0.65 0.20 0.45 0.30 Longitudinal extent of load area [m], la 3.30 3.70 3.70 2.55 2.55 2.50 2.50 4.00 4.00 2.60 Pressure Type Sea LPD Pitch LPD Pitch LPD Slam LPD Pitch Pitch Magnitude [kN/m2] 30.3 271 136.5 271 59.3 271 38.2 271 71.1 71.1

Table 29. Minimum bottom girder scantlings.

Bottom gi rde rs 1 2 3 4 5 6 7 8 9 10 Geometry Flange thickness [mm], tfl 2.5 25.0 2.5 25.0 2.5 25.0 3.3 25 2.7 2.9 Web thickness [mm], tw 2.5 21.0 2.5 7.8 2.5 7.3 4.6 25.3 3.9 2.5 Flange width [mm], bfl 40 217 40 98.5 40 94.3 300 256 300 40 Web height [mm], hw 350 350 350 350 350 350 350 350 350 350 Constraints (% of allowable) Beam deflection 92.1 100.0 87.9 100.0 57.0 100.0 47.1 100.0 79.6 100.0 Flange stress 28.0 6.1 76.3 6.1 55.9 6.1 24.3 6.2 26.1 36.7 Face stress 41.9 72.7 71.6 72.8 57.9 72.8 100.0 72.7 100.0 54.1 Web stress 4.9 20.9 28.0 21.0 18.6 21.0 17.8 20.9 16.6 6.7 Web shear 3.5 2.6 9.1 4.8 9.6 5.0 13.3 2.3 8.8 6.3 Min. fibre weight flange 100.0 10.1 100.0 10.1 100.0 10.1 78.0 10.1 94.0 87.8 Min. fibre weight web 100.0 12.1 100.0 32.7 100.0 34.7 55.5 10.0 65.6 100.0 Weight [kg] 32.7 153.2 36.7 43.3 25.3 40.3 129.6 197.1 175.2 13.0

Table 30. In-data for floor scantlings.

Bottom f l oor 1 Longitudinal extent of load area 2.5 Load breath 2.5 Lenght of beam 2.7 x (loadpoint) [m] 9.53 z (loadpoint) [m] 0 Local deadrise angle [deg] 10 Pressure type Pitch Magnitude [kN/m2] 158

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Table 31. Minimum scantling requirements for floors. Bottom f l oor Geometry Flange thickness [mm] 19.7 Web thickness [mm] 41.7 Flange width [mm] 300 Web height [mm] 450 Constraints (% of allowable) Beam deflection 9.9 Flange stress 17.5 Face stress 100.0 Web stress 22.5 Web shear 5.4 Min fibre flange 12.9 Min fibre web 6.1 Total weight [kg] 228.5

5.5.2. Side

The side scantlings are done in the same manner as the bottom, however the design pressures are significantly smaller and consist solely of the sea pressure at different levels. The side structure is divided into structural members according to the structural arrangement.

This results in a total weight of 776.2 kg for the side panels of one hull. The areas surrounding the crossbeams could require additional material to handle the local loads; a discussion of additional structural weight follows in section 5.6.

The total weight of the side girders for one hull is 91 kg. The total weight if the side structure for on hull is then 887.8 kg. The in-data and results of these calculations are displayed in table 32-36.

Table 32. Side panels input. Side pane l 1 2 3 4 5 6 7 8 9 10 Indata Load point [m], x 1.66 5.15 8.27 10.80 13.86 17.23 1.66 5.15 8.27 10.80 Load point [m], z 0.47 0.47 0.47 0.47 0.47 0.47 1.60 1.60 1.60 1.60 Panel length [m] 3.31 3.67 2.55 2.43 4.10 2.60 3.31 3.67 2.55 2.43 Panel breadth [m] 1.00 1.00 1.00 1.00 1.00 1.00 1.20 1.20 1.20 1.20 Pressure Type Sea Sea Sea Sea Sea Sea Sea Sea Sea Sea Magnitude [kN/m2] 21.08 21.08 21.08 21.15 21.33 21.53 11.14 11.14 11.14 11.22 Side pane l 11 12 13 14 15 16 17 18 Indata Load point [m], x 13.86 17.23 1.66 5.15 8.27 10.80 13.86 17.23 Load point [m], z 1.60 1.60 2.60 2.60 2.60 2.60 2.60 2.60 Deadrise [deg], β 20.00 20.00 10.00 10.00 10.00 15.00 20.00 20.00 Panel length [m] 4.10 2.60 3.31 3.67 2.55 2.43 4.10 2.60 Panel breadth [m] 1.20 1.20 0.75 0.75 0.75 0.75 0.75 0.75 Pressure Type Sea Sea Sea Sea Sea Sea Sea Sea Magnitude [kN/m2] 11.40 12.39 14.28 14.28 14.28 14.39 14.64 14.92

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Table 33. Results for side panels. Side pane l 1 2 3 4 5 6 7 8 9 10 Geometry Face thickness [mm], tf 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 Core thickness [mm], tc 10.3 10.4 10.2 10.2 10.5 10.4 9.4 9.5 9.3 59.4 Constraints (% of allowable) Panel deflection 100.0 100.0 100.0 100.0 100.0 100.0 99.9 100.0 100.0 100.0 Core shear 81.9 82.3 80.4 80.2 83.1 81.4 55.1 55.6 53.8 53.6 Face stress 67.4 67.3 67.1 67.1 67.7 67.8 54.9 55.1 54.4 54.3 Local buckling 16.7 16.7 16.7 16.7 16.8 16.8 13.6 13.7 13.5 13.5 Min. fibre weight 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 Weight [kg] 21.7 24.1 16.7 15.9 27.0 17.1 25.5 28.3 19.6 61.0 Side pane l 11 12 13 14 15 16 17 18 Geometry Face thickness [mm], tf 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 Core thickness [mm], tc 9.7 9.6 4.9 4.9 4.8 4.9 5.0 5.0 Constraints (% of allowable) Panel deflection 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 Core shear 56.5 54.9 80.3 80.5 79.5 79.6 81.6 81.2 Face stress 55.7 55.5 48.9 48.8 49.0 49.2 49.2 50.0 Local buckling 13.8 13.8 12.1 12.1 12.2 12.2 12.2 12.4 Min. fibre weight 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 Weight [kg] 31.7 20.1 14.1 15.6 10.9 10.4 17.5 11.1

Table 34. Input for side girder scantlings.

Side gi rde rs 1 2 3 4 5 6 Indata Load point [m], x 1.66 5.15 8.30 10.80 14.10 17.30 Load point [m], z 1.00 1.00 1.00 1.00 1.00 1.00 Beam length [m] 3.31 3.67 2.50 2.50 4.00 3.31 Load breadth [m] 1.10 1.10 1.10 1.10 1.10 1.10 Longitudinal extent of load area [m], la 3.31 3.67 2.50 2.50 4.00 3.31 Pressure Type Sea Sea Sea Sea Sea Sea Magnitude [kN/m2] 16.42 16.42 16.42 16.49 16.69 16.88

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Table 35. Side girder scantlings. Side gi rde rs 1 2 3 4 5 6 Geometry Flange thickness [mm], tfl 3.0 4.0 1.7 1.7 5.3 1.7 Web thickness [mm], tw 1.7 1.7 1.7 1.7 1.7 1.7 Flange width [mm], bfl 40.0 40.0 226.2 40.1 40.0 40.0 Web height [mm], hw 200.0 200.0 200.0 200.0 200.0 200.0 Constraints (% of allowable) Beam deflection 100.0 100.0 84.4 84.8 100.0 86.7 Flange stress 98.6 95.2 84.7 85.1 90.9 87.1 Face stress 70.0 77.0 55.9 56.2 85.4 57.5 Web stress 44.1 39.2 39.3 39.5 33.3 40.4 Web shear 16.7 18.5 12.6 12.7 20.5 13.0 Min. fibre weight flange 57.2 42.3 100.0 100.0 32.1 100.0 Min. fibre weight web 100.0 100.0 100.0 100.0 100.0 100.0 Weight [kg] 8.1 9.2 5.9 5.9 10.3 5.9

Table 36. Input and results for side frame.

Side f rame 1 Longitudinal extent of load area 2.5 Load breath 2.5 Lenght of beam 3 x (loadpoint) [m] 9.53 z (loadpoint) [m] 1.5 Pressure type Sea Magnitude [kN/m2] 12 Geometry Flange thickness [mm] 2.5 Web thickness [mm] 2.5 Flange width [mm] 40 Web height [mm] 300 Constraints (% of allowable) Beam deflection 28.3 Flange stress 82.5 Face stress 92.5 Web stress 25.1 Web shear 11.2 Min fiber flange 100.0 Min fiber web 100.0 Total weight [kg] 12.8

5.5.3. Deck 1 The scantlings of the panels of deck 1 are based on the pressures stipulated by DNV, in this case the sea pressure at the considered load point. These scantlings are not taking into account the extreme local loads imposed on the structure by the crossbeams, so the weight acquired here must be observed with some criticism.

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The total weight for the panels in deck 1 is then 249.4 kg. The results of these calculations give a total weight of the girders for one hull as 106.6 kg. This gives a total weight of deck 1 for one hull as 356.1 kg. The input and results for deck 1 are presented in table 37-40.

Table 37. Input for scantling calculations of deck 1.

Deck 1 pane l 1 2 3 4 5 6 7 8 9 Indata Load point [m], x 1.60 5.20 9.70 14.00 14.20 17.40 1.60 5.20 9.70 Load point [m], z 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 Deadrise [deg], β 10 10 10 15 20 20 10 10 10 Panel length [m] 3.31 3.67 5.00 2.10 4.00 1.25 3.31 3.67 5.00 Panel breadth [m] 0.50 0.70 0.80 0.50 0.50 0.40 1.10 1.10 1.10 Pressure Type Sea Sea Sea Sea Sea Sea Sea Sea Sea Magnitude [kN/m2] 11.4 11.4 11.4 11.7 11.7 11.9 11.4 11.4 11.4

Table 38. Scantlings for deck 1.

Deck 1 pane l 1 2 3 4 5 6 7 8 9 Geometry Face thickness [mm], tf 2.11 2.11 2.11 2.11 2.23 2.11 2.11 2.11 2.11 Core thickness [mm], tc 1.0 2.5 3.6 1.0 1.0 1.0 6.8 6.9 6.9 Constraints (% of allowable) Panel deflection 85.6 100.0 100.0 87.1 78.5 49.5 100.0 100.0 100.0 Core shear 88.0 81.9 77.2 89.1 87.2 71.3 65.0 65.4 66.2 Face stress 28.1 37.0 39.6 29.0 26.2 18.8 47.3 47.3 47.2 Local buckling 7.0 9.2 9.8 7.2 6.5 4.7 11.7 11.7 11.7 Min. fibre weight 100.0 100.0 100.0 100.0 94.5 100.0 100.0 100.0 100.0 Weight [kg] 20.8 33.6 53.6 13.2 26.6 6.3 26.3 29.2 39.8

Table 39. Input for scantling calculations of deck 1.

Deck 1 gi rde rs 1 2 3 4 5 Indata Load point [m], x 1.65 5.16 9.52 14.40 17.50 Load point [m], z 2.50 2.50 2.50 2.50 2.50 Deadrise [deg], β 10.00 10.00 10.00 20.00 20.00 Beam length [m] 3.30 3.67 5.00 4.00 2.50 Load breadth [m] 0.85 0.90 1.00 0.50 0.40 Longitudinal extent of load area [m], la 3.30 3.67 5.00 4.00 2.50 Pressure Type Sea Sea Sea Sea Sea Magnitude [kN/m2] 11.4 11.4 11.4 11.7 12.0

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Table 40. Scantlings for deck 1. Deck 1 gi rde rs 1 2 3 4 5 6 Geometry Flange thickness [mm], tfl 1.7 1.7 1.7 1.7 1.7 1.7 Web thickness [mm], tw 1.7 1.7 1.7 1.7 1.7 1.7 Flange width [mm], bfl 40 40 40 40 40 40 Web height [mm], hw 300 300 300 300 300 300 Constraints (% of allowable) Beam deflection 36.5 44.0 67.0 57.5 24.8 36.5 Flange stress 45.2 58.5 100.0 40.3 13.1 45.2 Face stress 22.7 27.2 44.1 24.2 9.9 22.7 Web stress 23.4 31.1 53.9 19.6 5.6 23.4 Web shear 6.0 7.0 10.6 4.4 2.2 6.0 Min. fibre weight flange 100.0 100.0 73.7 100.0 100.0 100.0 Min. fibre weight web 100.0 100.0 100.0 100.0 100.0 100.0 Weight [kg] 11.55 12.81 17.62 13.96 8.72 11.55

5.5.4. Weather deck

The scantlings for the weather deck are determined in the same manner. The total weight of the panels for one hull turns out at 158.4 kg, for the girders 41.8 and the web frame 52.9 kg. The total weight of the weather deck for one hull is then 253 kg. The input and results for the weather deck are displayed in table 41-45

Table 41. Input for weather deck scantlings. Weathe r deck pane l 1 2 3 4 5 6 7 8 9 Indata Load point [m], x 1.60 4.60 8.35 10.40 12.85 16.60 1.60 4.60 8.35 Load point [m], z 3.85 3.85 3.85 3.85 3.85 3.85 3.85 3.85 3.85 Deadrise [deg], β 10 10 10 15 20 20 10 10 10 Panel length [m] 3.30 2.60 1.50 1.40 2.50 2.60 3.30 2.60 1.50 Panel breadth [m] 1.00 1.20 1.30 1.30 1.30 0.30 1.00 1.20 1.30 Pressure Type Sea Sea Sea Sea Sea Sea Sea Sea Sea Magnitude [kN/m2] 16.9 16.9 16.9 16.9 17.2 17.5 16.9 16.9 16.9

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Table 42. Scantling results for weather deck. Weathe r deck pane l 1 2 3 4 5 6 7 8 9 Geometry Face thickness [mm], tf 1.16 1.16 1.16 1.16 1.16 1.16 1.16 1.16 1.16 Core thickness [mm], tc 11.5 15.2 14.4 13.4 17.3 1.4 11.5 15.2 14.4 Constraints (% of allowable) Panel deflection 100.0 100.0 100.0 100.0 100.0 81.6 100.0 100.0 100.0 Core shear 62.0 54.9 50.5 51.8 52.6 100.0 62.0 54.9 50.5 Face stress 74.1 80.7 75.1 73.5 84.1 34.6 74.1 80.7 75.1 Local buckling 18.4 20.0 18.6 18.2 20.9 8.6 18.4 20.0 18.6 Min. fibre weight 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 Weight [kg] 17.2 18.1 11.1 10.0 19.9 2.8 17.2 18.1 11.1

Table 43. Input for weather deck scantlings.

Weathe r deck gi rde rs 1 2 3 4 5 6 Indata Load point [m], x 1.60 4.60 8.35 10.40 12.85 16.60 Load point [m], z 3.85 3.85 3.85 3.85 3.85 3.85 Deadrise [deg], β 10 10 10 15 20 20 Beam length [m] 3.30 2.60 1.50 1.40 2.50 2.60 Load breadth [m] 1.00 1.20 1.30 1.30 1.30 0.30 Longitudinal extent of load area [m], la 3.30 2.60 1.50 1.40 2.50 2.60 Pressure Type Sea Sea Sea Sea Sea Sea Magnitude [kN/m2] 16.9 16.9 16.9 16.9 17.2 17.5

Table 44. Scantlings for weather deck girders.

Deck 1 gi rde rs 1 2 3 4 5 6 Geometry Flange thickness [mm], tfl 1.5 1.2 1.2 1.2 1.2 1.2 Web thickness [mm], tw 1.2 1.2 1.2 1.2 1.2 1.2 Flange width [mm], bfl 40 40 40 40 40 40 Web height [mm], hw 300 300 300 300 300 300 Constraints (% of allowable) Beam deflection 72.7 54.3 24.2 22.2 52.3 65.1 Flange stress 100.0 87.0 34.0 30.2 89.3 23.5 Face stress 65.0 63.3 46.7 44.6 69.2 24.2 Web stress 46.7 38.3 7.4 5.5 37.9 7.9 Web shear 15.1 14.2 8.9 8.4 15.1 3.7 Min. fibre weight flange 78.9 100.0 100.0 100.0 100.0 100.0 Min. fibre weight web 100.0 100.0 100.0 100.0 100.0 100.0 Weight [kg] 9.96 7.80 4.50 4.20 7.50 7.80

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Table 45. Scantlings for weather deck web frame. Weathe r deck beam 1 Longitudinal extent of load area 4 Load breath 4 Lenght of beam 2.75 x (loadpoint) [m] 9.53 z (loadpoint) [m] 3.85 Local deadrise angle [deg] 10 Pressure type Sea Magnitude [kN/m2] 16.9 Geometry Flange thickness [mm] 8.9 Web thickness [mm] 11.6 Flange width [mm] 150 Web height [mm] 300 Constraints (% of allowable) Beam deflection 9.5 Flange stress 19.5 Face stress 100.0 Web stress 21.1 Web shear 5.0 Min fiber flange 13.1 Min fiber web 10.0 Total weight [kg] 52.9

5.5.5. Bulkheads The bulkheads are dimensioned to the sea pressure at the relevant load point; in this case the load points are taken at middle of the panels.

It can be observed from this that in some cases it is the minimum allowable pressure that is the governing load case. Local loads originating from the crossbeams are not included in these scantlings. The total weight of the bulkhead panels for one hull is 136.2 kg.

This gives a total weight of the bulkheads for both the panel and beams of one hull to 191.8 kg. The input and results for the bulkhead scantling calculations are presented in table 46-49.

