Development of an adaptive roll stabilization system for fishing vessels

Development of an Adaptive Roll Stabilisation System for Fishing Vessels

E.B. Jones, B.N. Webster, R.W. Birmingham, A.P. Roskilly,

School of Marine Science & Technology, University of Newcastle upon Tyne, UK.

Summary

Although significant advances have been made in fishing vessel safety, fishing still remains a highly dangerous profession. One of the fundamental means by which the operation of fishing vessels can be improved is through reduction in the roll motion. Excessive roll not only increases fuel consumption but also makes working on deck hazardous, affecting the efficiency and safety of the crew. This paper describes a research and development programme being undertaken in the School of Marine Science & Technology at Newcastle University, which is exploring the use of novel control strategies for roll stabilisation tanks. The results of two control studies are presented - a simulation study of intermittent flow control within a U-tube and an experimental study on continuous flow control within a free-surface tank. The ultimate aim of the project is to develop an anti-roll system that can adapt to changing load and sea conditions, requiring minimum intervention from the crew.

Introduction

Investigations into roll reduction by means of liquid filled tanks dates back to the 1880’s and the work of Froude and Watts on the use of rectangular free-surface tanks. This was followed in 1911 by the development of the U-tube tank by Frahm, which proved more amenable to mathematical analysis, although neither design has proven especially popular due to the emergence of activated fin stabilisers. Valuable design data on the use of free-surface tanks was provided by an experimental study undertaken by Van den Bosch and Vugts (1966) into the non-linear wave phenomena, some of which are illustrated in figure (1). The results provided a valuable guide to the dimensioning and location of the tanks, as well as the magnitude and phase of the stabilising moments produced, and led to renewed interest in the field. More recent studies, aided by improvements in computational resources, have focussed on improved mathematical modelling of the free-surface water motion. Research of note includes that by, Armenio (1996), van Daalen et al (2001), Kim (2002) and Souto (2002). In addition some studies (Spanos 2001) have looked at the effect of water on the deck of small vessels, a problem which is similar in nature to free surface stabilisation tanks. A recent review of developments in roll stabilisation of fishing vessels was given by Helmore (2001).

On fishing vessels the need for an effective roll stabilisation system is widely recognised, as the crew are involved in some of the most gruelling work regularly performed at sea. Excessive roll not only increases fuel consumption but also makes working on deck hazardous, effecting the efficiency and safety of the crew. The benefits of a stabilisation device are clear: an increase in personal safety, higher individual productivity, and extended operational windows for the vessel. An additional and unexpected economic benefit for a stabilised ship is the ability to shut the propulsion plant down and drift (when unable to work in severe weather), this providing considerable savings in fuel, (Martin, 1994).

For a roll damping system on a motor vessel to be effective it must be able to satisfy a number of criteria, including:

• Operational even at low or zero speeds

• Efficient for many loading and weather conditions • Inexpensive to install and maintain

• Trouble-free in normal use

The first factor is particularly important for vessels that are stationary for long periods of time, such as fishing vessels, research vessels, and some recreational craft, for example when moored at anchor. For such craft some existing methods of roll stabilisation will therefore not be appropriate because devices such as fin stabilisers, and to some extent bilge keels, experience a degradation in performance at low vessel speeds. Whilst they still provide hull damping the dynamic lift, which is the primary mode of anti-roll operation, is lost. However there has been some recent work investigating the use of rotating fins to produce an anti-roll moment for stationary motor yachts, (Dallinga, 2002). For fishing vessels there is the additional disadvantage of nets being fouled by bilge keels and fin stabilisers, and so the natural choice for a versatile and economical roll reduction system is an anti-roll tank.

