Trans RINA, Vol 152, Part A4, Intl J Maritime Eng, Oct-Dec 2010
Equation 1 is solved, for six degrees of freedom using six simultaneous
amplitude in order to evaluate the nonlinear roll damping forces. Therefore a final solution is
equations, by first estimating the roll obtained after
iterating until, for a given set of conditions, the roll amplitude converges.
Twelve coupled equations of motions are solved to determine the motions of two ships in waves, for the full 6 degrees of freedom of each ship. This ensures that the presence of both ships simultaneously within the wave field is represented.
The matrices and vectors are divided into terms
dependent on ship a and ship b, with corresponding superscripts added to terms. For example, the added mass and damping sub-matrices [Aab] and [Bab] represent the forces on ship a due to the motions of ship b. The hydrodynamic components A, B and F are then computed by solving a model consisting of two ships with 12 radiation modes.
Reproducing the approach used for single vessel
motions, the nonlinear roll damping forces for two ships are evaluated by solving Equation 2 iteratively until the roll motion amplitudes for both ships converge.
⎡m A ba
a
⎢ ⎣
+ A aa m A b + A ab bb ⎤
⎥ ⎦
⎩ ⎨ ⎧
η η
b a
⎭ ⎬ ⎫
+ ⎡C
⎢ ⎣
3.
+ ⎡B B
⎢ ⎣
a 0 C aa ba
0 ⎤ a
⎥ ⎦
⎩ ⎨ ⎧
η η
B ⎤ bb
ab B
b a
⎭ ⎬ ⎫
EXPERIMENTAL PROGRAM
The model tests had two main aims. Firstly, to measure the motions of two realistic vessels operating side-by- side and investigate the influence of various parameters, including wave period, longitudinal
separation and supply ship displacement. Secondly to obtain data to
Table 1: Ship and Model Particulars Frigate
LBP (m) Beam (m) Draft (m)
Roll Gyradius (m) Pitch Gyradius (m) Yaw Gyradius (m) LCG (m) from MS
VCG (m) CB
∆
1.578 108.9 2.455 0.198 13.7 0.064 4.45 0.074 5.17 0.364 25.5 0.364 25.5 -0.048
-3.345 Tanker (MO)
Model Full Scale Model Full Scale 171.9
Tanker (FL)
0.44 30.8 0.44 0.111 0.167 0.631 0.631
TCG (m) 0 0 0 0 0.086 6 0.113 0.481 0.481 0.704 10.324 kg 3630 t
©2010: The Royal Institution of Naval Architects 7.9 0.704
Model Full Scale 171.9 30.8
2.455
7.8 0.145 11.7 44.2 44.2
0.167 0.631 0.631
0.086 6.013 0.072 0
0.125 0.724
10.15 11.7 44.2 44.2
5.025 0
8.8 0.724 92.9 kg 32661 t 112.56 kg 39574 t A-183
⎥ ⎦
⎩ ⎨ ⎧
⎩ ⎨ = ⎧
η η
F F
b a
b a
⎭ ⎬ ⎫
⎭ ⎬ ⎫
(2) 3.2 EXPERIMENTAL SET UP
The experiments were conducted in the AMC’s towing tank. This facility is part of the Australian Maritime Hydrodynamics Research Centre (AMHRC) which is a collaborative research organisation established by the AMC, DSTO and the University of Tasmania. The towing tank is 100 m in length, 3.6 m wide with a water depth of up to 1.6 m. Waves are generated by a hydraulically operated wet backed, single flap paddle. A wide variety of wave forms can be generated by the paddle including regular and irregular wave systems.
Both models were towed using a two post system, utilising a ball joint forward, and a ball joint and slide aft. The ball joints were located on the roll axis of the model. This system allowed the models to move freely in heave, pitch and roll whilst being constrained in surge, sway and yaw. The heave, pitch and roll motions of the vessels were measured using a total of eight linear voltage displacement transducers (LVDTs). Four LVDTs were fitted to each model: fore and aft LVDTs were attached to the fore and aft posts, while the port and starboard transducers were attached via a string and pulley system to the model topsides.
further validate the three-dimensional panel method seakeeping theory.
3.1 MODEL DETAILS
The 1:70 scale ship models selected for the experimental programme were a frigate and a supply tanker typically used by the RAN. The supply tanker was tested at two displacements: minimum operating (MO) and full load (FL). Both the model and full scale particulars of the ships are shown in Table 1. The frigate model was fitted with bilge keels which were 205 mm in length and 17 mm in depth.
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