Table 46. Input for bulkhead scantling calculations. Bulkhead 1 2 3 4 5 Panel number 1 2 3 1 2 3 1 2 1 2 1 Load point [m], x 0.00 0.00 0.00 3.30 3.30 3.30 6.90 6.90 11.80 11.80 15.70 Load point [m], z 1.7 1.7 3.3 1.7 1.7 3.3 1.7 1.7 1.7 3.3 1.7 Deadrise [deg], β 10 10 10 10 10 10 10 10 15 15 20 Panel length [m] 2.20 2.20 2.10 2.79 2.79 2.50 2.90 2.90 2.80 2.20 3.00 Panel breadth [m] 0.48 1.10 0.76 0.54 1.20 0.82 0.74 1.10 1.10 0.90 0.40 Pressure Type Sea Sea Sea Sea Sea Sea Sea Sea Sea Sea Sea Magnitude [kN/m2] 10.3 10.3 6.5 10.3 10.3 6.5 10.3 10.3 10.4 6.5 10.6

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Table 47. Scantling results for bulkhead panels. Bulkhead 1 2 3 4 5 Panel number 1 2 3 1 2 3 1 2 1 2 1 Face thickness [mm], tf 1.16 1.16 1.16 1.16 1.16 1.16 1.16 1.16 1.16 1.16 1.16 Core thickness [mm], tc 2.2 9.9 4.0 2.8 11.5 4.6 5.1 10.0 10.1 5.4 1.5 Constraints (% of allowable) Panel deflection 100 100 100 100 100 100 100 100 100 100 100 Core shear 70.1 44.7 44.4 12.5 11.8 11.5 56.9 46.1 46.2 40.5 78.1 Face stress 39.6 60.5 40.7 57.1 60.0 61.0 50.0 61.4 61.7 44.3 36.2 Local buckling 9.8 15.0 10.1 17.0 17.8 18.1 12.4 15.2 15.3 11.0 9.0 Min. fibre weight 100 100 100 100 100 96.9 100 100 100 100 100 Weight [kg] 3.9 12.0 6.4 5.8 17.5 8.4 9.0 15.9 15.4 8.4 4.3

Table 48. Input for bulkhead beam scantlings.

Bulkhead 1 2 3 4 5 Load point [m], x 0 3.3 6.9 11.9 15.7 Load point [m], z 1.7 1.7 1.7 1.7 1.7 Deadrise [deg], β 10 10 10 15 20 Beam length [m] 2.4 2.8 2.9 2.8 3.2 Load breadth [m] 1.1 1.2 1.1 1.1 0.4 Longitudinal extent of load area [m], la 2.4 2.8 2.9 2.8 3.2 Pressure Type Sea Sea Sea Sea Sea Magnitude [kN/m2] 10.3 10.3 10.3 10.4 10.6

Table 49. Scantling results for bulkhead beams.

Bulkhead 1 2 3 4 5 Geometry Flange thickness [mm], tfl 1.2 1.2 1.2 1.2 1.2 Web thickness [mm], tw 1.2 1.2 1.2 1.2 1.2 Flange width [mm], bfl 40 40 40 40 40 Web height [mm], hw 250 250 250 250 250 Constraints (% of allowable) Beam deflection 43.5 56.6 9.5 57.1 82.7 Flange stress 53.2 78.2 19.5 72.7 35.9 Face stress 38.9 49.6 100.0 45.5 28.7 Web stress 23.4 37.0 21.1 34.6 14.9 Web shear 8.8 11.2 5.0 10.4 4.4 Min. fibre weight flange 100.0 100.0 13.1 100.0 100.0 Min. fibre weight web 100.0 100.0 10.0 100.0 100.0 Weight [kg] 6 7 7.3 7 8

5.6. CONCLUSIONS AND DISCUSSION The aluminium scantlings where done at a more preliminary design stage to allow for a more detailed comparison of weight between the two different material concepts. The results do give a preliminary weight as well as centre of gravity and moments of inertia, important at other stages in the design spiral. The scantlings for the bulkheads of the aluminium craft are not yet determined but a weight estimate for these are done. There are several other aspects that affect the accuracy of the results. For the aluminium version:

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• The structural arrangement was preliminary and an additional deck is likely to be fitted, increasing weight.

• No account is taken for the local loads introduced by the crossbeams. • The pressure due to the craft standing of the well deck is not taken into account, but the beaching

pressure is used in the bottom of the aluminium craft.

However, using these preliminary scantlings an indication of the structural weight can be obtained, this amounts to a total weight of 13726 kg for the entire craft. Additional mass calculations can be found in section 6.2.

The scantlings obtained for the carbon composite version give the first estimate of the structural weight for the entire craft to 6094 kg. This is likely to increase substantially due to several reasons:

• No account is taken for the local loads introduced by the crossbeams. • The core thicknesses will be more uniform throughout the craft, possibly with different density in

different areas. • Face thicknesses could increase to make the craft more durable with respect to e.g. tool dropping,

wear etc. • Manufacturing method affect fibre to resin ratio and hence weight. • Local reinforcements and transitions between different structural members are not accounted for. • Some core thicknesses are not realistic, such as 1 mm core. This also violates the sandwich

assumptions and should probably be considered as single skin laminates.

According to Jesper Lodenius at SSPA a standard procedure, used by among other Swedish defence material administration, is to allow for a 15 % margin in structural weight. In order to address this and be slightly more conservative an addition of 20 % is made to the structural weight obtained by the DNV scantlings. This gives a total structural weight for the composite version as 7313 kg for the entire craft.

A problem encountered when determining the scantlings for both the aluminium and the composite craft is the issue of robustness. The nature of this craft is such that it will sustain severe impacts due to beaching and docking and it is not only the material concepts ability to handle these impacts, but also the reparability of the material that needs to be considered. This issue is especially difficult to deal with when it comes to the composite craft.

It is the authors’ opinion that the robustness of the craft is not completely accounted for in the DNV minimum fibre weight requirements. However, in this case the scantlings of almost every structural member are governed to some extent by this restriction. Several questions then need to be raised:

• How have these requirements been developed and what are they trying to capture? • Which type of crafts are they applicable on, could there be a difference depending on the

intended use? • Are they actually relevant in any case? • Is the issue of manufacturing accounted for, is it actually possible and reasonable to manufacture

laminates less than 1 mm thick? • The requirements are only stipulated for glass or carbon fibre, there could be other types of

materials that have better properties in some special aspects, how should they be dealt with?

An interesting study that lies outside this project, but is highly relevant should be to formulate these criteria or an additional robustness criteria taking e.g. craft type into consideration. It is natural that a pleasure cruising boat doesn’t obtain the same wear and tear as an e.g. military craft.

The other conclusion of the scantling calculations is that using a carbon composite structure instead of aluminium not only reduces weight by almost 47 % without adding any weight margin to the aluminium concept, in reality it could be even more. The structure itself is also more simple and a positive effect of this could be reduced manufacturing costs and perhaps, even though the material itself is more expensive, a cheaper craft. These facts together with the fact that overall weight is critical due to the limiting draught criteria, makes the material choice fall on the carbon composite version.

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6. MASS ANALYSIS A critical step in the design process is to find a first estimation of the crafts weight. This estimation is necessary for several reasons. It’s important for the determination of resistance and thus the required propulsive power and also to determine the hydrostatics of the craft. The draught is especially critical in this application since both the well deck and the shoreline compatibility sets restrictions on this entity. The mass analysis is also important in order to determine the seakeeping characteristics of the craft, since the mass distribution, i.e. the radius of gyration, plays a vital role in these calculations.

A structural mass for both of the material concepts is also needed in order to evaluate these against each other.

6.1. METHOD The unconventional nature of this particular craft makes the initial estimations on structural and systems weight difficult. In the first evaluation lap of the design spiral a semi-empirical model is used, the structural weight and system specifications are then updated as scantling results are presented. There are four distinct cases to evaluate; loaded with platform in the raised position, loaded with the platform in its lowered position, unloaded with the platform raised and finally unloaded with the platform in its lowered position.

The model used here for the first estimation of the weight is developed by A.F. Molland [14] and is a mathematical model based on catamarans ranging from 50 to 100 meters in length and a demihull separation ratio from 0.2 to 0.26. It is also based on Loyds Register of Shipping – Rules for classification of special service craft. The model is limited to aluminium only, however this gives an indication of the craft weight for the first lap in the design spiral.

The weight of the structure is determined based on the main particulars (length over all, beam of ship, beam of one hull, height and draft). The weight of the equipment is a function of craft length and breadth i.e. an area weight for service. The engine weight is estimated from the type of engine system used, e.g. gas turbine or diesel engine and required power originating from engine catalogs and High Speed Marine Transportation, Jane’s Book (1996 – 1997). The model is based on engine weights from a number of different manufacturers (MTU, Caterpillar, Zvezda and Wärtsila). In similar way estimations on propulsion systems and operational weight, such as water, fuel etc. is made. For a complete description of this model refer to Appendix 2.

The scantlings of the different material concepts provide the structural mass; these together with the masses of the selected propulsion and cargo handling systems provide the total mass of the craft. The moments of inertia and in the end the radius of gyration is a calculated using different tool depending on the material concept.

For the FRP structure the weight of each structural member is determined by the scantlings where these members are simplified, hence the weight and size of the structural members is idealized, this results in a small error being made in these calculations. Also, the only contribution to the radius of gyration that’s taken into account is the Steiner contribution. This is a reasonable assumption for parts of the structure at some distance from the centre of gravity, but not for structure close. This gives a slightly lower moment of inertia than in reality.

The aluminium structure is evaluated using the CAD software SolidEdge [9], which provides global centre of gravity and radius of gyration for the structure. Since the complete structure is modelled including stiffeners, these results are very accurate compared to the composite calculations.

Excel calculations are then used to account for the different system installed and for the cargo, where the moment of inertia is calculated about the local centre of gravity for each item and then moved to the global centre of gravity using Steiner’s theorem.

6.2. RESULTS The results are presented for the four different load cases for both material concepts, with the radius of gyration only for the transportation mode, i.e. when the platform is raised with and without cargo. Complete mass distributions and calculations can be found in Appendix 3. The total structural weight for the aluminium concept is 13.73 tonne and 7.31 tonne for the carbon composite version with an addition

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of 20 %, detailed results can be found in section 5 on scantlings. Besides the addition to the structural weight a margin of 15 % is added to the total weight of the craft, excluding the cargo. This is so that e.g. wiring, piping and ventilation is taken into account. The figure 15 % is used as a typical addition by FMV and is reasonable according to Jesper Lodenius at SSPA.

6.2.1. Load case 1 – Loaded transportation mode The results for load case 1 are presented in Table 50.

Table 50. Compilation of results for loaded transportation mode. Aluminium Composite Total mass, W [ton] 123.0 115.6 Longitudinal centre of gravity, LCG [m], from A.P. 8.06 8 Vertical centre of gravity, VCG [m], from B.L. 4.19 4.35 Transverse centre of gravity, TCG [m], from C.L. 0 0 Pitch radius of gyration, K [%], in percent of LWL 20.5 20.9

This shows that the composite structure would save at least 6 % in total weight. The aluminium craft has a slightly lower centre of gravity, but stability should not be critical since it is a catamaran. The radius of gyration for the two different material concepts is just about the same.

6.2.2. Load case 2 – Loaded beaching mode There is a significant change in both longitudinal and vertical centre of gravity once the platform is lowered in the beaching mode of operation. This load case is presented in Table 51.

Table 51. Compilation of results for loaded beaching mode. Aluminium Composite Total mass, W [ton] 128.1 120.7 Longitudinal centre of gravity, LCG [m], from A.P. 9.7 9.74 Vertical centre of gravity, VCG [m], from B.L. 2.19 2.22 Transverse centre of gravity, TCG [m], from C.L. 0 0

6.2.3. Load case 3 – Unloaded transportation mode Load case 3 is presented in Table 52.

Table 52. Compilation of results for unloaded transportation mode. Aluminium Composite Total mass, W [ton] 61.0 53.7 Longitudinal centre of gravity, LCG [m], from A.P. 8.23 8.11 Vertical centre of gravity, VCG [m], from B.L. 2.45 2.56 Transverse centre of gravity, TCG [m], from C.L. 0 0 Pitch radius of gyration, K [%], in percent of LWL 26.15 27.4

6.2.4. Load case 4 – Unloaded beaching mode Load case 4 is presented in Table 53.

Table 53. Compilation of results for unloaded beaching mode. Aluminium Composite Total mass, W [ton] 66.1 58.7 Longitudinal centre of gravity, LCG [m], from A.P. 8.48 8.4 Vertical centre of gravity, VCG [m], from B.L. 1.61 1.61 Transverse centre of gravity, TCG [m], from C.L. 0 0

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7. HYDROSTATICS There are two factors that significantly affect the hydrostatics of the FLCU, the varying beam and the movable platform. It is hence necessary to investigate the transverse stability and the floating positions in the different modes.

7.1. METHOD To evaluate the hydrostatics of the LCU, calculations were made with the developing tool Hydromax from Maxsurf. The basic input is the geometry of the hull. Three types of analysis can be made in the Hydromax; upright hydrostatics, equilibrium condition and large angle stability. For upright stability, calculation of displacement, centre of buoyancy and other hydrostatic data were made. The basis is a fixed zero heel angle, a user defined trim angle and a set of depths for which results are generated. The equilibrium analysis uses load cases to calculate the displacement and the location of center of gravity. This is performed by iterations as the program searches for the heel, trim and draft that satisfy equilibrium.

For the large angle stability, displacement and center of gravity are specified in load cases. Hydromax, then calculate the righting lever arm and other hydrostatic data at different heel angles by balancing the displacement generated by the load case against the hull buoyancy. The results can then be viewed as a table output and a graph of the GZ-curve (distance between center of gravity and center of buoyancy as function of heel angles). Further, the results can also be directly evaluated against different stability criteria.

One of the benefits with Hydromax is its ability to analyze multihull stability. This is achieved by taking the total waterline beam of the immersed portions of the hull sections to calculate the block coefficient and other hydrostatic data.

7.2. FLOTATION AND TRIM The FLCU has a fairly unconventional mass distribution since the main cargo is approximately 50 % of the displacement and is concentrated to a relative small volume. Thus a small change of the cargo position will change the trim significantly. This is exactly what happens during the movement of the platform since it will move in both longitudinal and vertical direction. The equilibrium calculations were used to evaluate the geometry of the platform and need for ballast to obtain approximate zero trim at different load cases. For the equilibrium analysis the LCU was evaluated with the platform in both upper and lower position with and without the primary cargo.

The results are presented in the following two sections as figures showing the floating position in side views and hydrostatic data tables. When the platform is lowered, ballast of 2.5 tones in each hull is necessary to obtain a zero trim. With the platform raised there is no need for ballast. The trim is in loaded condition zero and slightly aft in unloaded condition. The fuel level is not taken into consideration since the tank is placed at the center of gravity. Thus the influence of the fuel level is assumed to be neglectable to the trim.

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7.2.1. Platform raised

Figure 15. Side view, in loaded condition, the blue line is the water line. The platform is intentionally left out.

Figure 16. Side view, in unloaded condition, the blue line is the water line. The platform is intentionally left out.

Table 54. Hydrostatic data platform raised

l oaded condit ion unloaded condit ion Draft Amidship, [m] 1.716 0.908 Displacement, [tonne] 115.7 53.68 Draft at F.P, [m] 1.716 0.884 Draft at A.P, [m] 1.716 0.933 Trim (+ve by stern), [m] 0.000 0.049 W.L. Length, [m] 18.542 18.738 Waterplane. Area, [m2] 74.041 76.690 Prismatic coefficient, [-] 0.704 0.662 Block coefficient, [-] 0.647 0.556 GMt corrected, [m] 9.040 25.742 GML corrected, [m] 9.436 28.444 KMt, [m] 13.393 28.307

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7.2.2. Platform lowered

Figure 17. Side view, in loaded condition, the blue line is the water line.

Figure 18. Side view, in unloaded condition, the blue line is the water line.

Table 55. Hydrostatic data l oaded condit ion unloaded condit ion Draft Amidship, [m] 0.920 0.479 Displacement, [tonne] 120.7 58.69 Draft at F.P, [m] 0.928 0.243 Draft at A.P, [m] 0.912 0.715 Trim (+ve by stern), [m] -0.016 0.472 W.L. Length, [m] 18.744 20.108 Waterplane. Area, [m2] 76.611 154.399 Prismatic coefficient, [-] 0.788 0.599 Block coefficient, [-] 1.223 0.490 GMt corrected, [m] 9.074 23.222 GML corrected, [m] 10.277 67.591 KMt, [m] 12.813 26.052

7.3. LARGE ANGLE STABILITY The large angle stability analysis was done for the case with the hulls in an inboard position (docking mode) as well as an outboard position (transportation mode) with and without cargo in each case. As evaluation criteria the IMO HSC 2000 [48] annex 7 and annex 8 were used. Annex 7 normally applies to multihull ships and annex 8 to monohull ships. However, this is not a strict definition and the code gives a guideline that indicates what annex to use. This guideline is shown in Table 56.

Table 56. IMO HSC 2000 rule application guideline

WL WPB A!"

GMT

7! 7> 3! annex 8 annex 8 or annex 7

3> annex 8 or annex 7 annex 7 Where GMT is the transverse metacentric height in m, WLB is the beam of the craft in m, WPA is the water

plane area in m2 and ! is the volume displacement in m3. The LCU conforms to annex 7 for all modes but the loaded docking mode that strictly conforms to annex 8.

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For both annexes a similar weather criterion is used for evaluation. The criterion is the same as normally used for larger ships in the IMO A749 criteria. This criterion takes a worst wind, Vw (IMO notation in m/s) scenario in to account, which will correspond to a pressure in Pa. This pressure is assumed to act over a projected area giving a force resultant that will heel the craft with a certain lever arm. For this case the worst steady wind is set to 20 m/s. The rule also stipulates that wind gusts should be taken into consideration by a factor of 1.5 times the steady wind. Hydromax automatically calculate the projected lateral area of the hull. Additional area is for the platform approximated to 18 m2 and for the tank to 32 m2. The criterion is that the craft may not heel more than 10 degrees when subjected to a wind gust.

The rest of the criteria differ between annex 7 and 8 even though the basis is the same. They are likely based on the IMO A749 but with other requirements. In annex 7 the criterion 1.4 is not considered since it takes heeling due to passenger crowding and high speed turning into consideration. The passenger criterion is irrelevant and the cargo will be secured. The heel due to high speed turns needs a turning radius as input which is difficult to assess a representative value of in this stage of the design.

The results of the most critical load case are shown in the following sub section by summarizing criteria’s and corresponding value. A corresponding GZ-curve is also shown. For a more comprehensive review of the criteria refer to IMO HSC2000.

7.3.1. Loaded docking mode As previously discussed, this case does apply to IMO HSC2000 annex 8 that normally is used to evaluate monohull ships. This is due to the fairly small beam and the large displacement of the craft. The results are shown in Table 57 and Figure 19.