Anti-Roll Tank Operation

Anti-roll tanks generally fall into two categories – Free surface and U-tube. Free surface tanks are simple rectangular containers with a central obstruction to impede the flow of water. U-tube tanks consist of two separate tanks connected by a water conduit at the base and an optional air conduit in the roof, with valves or baffles in the conduits to alter the fluid flow. The operation of an anti-roll tank is classified as either active, in which the water in the tanks is pumped from one side to the other, or passive, in which the water flows under the influence of gravity. Free-surface tanks are therefore, by definition, passive. The major roll stabilisation effect comes from the mass moment of the water and the creation of a significant anti-roll moment requires a large amplitude of motion coupled with a significant phase difference between the water and the ship roll. For an active U-tube system this is easily achieved but the pumping systems are bulky and expensive to run. Consequently passive anti-roll tanks are far more common on fishing vessels and the creation of an effective anti-roll moment is more complicated.

Ships experience the largest roll amplitude when the frequency of roll is close to the ship natural roll frequency, a condition known as resonance. Since both free-surface and U-tube tanks exhibit oscillatory behaviour, the most common design procedure for passive tanks is to choose the geometry so as to give a tank natural frequency close to that of the ship (Bosch, 1966(b)), (Bell,1966). For a free-surface tank the worst ship roll will then co-incide with the formation of a hydraulic jump, or bore, which creates a sizeable anti-roll moment. For a U-tube rolling at its natural frequency the water in the tank will oscillate with almost maximum amplitude and a phase lag of ninety degrees, again creating an effective anti-roll moment. Whilst this strategy is effective at reducing the roll at resonance, it can actually increase the roll amplitude at other wave frequencies. This is a particular problem at low wave frequencies when the ship is rolling slowly, since the water in the tank will then be closely in phase with the ship roll. This potentially dangerous situation has been resolved in commercial passive U-tube systems (Honkanen, 1990) by using valves in the air duct to reduce the flow of water, thereby extending the effective period of the tank. Installing the valve system in the air channel avoids the high forces and water hammer effects that would be involved with valves in the water channel, although the compressibility of the air adds extra complexity to the control system. The other drawback of passive-tanks is that if the vessel takes on cargo, such as fish, the ship’s natural roll frequency will change and the tank will no longer be correctly tuned. One option is to change the depth of water to alter the tank natural frequency, although this will inevitably be slow and

require expensive automated pumping systems to be installed, and it is therefore more practical to change the natural frequency with baffles.

Whilst tanks of this type are already available the concept is currently only applied to U-tube tanks of known geometry that have well-defined flow characteristics. To make a frequency adaptive roll stabiliser more applicable to fishing vessels, the majority of which are already fitted with simple free-surface tanks, will therefore require a control system which can adapt to tanks of varying geometry with minimal prior knowledge of the vessel. This is the primary objective of the research programme currently underway at the University of Newcastle aimed at developing a generic controlled-passive stabiliser system.

Tank Control Strategies

To assist in the development of the roll stabilisation system a working fishing vessel – the 56 metre stern trawler Forever Grateful – is being used as a test bed for the prototype system. The vessel is shown in Figure (2). The main particulars are shown in Table (1). The ship is currently fitted with a stability tank (Beam (X)=8m, Height (Y)=3.5m, Longitudinal Length (Z)=1.8m), located 10 metres above the keel and using a central partition containing two large holes to act as a baffle. Half-filled the tank will contain 26 tons of water whilst the displacement of the vessel varies between 2000 and 3000 tons, depending on the loading condition. The tank geometry presents three possible options – keep the existing partition to divide the tank into two sections, replace the central partition with two side partitions to divide the tank into three sections, or fit a box construction in the roof to create a rudimentary U-tube. For simplicity, the flow of water will be controlled by a set of vertical vanes rotated between 0 degrees (fully closed) and 90 degrees (fully open), as shown in Figure (3). The initial design for the vane mechanism involves a hydraulic actuator situated on top of the frame, with a simple position transducer providing the feedback signal. Whilst the double-partition design has useful stabilising properties (MER, 1993), it would require two sets of vanes and will therefore not be considered on the grounds of cost. The practical alternatives are therefore a single partition or a pseudo U-tube, where the single-partitioned tank will hold a large volume of water but will have less well-defined flow characteristics than the U-tube. This paper examines both geometries and two possible methods for controlling the vanes – one adopting an on-off approach and the other a proportional strategy – resulting in intermittent or continuous water flow respectively.

