Trans RINA, Vol 152, Part A4, Intl J Maritime Eng, Oct-Dec 2010 in the cable connection. If the relative motions of the


ships become too large the hose may dislodge or the cable break, a serious safety issue.


Traditionally Commanding Officers (COs) have relied on their own knowledge and experience to determine the suitability of conditions to undertake RAS. Operator guidance is therefore required for use by COs of the ships in the selection of suitable conditions for replenishment


operations. Several key factors may


influence the overall successful outcome of this type of operation; these include vessel loading condition, wave height and period, ships heading and speed as well as the longitudinal and lateral separation of the vessels.


The hydrodynamic response of two bodies in close proximity is a complex hydrodynamic interaction problem; so it is not surprising that only limited research has been conducted into this field. Much of the work has focussed on


the interactions between two moored


vessels, a situation often found in the offshore oil and gas industry. Many of the developments in this field are extensions of


the seminal work of Ohkusu [1, 2, 3].


Ohkusu [1] commenced by developing a method, based on Ursell’s [4] classical solution for a single heaving cyclinder, to the case of two cylinders in a catamaran configuration. Using a combination of


the multipole


method and strip theory, Ohkusu [3] calculated the response of ship-like bodies at zero speed in beam seas. Kodan [5] subsequently extended Ohkusu’s method to study the motions of two bodies in close proximity in oblique seas.


experimental data was used to validate a theoretical ship motion prediction method, using a 3-D zero-speed Green function with a forward speed correction in the frequency domain [16].


One perceived shortcoming of the work of Andrewartha et al. [15] was the use of a containership model, a vessel type not used for RAS supply operations by the Royal Australian Navy (RAN). This has been rectified in the current work, where a model of a typical replenishment tanker, as utilised by the RAN, is tested in simulated RAS operations with a representative frigate. Full scale RAS manoeuvres conducted by the RAN have drawn attention to the possibility of a significant influence of the displacement of the supply vessel on the motions of the receiving ship.


This work therefore extends the


previous study by testing the supply vessel in two realistic loading configurations.


Similarly Buchner et al. [6] extended the


numerical model of van Oortmerssen [7] for the time domain simulation of a side-by-side offloading operation and compared the results favourably with model experiments.


Fang and Kim [8], Fang [9] and Chen and Fang [10, 11, 12] extended the work of Kodan [5] by developing a three-dimensional panel method including forward speed and


dimensional


hydrodynamic interaction effects. panel


codes were also Three- developed


independently by McTaggart et al. [13] and Wang et al. [14]. Due to the complexity of the set-up there has been very limited experimental testing to obtain data to validate theoretical predictions. Kodan [5] conducted model


tests at zero forward speed only;


This paper reports on both numerical and experimental analyses. Model tests were conducted where the motions of both vessels were recorded and the influence of various parameters, including longitudinal separation and supply ship displacement, on the ships’ motions studied. These motions were then used to estimate extreme roll motion of the frigate and the relative motions between the ships in a series of realistic operating conditions. The data obtained from the experimental study has also been used to further validate a theoretical prediction method. Once fully validated the three-dimensional panel method seakeeping code can be used as part of the development of operator guidance tools for vessels operating in close proximity to each other.


2. THEORETICAL PREDICTIONS


The theoretical predictions were made using a potential flow, three-dimensional panel method seakeeping code, FD-Waveload [16]. It is based on the zero-speed Green function with a forward speed correction (a modification of the hull boundary condition only) in the frequency domain. The motions of a single vessel in waves are governed by the equation of motion given in Equation 1 [17]:


[m A  + Bη η η + C + whilst


McTaggart et al. [13] conducted semi-captive model tests with the two models constrained in surge, sway and yaw for forward speeds of up to 12 knots in head seas.


The Defence Science & Technology Organisation


(DSTO) and the Australian Maritime College (AMC) have established a collaborative research program to study the hydrodynamic interactions between vessels whilst travelling in close proximity. Andrewartha et al. [15] conducted a series of simulated RAS model tests using an S-175 container ship and frigate to investigate a series


of parameters, including transverse longitudinal separation, on the ships’ motions. The


where [m] is the ship inertial matrix, [A] is the added mass matrix,


{ }η  is the velocity vector and {} [B] is the damping matrix, [C] are


hydrostatic stiffness terms and {F} is the wave exciting force vector which includes terms due to both incident and diffracted waves, { }η


 is the acceleration vector, ηis the displacement


and


vector. The damping matrix includes terms due to wave radiation, lift forces, and viscous forces; the viscous roll damping consists of contributions from bilge keels, eddy- making resistance of the hull, hull viscous effect of other appendages.


friction and the ]{ } [ ]{ } []{} { }F = (1)


A-182


©2010: The Royal Institution of Naval Architects


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