Table 57. Stability criteria, loaded condition, docking mode

HSC 2000 Annex 8 Monohul l . Inta c t Value Uni t Actual Sta tus

1.1 Weather criterion from IMO A.749(18)

Angle of steady heel shall not be greater than 10 [deg] 8.7 Pass

1.2 Area 0 to 30 or GZmax

shall not be less than 3.151 [m.deg] 4.955 Pass

1.3 Area 30 to 40

shall not be less than 1.719 [m.deg] 3.275 Pass

1.4 Max GZ at 30 or greater

shall not be less than 0.2 [m] 0.393 Pass

1.5 Angle of maximum GZ

shall not be less than 15 [deg] 31.2 Pass

1.6 Initial GMt

shall not be less than 0.15 [m] 0.366 Pass

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Figure 19. GZ-curve loaded condition docking mode,

7.4. DISCUSSION As can be seen in the results from the 4 stability cases, the FLCU does fulfill all requirements. It is also easy to see that the most critical case from a stability point of view is the loaded condition in docking mode. Even though the craft fulfills all requirements, it is quite sensitive in this mode. For example an increased worst wind from 20 to 25 m/s would mean that the craft would fail that criterion. It is also important to remember that the criteria are static. Although the area criterion 1.2 in annex 8 somehow should represent dynamic properties such as resistance to dynamic disturbances from wind and waves, it is not a guarantee that it will do that. The criteria should be treated as necessary but not always enough. A further investigation of the dynamic properties could be done by sea keeping analysis or model trials, which is highly recommended for the critical case before doing a final design.

The rest of the analyzed cases show increased transverse stability properties. For the most extreme condition (transportation mode with no cargo) is the GZ-curve fairly steep and has an impressive metacentric height of 25 m.

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8. RESISTANCE The purpose of the resistance calculations is to determine the required propulsive power of the craft and thus the engines and propulsion system so that the craft will fulfil the specification of requirements.

The multihull configuration offers an advantage when it comes to propulsive resistance. Due to the slender nature of the hulls the free surface disturbance is less than for a conventional monohull and thus the wave-making resistance is reduced. There are a number of ways to further reduce this disturbance, e.g. using a SWATH configuration, hydrofoils or making the multihull planning. Another way to further reduce this wave making is to make the demihulls asymmetric and thus minimising the adverse interference between the demihulls. The catamaran analysed here could be classified as a semi-displacing craft since the Froude number is in the region between 0.7-1.0 and the hulls generate a not negligible dynamic lift. The hull shape is rather conventional with U-shaped sections turning more V-shaped towards to the bow. According to Insel [20] the interference resistance in this speed regime is less pronounced and the demihulls are hence symmetric.

The resistance estimation of a displacing/semi-displacing catamaran configuration follows the same standard as for conventional monohulls with two differences. First there is body interference between the demihulls. The result of this is that the flow around a demihull is asymmetric about the centre line of the hull. This has several implications on the resistance, the following are some the primary effects [20].

• The flow velocity around the demihull could increase due to the Venturi effect between the two hulls. Basically this means that due to continuity the velocity must increase at the constriction between the hulls and the pressure decrease due to the conservation of energy. This modifies the frictional resistance as well as the form factor.

• Due to the asymmetric flow, a cross flow below the keel causing vortices and resulting in induced resistance. This also has effects at the transom where the cross flow could cause induced resistance.

The second implication of the catamaran configuration is wave interference. This is a result of the two wave systems caused by the demihulls interfering with each other. This has some implications on resistance.

• The wave formation of a demihull may, due to the presence of another hull, be different than that for the demihull in isolation. This could cause an adverse or positive effect on the wave making resistance.

• Superpositioning the divergent bow waves between the hulls could cause a high breaking wave causing spray and increase viscous resistance.

8.1. METHODS A critical part of the design spiral is to determine the resistance or ultimately the required propulsive power for the considered vessel. Although catamaran hull forms have been around for a long time, simple methods for prediction of their resistance are harder to find than for conventional monohulls. The main difference between typical catamaran hull and monohull is its high length to beam ratio, i.e. the slenderness of the demihulls and naturally this has effects on the selection of method used for analysis. In general there are four levels of analysis available: the first is comparing the design with similar designs, second the use of semi-empirical methods and CFD methods ranging from potential flow models to Navier-Stokes formulations. In addition to this model experiments could be used to determine the resistance of a particular craft. The method of choice is largely dependent on the phase of the design process and the time available. At initial studies methods one and two are usually employed, the third method could be used when refining the hull shape. Before commencing to build the particular craft, the results are usually validated using model trials.

At the initial design stage the resistance of the FLCU is evaluated with a semi-empirical method, once the geometry of the hull has been determined the slender body method is used. Since this particular catamaran is on the limit of validity of these methods it is of importance to obtain results from as many sources as possible in order to make a qualitative comparison and judgement of the results.

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8.1.1. Semi empirical method This chapter describes the semi-empirical method used for resistance prediction in the preliminary design phase.

In general the calm water resistance of a vessel could be divided into the following major components; viscous resistance and wave resistance. Estimating the viscous resistance is done using the ITTC-1957 line together with a form factor to account for the voluminous shape of the submerged body. This factor could, according to [12], be calculated as a function of waterline length and displacement and is assumed to be constant over the entire speed range. This is not without controversy and e.g. Armstrong proposed a different approach with a speed depended form factor for catamarans described in [10].

For catamarans this factor is generally complemented with a factor taking viscous interference between the demihulls into consideration. This is due to the flow velocity augmentation that the demihulls percept due to the vicinity of another hull. The wave-making resistance coefficient is also complemented with an interference factor due to the twin-hull configuration, according to Insel & Molland [11] beneficial interference could be found at Fn=0.35-0.42 while adverse interference could befound at both sides if this speed range. However it is suggested by Insel & Molland that the wave-making interference could be neglected above a certain speed that is demihull separation, S, and L/B dependent. For this particular craft with S/L=0.5 and L/B=6.5, the Froudes number 0.8, corresponding to the design speed, seems to be well above this limit.

The wave resistance is somewhat more difficult to calculate and in the preliminary design phase a semi-empirical model developed by Sahoo, Brown & Salas 2004 [10] is used. This model is based on a research program devised to examine variations in wave resistance due to change of the main particulars of the catamaran hull. The validity range of this method is described in Table 58.

Table 58. Range of parameters for the Sahoo, Brown & Salas 2004 series. Geometric parameters L/V1/3 L/b b/T CB Fn

Range of application 8.22-11.2 10-15 1.5-2.5 0.4-0.5 0.2-1.0

The wave resistance coefficient can then according to Sahoo, Brown & Salas be described as

CWcat = eC1 (L / b)C2 (b / T )C3 CBC 4 (L / V 1/3)C5 iE

C6!C7 (s / L)C8 , (1),

where iE is the half angle of entrance and β the deadrise angle at midship. This coefficient is taking the interference between the demihulls into consideration. The coefficients C1-C8 may be found together with a complete description of the method in Appendix 0. The total resistance coefficient of the catamaran can hence be calculated according to

CT = (1+ !int erk)CF + CWcat , (2)

where the parenthesis contains the interference corrected, βinter, form factor, k, described earlier.

8.1.2. Slender body method The slender body method is based on a linearised analysis of the far field wave pattern generated by an arbitrary array of Kelvin sources in a finite channel. It was developed for multihulls by A.F. Molland [13] and later refined by many researchers dealing with some of the problems the method presents. For the linearised potential theory the following assumptions are made:

• The fluid is invicid, incompressible and homogenous. • The flow is steady and irrotational. • Surface tension can be neglected. • The free surface elevation is small compared with wave length and with no breaking wave

present. • All the energy causing free surface waves can be measured by examining the far field wave

system.

Slender body assumptions are used to relate source strength to hull form shape. The sources and sinks are placed on the centre plane of the hull and their strength and distribution is such that that the flow velocity

43

normal to the fictive hull surface is zero. The method calculates the total dissipated energy radiating from the hull in the far field wave system and thus the wave resistance of the craft. To this an addition of the viscous resistance with form factor, taking viscous interference into account, according to ITTC ’57 must be made to obtain the total resistance of the craft.

This method is implemented in the Maxsurf Hullspeed program and is used to analyse the resistance of the FLCU. In addition to the original formulation by Molland an addition is made with respect to the transom of the craft. In order to model the transom running dry at higher speeds a virtual transom is added where the reattachment of the flow is moved from the transom to a point 6 times half the width of the transom. This has proven to give good results in the higher speed range [21].

According to P. Couser [21] the suggested lower limit for the slenderness ratio defined as

Rslender =L

Vdemi1/3 , (3)

where V denotes the volume displacement of a demihull, is between 4-5. This limit is however dependent on Froude number and this ratio should be larger when to speed increases. For a Froude number of 1.0 an acceptable lower limit would be 7.5. The FLCU has a slenderness ratio of 4.8 and is thus on the lower acceptable limit so results should be treated with caution.

8.2. RESULTS

All the relevant input data for the catamaran can be found in section 3. The results for the landing craft using the slender body method, the semi-empirical method and calculations made by Rolls Roys on the particular catamaran are presented in Figure 20. The method of calculation for the latter is however unknown but serves as a third part reference.

Figure 20. Comparison of resistance for different methods at fully loaded condition.

The methods show good correlation up to 13 knots, and then however the spread is large. The main particulars of the FLCU are outside the range of parameters and since the method is regression based there is no justification for the use of these results. The results obtained from Rolls Roys together with the comments from their engineer saying that our calculations where a bit conservative is interesting, but the method they used is however unknown. The slender body method yields the highest resistance and to be conservative this resistance will be used as reference. The result of this decision is that the weight of the craft is likely to increase due to a higher required propulsive power. This could the yield a negative design

44

spiral where weight and hence resistance increase for each iteration. The resistance plotted is the sum of the wave-making resistance and the frictional resistance.

Now using this as input a more detailed analysis of the different resistance components of the catamaran is made dividing the resistance into different components and adding wind resistance and added wave resistance (Figure 21).

Figure 21. Resistance components of the landing craft at full load.

The added wave resistance is gathered from the linear strip theory and is only valid until roughly 13 knots. The wind resistance is calculated according the ITTC procedure [49]. According to this figure the dominating resistance component at higher speed is the wave resistance. At design speed and full load the resistance amounts to 115 kN. These calculation where confirmed by Hans Liljenberg at SSPA.

8.2.1. Powering and propulsion Using the resistance calculations from the previous section a suitable engine and propulsion is selected. Due to the nature of the craft and the requirement for it to be able to stand on the bottom and on the welldeck the most natural choice is a water-jet propulsion system.

To determine the required engine power the efficiency of the propulsion system must be calculated. According to Molland [14] the overall water-jet efficiency as a function of ship speed, vs, can be calculated as

!D =1

1+ 8.64 / vs (4)

According to this the efficiency at design speed is 0.54, to this an additional 3 % of mechanical gearbox losses is added. Hence the total efficiency is 0.53. Using this the minimum required power of the selected engines is 2160 kW, this gives 1080 kW per engine. This value is confirmed by Hans Liljeberg at SSPA in Gothenburg, which declares that the efficiency would go from 50 % in the lower speed regime to almost 60 % in the higher speed regime.

The selected engine is the MTU 12 V 2000 M93 with a power rating of 1340 kW, additional data may be found in [22]. This is somewhat more than the minimum requirement but gives an additional safety margin. In consultation with Rolls Roys the Kamewa 56A3 water-jet system was chosen, additional data can be found in [23]. This is a larger unit than the listings specify, but was recommended due to the non-

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planing characteristics of this particular craft. Rolls Roys also supplied the delivered propulsive power based on the engine selection made above, the results of this is plotted in Figure 22. This indicates that the design speed will be met with the selected components by a small margin.

Figure 22. Required and delivered power at full load.

The MTU engine has a fuel consumption of 341 litres/hour at the rated power. According to the specification of requirements the craft has to be able to make a round trip to the shore without refuelling. This is a total distance of 60 NM. The craft travels at 20 knots from the LPD to the shore fully loaded, but once unloaded it does at least 30 back from the shore. This gives that the total time for a single round-trip is 2.5 hours. This gives a total fuel consumption of 1705 litres for both engines, which with a density for diesel of 0.85 kg/m2 gives a total mass for the fuel of 1450 kg. This is conservative since the engines are not likely to work at the full rated power on the return-trip from the shore. The fuel tanks are however constructed to give a range of 2 return trips, i.e. 1.75 m3 per fuel tank. This gives a range of 100 NM at full load according to the specification of requirements.

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9. MANOEUVRING An accurate calculation of manoeuvring properties for a catamaran propelled with water jet is fairly complex. Most available methods are developed and verified for standard propelled merchant ships and thus not applicable to the LCU. To obtain reliable results model trials should be carried out. It is however possible to estimate the course stability of one hull which will give an indication of course stability properties for the whole craft. According to Dubrovsky and Lyakhovitsky [27] a multihull ship shows the same tendency as monohull ships with increasing stability for increasing length over beam relationships and decreasing beam over draught relationships. Fossen et.al [28] derived an expression for early design stability judgement of a monohull craft,

4

21 (5.23 3.88 0.0050 ( ) ) 0Cb BT LTLT

! " # $ # # + # =% &' (, (5)

where ,l ul

LLTd

= and ,l ul

bBTd

= . The variable L refers to the length between perpendiculars, b is the

beam of one hull and d is the draught in loaded an unloaded condition (index l & ul). The equation can be plotted as a stability border, which is done for the FLCU block coefficient, Cb in Figure 23. Note that the L/b relationship is used for the x-axis by the calculation as

L LTb BT= . (6)

This was done to make it easier to relate course stability tendencies to the conclusions drawn by Dubrovsky and Lyakhovitsky [27].

Figure 23. Stability boundaries for the LCU

From this it is apparent that the FLCU would maintain a steady course in loaded but not in the unloaded condition. Following this rough estimation gives the conclusion that course-stabilizing equipment probably is necessary. Hans Liljenberg at SSPA also confirms this. To increase stability, fins could be installed in the stern. The detailed solution for this is however not treated since it would be too unreliable without the results from model trials or more comprehensive calculations.

Since the LCU is propelled by a Kamewa waterjet, forward and reversed manoeuvres is controlled by a ladle and turning by a nozzle. Booth these are moved by hydraulic cylinders, which are powered from a hydraulic pump fitted to the transmission at the engine. It could probably share pump with the hydraulic cargo handling system. An alternative would also be to fit the transmission with two separate pumps to get more redundancy. It is however desired to have the manoeuvring system connected directly to the engine and not use electric pumps since this will be a much safer system.

47

The manoeuvring control system is intended to be connected to an automation computer, which makes it possible to control each water jet manually as well as automatic. It will also be fitted with a proper autopilot. None of these systems will be further analysed since they are to a great extent custom designed and hence not relevant at this stage in the design process.

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10. SEAKEEPING In order for the FLCU to fulfil its mission under the required circumstances an assessment of the craft’s seakeeping characteristics needs to be done. This section gives a detailed account of the different methods available, their limitations and possibilities. The final section presents the results for the landing craft and a discussion around these.

Basically the seakeeping assessment of a vessel can be divided into three fundamental parts [35]: • Estimation of the likely encountered environmental conditions at the area of operation, i.e. wave-

spectrum and limiting sea-state. • Prediction of the response characteristics of the vessel. This can be done in several ways ranging

from experience, tank testing to various numerical techniques. • Specification of criteria to assess seakeeping behaviour. This could for example be vertical

acceleration, angular accelerations or relative motions at various locations of the ship.

The first part of this section presents some of the numerical methods available for evaluation of seakeeping characteristics for a non-planing, high-speed catamaran. It contains a brief overview of the methods, their limitations and advantages. Second, the criteria’s for evaluating the landing craft’s seakeeping behaviour will be presented and discussed together with the environmental conditions for this particular application. Finally the results of the seakeeping analysis are presented together with an evaluation of the methods and their applicability for this particular craft.

10.1. FUNDAMENTAL HYDRODYNAMICS FOR BODY AND WAVE INTERACTION

10.1.1. Linear and non-linear considerations

Regarding linearity and non-linearity there are many things to consider. The problems can be divided into free surface, body and other non-linear effects. For the free surface the following observations can be made [36, 37, 38].

• A water surface most often contains breaking waves and splashes. These effects are non-linear and cannot be captured using the potential flow theory.

• There could be non-linear interactions among different wave frequencies, which could result in amplification of the existing amplitude and/or the creation of new wave components.

Some of the important body non-linearity’s can be described as

• Interaction of steady and unsteady wave flows.

• Geometry changes such as a flared bow or overhanging stern cannot be described by the linear equations of motion. Even worse is the effect of a planning craft where the hull partially or completely leaves the water surface

• For a fast semi-displacing craft the wave-elevation along the hull is in the order of magnitude as the width of the hull. This implies that the changes in the longitudinal direction are not negligible and not linear.

Most of the methods used in seakeeping assessments are linear, which allows the equations of motion to be solved in the frequency domain. Non-linear simulations must be performed in the time-domain. The main concern here will be to describe the methods involving the linear equations of motion. This seems to be appropriate for analysing a semi-displacing catamaran in a moderate sea-state, where some of the non-linear effects described earlier, such as effects of hydrodynamic lift, perhaps are less important [37].

10.1.2. Basic hydrodynamics Before the different methods of calculating the seakeeping behaviour of a craft propagating in waves the problem itself is described. The fundamentals of waves and wave/body interaction are outlined in order to get an understanding of the different problems that needs to be solved. The outline is on a larger perspective and the details of e.g. modelling a wave are not described.

49

When analysing the motion of a ship in waves one of the sought after entities are the particle velocity and the pressure field as a function of location and time and ultimately the motions of the craft.

u = u x ,t( ) and p = p x ,t( ) , (7, 8)

where the components of u often is expressed as

u = u u,v,w( ) (9)

Newton’s equation for conservation of momentum for a volume of water, V, can be expressed as [39]

! Dudt

dV = Fe"V# , (10)

where ρ is the density and Fe is the sum of all the forces acting on the volume of water. According to this equation the mass of the particles times the particle accelerations equals the external forces acting on the fluid volume. These external forces can be divided into volume and surface forces. The volume forces would be gravitational or inertia forces and the surface components consist of pressure forces normal to the fluid and frictional forces tangential to the surface of the fluid. Using this the equations of motion or the Navier-Stokes equations can be written as

! DuDt

= "#p + µ #2u +13# #u( )$

%&'()+*# #u( ) + !F , (11)

where µ is the viscosity and θ a elastic viscosity coefficient. F is the external volume force. A complementary equation is obtained from the law of continuity which states that the change of mass in a bounded volume must be equal to the flow through the boundary surface of the same volume, this can be formulated as

ddt

!dV = " !u #ndSS$

V$ (12)

This can for the case of incompressible flow be simplified to

!u = 0 (13)

and the Navier-Stokes equations can be simplified to

! DuDt

= "#p + µ#2u " !gez , (14)

where the volume force F is represented by the gravitational force field. These equations suffice in principle to describe any flow phenomena regarding the flow around a ship, in the far field, boundary layer and wake. However, every single small fluctuation in these local areas might not be of that much interest. Hence a technique where the calculations are averaged over time intervals, which are long compared to these small fluctuation, but short, compared to the wave periods was developed [36]. This is called the Reynolds Averaged Navier-Stokes (RANS) equations. To solve these equations require significant computing power and time and its use is hence limited.