Intermittent Flow

Since the mass moment provides the majority of the roll reduction effect, the intermittent flow control strategy will attempt to maximise this by trapping as much water as possible on the side that opposes the roll. Thus as the ship rolls to port the majority of the water will be held in the starboard tank. As the roll approaches the maximum port roll angle the vanes are opened, thereby transferring the water into the port tank ready for the roll to starboard. A proto-type U-tube stabiliser of this type (Terao, 1986) has already been tested on a twelve metre vessel and the reported results indicate that the worst-case roll with the control system activated was approximately 40% of the worst roll with the vanes kept shut and 65% of the worst roll with the vanes kept open. Theoretically this strategy could be applied to either a partitioned or U-tube shaped tank, and one of the project goals is to create a SIMULINK model of the irregular water flow which would result. In the absence of a completed mathematical model the concept was evaluated on a pseudo U-tube through simulation, assuming that the water oscillates according to standard U-tube theory.

Continuous flow

In contrast to the intermittent method, where the vanes are either open or closed, the continuous flow strategy will involve various intermediate vane angles in order to modify the flow proportionally. Due to the difficulty in accurately modelling fluid flow through partially opened vanes this control method was evaluated experimentally using a scale model of the ship and

tank, and the effect of different vane angles over a range of wave periods was analysed. Whilst this method is also applicable to either type of tank it was tested on a partitioned design in order to assess the effect of the hydraulic jump phenomenon.

Intermittent Flow Simulation Study

Coupled Ship & U-tube Model

The theory describing coupled ship & U-tube systems is well developed (Chadwick, 1954), and treats the motion of the water in the columns as a tank angle (_{φ) relative to the deck of the ship} which is inclined at roll angle (θ). The differential equations describing the ship and tank roll are:

φ

φ

θ

θ

θ

S S W ST ST S B C M J C

J &&+ &+ = − &&− (1)

θ

θ

φ

φ

φ

T T ST ST T B C J C

J &&+ &+ =− &&− (2)

where the ship is assumed to be rolling about the combined centre of gravity (G) of the ship and tank. The coupled ship inertia when fitted with a tank mass (m) with centre of mass (O) is:

(

₁

)

_k2 _GG'2 _mGO2

JS = +

δ

∆+ ∆+ (3)

where (δ) is the added mass fraction, (k) is the radius of gyration, (∆) is the ship displacement and (G’) is the centre of gravity of the ship with the tank empty. The ship coefficients are defined using the metacentric height (GM) and ship roll damping ratio (ηs) as:

(

m

)

GM g C_S = ∆+ . (4) S S S S J C B =2

_η

(5)

and the wave moment is generally approximated to:

(

m

)

GM.g Sin( t)

MW = ∆+

ψ

A

ω

(6)

The tank coefficients are related to the geometry of the U-tube, with dimensions shown in Figure (4), by:

(

X W

)

WZ _g C C_{T ST }      ₋ = = 2 2

ρ

₍₇₎

(

)

    + −       ₋ = 2 2 2 2 ) ( 2 W H h W X WZ W X qW BT

ρ

(8)

(

)

    − ₊       ₋ = W H h W X WZ W X W JT 2 ) ( 2 2

ρ

₍₉₎

(

X W

)

WZ

₍

_{DG H}

₎

JST = − +

2

2

ρ

₍₁₀₎

where the distance from the centre of roll (G) to the centre of the duct (D) will be negative if the tank is placed above the roll centre. Using the definitions of (JT) and (CT) the natural frequency

of the U-tube is then:

Hh W Z W gh T 2 ) ( 2 2 2 + − + =

ω

(11)

