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The design process of foil-assisted catamarans (FAC) contains several interlinking design proc- esses. Such processes pertain to the various sub-components of the FAC, such as catamaran demi-hull forms, lift generating devices, propulsion machinery, propulsors, the various fluid transfer systems, crew accommodation and or cargo securing arrangements, amongst others. The processes are interlinked as outcome of one design process influences the other. For example, the hull-form design influences resistance at service speed and consequently influences the choice and geometry of the propulsor and propulsion machinery powering characteristics. This linking influence therefore forces the complete ship design process to be an iterative process. The various established design stages, i.e. conceptual, tender and production design phases, is a good indication of this iterative nature. The conceptual design process of FAC containerships fuelled by LH2 is described in this chapter, whilst the hydrogen fuelling of such ships has been discussed in the preceding chapter. The design processes required in the conceptual phase of FACs are discussed in this Chapter, such as the basic force and moment equilibriums, estimation of resistance and propulsion power requirements as well as estimation of lightship and deadweight. The subject of motion behaviour in an irregular seaway, such as found on potential target routes of FAC containerships, is also touched upon. Chapter 4.2 describes the results of this interlinking conceptual ship design process, i.e. the LH2 fuelled FAC containership.

Foil-assisted craft are part of a larger family of available “hybrid fluid-borne vehicles”69 _which combine powered and un-powered lift with static buoyancy lift to form a wide array of available hybrid ship designs, according to Meyer (1991). These ship designs can be classified using a sustention triangle, as is indicated in Figure 3.1. This triangle indicates the three forms of lift along its vertexes. The x-vertex indicates buoyancy lift whilst the y-vertex presents dynamic lift and the z-vertex powered lift. Powered lift is associated with lift generated through active ma- chinery, such as fans. A typical example of a 100% powered lift vehicle is an air-cushion vehicle. Un-powered lift is lift generated through devices attached to the hull or the hull itself, i.e. planing hull-forms and hydrofoil vessels. The sustention triangle was used in naval research in the USA during 1970s to identify various hybrid ship types for naval applications as discussed by Meyer. Examples of ship types identified from this study, such as the SWASH, HYSWAS, SWAACS and HYACS ship types have been described in Section 1.2.1. Interestingly, Meyer also includes a Large Hydrofoil Hybrid Ship (LAHHS) consisting of a single torpedo shape, providing 70% overall lift through static buoyancy, and several large hydrofoils, providing the remaining 30% lift through dynamic means. This hybrid ship type resembles the FAC containership concept in that

it provides combined buoyancy and dynamic lift; however, the FAC provides this buoyancy lift via two catamaran hulls. The work by Meyer clearly illustrates that the FAC concept fits into an existing family of hybrid marine vehicles and that a framework for identifying and positioning this ship type exists within the literature.

[HOVERCRAFT] [HYDROFOIL] x y z (0,0,10) (0,10,0) (10,0,0) x = 0 x = 2 x = 4 x = 6 x = 8 x = 10 y = 0 y = 2 y = 4 y = 6 y = 8 y = 10 z = 0 z = 2 z = 4 z = 6 z = 8 z = 1₀ [DISPLACEMENT SHIP]

INCREASING PASSIVE LIFT

IN C R E A S IN G B O U Y_A N C_Y IN CR EA SIN G P OW ER ED LIF T

Figure 3.1: Sustention triangle identifying different hybrid ship design with dynamic or static lift support [from Meyer (1991)]

3.1

Force and moment equilibriums

FACs operate in two distinct modes, the initial mode in which the vessel is at rest floating on the deeper draught (Tf) and the second mode operating on its design Froude displacement number

and reduced dynamic draught (Tdy). In both modes the FAC is in a force and moment equilib-

rium, albeit in the second mode this equilibrium can be considered a quasi-static equilibrium. Equations describing both equilibriums are presented in this section in addition to forces at play in dynamic conditions.

3.1.1

Static floating conditions

The static floating condition with draught Tf should generally be in a zero trim condition70, but

more importantly, the buoyancy of the catamaran demi-hulls should be able to carry the ship weight (W). This static floating condition is indicated in Equation 41 describing that combined buoyancy mass of two demi-hulls, attached foils and entrained water of waterjets should equal ship weight. As this equation describes the zero speed situation there is thus no dynamic lift component whilst the trim of the ship is evaluated through Equation 42. The hydrostatic charac- teristics of the ship, utilized in Eq. 42, correspond to two demi-hulls and are determined at the floating draught Tf.

W=2A 5b _DH +5_F @5_{W J}cAρ_sw= ∆@ A_T f (41)

t

=

∆

LCB@LCG

MTC

As noted previously, the trim in this floating condition should approximate zero and subsequently the longitudinal centre of buoyancy (LCB) should match the LCG position of the vessel. An accurate estimate in this early design process of both W and LCG values aids in the accurate development of the hullform design. This hullform design provides volumes of the demi-hulls and the position of LCB and various design iterations may be required to obtain a zero trim floating condition.

3.1.2

Quasi-static conditions

A quasi-static condition describes the forces and moments acting on a body isolated on a single time unit t. For such a condition to exist all forces and moments acting on the body need to be in equilibrium. In case of a FAC design application this equilibrium refers to the force acting along the z-axis and various moments about a fixed point. Assuming that the length axis corresponds to the x-axis, the beam axis corresponds to the y-axis then quasi-static force equilibriums also exist along these axes. It is obvious that the propulsion drive force is in equilibrium with the complete resistance of the ship along its x-axis and this equilibrium is not considered here. Similarly, no significant forces are acting along the y-axis of an FAC ship and hence this quasi-static condition is also not considered. The quasi-static condition along the z-axis, which is speed dependent, has to be considered to evaluate the foil lift, buoyancy forces of the demi-hulls and the weight of the ship. This quasi-static condition is captured in Equation 43, which simply states that the summa- tion of all foil and displacement buoyancy lift forces acting in the positive direction along the z- axis should equal the weight of the vessel, acting along the negative direction of the z-axis. The quasi-static equilibrium occurs at the dynamic draught Tdy and subsequently all hydrostatic

characteristics of the demi-hulls are associated with this draught. This applies in particular to the displacement figure indicated in Equation 43, while the ships weight remains unchanged.

F_V = X i=1 i F_F i h j i k+g∆ H L J I M K T_{d y} @g W=0 ₍₄₃₎

Foil lift of individual foils are determined here using a method described by Oossanen and Van Manen (1988). This method is utilized for its ease of use in the initial design stages instead of the more elaborate computational methods, see Andrewartha and Doctors (2001). Equation 44 allows determination of the lift curve coefficient of a hydrofoil located close to a free-surface based on foil characteristics, such as aspect ratio (AR), sweep angle (Λ) and depth correction factor P indicated separately in Equation 45. This depth correction factor utilizes the local foil

submergence (i) to its chord ratio (c) as input. Additional coefficients are required in Equation 44, such as σ and ζ representing Munk’s interference and foil planform correction factors respec- tively. Values for Munk’s interference factor may be obtained from the classic aerodynamic textbook by Von Mises (1945). The three-dimensional lift coefficient at the correct angle of attack of the foil is then determined using Equation 46. Individual foil lift can subsequently be deter- mined utilizing local flow conditions with this lift coefficient.

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