By further omitting the viscosity in these equations and thus being unable to represent the flow in the wake or the boundary layer where viscosity and hence friction plays a vital role. These equations turn into what is called the Euler equations. Equation (14) can now be written as

! DuDt

= "#p " !gez (15)

By neglecting the viscosity and thus the ability to represent the boundary layer allow for a coarser grid and reduced computing power.

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By assuming that the flow is irrotational. i.e. that the fluid particles doesn’t rotate about its own axis, wich is true for this application in areas outside the boundary layer. However, this information is already lost since viscosity is neglected. There exists a velocity potential, φ, which is defined as

u = !" (16)

Using this the Euler equation can be integrated, turning into the Bernoulli equation

! "#"t

+12!$# %$# + p + !gz = C (17)

and the equation of continuity (13) transcends into the Laplace equation

!2" = 0 (18).

So by calculating the total velocity potential and the constant C, the pressure can be determined at any location in the fluid using the Bernoulli equation. The Laplace equation is linear, which allows solutions to be superimposed on each other.

However since neglecting viscosity and assuming irrotational flow, splashing or breaking waves cannot be modelled using the potential theory. This means that the waves that can be modelled have a small height compared to length and that the wave-slope is small. It can then be shown that the acceleration of the fluid particles are a lot larger than the velocity direction squared. The effect of this is that the time-derivative of the velocity potential is many times larger than the square of the gradient of the velocity potential, hence this term can be neglected in the Bernoulli equation, making it linear.

Another important effect is that the boundary conditions on the free surface can be linearised on the mean surface instead of the unknown surface. Potential flow is the foundation of most seakeeping prediction techniques.

10.1.3. Linear ship motions The ship can be considered as a rigid body with a coordinate system with the origin at the mean free surface when the ship is a rest. The z-axis goes through the centre of gravity of the ship and the coordinate system travels with the same speed as the ship, V, but does not oscillate with the ship (Figure 24)

Figure 24. Definition of coordinate system.

The directions defined are η1 = surge, η2 = sway, η3 = heave, η4 = roll, η5 = pitch and finally η6 = yaw.

The motions of the ship in the translating directions of freedom (surge, heave and sway) can be described starting with Newton’s second law

F = m!!! (19)

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and for the rotating directions of freedom the equations is written as

F = I !!! , (20)

where F represents both forces and moments. The problem is normally divided into two different problems, which is possible due to the linear approximations

• The forces and moments acting on the ship by the incident waves when it’s restricted in movement, except for forward speed. These force and moments are called the wave excitation loads and consists of the Froude-Kriloff forces originating from the pressure field caused by the waves and the diffraction forces originating from the waves reflected on the ship.

• The forces and moment acting on the ship when it is oscillating in a calm surface with the wave excitation frequency. This generates radiated waves and the loads are identified as added mass, damping and restoring forces and moments.

The resulting equations of motion are two systems of three coupled linear equations of motion

M jk + Ajk( ) !!!k + Bjk !!k + Cjk!k"# $% = Fjei&et j = 1,...,6( )

k=1

6

' (21)

Matrices M and I represents the mass and inertia terms, B the damping terms and C the restoring forces terms. F represents the forces and moments due to the incident wave and diffraction. These equations can now be solved in the frequency domain. The problem to solve is hence first to determine the Froude-Kriloff and diffraction forces, i.e. determine the pressure at any given position of the hull and determine the mass/inertia, damping and restoring forces coefficients. Note that these equations have assumed that e.g. the damping is linearly proportional to the velocity and that the restoring forces coefficient is linearly proportional to the position of the ship, this is not true for e.g. a V-shaped hull. It is also assumed that the roll damping is linearly proportional to the roll angular velocity.

There are several different methods to solve these unknown forces and coefficients; a survey of methods applicable on a semi-displacing catamaran follows.

10.2. SURVEY OF METHODS This section outlines some of the most important and well-used methods for assessing seakeeping behaviour. Especially considered is the methods applicability on a high-speed non-planing catamaran like the FLCU.

10.2.1. Linear Strip Theory

The by far most commonly used method for seakeeping analysis is the Linear Strip-Theory as proposed by Salvetsen [40]. This theory has proven to be accurate and extremely efficient in determining seakeeping properties for conventional ships. However it has its limitations. The theory is linear in all respects; the effects of the method being fully linear means that a number of simplifying assumptions have been made, it is not the intent here to account for all of these, but rather to highlight some of the different modelling aspects when using the strip-theory so that a comparison to other methods is possible.

The linear strip-theory is based on potential flow and the total velocity potential for a ship travelling in elementary waves may be written as [36, 40]

!t = ("Vx + !s ) + (!w + !I ) (22),

where –Vx is the potential of the undisturbed steady flow with the ship speed V and φs is the potential of the steady flow disturbance, e.g. the disturbance due to the presence of the hull. In strip theory this term is completely omitted and the only consideration for forward speed is due to the undisturbed uniform flow.

Here φw is the potential of the undisturbed wave and φI the remaining unsteady potential, i.e. the potential due to the movement of the hull and the diffraction potential.

These potentials can be superimposed since the Laplace equation, describing the continuity of mass, is linear with respect to φt. This is a central part of the model since the problem can be divided into two parts; one part where the forces and moments due to the ship oscillating in an undisturbed surface can be

52

determined and the second part where the forces and moments due to the incident wave, when the ship is assumed fixed can be determined.

The method is not fully 3-D since the potentials φI and φw and hence the forces of the waves acting on the hull and the flow due to the presence of the hull itself are calculated at 2-D strips along the longitudinal axis of the hull and then integrated along the length of the hull (Figure 25).

Figure 25. Illustration of a ship divided into transverse strips.

This means that the e.g. exciting forces, damping and added mass coefficients are calculated in an isolated 2-D strip, that’s not affected by the steady flow in the longitudinal direction due to the forward motion of the ship. Further it is the static draught that is used in these calculations and not the actual free surface elevation at the considered position along the hull. So no interaction is taken into account between the local steady flow and the flow due to the motion of the hull.

These coefficients are usually calculated by forcing an oscillation in the considered direction on a sime-circle at a free surface. The problem is then to determine the velocity potential of the oscillating semi-circler and once this is determined the added-mass, damping and excitation can be calculated using the Bernoulli equation.

There are several techniques to determine these quantities with varying accuracy. The fastest, which is used in Maxsurf Seakeeper, is the Lewis form method. This analytical technique maps an arbitrary ship’s section to a unit semi-circle centred at the origin. The analytical solution of the potential flow formulation for a unit circle may then be applied to an arbitrary hull form. Here a section that is equal in beam, draught and area, but not in shape as the real ship section represents the hull. The Lewis mapping is the simplest form of mapping using only three parameters, using more parameters yields a section more true to the actual section geometry [45].

Also common, but requiring more computational power is the use of close-fit methods such as the Frank close-fit method. The velocity potential and hence the coefficients are then determined using a 2-D panel method where the section is represented by a number of points with straight line segments connecting these. Pulsating sources are then distributed along this boundary and the potential is calculated using the appropriate boundary conditions. These are claimed to be slightly more accurate than the conformal mapping methods [36].

The consideration of forward speed is accounted for in the linear strip theory using the encounter frequency of the waves as well as using approximate speed corrections on the added-mass and damping coefficients.

To summarize the above and put things in a context of a catamaran travelling at Fn=0.75-0.8 one can conclude that there are several reasons to be careful with the results obtained by the linear strip theory.

• No account the interaction between the local steady flow and the flow due to the motion of the hull. In this application, especially due to high speed, the free surface disturbance and effect on the local flow will be significant [41]. The determination of the hydrodynamic coefficients and forces at the non-disturbed surface could then differ significantly due to e.g. the wave elevation profile along the hulls.

• The implementation made in Seakeeper only considers one demihull in isolation. This has significant implication on e.g. the hydrodynamic coefficients of added-mass and damping. This is especially dominant when there is no or low forward speed, when the strip theory in general gives

53

good predictions. In beam seas the effect of blanketing of the incident waves of one hull could also be significant, this is not considered in the Seakeeper software.

• Since the 2-D coefficients of added-mass and damping are obtained at zero forward speed they are strongly affected by the wave resonance between the hulls. This can e.g. mean that the added-mass is negative or that the damping coefficient is zero at some frequencies due to what’s referred to as wave-trapping (roll-motion) or piston mode resonance (heave motion). In reality this would not occur to an equally large extent when the ship is moving forward since the waves are swept downstream (in a ship frame of reference), especially at high speed when the linear strip-theory is not valid [37]. It is suggested that it is more accurate to neglect hull interaction in the damping and added mass coefficient calculations when applying strip-theory to a catamaran.

• Since no account is taken to the steady flow disturbance, the method does not consider hull attitude, e.g. trim or sinkage, which is significant and could affect the results substantially, especially for catamarans [41].

• The method assumes slenderness, this means that the dimension of the cross-sections are small compared to the length of the hull and that the changes of the geometry and the potential in the longitudinal direction is small. This assumption allows the flow at these cross-sections to be considered as 2-D.

• The conventional strip theory assumes small motions and wave heights, and therefore a linear relationship between the two.

10.2.2. High Speed or 2.5D Strip Theory The method has since then been refined ad developed by several researchers, e.g. Zhao & Faltinsen [43].

The conventional strip-theory neglects the local steady flow around the ship and the unsteady waves generated by the ship are assumed to propagate perpendicular to the longitudinal axis of the ship. The 2.5-D theory on the other hand does take the steady flow around the ship into account. It is assumed that the flow at a certain section is affected only by the flow of a section upstream and that there’s no influence of the ship upstream of the bow. The numerical solution then starts at the bow and steps downstream truncating just prior to the stern. The reason it’s called the 2.5-D theory is that it combines the 2-D-Laplace equation with 3-D free-surface conditions.

The 3-D free surface conditions are used to step the solutions of the free surface elevation and the associated velocity potential due to the steady flow. The total velocity potential for each cross section is then obtained using the 2-D Laplace equation.

The calculation scheme is to first solve the steady flow problem for the ship, an effect of this is that the wave-making resistance, running trim and draught is determined. The unsteady part is then solved, but with the free-surface boundary condition linearised about the steady flow solution instead of the undisturbed mean surface as in the conventional strip method. This also means that the steady free surface could be solved as a non-linear problem. According to Faltinsen and Zhao the use of a non-linear free surface shows better agreement with experimental results.

However this method also has its limitation.

• The equations of motions are still linear and hence it assumes small motions and small wave heights

• The sides of the craft must be near vertical if the method proposed by Zhao & Faltinsen [43] is to be used. This is required anyway since the equation of motions is linear and e.g. the heave restoring force on a v-shaped hull is depended on the vertical position squared [44].

• The speed has to be high; this is partly due to the neglecting of transverse waves, but also the fact that the method assumes a dry transom, an Fn>0.4 or 0.5 is suggested depending on the source. A further requirement on high speed is also set by the inability to completely capture the interaction between the demihulls, now when in the high-speed regime the radiated waves are completely swept downstream.

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• The interaction between the demihulls is not captured completely, only the interference due to a superposition of the demihull results can be obtained. The interaction effect is less pronounced for higher speed, but it also depends on a number of other parameters such as demihull separation. There have however been attempts to use a time-domain High Speed Strip Theory, which includes the interaction between the demihulls. However the results confirmed that this effect was weak at high speeds [37].

10.2.3. 3-D Linear Boundary Element or Panel Methods With the aid of more computer power, the possibility to use 3-D predictions methods has been made available. There are primarily two different types of approaches used, the Green Function Method (GFM) and the Rankine Panel Method (RPM), the most popular of these being the RPM method [36]. Both of these methods can be used to solve for the unknowns in the linear equations of motion in the frequency domain. The equations of motion are still considered to be linear, but instead of dividing the hull into strips and integrating over the entire length, the potential flow around the hull is calculated in 3-D. That means that the total velocity potential is solved in 3-D and that it is possible to account for all linear effects of interaction between both the steady and unsteady flow as well as all interaction between the demihulls.

The RPM method divides the total velocity potential like earlier as

!t = "Vx + !s( ) + !w + !I( ) (23)

In the same manner as for the 2.5-D method, the steady potential, ϕs, can first be solved using non-linear calculations and thus also finding wave-resistance, trim and running draught. The incident wave potential is also known and the remaining unsteady potential is divided into diffraction and radiation components

!I = !d + !iuii=1

6

" (24)

The potentials are solved using the Laplace equation with the following boundary conditions

1. Water doesn nott penetrate the hull. 2. Water doesn not penetrate the free surface 3. At the free surface there is atmospheric pressure. 4. Far away from the ship, the flow is undisturbed. 5. Waves generated by the ship radiate away from the ship. 6. No waves are reflected at the boundary of the domain. 7. For antisymmetric motions a Kutta condition is enforced at the transom. 8. Forces and moments not in equilibrium results in ship motions.

To determine the diffraction potential all motions are set to zero. To determine the different radiation potentials, the corresponding velocity, ui, is set to one and the other velocities, the diffraction and incident wave potentials to zero. The velocities are then determined using the momentum equations, i.e. Newton’s second law. The method includes the interaction between the unsteady and the steady flow.

But this method as the strip-theory also has limitations or issues that has to be dealt with. For low speed and moderate motions the method provides very accurate results and don not have the problems associated with resonance between the demihulls encountered in the linear 2-D strip-theory. However, for high-speed the situation is a little bit different. The problem relates to the way in which the transom is treated. Faltinsen [37] showed that a 3D RPM method doesn’t provide much better results than the conventional strip-theory in a high-speed, semi-displacing application. In this study, [37], the transom of the ship is assumed to be “wet”, so the flow adheres to the transom even at high-speed, which is not true. An important effect of hull lift damping was thus neglected and the results were poor. It is however stated that this can be dealt with by enforcing a Kutta condition at the transom for all motions, allowing the flow to smoothly detach from the transom in a manner more true to the actual situation.

A main disadvantage of using the RPM method is that it requires significant computer power, since both the hull and the free surface must be discretized. The computing time is in the order of several magnitudes longer than e.g. the 2.5D strip theory.

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The GFM approach distributes panels on the mean wetted surface of the hull, i.e. the calm water floating position of the hull. The velocity potential of each panel fulfils the Laplace equation and the radiation condition, i.e. the continuity of mass and that the waves are propagating in the right direction. Using this method there is no need to discrestize the free surface, this reduces computations time. Usually the GFM omits the steady disturbance, φs, completely, which is questionable especially at higher speeds.

10.2.4. Summary To summarize the above and put it into context of a semi-displacing catamaran such as the FLCU it can be concluded that

• The standard strip-theory is not suitable to analyse the motions of a high-speed catamaran in seaway. There are several reasons for this, as stated above, but the primary ones are that: No account of the steady disturbance due to the forward speed of the ship is taken, this implies low speed. The coefficients needed to solve the linear equations of motions are evaluated at zero speed, this can lead to resonance effects between the two demihulls such as wave-trapping or piston-mode resonance. It was concluded that when analysing a catamaran one should only consider one demihull when determining the hydrodynamic coefficients.

• The most accurate results that can be obtained from the strip-theory are the head seas case, when modelling one demihull only.

• The 2.5-D theory yields excellent results as long as the sea-state and motions are moderate. The difference is that this method actually accounts for the steady disturbance of the ship at forward speed and the interaction between this and the unsteady flow. The method is slower than the conventional strip-theory especially if calculating the steady disturbance using non-linear theory.

• The 3-D methods can provide excellent result with the same restrictions on sea-state and motion amplitudes. No resonance effects are present, but it is important to deal with the flow separation at the stern. The main drawback is computation time, which is in the order of several magnitudes greater than for the strip-theory approaches.

10.3. SEAKEEPING ANALYSIS OF THE FLCU An assessment of the seakeeping characteristics of the FLCU is made with the use of the linear strip-theory. It was concluded that this is not optimal tool for this analysis, but it is the only means available at this time. The analysis is done in head and beam seas using the Maxsurf Seakeeper program [45], which has the theory according to Salvetsen [40] implemented. The 2-D hydrodynamic coefficients are calculated using the conformal mapping method with five parameters. This yields geometrical sections more true to the actual shape of the hull (Figure 26).

Figure 26. Mapped and true sections of the FLCU. Left using 5 parameters conformal mapping and right 3 parameters Lewis

mapping. Green lines represents mapped sections.

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When modelling a catamaran in Seeakeeper only one hull is considered, this has proved to give reliable results for coupled heave and pitch in head seas, with the limitations mentioned previously. It is also possible to model uncoupled roll motions, the method that Seakeeper uses is to still only consider one hull but the real separation between the demihulls are used to calculate the actual metacentric height. The method used by Seakeeper is basically to model the roll motion as an alternative heaving of the two demihulls. The added mass and damping for the roll motion is then the same as for the added mass and damping of the heave motion of one hull.

10.3.1. Environmental conditions and seakeeping criteria The FLCU is according to the specification of requirements to be able to operate at full speed in seastate 3; this means a significant wave height between 0.5-1.25 m. Using only the definition of seastate poses a problem since it is an interval, here it is chosen to stay conservative and select the maximum interval value. The ITTC 2 parameters Bretschnider spectrum is used to model the energy distribution at different frequencies in the required sea-state. The advantage of using this spectrum is that the significant wave height and modal period can be modified to adapt the spectrum to the wave statistics at a certain location [44]. The analysed case is load case 1 as described in section 6.

The FLCU is analyzed at mean zero-crossing periods between 4-10 s, this corresponds covers the most common periods for both the North Atlantic and the Baltic Sea for this particular significant wave-height.

There are two especially limiting criteria for the FLCU; slamming on the cross structure bottom and emergence of the water-jet intake pipe. This means that the relative motion of a point located at the bottom of the cargo platform must be less than the vertical clearance to the surface when the craft is fully loaded. For the water-jet intake the relative motion must be less than the draught of the hull at that position. The input and locations are presented in Table 59.

Table 59. Input for seakeeping analysis. Input Spectra ITTC two param. Bretschnider Modal period 4, 6, 8 [s] Significant wave height 1.25 [m] Directions 180, 90 [°] Points o f i nte res t X [m] relative A.P. Z [m] relative B.L. Cargo platform 17 3.8 Water-jet intake 1 0.4 Bridge, i.e. tank cockpit 8 5.5

In addition to these criteria the FLCU is also evaluated against the NORDFORSK criteria for small fast crafts [46]. Since the craft is autonomous there is no bridge in a common sense, the location at which to apply the NORDFORSK criteria is then more natural to be in the tank cockpit where the personnel is situated. The limits for the FLCU are presented in Table 60.