The steady-state solution for the ship roll angle is obtained by assuming that the ship and tank will oscillate sinusoidally with amplitudes (θA) and (φA) at the same frequency (ω) as the wave

moment, with the tank roll lagging the ship roll by a phase angle (ε). The amplitude ratio for the ship and wave slope can then be expressed as:

(

)

(

)

1 2 2 2 2 2 . Ω Ω + − + + ∆ =

ω

ω

ψ

θ

S S S A A J C B g GM m (12)

(

)

(

₂

)

2 2 2 2 2 1

ω

ω

ω

T T T ST ST J C B J C − + − = Ω (13)

(

2

)

2 2

(

2

)(

2

)

2 = CST −JST

ω

+2BSBT

ω

−2CS −JS

ω

CT −JT

ω

Ω (14)

and the amplitude ratio for the ship and tank is then simply:

1 Ω = A A

θ

φ

₍₁₅₎

with a ship-tank phase difference of:

( )

_ω

2

ω

ε

T T T J C B Tan − − = (16)

On-Off Control Algorithm

The success of the intermittent flow method is dependent on the depth of water within the tank and correct timing of the opening of the vanes.

The optimum filling depth for the U-tube is calculated from the condition when one column is completely full and the other completely empty whilst still maintaining a full duct – corresponding to the maximum stabilising moment. For a U-tube of height (Y) and duct height (h), the optimum level depth of water (H) in the columns is therefore simply 0.5 x (Y+h). For an oscillating U-tube with a well-defined natural period the timing is relatively straightforward if the next ship roll period, and hence the time of the next peak, can be adequately estimated. For modest damping within the tank the damped natural period is very

close to the un-damped natural period and the water column will take approximately half this time to flow from one side to the other. Opening the vanes a quarter of the damped period before the estimated time of the peak roll will therefore ensure that the flow ‘straddles’ the peak, giving an effective phase lag of 90 degrees. The U-tube natural period thus represents the absolute minimum roll period for which this method can be used, with the vanes permanently open.

Simulation Parameters

The intermittent flow scheme was tested using a SIMULINK simulation of the Ship & U-tube system with geometric data from the fishing vessel Forever Grateful and real loading conditions, listed in Table (2). The effect of closing the vanes was modelled by increasing the damping coefficient in equation (8). Two different loading conditions (3) & (13) were chosen from Table (2) to evaluate the stabiliser performance, relating to leaving port with refrigeration salt water in the forward and mid fish holds (LC 3), and arriving in port with a medium catch of fish (LC 13). Typical wave periods were selected ranging from 8 to 14 seconds, which had a bearing on the chosen dimensions of the U-tube framework within the existing rectangular tank. A U-tube natural period of no more than the shortest ship roll period is required, whilst adhering as far as possible to the relationship between (H) (Y) & (h) for maximum volume difference. The selected dimensions (W=2, H=2, h=0.5) were chosen to give a natural period of 7.5 seconds. However, the mass of water contained in this tank would be 18.45 tons which is only 0.6% of the maximum ship displacement, which must be taken into account when assessing the results. Since the controller requires reasonably large wave heights in order to generate the maximum volume difference across the tank it was tested on wave heights of both 1 and 4 metres. The results for a standard U-tube stabiliser with a fixed geometry were also included to provide a fixed reference against which the performance of the controlled U-tube could be measured. This standard U-tube was tuned to a mid-range period of 10.0 seconds to provide reasonable performance across the chosen frequency range, with the fixed dimensions (W=2.5, H=1.82, h=0.3) enclosing the same volume of water as the controlled tank. The results using a ship damping ratio (ηS) of 0.1 are shown in Figure (5), including the consequences of keeping the

vanes permanently open or closed. The out to out roll is expressed in terms of amplification of the maximum wave slope, calculated using the deep water expression for wavelength.

Intermittent Flow Results

The minimum wave period of 8 seconds is on the very limit of the operational range of the intermittent flow controller, and stable control operation was only achieved for periods of 9 seconds and above. For a wave height of 1 metre the controller appears to give excellent roll reduction for both loading conditions, generating only 30% of the roll amplification obtained with the water held statically in the tanks. Since the geometry was chosen to create a short tank natural period the open flow response is good at short wave periods but becomes progressively worse as the period lengthens and the water distribution becomes synchronised with the ship roll. Not surprisingly the fixed U-tube functions best under loading condition 3 around a wave period of 10 seconds, for which situation it was tuned, although the minimum roll amplification rises to 55% of the value with the vane closed. The apparent inability of the tuned U-tube to out-perform the intermittent flow scheme, even at the resonant frequency, is due to the use of a small wave height which only generated a maximum out to out roll of 12 degrees with the vanes closed. At these small roll angles the fixed U-tube was incapable of creating the same volume difference across the tank as the intermittent flow method. The results for a wave height of 4 metres therefore give a more realistic measure of performance, with maximum out to out rolls of up to 50 degrees with the vanes closed. At these amplitudes the tank will become saturated for both the intermittent-flow and fixed U-tube, and hence the responses around 10 seconds at loading condition 3 are virtually identical. The real benefit of the controller only becomes apparent for loading condition 13 where the long resonant period of the ship allows the intermittent anti-roll moment to work most effectively, flattening the maximum amplification to

28% of that for a closed vane. Conversely the fixed U-tube performance deteriorates markedly under these conditions as the short tank natural period cannot generate the required phase lag at the longer ship natural period.

Continuous Flow Experimental Study

To assess the feasibility of using the continuous flow control method a (13:1) scale model of the passive stability tank installed on the fishing vessel Forever Grateful has been constructed, with a range of sensors installed inside the model tank to measure the various physical parameters, including height of tank water, air pressure, water flow velocity and differential water pressure. The model stability tank was mounted on a box barge of the same beam and fitted with a central dividing partition into which the vanes of the flow baffle were inserted. A range of experimental runs were carried out in regular waves for different tank filling depths and baffle angles, as well as with the partition removed. Figures (6) and (7) show the experimental setup of the test barge and the model anti-roll tank. The outcome of these tests was used to determine whether altering the vane angles can compensate for the changes in the ship roll dynamics under different loading conditions.

Experimental Parameters

The model baffles are shown in Figures (8) and (9) with vanes arranged at a range of angles (90º, 60º, 45º, 30º and 15º), representing the different settings that could be adopted to alter the flow characteristics of the tank. Table (3) shows the four different loading configurations tested. The first configuration (1) represents the unloaded barge fitted with a 4 kg tank of water. The natural free-surface period of the tank (1.75 s) was then just above the barge’s modified natural period (1.7 s). The barge was then loaded with weights to produce a stiff condition with reduced natural period (2) and a tender condition with extended natural period (4). Configuration (3) was achieved with weights and 6 litres of water in the tank so that the tank’s free surface natural period (1.46 s) once again matched the barge’s modified natural period (1.50 s), but with altered GM.

Continuous Flow Results

The results in figures 10, 11, 12 & 13 show the peak to peak roll amplitude non-dimensionalised with respect to the response for the tank with no partition present, i.e. a purely free surface tank. Presented in this way it becomes immediately apparent which baffles produce a lower roll response than the free surface tank. In all cases, at the barge’s natural period the free surface tank performs better than the partitioned tank. From studying video recordings of the tests it is apparent that the hydraulic jumps and bores produced at these periods impact the solid section of the partition above the vanes, and hence the maximum transfer of water across the partitioned tank is not achieved. This problem can be easily rectified in practise by increasing the height of the vanes to allow bores to travel through them, thereby improving the effectiveness of the baffle in comparison with the free-surface.

Despite this design flaw, the responses at periods below the barge’s natural period show that the use of baffles with a reduced opening (B15) do improve slightly on the purely free-surface tank. The advantage of using baffles at wave periods above the barge’s natural roll period was harder to judge due to the reduced roll amplitude of the barge, although in general the more open vanes seemed to perform the best. This result addresses one of the main problems of free surface tanks - that they can worsen the roll motion of a vessel away from the period to which they are tuned. Hence it appears that over a range of wave periods and loading conditions differently angled vanes can be implemented to optimise the system’s roll reduction effect.