Table 60. Seakeeping criteria limits. Cri te ria Vertical acceleration F.P. 0.65g = 6.38 [m/s2] RMS-value Vertical acceleration tank cockpit 0.275g = 2.7 [m/s2] RMS-value Lateral acceleration tank cockpit 0.1g = 0.98 [m/s2] RMS-value Roll 4° [°] RMS-value Platform relative motion 2.1 [m] Max value, 4 times RMS Water-jet emergence 1.6 [m] Max value, 4 times RMS

The speed at which these criteria should be evaluated is 20 knots, but due to the limitations of the method available these speeds are not likely to provide any accurate results. The responses obtained at these speeds are usually over predicted according to literature such as [35]. The analysis is however performed at speeds ranging from 0.2 < Fn < 0.8. A reasonable upper limit for the validity of the strip method is according to the previous chapter in the region of 0.4 – 0.5 depending on the source of information. This means a speed between 10.5 – 13.1 knots. A comparison of maximum vertical acceleration at the centre of gravity between the seakeeping analysis and the DNV rule formulations is also done.

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Other required information besides the geometry of the hull is the displacement and radius of gyration obtained in section 4. The craft is evaluated at full load, i.e. load case 1. The radius of gyration in the roll direction is assumed to be 37.5% of the total beam [45].

10.3.2. Seakeeping characteristics of the FLCU Using the strip-method to analyse the seakeeping characteristics of the FLCU yields the following results in relation the limiting

criteria ( Table 62-

Table 64).

Table 61. Results of seakeeping analysis for the FLCU at 4 s mean zero-crossing period. Spe ed [knot s , (Fn) ] 5, (0.2) 13.1, (0.5) 20, (0.76) Cri te ria Heading 180° Vertical acceleration F.P. 2.53 3.14 3.16 Pass Vertical acceleration tank cockpit 1.13 2.12 2.37 Pass Lateral acceleration tank cockpit 0.3 0.36 0.36 Pass Roll 0 0 0 Pass Platform relative motion 2.46 2.6 2.4 Fail Water-jet emergence 1.36 2.24 2.36 Fail Heading 90° Vertical acceleration F.P. 1.28 Pass Vertical acceleration tank cockpit 0.98 Pass Lateral acceleration tank cockpit 1.7 Fail Roll 0.64 Fail

Table 62. Results of seakeeping analysis for the FLCU at 6 s mean zero-crossing period.

Spe ed [knot s , (Fn) ] 5, (0.2) 13.1, (0.5) 20, (0.76) Cri te ria Heading 180° Vertical acceleration F.P. 1.4 2 2.3 Pass Vertical acceleration tank cockpit 0.67 1.4 1.9 Pass Lateral acceleration tank cockpit 0.16 0.22 0.25 Pass Roll 0 0 0 Pass Platform relative motion 1.32 1.63 1.7 Pass Water-jet emergence 0.7 1.37 1.69 Fail Heading 90° Vertical acceleration F.P. 0.4 Pass Vertical acceleration tank cockpit 0.5 Pass Lateral acceleration tank cockpit 0.32 Pass Roll 5.6 Fail

Table 64. Results of seakeeping analysis for the FLCU at 8 s mean zero-crossing period.

Spe ed [knot s , (Fn) ] 5, (0.2) 13.1, (0.5) 20, (0.76) Cri te ria Heading 180° Vertical acceleration F.P. 0.81 1.22 1.46 Pass Vertical acceleration tank cockpit 0.42 0.88 1.2 Pass Lateral acceleration tank cockpit 0.09 0.13 0.15 Pass Roll 0 0 0 Pass Platform relative motion 0.8 1.0 1.2 Pass Water-jet emergence 0.4 0.8 1.04 Pass Heading 90° Vertical acceleration F.P. 0.25 Pass Vertical acceleration tank cockpit 0.3 Pass Lateral acceleration tank cockpit 0.52 Pass Roll 0.19 Pass

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The results are encouraging; the FLCU passes most of the limiting criteria at all speeds. However, as mentioned previously the validity of the results at higher speeds, especially at 20 knots is questionable. For lower speeds they do give an indication of the seakeeping characteristics of the craft. The maximum values are taken as 4 times the RMS value. The mean zero-crossing period for waves between 0-2 m during the winter months in the North Atlantic is 8.2 s. This is rather long compared to e.g. the most common wave in the Baltic Sea, where the period is between 3.5-4 s. This study indicates that at lower encounter frequencies, the FLCU will experience problems with fulfilling the criteria. However, according to the previous discussion, the FLCU is not likely to operate in the Baltic Sea and if it would do so operational restrictions may be used.

The vertical accelerations can be compared with the value stipulated from DNV, which states that the vertical acceleration is 10.1 m/s2 with a 1 % risk of being exceeded in the worst operating condition. However, since DNV does not state during what time period this measurement is given it is difficult to do a proper comparison to the results obtained in the seakeeping analysis. The craft has no problem fulfilling the NORDFORSK criteria, except for the high-speed case, but the results at that regime are very uncertain. The only problem is fulfilling the rolling criteria, but again the method used here is highly simplified and further studies needs to made to draw proper conclusions.

The interesting results are for the head seas case; it can be determined with a higher accuracy that the platform clearance is enough to fulfil the seakeeping criteria.

The response amplitude operator for the FLCU at 13 knots in head seas is presented in Figure 27. It also displays the energy density of the spectrum, i.e. the energy content of the different wave components. It can be observed that the response spectrum peaks at an encounter frequency of 4 s and that this poses some problems for the FLCU to fulfil all seakeeping criteria at this wave-period.

Figure 27. Response amplitude operator at 13 knots and head seas.

10.3.3. Conclusions A simplified analysis for initial investigation of the seakeeping characteristics of the FLCU has been made. The results are not conclusive and further studies are required, but lies outside this investigation. It does however give an indication that the proposed design has got the potential to fulfil the seakeeping requirements according to the specification of requirements.

Efforts have also been made to find proper tools to analyze the seakeeping for a craft of this particular kind. The conclusion is that the most cost effective method is the 2.5-D strip theory as developed by Zhao & Faltinsen [43]. A further final step would be to use model tests to verify and further refine the results of the seakeeping analysis.

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11. STRUCTURAL DESIGN CARGO PLATFORM This section outlines the structural design of the cargo platform. The conceptual function and purpose of the cargo platform is outlined in part I of this report and a more detailed presentation is made in the following text.

The cargo platform has several functions regarding the performance of the craft. Its primary purpose is naturally to support the cargo under transit to and from the shoreline, but it also serves an important role in a hydrostatic perspective. The following list compiles the most important requirements on the cargo platform function.

The landing craft’s cargo platform shall • Be able to support the weight of the primary and secondary cargo at the specified design

acceleration • Provide means to load and unload cargo at shoreline and in the landing platform dock • Provide means for cargo to transit from one LCU to an adjoining LCU • Be lightweight • Provide enough reserve buoyancy to ensure that the LCU meets the specified draft when landing

or docking • Be able to be raised or lowered to ensure that the LCU meets the specified draft when landing or

docking • Be able to be raised enough to ensure that the bottom clears the water surface at the specified

operational and survival sea-state • Shall fulfil all requirements of the DNV High Speed Light Craft & Naval Surface Craft rules

Besides these requirements consideration needs to be taken to geometrical limitations, such as the LPD limitations.

11.1. GENERAL & STRUCTURAL ARRANGMENT PLATFORM The platform is essentially a large beam simply supported at points 1 and 2 (Figure 28). The width of the platform is determined by the primary cargo, which has a vehicle width of 3.8 m. In addition to this a minimum manoeuvring margin of 0.3 m on each side is needed according to Christer Nedin at FMV. Hence the total minimum width of the platform is 4.4 m. The platform width has several implications on the performance, weight and safety of the craft. Keeping the platform at minimum width results in lower loads on the crossbeams, thus reducing weight. However reducing overall breadth results lower stability for the craft. This may not be critical in transit mode, but in docking mode this needs to be considered. The distance between the demihulls also has implications on resistance. Attachment point to secure the cargo must also be fitted, but this is outside this study.

The length of the platform is largely dependent on the loading of the craft and the ability to transfer vehicles between two crafts in the well deck. The overall length is 19 m and this gives that a flap with a minimum length of 1 m needs to be fitted at the bow of the platform. This flap will not only serve as a bridge connecting two crafts in the well deck, but also help the vehicles to disembark safely at the shore.

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Figure 28. General and structural arrangement of platform

The top plating of the platform needs to be able to support the pressure exerted by the primary cargo. Three stiffeners are placed with a spacing of 500 mm, this provides excellent support for the cargo since two of these stiffeners will be situated below the tracks. This divides the plating into smaller segments where the plating width is 500 mm in the outer part of the platform and 760 mm on both sides of the centre girder. The cross-sections of the top stiffeners are assumed to be constant throughout the length of the platform. The stiffeners in the bottom are spaced in the same manner as for the top plating, but the cross-section of these may vary due to the different loading scenario.

The global strength of the platform is supplied by the longitudinal centre girder, G1, and to some extent the outer girder, G2. But because of practical requirements the outer girders needs to be cut out and thus reducing the web from 800 mm to only 100 mm and imposing a significant break in continuity and load carrying ability. To reduce this discontinuity the outer girder is raised at points 1 and 2.

The structure also has a grid of transverse floors with the purpose of transferring load to the centre and outer girder.

11.2. MATERIAL The platform is constructed using aluminium and steel. This material concept is chosen for several reasons. The platform will be subjected to extreme loads when landing and standing at the shore, due to this the centre girder is constructed by steel. The platform also needs to be tough due to the abrasion and local loads imposed by the cargo, well deck and shore. Aluminium is used wherever possible to reduce weight. The material properties are outlined in section 4.

11.3. SCANTLINGS METHOD PLATFORM The cargo platform is designed according to the specification of requirements, determined by cargo loads, sea loads, buoyancy and operation. The minimum plating thickness and stiffener sectional modulus due to cargo loads on the platform is determined using DNV HSC & NSC §5:7. A detailed investigation of the required scantlings of the platform is performed using FEM calculations, this allows for weight reduction and consideration of global stiffness and strength, which is of utmost importance for the operability of the craft. This is also necessary due to the unconventional nature of the craft and the boundary conditions applied on the platform.

11.4. LOADS The cargo platform must, according to the specification of requirements, be able to support both the primary and the secondary cargo as well as handle the potential slamming loads on the bottom of the

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structure according to DNV. There is also a need to consider local loads due to beach landing and rough cargo handling.

11.4.1. Cargo loads The primary cargo, battle tank 122, has a mass of 62.000 kg, this mass is distributed on its tracks. This gives a pressure of p0=9.4 N/cm2 exerted by the tank on the platform structure. The secondary cargo, the 9040C, has a mass of 28.000 kg, a track width of 533 mm and a ground contact length of 4480 mm. This results in a ground pressure of 5.8 N/cm2. The heavier battle tank 122 hence determines the platform scantlings. The pressure exerted by the tank of the cargo platform, according to DNV HSLC & NSC §5:2:3, described as

ptracks =p0 9.81+ 0.5av( )

9.81 [kN/m2 ] (25),

where av is the design acceleration at the considered longitudinal position of the platform and is chosen as the centre of gravity for the tank x=9.65 m. The magnitude of this is 10.4 m/s2. This results in a design pressure of ptracks,MAX=215.5 kN/m2. This pressure should be applied at the contact surface of the tank when it is in transit position. The ground pressure of ptracks,NOM=94 kN/m2 should also be applied at 2 other positions of the platform to simulate embarkation and disembarkation at the LPD or when transferring a tank from one LCU to another.

11.4.2. Beaching The final load that should be applied to the platform is the beaching load. This load originates from the contact with the beach and is calculated according to DNV NSC §5:14:3 as

pbeach = 3.2 !bcontact

[kN/m2 ] (26)

This should also be applied together with the tank track loads. The magnitude of this load is 81.4 kN/m2.

11.4.3. Disembarkation The final load case is determined by the disembarkation of the tank. At this point the platform rest on the bottom and the tank still stands on it. This compresses the platform under great stress. Assuming a load area of 6.8 m2 when the tank rolls of the platform give an estimated contact pressure of 89.4 kN/m2. This is slightly higher than the beaching pressure., but it is very much dependent on the chosen load area.

11.4.4. Summary Now all the relevant loads on the cargo platform have been determined and two different approaches are used to determine the scantlings of the platform. The global loads are assumed to be handled by the crossbeams, which are not included in this analysis, but can be found in section 12. First the general thicknesses are determined using the DNV rules, these are then crosschecked with direct calculations using FEM software. For the direct calculations the following load cases can be identified ( Table 64).

Table 64. Definition of load cases for platform. Load case Ptracks,NOM

[kN/m2] ptracks,MAX

[kN/m2] pdisembarkation [kN/m2]

Pbeach [kN/m2]

1, Transit 215.5 2, Beaching 94 81.4 3, Disembarkation at shore 94 89.4

Load case 1 describes the craft in transit at full speed, load case 2 models the landing of the craft against the shore. Load case 3 describes the embarkation of the cargo and essentially applies the nominal track pressure when the craft is at rest on the shore.

11.5. DNV SCANTLINGS Due to the special nature of the FLCU cargo platform the applicability of the DNV rules should be carefully monitored. There are two cases to evaluate, where the platform plays two different structural

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roles. The first case, when the craft is in transit with the platform raised it can be regarded as a deck and cross-structure between the hulls. In this case the applicable load would be the loads imposed on the platform by the cargo.

The second case is when the platform has been lowered, at this stage the craft travels at reduced speed and the platform now acts as the bottom structure of a hull. The relevant loads acting at this stage is the nominal cargo pressure and the beaching pressure described in the previous section.

11.5.1. Method First the design acceleration is determined according to DNV HSLC rules and the loads are then calculated according to the previous section. The maximum pressures and loads from these calculations are then used as input in the scantling equations to determine minimum thickness and sectional modulus for the considered structural member. The platform is divided into plates, girders, floors and stiffeners according to Figure 28.

The scantlings obtained here will be used as a first estimate in the direct calculations where global stiffness and strength is evaluated. Further discussions on the design acceleration may be found in section 5.

11.5.2. Plates Plates P1-P4 are defined with the required input in Table 65. These plates represent the different loading scenarios for different parts of the platform plating. For the top plate, P1, the dimensioning load is the track load from the tank 122. P2 and P3 represents the plates on the bottom of the platform where only the sea pressure needs to be taken into account and plate P4 represents the plate taking the beaching impact when landing the craft (Figure 28).

The minimum thickness of the plating supporting cargo on wheel or tracks is according to DNV HSLC & NSC §5:2:3 determined as

tmin =77.4ka kwcsp

m! (27),

where

ka = 1.1! 0.25 s l , max 1, min 0.85

S is the stiffener spacing and l the stiffener length. Kw is determined according to

kw = 1.3! 4.2as+1.8"

#$%&'

2 , max 1. (28),

where a is the longitudinal extent of the load area parallel to the stiffeners. The considered pressure is noted p and c is equal to the stiffener spacing, s, if extent the load area perpendicular to the stiffeners, b, is larger than the stiffener spacing and equal to b if the extent is smaller than s. σ is the allowable stress and can be found in section 4 for the considered materials. For values of the ratio b/s larger than 1, m is equal to 13.57.

The method for determining minimum plating thickness of the bottom plates is described in DNV §3:3.

Table 65. Input for plates. Plate 1 2 3 4 Longitudinal position, x [m] 9.65 9.65 9.65 17.65 a [m] 1.6 1.6 1.6 1.61 b [m] 0.5 0.5 0.76 0.76 Pressure type Cargo Sea Sea Beach p [kN/m2] 142.4 20.6 20.6 81.4 t_min 11.2 5.5 6.9 20

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The results for minimum thicknesses of the plating is found in the final row of Table 65 and for plate number 4 an addition of 20 % is made according to DNV §5:7:4.

11.5.3. Floors For the girders and floors the pressures for a section below the tank and one section at the forward part of the platform is evaluated. The maximum pressure is the chosen for a sample calculation of one floor, F1. The pressures considered are the cargo pressure and beaching pressure. The input for F1 is presented in Table 66.

Table 66. Input for floor. Member F1 Longitudinal position 9.65 Vertical position 4 Spacing 1.6 Span 2.26 Longitudinal extent of load area 5 Transverse extent of load area 0.63 Plate thickness top 11.2 Plate thickness bottom 5.5 Pressure 142.4

The results are presented in Table 67. However it should be pointed out that the platform doesn’t act as a typical hull section, it might be more correct to interpret the platform as a hull girder and consider its global stiffness and strength, this is dealt with in the direct calculations. The results for the floor should hence be treated with some degree of conservatism.

Table 67. Results for F1. Member F1 Zmin [cm3] 247.2 Zcalc [cm3] 2718 Web height hw [mm] 800 Web thickness tw [mm] 4 Effective flange breath bf [mm] 0.8 Flange thickness top [mm] 11.4 Flange thickness bottom [mm] 5.5

11.5.4. Stiffeners In the same manner as for the plates, three sections of the longitudinal stiffeners are selected to represent the platform structure in the scantling calculations, S1-S3. S1 is a stiffener placed below the tank tracks and S2 in the forward part of the bottom, where heavy impacts from either the beach or slamming will occur. S3 represents the stiffeners in the bottom only exposed to the sea pressure. The required input for the calculations of S1-S3 is presented in Table 68.

Table 68. Input for stiffeners. Sti f f e ner 1 2 3 Longitudinal position x [m] 9.65 17.65 9.65 Stiffener spacing s [m] 0.5 0.76 0.76 Stiffener span l [m] 1.6 1.6 1.6 Longitudinal extent of load area a [m] 1.6 1.6 1.6 Transverse extent of load area b [m] 0.63 0.76 0.76 Plate thickness tp [mm] 11.2 20 6.9 Pressure p [kN/m2] 142.4 81.4 20.6

The minimum section modulus for a stiffener supporting a cargo deck, stiffener 1, is according to DNV §5.2.3 calculated as

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Zmin =1000kzlcdp

m!+ Zk [cm3] (29)

The calculation method for the stiffener number 2 may be found in DNV §3:3:5, describing the bottom scantling method.

For stiffener S1-S3 the following results are obtained (Table 69).

Table 69. Stiffener scantlings. Stiffener 1 2 3 Zmin [cm3] 126.8 181.6 82.7 Zcalc [cm3] 127.0 183.0 85.1 Web height hw [mm] 120 125 100 Web thickness tw [mm] 8 10 8 Flange breath bf [mm] 80 100 80 Flange thickness [mm] 12 12 10

11.5.5. Conclusions The results and calculations presented above for the cargo platform are representative for the entire platform and the complete scantlings for the platform could be found from these in all respects but for the girders and floors. When observing this structure from a DNV rule point of view it is very much realistic to apply the plating and stiffener calculations. These results provide a good starting point for the local loads imposed on the structure by the cargo, the sea and the beaching manoeuvre. However for the girders and floors one should be careful with the results. The rule calculations assume that these members are a part of a larger structure and that the boundaries are stiff or semi-stiff, as a shipside or bulkhead. This is not the case for the platform and it should rather be treated as a hull girder or a beam. To accurately determine the stiffness and strength of the entire platform direct calculations are made with the use of the local scantlings as initial input.

11.6. DIRECT CALCULATIONS The aim of the direct calculations is to analyse the global and local stiffness and strength of the platform under a number of different loading conditions. It allows for, as opposed to the DNV formulations, the introduction of multiple loads to simulate the actual loading of the platform in a more realistic manner. The purpose of the modelling is to obtain accurate global as well as local displacements and stresses. Local stresses at joints, corners and interaction between lever arms and platform is not analysed at this stage, but problem areas may however be identified. The FEM-calculations are done using Abaqus CAE [47]. The results of this analysis should be sufficient to with a high degree of certainty assure that the platform can be constructed to meet the specification of requirements and obtain a realistic weight estimate of the entire platform.

11.6.1. Model One of the most important issues of FEM-modelling is to determine the extent of the model. In this case it is rather straightforward. Since the required results are both global and local stresses and displacements and the platform could be regarded as a simply supported beam the entire platform is modelled. In order to reduce computing and modelling time symmetry can be used about the centreline of the platform. The model is then fully 3-D, where every part but the local stiffeners are modelled with its actual geometry. The model is presented in Figure 29. Local radiuses and some more complex geometries of the different parts are somewhat simplified.

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Figure 29. FEM-model of one side of the platform. Forward to the left.

11.6.2. Mesh size Since the main purpose of the FEM calculations is to provide both the global and local displacements and stresses the mesh should be of medium to fine size depending on the area being modelled. The model is meshed part-by-part to obtain good mesh sizes independent of part size. The mesh is also refined in areas with high stress gradients to give more accurate results but still keep the calculations fast.

11.6.3. Elements The platform is modelled by the aid of several different FEM-elements. For the plating, girders and floors shell elements are used. The type used here is a conventional 4-node shell element with reduced integration. This type of element can model both in-plane and lateral properties, which is required when applying e.g. a lateral surface pressure. However to accurately calculate the lateral displacements all the stiffeners need to be modelled. The longitudinal stiffeners are modelled used a 3-D, 2-node linear beam element. This makes modelling easy and reduces computing time. It is however important to accurately offset these elements from the shell element so that the stiffener actually is placed in the correct side of the panel and not in the centre plane. These elements are compatible with the shell elements. A tie constraint is used to connect the beam elements to the shell elements; this constraint prevents both translation and rotation at the intersection or connection of the different structural members.

For the structural parts connecting the arm to the platform 4-node linear tetrahedron 3-D elements are chosen, mainly due to modelling issues. To connect these elements to the plating/shell elements a shell-to-solid coupling is used. This will couple the displacement and rotation of each shell node to the average displacement and rotation of the solid surface in the vicinity of the shell node.

11.6.4. Application of load All the loads are applied as surface pressures on a partitioned part of the top or bottom surfaces. The hydrostatic pressure on the platform when lying at the beach is applied as a function of water depth. The platform is assumed to have its waterline at the top of the upper plating. Figure 30 shows the different load cases investigated.

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Figure 30. Load cases 1-3 for FEM calculations.

11.6.5. Boundary conditions The boundary conditions are well defined and symmetry is used along the centre line of the platform. The platform is simply supported at the points indicated in Figure 31. In reality these points are restricted to some extent in the rotation about the longitudinal X-axis due to the presence of the lever arms. The rotation of these arms could be determined using a global model and then applied at the elements building the attachments for the lever arms. By assuming a simply supported boundary condition the displacements could be slightly over-predicted.

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Figure 31. Boundary condition for FEM calculations.

11.7. RESULTS The following is a discussion of the results from the direct calculations on the cargo platform. The final scantlings and weight is also presented.

11.7.1. Load case 1 Using the input from the scantlings according to DNV for the plating and stiffeners resulted in a well-balanced structure, however slightly heavy. For load-case 1 the maximum Von Mises stress in the stiffeners is 128 MPa, and 60 MPa for the plating below the tank tracks. This indicates that reducing plating thickness and increasing the stiffeners sectional modulus could achieve a more balanced and lighter structure. The results for the stiffeners and plating do however show excellent conformation with the results obtained using the DNV calculation method. The transverse floors could be lightened considerably if only considering this load-case since the stresses on these are well below the maximum allowable stress of 128 MPa. The critical areas with respect to stresses can be identified as the centre girder, stiffeners and the areas surrounding the cut-out for the transverse crossbeams. Figure 32 displays a schematic image of the Mises stress distributions in the platform.

Figure 32. Stress distributions (MPa) of the platform for loadcase 1 [Mpa].

Further it can be observed that the stresses on the centre girder are well within the limits of the allowable stresses for steel. The stresses at the crossbeam attachment points 1 and 2 according to Figure 31 is locally very high, but this is due to the manner in which the boundary condition is applied, to further refine this local analysis a boundary condition more true to the actual local situation could be applied. It is here judged that this simplified boundary condition is adequate to represent the global stresses and stiffness of the platform.

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The vertical displacements of the platform is also of interest and in load case 1 the maximum displacement of the platform itself is 10 mm, this is only 0.125% of the free length between the supports. The maximum displacement overall is for the plates below the tank 15 mm, but the plate itself only bends 5 mm.

11.7.2. Load case 2 The beaching load case is very critical; the pressure exerted at the forward part of the platform is extremely high and works together with the tank pressure to bend the platform. Again the local scantlings using the DNV formulations provides adequate strength with stresses in the stiffeners and plates, except in areas surrounding the forward cut-out. This area has room for improvement and weight reduction by balancing the structure, i.e. making the stresses in the stiffeners and plates more equal, even reducing the stiffener cross-section and plating thickness. There is also a need for some redundancy in the plating due to the extreme chafing produced by the contact with the shore. Figure 33 displays the displacements at the attachment points of the crossbeams; even though the boundary condition is simplified it indicates that the magnitude of these displacements are manageable. The maximum displacement is in the forward part of the platform, which moves 113.5 mm in the vertical direction.

Figure 33. Vertical displacements in millimeter due to load case 2 [mm].

The most critical stresses are those in the centre girder in the area around the cut-out. This area is reinforced with thicker plating to reduce stress levels to the maximum allowable stress for steel. The areas surrounding the cut-out on the outside of the platform is also reinforced with steel plating. The most effective way deal with these large stresses is not fully addressed here. However a simple approach to reinforce locally is used to show that the stress levels are manageable. The Von Mises stress levels in the floors are no higher than 75 MPa, and are displayed in Figure 34.

Figure 34. Von Mises stress in the floors due to loadcase 2 [mm].

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A more intelligent and refined design could dramatically reduce the weight of the platform.

11.7.3. Load case 3 This load case is not as critical to the structure as load case 2, but it stresses the structure in a different way than the two previous load cases. Since the forward part of the platform is resting on the shore, the stresses on the transverse floors increases due to the compression. It was suggested is load case 1 that the floor could be lightened by removing parts of the structure, this is not the case in this area. A further refinement of this analysis would be to model the contact pressure between the shore and the platform, in this study the DNV minimum plating thicknesses due to beaching are used in this area of the platform.

11.7.4. Discussion & Scantlings The direct calculations together with the DNV scantlings provide the initial scantlings of the platform (Figure 35). Using these two methods it’s proven that that the load cases are manageable and that the platform can be constructed to a total weight of 13 ton. As discussed previously there are room for vast improvements of the structural design, especially since the problem areas are identified through the FEM analysis. Further the stiffeners and plating in some areas can be reduced in section and thickness and still comply with the maximum allowable stresses according to the DNV safety factors and material properties. The weight optimisation of the platform structure lies outside the scope of this study, but might prove to be necessary in the next design iteration. The direct calculations also show that the load transfer from the structure supporting the arms to the platform itself is manageable, the local deformations and stresses are within the limits set by the choice of material, in this case structural steel.

Figure 35. Scantlings for cargo platform .

The proposed platform design fulfils the specification of requirements. It can handle both the primary and the secondary cargo, it provides a conceptual mean to load and unload cargo at the shore or LPD. It is as lightweight as possible with the means and time available, however weight can be saved with further studies. It provides a reserve buoyancy of 60 ton, thus reducing draft when landing to less than 1 meter. The design allows the platform to be raised and lowered and it fulfils the relevant requirements of the DNV HSLC & NSC rules.

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12. CARGO CONTROL SYSTEM (CCS) DESIGN A conventional catamaran does usually have a large and flat cross structure, completely fastened to the hulls with lots of elements contributing to the global strength and stiffness of the craft. This should be compared to the unconventional design of the FLCU which only has four attachment zones for the cross structure. At each zone, a CCS is fitted with the task to act as the link between platform and hulls and to enable the transformation between the FLCU modes. The system will operate in an extreme environment and be subjected to heavy loads due to waves, cargo and beach contact. A natural consequence of this is that the design must be strong, robust and stiff. It is hence obvious that the CCS design is one of the crafts most important and critical design areas.

A complete detailed design of the CCS would be a fairly complex task, too comprehensive for this study. Hence, the main parts of the analysis were done in a global sense, with the overall goal to provide dimensions and masses of the different components in the CCS.

This section will focus on the design. The principal function of the CCS is more thoroughly described in part I of this report. It is also important to stress that the CCS is designed for the carbon sandwich hull version.

12.1. CCS DESIGN AND DEFINITIONS In Figure 36, a complete picture of the CCS, its dimensions and part definitions is shown.

Figure 36. General arrangement drawing of aft station CCS, side, top and 3D view, all measurements in mm

The CCS design can be divided in two sections, the structure and the system. The structure section includes coarse design of all beams in the CCS, detailed analysis of the connection between platform tube beam and lever arm, and also an analysis of the global stiffness. The system section includes design of hydraulic cylinders and the locking device.

12.2. CCS COARSE STRUCTURAL DESIGN AND GLOBAL STIFFNESS The general aim with the structural design is to dimension the CCS beams, calculate the global displacements of the hulls and get data of how the loads transfer between the CCS parts. The final aim is important in data to the design of the systems and for more detailed structural analysis.

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For the main part of the analysis a global FEM-model was developed in ABAQUS. The connection between the platform tube beam and the lever arm were also analyzed in detail.

12.2.1. Extent of model The model consists of 2 sub-parts; the hull structure and the CCS beams. The geometry of the hull is modeled as an elongation from the mid ship section and the CCS beams is modeled with wires. The later makes it possible to represent the beam dimensions i.e. profile and geometry by the use of beam elements. The idealization of the structure is shown in Figure 37.

Figure 37. Structure idealisation with the CCS beam profiles rendered.

The geometry idealization is also shown with its dimensions and definitions in Figure 38.

Figure 38. Geometry idealisation, definitions and measurements in mm (coordinate system marked in red)

The hull structure was further simplified by only including the primary members. Since the scantlings of the hull structure obtained in section 5 should be treated as minimum requirements, the hull structure used in the model is balanced to more realistic dimensions. The final dimensions are shown in Table 71 for each hull structural element.

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Table 70. Hull structure dimensions Bottom Pla t in g Bottom gi rde rs Face thickness [mm], tf 1.7 Flange thickness [mm], tfl 25 Core thickness [mm], tc 17 Web thickness [mm], tw 10 Flange width [mm], bfl 250 Deck pla t in g Web height [mm], hw 350 Face thickness [mm], tf 2.11 Core thickness [mm], tc 15 Deck g irde rs Flange thickness [mm], tfl 1.5 Side pl at i ng Web thickness [mm], tw 1.2 Geometry Flange width [mm], bfl 40 Face thickness [mm], tf 1.7 Web height [mm], hw 300 Core thickness [mm], tc 10 Bulkhead Sti f f en er s Bulkhead Pla t in g Flange thickness [mm], tfl 2.5 Face thickness [mm], tf 1.2 Web thickness [mm], tw 1.2 Core thickness [mm], tc 10 Flange width [mm], bfl 40 Web height [mm], hw 250

12.2.2. Material The CCS was only developed for the carbon fiber sandwich hull alternative. The material properties for the hull structure are the same as defined in Table 10-14 in section 4. Material.

All parts of the CCS is designed in high tensile steel NV-500. The reason for choosing this fairly exclusive steel was primary to reduce weight. The tensile strength is almost 40 % better than normal constructional steel with comparable E-modulus. It might be possible to design at least some parts in other materials such as carbon fiber in order to reduce weight even more. This would however make the design more complex. Another critical factor with the use of other materials would be robustness. Especially the lever arms and the platform tube beams will be very exposed to local impacts such as rocks or a bad maneuvered battle tank.

The material properties and allowable stresses are the same as presented in Table 18 and Table 19 in section 4. Material.

12.2.3. Design loads Realistic design loads is an issue for a craft such as the FLCU. In this first step it was decided to use the global catamaran cross structure design loads as stipulated by DNV HSLC & NSC rules [33]. They give three design moments, twisting moment in pitch Mp, twisting moment in roll Mt, and transverse bending moment Ms. The definitions of the moments are shown in Figure 39.

Figure 39. Definition of DNV cross structure design moments [33]

The loads are calculated from expressions depending on design acceleration, main dimensions and factors decided by area notation. They are for this case shown in Table 71.

Table 71. DNV cross structure design moments Mp [kNm] 2630 Mt [kNm] 2432 Ms [kNm] 1297

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As one can see, the loads are fairly heavy. Both the pitch and twist loads represent load cases due to dynamic loads from waves whereas the transverse bending moment represents the static still water load. It is important to keep in mind that especially the dynamic loads are relatively uncertain estimations. A study presented at the conference FAST 99 by Heggelund [32] showed that the DNV load estimations could be more than twice as high as the real loads. Thus model basin trials or more accurate seakeeping calculations should be carried out before doing a final design of the system.

12.2.4. Load application The DNV global loads need to be applied in a realistic way. Since they in reality depend on the pressure distribution along the hulls they are recalculated and applied to the model as pressures. The geometry of the cross structure beams makes the load transfer between them fairly complex.

The pitch load case is recalculated as a pressure distribution in the following manner. The moment is treated as a force pair acting from the aft and the bow of the LCU. These forces are then distributed as a linear varying load along the ships bottom. The principal behind this load case is shown in Figure 40.

Figure 40. Load distribution for the pitch load case

The function f(x) [N] describing the force distribution is calculated through moment equivalence as

2 2

3 32 ( )3 2 2

p pp

M MM q l l q f x x

l l= ! ! " = # = (30).

From this follows that the pressure distribution p(x) [Pa] can be written as

2

3 1( )2

pMp x xl l b

=!

(31),

where b is the beam of one demihull. Since the twist moment Mt in the end will affect the structure in the same way as the pitch moment, it can be treated likewise. The moment is idealized as a force pair, acting in the outer side of each hull in the bow and the aft. The final distribution is then derived in the same way as for pitch moment.

The transverse bending moment is distributed evenly in both transverse and longitudinal direction over the bottom. The principal is shown in Figure 41.

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Figure 41. Pressure distribution for the transverse bending load case.

To calculate the pressure, the bending moment is idealized as a line load acting through each of the hull centrelines. This line load is then distributed evenly over the bottom as a pressure.

12.2.5. Boundary conditions Since the craft is symmetric along the platform centerline, only half of it is included in the calculation. The boundary conditions are shown in Figure 42. To make it easier to overview, both the real geometry and the model is shown with corresponding boundary condition. It should also be mentioned that the boundary conditions are the same at bow and aft station.

Figure 42. Boundary conditions

The meanings of each boundary condition are explained in Table 72.

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Table 72. Boundary conditions BC Nr. Type Physical representation 1 Clamped Welded connection between platform tube beam

and platform center girder. 2 Fixed in Z-direction Connection between platform tube beam and

platform. 3 Free to rotate around X-axis, all other

degrees of freedom tied between lever arm and platform tube beam.

Connection between lever arm and platform tube beam which is free to rotate around the platform tube beam.

4 Translations and rotations tied between the two lever arm parts

Connection between lever arm parts

5 Translations and rotations tied between the two lever arm parts

Connection between lever arm and hull tube beam

6 Translations tied to hull structure over a length equal to the width of the hull tube beam supports

The layered connection between hull tube beam and hull structure.

7 Rotation around X-axis fixed The locking device

For the connections between the different hull structural elements, the ABAQUS tie command was used. This constraint connects the degrees of freedom between the parts in an ABAQUS assembly. The connection is independent of the mesh and can tie both translations and rotations.

12.2.6. Element type and Meshing The hull structure is modeled with shell elements. The element used is a 4-node shell element in ABAQUS named S4R. It can model both in plane and lateral properties. The element can represent the carbon fiber sandwich material fairly well by taking cross section data i.e. lamina and core thicknesses as input. It is also not too time consuming to calculate. The lay-up of the faces and the properties are equal to the ones defined in the material selection chapter.

The beams are modeled with beam elements in ABAQUS named B31. They are represented by wires in the model geometry and the beam properties are represented by giving the beam profiles as in data to the element. From calculations with beam elements in plane stress and rotational shear stress as well as section force, (in plane) sectional moments and displacements can be obtained.

The hull is meshed with a medium size mesh and as far as possible is a quad mesh used with approximate size of 10 x 10 cm. The beams are meshed with a finer size.

12.2.7. Results CCS Beam dimensions Calculations were carried out for both the transverse bending and the pitch load case. The twist load case was not considered since it loads the structure in the same way as the pitch load case and was in the same magnitude. The pitch load case loads the structure more compared to the transverse bending load case and is hence dimensioning for the CCS beams.

The final dimensions of the CCS beams are summarized in Table 73.

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Table 73. Dimensions of CCS structure Station Part Profile Dimension of profile

(radius /width x height) [mm] Thickness [mm]

Weight [kg]

Bow Hull beam tube 250 25 975

Lever arm long part rect. 600 x 500 20 1055

Lever arm short part rect. 600 x 650 15 170

Platform beam tube 250 23 807

Aft Hull beam tube 250 20 782

Lever arm long part rect. 600 x 500 15 791

Lever arm short part rect. 600 x 650 15 170

Platform beam tube 250 15 537

The results show that, the bow station is in general made out of thicker dimensions than the aft station. This is due to the position further away from ships center compared to the aft station, which for the pitch load case loads the CCS structure more. For both stations is the hull beam subjected to the largest stresses.

The beam with the highest stress is the bow hull beam, which has a maximum stress level of 315 MPa which is 15 MPa under the requirement. The aft hull beam is in the same stress region as well as both lever arms. The platform tube beams are not especially heavily stressed. The reason is that the boundary conditions not really distribute the loads realistic. It was thus decided to analyze those beams and the connections to the lever arms in detail. Another synergy with this selection is that it can include contact analysis between the lever arm and the platform tube beam. It will also serve as an indication that the dimensions retrieved in the global analysis are plausible.

12.2.8. Results global stiffness One of the aims with the model was to investigate the global stiffness of the FLCU. The global displacements for the transverse bending load case are shown in Figure 43 and for the pitch load case in Figure 44.

Figure 43. Displacement in Y-direction [mm] due to transverse bending load, grid shows undeformed state

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Figure 44. Displacement in Y-direction [mm] due to pitch load, grid shows undeformed state

The displacement is different in the bow and the aft due to the unsymmetrical placed bow and aft stations. The difference in displacement between the bow and the aft is about 400 mm in the Y-direction for the pitch load case. For the other directions the displacements are relatively small and in the magnitude order of 50 mm. The displacements are quite small for the bending load case compared to the pitch load case. It is however interesting to observe how the placement of the cross structure beams affects the global displacement.

One important thing to keep in mind with this analysis is that it only gives an indication of the global stiffness since the full deformation of the hull structure is not included. The boundary condition number 7 locks the hull tube beam in the rotational degree of freedom. The negative consequence of this is that the moment acting around this beam is not distributed out in the hull structure as it does in reality. Nevertheless, the reaction moment given by this boundary condition is important information for the design of the braking system and the structure which it connects to. It is for the pitch load case 1185 kNm.

12.3. DETAILED ANALYSIS OF CONNECTION BETWEEN PLATFORM TUBE BEAM AND LEVER ARM The connection between platform tube beam and lever arm was chosen for more detailed analysis with the purpose of verifying the platform tube beam dimensions obtained in the global coarse analysis and to check the contact pressures between the lever arm and the platform tube beam.

This was done with a detailed FEM model developed in ABAQUS.

12.3.1. Extent of model The connection between lever arm and platform tube beam is basically a bush in the short part of the lever arm. This bush is fitted around the platform tube beam with a tolerance of about 0.1 mm. A picture of the model extent is shown in Figure 45.

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Figure 45. Extent of model

The platform tube beam geometry is idealized with a surface and the lever arm beam with a solid. The use of solid is a step from reality but is easier to model and mesh on the cost of calculation time. The primary task for the lever arm is to transfer a contact pressure to the platform tube beam and thus is the use of a solid idealization good enough.

The following figure shows the geometry of the model with measurements, coordinate system, and definitions used in the further sections.

Figure 46 2D-drawing of model extent with measurements in

12.3.2. Loads The loads were taken from the global model as turning moments around the Y- and X-axis and are to be seen in Table 74.

Table 74. Lever arm loads Aft Bow Moment around X-axis [kNm] 212 212 Moment around Y-axis [kNm] 365 241

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The moments around the Y-axis are larger and will thus be used in the calculations. This neglects from collaboration effects but makes the result easier to verify by analytical calculations. It is also important to keep in mind that these moments are taken from the global FEM-calculation. The beam elements used could not return transverse forces, hence only bending moments were used.

12.3.3. Load application The loads are applied to a reference point at the bottom surface of the lever arm part (marked in Figure 46). To avoid singularity the degrees of freedom for the bottom surface of the lever arm part is constrained to move similar with the reference point. This will distribute the load over the whole bottom of the part.

12.3.4. Boundary condition The boundary conditions are marked in Figure 46 with BC1-3. BC1 correspond to the connection to platform center girder and is clamped to model the welded connection. The other end is modeled as simply supported and marked with BC2.

BC3 is the connection between lever arm and platform tube beam that is modeled with contact. For this Abaqus has fairly advanced possibilities. Here one of the simplest procedures was chosen. The interaction between the surfaces was modeled with a “hard” frictionless contact. This is the classical LaGrange multiplier method of constrained enforcement, which according to the documentation [47] will minimize the penetration of the surfaces and thus provide fairly good results. Since the contact is frictionless the lever arm must also be constrained not to translate in order to avoid gliding of the parts. Locking the translations in the same reference point as the load was applied to does this.

12.3.5. Element type and meshing The platform tube beam is modeled with a surface and thus the same shell element will be used as for the plating in the platform. The lever arm part is modeled with a normal solid 8-node linear element in ABAQUS named C3D8R.

The mesh was created regularly over the whole model with quadratic elements measuring approximate 20 mm at all sides. The meshed assembly of the model can be seen in Figure 47.

Figure 47. Meshed model

12.3.6. Analytical calculations To validate the numerical calculations an analytical contact analysis was carried out. It is based on an estimation of how the pressure distribution should look like. The idealization is shown in the following figure.

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Figure 48. Analytical model applied to the platform tube beam, seen from above

This was done by the pressure distribution p approximating as

Fpd t

=!

,

where F is the force given by the turning moment My divided by lever arm width (600 mm), d is the diameter of the beam and t is the approximated main pressure width. All variables can also be seen in Figure 48. The diameter is 500 mm and the width t was estimated to 30 mm. The moment of 365 kNm gave an approximate contact pressure of 40.5 MPa.

An analytical calculation was also done for the whole beam. The idealization is shown in the following figure.

Figure 49. Idealisation for the analytical calculation, coordinate system is the same as in Figure 46.

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The boundary condition in Figure 49 is to the right clamped which corresponds to BC1 in the FEM-model and to the left simply supported which corresponds to BC2. The load F was calculated from the moment of 365 kNm. The displacement in X-direction, plotted over the beam length is shown in Figure 50 together with the displacement from the FEM-calculations.

Figure 50. Displacement plotted over beam length. FEM-curve is from the path shown in Figure 50.

The shape of the displacement curve is fairly similar and also the point where the maximum occurs coincides. The FEM-calculation values are almost 40 % less than the analytical. Even though the relative difference in displacement is fairly high, the absolute difference of 0.6 mm should not be an issue. The maximum von Misses stress level is for the analytical calculation 221 MPa.

12.3.7. Results Calculations were made for the heaviest load case in Table 74 of 365 kNM. The thickness of the platform tube beam was varied until the maximum von Mises stress was in the magnitude of the allowable stress (see section Material for definition). The result showed that a thickness of 12 mm is well inside the margin. The stress distribution can be seen in Figure 51.

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Figure 51. Von Mises stress distribution in MPa, Coordinate system is the same as in Figure 45. The red dotted line represents

the path along which the displacement in X-direction is plotted in Figure 50.

The result of the contact pressure calculations is shown in Figure 52.

Figure 52. Contact pressure distribution in MPa, Coordinate system is the same as in Figure 45.

The pressure is distributed along two half planes of the beam as can be expected. The average pressure is 40 MPa which very well corresponds to the analytical estimation. The maximum pressure is 62 MPa, so the strength of the beams should be sufficient. This will imply that the thickness of the beams could be decreased to 12 mm, which would reduce the weight compared to the dimensions in Table 73. Since these calculations were made in a late stage, the new dimensions are not implemented in the design. They do nevertheless show that weight could be gained by detailed stress analysis.

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12.4. SYSTEM DESIGN

The design of the systems were limited to the hydraulic cylinders and the locking device with the purpose getting necessary dimensions and relate them to products available at the market and hence get data of the parts weight.

12.4.1. Load analysis of the CCS system The hydraulic cylinders are designed primarily to move the platform from raised to lowered position and vice verse. Since the movement is carried out slowly, the dimensioning load case is treated as static. It is also very important to stress that the loads used here assumes that each CCS station is loaded equally. This is a step from reality and the required forces should thus be treated as minimum requirements.

Figure 53. Dimensioning forces acting on the platform control system

The loads acting on one lever arm are shown in Figure 53. The required hydraulic force, Fh can be calculated through a moment equivalence calculation. The force Fp includes the mass of platform and cargo and the force Fa includes the mass of lever arm acting in the approximate centre of gravity of the part. The result of the calculations is that the force Fh should be at least 2250 kN which is equal to a moment Mb around the hull tube beam of 653 kNm.

The locking device main task is to lock the hull tube beam when the FLCU is under transportation. The required force was obtained from the previous global FEM calculation as a reaction moment at boundary condition 7 in Figure 42. It is also defined in Figure 52 as Mb and must be at least 1185 kNm.

12.4.1. Hydraulic cylinders design The design of the hydraulic system was done with calculations based on guidelines provided from the hydraulic company Hydraulsyd [24]. In data for the calculations was the required force, time to fulfill an elevation, cylinder diameter, engine range per minute and some safety factors. All in data can be seen in Table 75.

Table 75. Input for dimensioning of the hydraulic system Required force per cylinder 2250 kN (bow), 1125 kN (aft) Time to fulfill an elevation 60 s Rpm diesel engine 1800 rpm Mechanic efficiency 0,9 Volumetric efficiency 0,9 Efficiency for hydraulic pump 0,8 Safety factor against pressure loose 1,15

Primary purpose of the calculations was to get a rough estimation of hydraulic cylinder size and thus the weight of the system. The results of the calculations were matched with available product specification from Hydraulsyd and the main data of the final system can be seen in Table 76.

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Table 76. Main data of Hydraulic system

Cylinder aft Cylinder bow

Model, Hydraul syd 25 CA Model, Hydraul syd 25 CA

Cylinder diam. [mm] 200 Cylinder diam. [mm] 280

weight 0 mm length of stroke [kg] 122 weight 0 mm length of stroke [kg] 493

weight /100 mm length of stroke [kg] 14 weight /100 mm length of stroke [kg] 44

length of stroke [m] 0.6 length of stroke [m] 0.6

Total weight (one cylinder) [kg] 206 Total weight (one cylinder) [kg] 757 A pump suitable to power the cylinders from the engine gear box weights around 50 kg. The cylinders used for the aft station is in a medium range whereas the bow station cylinders are in the higher range of available products from Hydraulsyd. It is once again important to stress that the results should be treated as minimum requirements. If for example the design load would be doubled it would be a challenge to combine a larger and heavier system with the lack of space at the bow station. This does once again show how important realistic load cases are for the design of a craft such as the FLCU. The next step in the design would hence be to combine the necessary loads for platform elevation with the dynamic wave loads.

12.4.2. Braking system design The discs used as lever arms for the hydraulic cylinders will have cutouts in which a locking device could be pushed into. The principal function can be seen in Figure 54 [25].

Figure 54. Side view of Dellner brakes locking device [25].

The locking device is from Dellner-brakes which is a Swedish company specialized in designing brakes for demanding marine conditions. There are different models available. For this application, the model LM95 is reasonable choice since it can deliver 1000 kN locking force and the locking part is 95 mm wide. According to sales manager Peter Mikaelsson [26], a good rule of thumb is that the brake disc should be around 5 mm wider than the locking part and that one can expect an approximate breaking moment of the radius of the disc times the breaking force. This means that one unit could deliver approximately 500 kNm breaking force with a disc radius of 0,5 m.

Both stations have two locking devices that give them a locking force of 1000 kNm. It is obvious that this is too small to lock the turning moment, which is 1185 kNm. This is due to that the final dimensioning load, in a late stage of the design process was found higher than the first assumptions. Probably, the locking device could be used together with the lifting hydraulics that then gives another extra 653 kNm breaking moment and thus provide enough locking capacity. It is however desirable to have a locking system independent of the lifting system. One thing, which was discussed but not implemented, was to

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include disc brakes as well. This would increase the locking capacity and also make the system less vulnerable to failure of hydraulic tubes since it could lock the platform if one of the cylinders fails.

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13. REFERENCES 1. Royal Navy website about the Albion class, http://www.royalnavy.mod.uk/operations-and-

support/surface-fleet/assault-ships/albion-class/ , Available 2009-09-21 2. German company Schottel information about propulsion,

http://www.schottel.de/uploads/PDF1176992341.pdf, available 2009-09-21 3. Information about the French navy, http://www.netmarine.net/f/bat/sabre/caracter.htm,

available in 2009-09-21(in French only) 4. Combatant Craft of America information on U.S Landing Craft Utilities,

http://www.warboats.org/ , available 2009-09-21 5. Global Security information on the Zubr LCAC,

http://www.globalsecurity.org/military/world/russia/1232_2-specs.htm, available 2009-09-21 6. Royal Australian Navy information on Landing Craft Utilities,

http://www.navy.gov.au/HMAS_Balikpapan, available 2009-09-21 7. Försvarsmakten information on battle tank 122, http://www.mil.se/sv/Materiel-och-

teknik/Fordon/Stridsvagn-122/, available 2009-09-21 8. Försvarsmakten information on battle vehicle 9040C, http://www.mil.se/sv/Materiel-och-

teknik/Fordon/Stridsfordon-9040C/, available 2009-09-21 9. Solid Edge software 10. Prasanta K. Sahoo, Marcos Salas, Adam Schwetz, Practical evaluation of resistance of high-speed

catamaran hull form – Part I, 2007 11. M. Insel & A.F. Molland , An investigation into the resistance components of high-speed

displacement catamarans, 1991 12. A.F. Molland, J.F. Wellicome & P.R. Couser, Resistance Experiments on a Systematic Series of

High-Speed Displacement Catamaran Forms, Transaction of the Royal Institution of Naval Architects, Vol. 138, pp 55-71.

13. A.F. Molland, P.R Couser, Dr J.F. Wellicome, An improved method for the theoretical prediction of the wave resistance of transom-stern hulls using a slender body approach. Department of Ship Science, University of Southampton, U.K.

14. A.F. Molland, T. Karayanis, D.J Taunto and Y Sarac-Williams, Preliminary estimates of dimensions, powering, and seakeeping characteristics of fast ferries, Proceedings of the 8th International Maritime Design Conference, 5-8 may 2003, Athens, Greece

15. Toray Industries, http://www.torayca.com/index2.html, available 2009-12-14. 16. Green Marine, http://www.marinecomposites.com/, available 2009-12-14. 17. Introduction to the Mechanics of Composite Materials, course material SD2414 KTH. 18. Monica Norrby, Approximativ materialdata för material som kan utgöra en sandwichpanel. KTH

2008 19. A. Rosén, Guide to DNV HS, LC & NSC, KTH 2009 20. M. Insel, An Investigation of the resistance components of high speed displacing catamarans.

University of Southhampton 1990. 21. Mr P.R. Couser, Dr J.F. Wellicome and Dr A.F. Molland. An improved method for the

theoretical prediction of the wave resistance of transom-stern hulls using a slender body approach. Department of ship science, University of Southampton.

22. Technical Data Sheet 535 SP 0031 for MTU 12V 2000 M93, MTU Diesels 23. Fact sheet Kamewa Water-Jets, http://www.rolls-royce.com/Images/3026300_a_wj_fs_tcm92-

8767.pdf, available 2009-12-15 24. Hydraulsyd downloadable product overview,

http://www.pmchytech.com/Archive/Documents/Swedish/Produktoversikt.pdf , available 2009-12-14

25. Dellner-brakes product information, http://www.dellner-brakes.se/default.aspx?page=produkter_art&art=3 available 2009-12-14

26. Telephone discussion with sales manager Peter Mikaelsson at Dellner-brakes 27. V. Dubrovsky & A. Lyakhovitsky, Multihull Ships, Backbone Publishing company, 2001 28. Fossen, Thor I, Guidance and control of ocean vehicles, Chichester, Wiley corporation, 1994 29. Marinelog article about Brittish FLC PACSCAT,

http://www.marinelog.com/DOCS/NEWSMMIX/2009oct00121.html , available 2010-01-21

87

30. Youtube animation of PACSCAT scenario, http://www.youtube.com/watch?v=ZaPvUTuIMAQ available 2010-01-21

31. UN peacekeeping operations January 2010, http://www.un.org/en/peacekeeping/currentops.shtml, available 2010-01-25

32. Svein Erling Heggelund, Torgeir Moan, Stig oma, Global Structural Analysis of Large Catamarans, conference proceedings FAST 99.

33. DNV rules for classification of High Speed Craft & Naval Surface Craft, January 2006 34. M. Razola, Optimization of sandwich structures (unpublished), KTH 2009 35. P. Couser, Seakeeping analysis for preliminary design,

http://www.formsys.com/maxsurf/msdocumentation/technical-papers, available 2010-02-10 36. A.F. Molland, The Maritime Engineering Reference Book, ISBN: 978-0-7506-8987-8 37. Odd M. Faltinsen, Hydrodynamics of High-Speed Marine Vehicles, ISBN: 978-0-521-84568-7 38. Yifeng Huang, Nonlinear Ship Motions by a Rankine Panel Method, MIT 1997 39. K. Garme, Marin hydromekanik (Föreläsningsanteckningar), KTH, September 2008 40. Salvesen, Tuck & Faltinsen, Ship Motions and Sea Loads, SNAME 1970 41. D.S Holloway, A High Froude Number Time Domain Strip Theory Applied to the Seakeeping of

Semi-SWATH’s, University of Tasmania, November 1998 42. Yheoretical Manual of Strip Theory Program “Seaway for Windows”, J.M.J. Journée & L.K.M.

Adegeest, September 2003. 43. R. Zhao & O. Faltinsen, Numerical predictions of ship motions at high forward speed, Phil.

Trans. R. Soc. Lond. A (1991) 344, 241-252 44. A. Rosén, Sjöegenskaper, KTH 2008 45. Maxsurf Seakeeper Manual version 11.1, Formation Design Systems Pty Ltd 1998. 46. NORDFORSK, Assessment of ship performance in a seaway, ISBN: 87-982637-1-4 47. Abaqus/CAE User’s manual, version 6.7, DS Simulia Group 48. 2000 HSC Code, IMO, London 2001, ISBN 92-801-5122-3 49. ITTC – Recommended Procedures and Guidelines, Full Scale Measurements Speed and Power

Trials, Analysis of Speed/Power Trial Data, 7.5 2004

1. APPENDIX, SEMI-EMPIRICAL METHOD FOR ESTIMATION OF RESISTANCE The method for determining the viscous and wave-making resistance of a catamaran according to [10] is here described. The total resistance coefficient may be written as

CT = (1+ !interk)CF + CWcat (1),

where the viscous form factor corrected for interference can be written as

(1+ !interk) = 3.03(L / V 1/3)"0.4 (2).

The frictional resistance coefficient CF is expressed according to the ITTC 57 line as

CF =

0.075(log(R E ) ! 2)2

(3),

where RE is the Reynolds number calculated according to

RE =

vs L!

(4).

L is the waterline length, vs the speed expressed in m/s and ν the kinematic viscosity of water. The wave-making resistance coefficient is written as

CWcat = eC1 (L / b)C2 (b / T )C3 CBC 4 (L / V 1/3)C5 iE

C6!C7 (s / L)C8 (5)

where iE is the half angle of entrance and β the deadrise angle at midship. This coefficient is taking the interference between the demihulls into consideration. The coefficients C1-C8 are given in Table 77.

Table 77. Regression coefficients. Fn C1 C2 C3 C4 C5 C6 C7 C8

0.001 0.480 0.303 0.000 0.000 -4.124 -0.039 -0.199 0.037

0.002 0.406 0.000 0.000 0.656 -3.282 0.171 0.087 -0.089 0.003 0.350 0.000 -0.471 -0.963 -3.523 0.000 -0.688 -0.035 0.003 0.388 0.263 0.000 -0.600 -4.262 0.000 -0.337 -0.368 0.004 0.603 -0.110 0.000 0.000 -3.625 -0.061 -0.095 -0.314 0.005 1.055 0.000 0.082 -0.025 -3.617 0.000 -0.064 -0.181 0.006 0.419 0.154 0.185 0.000 -3.869 0.000 0.000 -0.069 0.006 -0.466 0.049 0.113 0.000 -3.322 0.089 0.000 -0.006 1.000 -1.221 0.000 0.081 0.000 -3.046 0.183 0.000 0.075

The validity range of the regression is displayed in Table 78.

Table 78. Range of parameters for the Sahoo, Salas & Schwetz method (2004).

Now using the total resistance coefficient the total resistance may be calculated according to

RT = 0.5!SWcatvs2CT (6),

where SWcat is the wetted surface of both hulls and ρ the density of water.

Geometric parameters L/V1/3 L/b b/T CB Fn

Range of application 8.22-11.2 10-15 1.5-2.5 0.4-0.5 0.2-1.0

2

2. APPENDIX, WEIGHT ESTIMATION MODEL This is a summary of the method developed by Molland [14]. The total mass of the ship can be calculated as

MT = M H + MO + M M + M DW , (1)

where M H is the mass of the hull in tonnes, MO is the mass of the outfit, M M is the mass of the engine

installation and M DW is the deadweight. The mass of the hull is calculated as

M H = 0.0064EC1.7 , EC ! 3025( )

M H = 0.39EC0.9 , EC > 3025( ) , (2)

where EC is the numeral equipment, which in term for a multi hull can be calculated as

EC = 2L(b + T ) + 0.85L(D ! T ) +1.6L(B ! 2b) . (3)

L is here the length over all, B is the beam measured from the most outer part of one hull to another, b is the beam for the single demihull. D is the vessels height including superstructure, which can be estimated as

D = 4 + 0.44B . (4) The outfit mass is at an early stage very much approximate, Molland however propose the following formula as a first estimation

MO = 0.03 ! L ! B . (5)

For the machinery the weight can be estimated as

M M = M D + MGB + MWJ + M Rm . (6)

M D is the mass of the engine and can be calculated approximate as

M D = 6.82

Pn

!"#

$%&

0.85

, (7)

where P is the power in kW and n is the range per minute.

MGB is the mass of gearboxes and is calculated as

MGB = 0.00348P0.75 . (8)

MWJ is the mass of the water jet and is calculated as

MWJ = 0.00018P1.18 . (9)

3

M Rm is the mass for the remaining machinery and calculated as

M Rm = 0.55( M D + MGB + MWJ ) (10)

The deadweight is the mass of the cargo, fuel, crew etc. Since the model was developed for passenger ferries it is not fully applicable on a LCU. In the deadweight the load of the cargo is for the case of a LCU dominating together with the fuel. The cargo load is known from the specification of requirements and the mass of the fuel is taken with an approximation based on the fuel consumption and the range.

4

3. APPENDIX, MASS DISTRIBUTION The following section presents detailed account of the mass distribution and radius of gyration for the two material concepts.

3.1. CARBON COMPOSITE VERSION Table 79-82 to relates to the carbon composite version and presents the mass distribution in the transportation mode and beaching mode at full load.

Table 79. Mass distribution of FRP concept in the fully loaded transportation mode.

Item Quanti t y Wei gh t [kg] LCG [m] f rom A.P. VCG [m] f rom B.L. Hull structure +20% 1 7312.8 9.2 1.45 Platform beam bow 1 1614 12.3 4.15 Platform beam aft 1 1074 3.85 4.15 Hull beam fwd 2 975 15.3 3.4 Hull beam aft 2 782 6.9 3.4 Lever arm beam fwd 2 1225 13.3 3.4 Lever arm beam aft 2 961 4.8 3.4 Engine, gearbox, coupling 2 3985 5.6 0.8 Platform 1 13000 8.97 4.1 Cargo 1 62000 7.90 5.9 Hydral fwd 2 757 14.5 3.2 Hydral aft 4 206 5.9 3.2 Water-jet 2 2230 0 0.5 Fuel 1 1450 8.3 0.25 Brakes aft 4 150 7.5 3.4 Brakes fwd 4 150 16.2 3.4 Addition for electrics etc 15% 1 5380.8 8.84 2.81 Total weight 115686 8.00 4.35

Table 80. Pitch radius of gyration about the transverse Y-axis at full load. Mass moment of inertia about CG [kgm2] 1754293 Pitch radius of gyration [m] 3.89 In percent of Lwl [%] 20.87

5

Table 81. Mass distribution of FRP craft in fully loaded beaching mode.

Item Quanti t y Wei gh t [kg] LCG [m] f rom A.P.

VCG [m] f rom B.L.

Hull structure +20% 1 7312.8 9.2 1.45 Platform beam bow 1 1614 12.3 1.05 Platform beam aft 1 1074 3.85 1.05 Hull beam fwd 2 975 15.3 3.4 Hull beam aft 2 782 6.9 3.4 Lever arm beam fwd 2 1225 13.3 1.85 Lever arm beam aft 2 961 4.8 1.85 Engine, gearbox, coupling 2 3985 5.6 0.8 Platform 1 13000 8.97 1 Cargo 1 62000 7.9 2.8 Hydral fwd 2 757 14.5 3.2 Hydral aft 4 206 5.9 3.2 Water-jet 2 2230 0 0.5 Fuel 1 1450 8.3 0.25 Ballast 2 2500 0.5 2.5 Brakes aft 4 150 7.5 3.4 Brakes fwd 4 150 16.2 3.4 Addition for electrics etc. 15 % 1 5380.8 8.84 2.81 Total weight 120686 9.74 2.22

Table 83–85 presents the mass distribution for the beaching mode and transportation mode at light condition.

Table 82. Mass distribution in the unloaded transportation mode.

Item Quanti t y Wei gh t [kg] LCG [m] f rom A.P.

VCG [m] f rom B.L.

Hull structure +20% 1 7312.8 9.2 1.45 Platform beam bow 1 1614 12.3 4.15 Platform beam aft 1 1074 3.85 4.15 Hull beam fwd 2 975 15.3 3.4 Hull beam aft 2 782 6.9 3.4 Lever arm beam fwd 2 1225 13.3 3.4 Lever arm beam aft 2 961 4.8 3.4 Engine, gearbox, coupling 2 3985 5.6 0.8 Platform 1 13000 8.97 4.1 Cargo 1 0 7.90 5.9 Hydral fwd 2 757 14.5 3.2 Hydral aft 4 206 5.9 3.2 Water-jet 2 2230 0 0.5 Fuel 1 1450 8.3 0.25 Brakes aft 4 150 7.5 3.4 Brakes fwd 4 150 16.2 3.4 Addition for electrics etc 15% 1 5380.8 8.84 2.81 Total weight 53686 8.11 2.56

6

Table 83. Moments of inertia in the unloaded transportation mode.

Mass moment if inertia about CG [kgm2] 1399495 Pitch radius of gyration [m] 5.11 In percent of Lwl [%] 27.36

Table 84. Mass distribution in unloaded beaching mode.

Item Quanti t y Wei gh t [kg] LCG [m] f rom A.P.

VCG [m] f rom B.L.

Hull structure +20% 1 7313 9.2 1.45 Platform beam bow 1 1614 12.3 1.05 Platform beam aft 1 1074 3.85 1.05 Hull beam fwd 2 975 15.3 3.4 Hull beam aft 2 782 6.9 3.4 Lever arm beam fwd 2 1225 13.3 1.85 Lever arm beam aft 2 961 4.8 1.85 Engine, gearbox, coupling 2 3985 5.6 0.8 Platform 1 13000 8.97 1 Cargo 1 0 7.9 2.8 Hydral fwd 2 757 14.5 3.2 Hydral aft 4 206 5.9 3.2 Water-jet 2 2230 0 0.5 Fuel 1 1450 8.3 0.25 Ballast 2 2500 0.5 2.5 Brakes aft 4 150 7.5 3.4 Brakes fwd 4 150 16.2 3.4 Addition for electrics etc. 15 % 1 5380.8 8.84 2.81 Total weight 58686 8.40 1.61

7

3.2. ALUMINUM CONCEPT Table 85-88 presents the mass distribution for the aluminum craft in at full load in both the transportation and beaching mode.

Table 85. Mass distribution for aluminium structure in fully loaded transportation mode.

Item Quanti t y Wei gh t [kg] LCG [m] f rom A.P. VCG [m] f rom B.L. Hull structure +20% 1 13727.0 9.2 1.45 Platform beam bow 1 1614 12.3 4.15 Platform beam aft 1 1074 3.85 4.15 Hull beam fwd 2 975 15.3 3.4 Hull beam aft 2 782 6.9 3.4 Lever arm beam fwd 2 1225 13.3 3.4 Lever arm beam aft 2 961 4.8 3.4 Engine, gearbox, coupling 2 3985 5.6 0.8 Platform 1 13000 8.97 4.1 Cargo 1 62000 7.90 5.9 Hydral fwd 2 757 14.5 3.2 Hydral aft 4 206 5.9 3.2 Water-jet 2 2230 0 0.5 Fuel 1 1450 8.3 0.25 Brakes aft 4 150 7.5 3.4 Brakes fwd 4 150 16.2 3.4 Addition for electrics etc 15% 1 6342.9 8.84 2.81 Total weight 123062 8.06 4.19

Table 86. Moment of inertia and pitch radius of gyration for the aluminium craft in fully loaded transportation mode. Mass moment of inertia about CG [kgm2] 1798335 Pitch radius of gyration [m] 3.82 In percent of Lwl [%] 20.49

8

Table 87. Mass distribution in the fully loaded beaching mode.

Item Quanti t y Wei gh t [kg] LCG [m] f rom A.P.

VCG [m] f rom B.L.

Hull structure +20% 1 13727 9.158080944 1.45 Platform beam bow 1 1614 12.3 1.05 Platform beam aft 1 1074 3.85 1.05 Hull beam fwd 2 975 15.3 3.4 Hull beam aft 2 782 6.9 3.4 Lever arm beam fwd 2 1225 13.3 1.85 Lever arm beam aft 2 961 4.8 1.85 Engine, gearbox, coupling 2 3985 5.6 0.8 Platform 1 13000 8.97 1 Cargo 1 62000 7.9 2.8 Hydral fwd 2 757 14.5 3.2 Hydral aft 4 206 5.9 3.2 Water-jet 2 2230 0 0.5 Fuel 1 1450 8.3 0.25 Ballast 2 2500 0.5 2.5 Brakes aft 4 150 7.5 3.4 Brakes fwd 4 150 16.2 3.4 Addition for electrics etc. 15 % 1 6342.9 8.84 2.81 Total weight 128062 9.70 2.19

Table 88-91 presents the mass distribution for the light condition in both the transportation and beaching mode.

Table 88. Mass distribution in the unloaded transportation mode.

Item Quanti t y Wei gh t [kg] LCG [m] f rom A.P. VCG [m] f rom B.L. Hull structure +20% 1 13727.0 9.2 1.45 Platform beam bow 1 1614 12.3 4.15 Platform beam aft 1 1074 3.85 4.15 Hull beam fwd 2 975 15.3 3.4 Hull beam aft 2 782 6.9 3.4 Lever arm beam fwd 2 1225 13.3 3.4 Lever arm beam aft 2 961 4.8 3.4 Engine, gearbox, coupling 2 3985 5.6 0.8 Platform 1 13000 8.97 4.1 Cargo 1 0 7.90 5.9 Hydral fwd 2 757 14.5 3.2 Hydral aft 4 206 5.9 3.2 Water-jet 2 2230 0 0.5 Fuel 1 1450 8.3 0.25 Brakes aft 4 150 7.5 3.4 Brakes fwd 4 150 16.2 3.4 Addition for electrics etc 15% 1 6342.9 8.84 2.81 Total weight 61062 8.23 2.45

9

Table 89. Moments of inertia in the unloaded transportation mode.

Mass moment of inertia about CG [kgm2] 1454175 Pitch radius of gyration [m] 4.88 In percent of Lwl [%] 26.15

Table 90. Mass distribution in the unloaded beaching mode.

Item Quanti t y Wei gh t [kg] LCG [m] f rom A.P.

VCG [m] f rom B.L.

Hull structure +20% 1 13727 9.158080944 1.45 Platform beam bow 1 1614 12.3 1.05 Platform beam aft 1 1074 3.85 1.05 Hull beam fwd 2 975 15.3 3.4 Hull beam aft 2 782 6.9 3.4 Lever arm beam fwd 2 1225 13.3 1.85 Lever arm beam aft 2 961 4.8 1.85 Engine, gearbox, coupling 2 3985 5.6 0.8 Platform 1 13000 8.97 1 Cargo 1 0 7.9 2.8 Hydral fwd 2 757 14.5 3.2 Hydral aft 4 206 5.9 3.2 Water-jet 2 2230 0 0.5 Fuel 1 1450 8.3 0.25 Ballast 2 2500 0.5 2.5 Brakes aft 4 150 7.5 3.4 Brakes fwd 4 150 16.2 3.4 Addition for electrics etc. 15 % 1 6342.9 8.84 2.81 Total weight 66061.9 8.48 1.61

10

4. APPENDIX, LARGE ANGLE STABILITY CALCULATIONS

4.1.1. Loaded docking mode The results of the stability evaluation are shown in Table 91 and Figure 55.

Table 91. Stability criteria, loaded condition, docking mode

HSC 2000 Annex 8 Monohull. Intact Value Unit Actual Status

1.1 Weather criterion from IMO A.749(18) Angle of steady heel shall not be greater than 10 [deg] 8.7 Pass 1.2 Area 0 to 30 or GZmax shall not be less than 3.151 [m.deg] 4.955 Pass 1.3 Area 30 to 40 shall not be less than 1.719 [m.deg] 3.275 Pass 1.4 Max GZ at 30 or greater shall not be less than 0.2 [m] 0.393 Pass 1.5 Angle of maximum GZ shall not be less than 15 [deg] 31.2 Pass 1.6 Initial GMt shall not be less than 0.15 [m] 0.366 Pass

Figure 55. GZ-curve loaded condition docking mode,

Note that the y-axis scale in the above figure is different from the following GZ-curves.

11

4.1.2. Unloaded docking mode The results of the calculations and criteria evaluations are shown in Table 92 and Figure 56. Note that this condition applies to IMO HSC 2000 annex 7 compared to the loaded condition in docking mode.

Table 92. Stability criteria, unloaded condition, docking mode

HSC 2000 Annex 7 Multihull. Intact Value Units Actual Status

1.1 Area 0 to 30 shall be greater than 4.685 [m.deg] 20.322 Pass 1.2 Angle of max. GZ shall not be less than 10 [deg] 20.2 Pass 1.3 Weather criterion from IMO A.749(18) Angle of steady heel shall not be greater than 10 0.8 Pass [deg] 1.5 Area between GZ and HTL

Criteria: Area between GZ and heeling arms shall not be less than Hpc + Hw 1.604 [m.deg] 11.679 Pass Ht + Hw 1.604 [m.deg] 11.679 Pass

The abbreviations Hpc and Ht in the above table mean height of lever arm due to passenger crowding and due to high speed turning respectively. These are in this case not treated further.

Figure 56. GZ-Curve unloaded condition docking mode

12

4.1.3. Loaded transportation mode

Table 93. criteria, loaded condition, transportation mode

HSC 2000 Annex 7 Mul t i hul l . Intac t Value Uni ts Actual Sta tus

1.1 Area 0 to 30 Pass shall be greater than 4.536 [m.deg] 35.022 Pass 1.2 Angle of max. GZ Pass shall not be less than 10 [deg] 20.8 Pass 1.3 Weather criterion from IMO A.749(18) Pass Criteria: Pass Angle of steady heel shall not be greater than 10 [deg] 0.4 Pass 1.5 Area between GZ and HTL Pass Criteria: Area between GZ and heeling arms shall not be less than Pass Hpc + Hw 1.604 [m.deg] 18.373 Pass Ht + Hw 1.604 [m.deg] 18.373 Pass

The abbreviations Hpc and Ht in the above table mean Height of lever arm due to passenger crowding and due to high speed turning respectively. These are in this case not treated further.

Figure 57. GZ-Curve loaded condition transportation mode

13

4.1.4. Unloaded transportation mode

Table 94. criteria, unloaded condition, transportation mode

HSC 2000 Annex 7 Mul t i hul l . Intac t Value Uni ts Actual Sta tus

1.1 Area 0 to 30 Pass shall be greater than 8.516 [m.deg] 25.57 Pass 1.2 Angle of max. GZ Pass shall not be less than 10 [deg] 11.1 Pass 1.3 Weather criterion from IMO A.749(18) Pass Criteria: Pass Angle of steady heel shall not be greater than 10 [deg] 0.2 Pass 1.5 Area between GZ and HTL Pass Criteria: Area between GZ and heeling arms shall not be less than Pass Hpc + Hw 1.604 [m.deg] 39.666 Pass Ht + Hw 1.604 [m.deg] 39.666 Pass

The abbreviations Hpc and Ht in the above table mean Height of lever arm due to passenger crowding and due to high speed turning respectively. These are in this case not treated further.

Figure 58. GZ-Curve unloaded condition transportation mode