Additional Design Considerations

Fail-Safe Condition

The presence of a baffled anti-roll tank means there is an additional free-surface acting to reduce the effective metacentric height of the vessel. When the system is operating under normal conditions this additional free-surface would not pose a threat to the stability of the vessel and indeed should be acting to reduce the roll response. However, in the case of a complete power black out on the vessel the free-surface may act in a way that worsens the motion of the vessel. Under these circumstances it is vital to remove the free-surface and improve the vessel’s stability. Although this may produce more severe accelerations the vessel will be in an inherently safer condition.

For the above reasons it is essential that the system be rendered inoperable in the event of power loss. This can be achieved in a number of ways. Firstly, closing the vanes within the tank, and thus reducing the area of the surface by half, will have the effect of quartering the free-surface effect on the vessel’s stability. This could be achieved by having a spring mechanism on the vanes which would automatically close them in the event of power loss. Secondly, and more importantly, the water should only be held in the tank if power is present, i.e. water dumping valves on the tank should be held closed under power, and open automatically due to the weight of water if power is lost. With the tank drained the detrimental free surface is removed entirely. Once power has been restored the tank could be refilled and normal operation restored.

Graphical Interface

The anti-roll tank system is intended to be operated with minimal human intervention. However, in order that the device is not treated as a black box that the crew neither trust or use, a visual computer interface is being developed that will provide stability information to the master of the vessel. This will display the tank’s current mode of operation and relevant information such as depth of water. It will also indicate estimates of the vessels effective metacentric height, and the impact of the system on the vessels motion.

Discussion

In relation to alternative stabiliser designs both the methods investigated show significant potential, although it must be noted that the results in this study were achieved under idealised circumstances with regular waves. A real ship would be subjected to highly irregular roll which will adversely affect both control methods.

The intermittent flow control method for an idealised U-tube produced a substantial roll reduction for all simulated conditions but for waves of any appreciable height it was most effective at long roll periods. The form of the control algorithm means that it is essentially independent of loading conditions and requires only simple feedback information – ship roll angle and tank water depth. Applying this method to a real tank is likely to be more complicated due to the absence of a well-defined flow period, and work is currently underway in developing an artificial neural network model of the water flow-rate from which the correct vane opening time can be calculated. The degree of oscillation obtained within a real tank is also likely to be less than that predicted by U-tube theory, and the simulation results must therefore be viewed as a theoretical upper limit on the potential roll reduction.

The experimental results from the partitioned tank model apparently suggest that the un-baffled free-surface tank outperforms the partitioned geometry for all but a few roll periods. However the results may have been affected by the low height of the vanes used and the fact that the model tank was scaled only by length, rather than dynamically. The over-whelming effectiveness of the hydraulic jump in reducing the roll may therefore not be translated to a real ship where the roll periods are much longer and the water motion in the tank less extreme. To apply the continuous flow control scheme in practise will involve evaluating the roll-reduction properties of different vane angles under various wave conditions in order to build up a database of optimum settings for the baffle. Whilst this makes the continuous flow scheme more complicated to implement than the intermittent flow scheme, it has the advantage that it can operate at short roll periods. Its operation at long roll periods is likely to be greatly inferior however, since the vanes must be almost closed to prevent the water motion becoming synchronised with the ship, thereby limiting the water transfer.

Conclusion

Ultimately a combination of the two control methods may prove the most effective – partially open vanes at short roll periods and open / closed vanes at long roll periods. The choice of geometry (partitioned or U-tube) will be dependent on the tank dimensions - the width and water depth determining whether a bore will form. The resultant anti-roll device will be applicable to a range of vessels, such as recreational craft, where roll reduction at low speeds is desirable.

References

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List of Symbols

θ = Ship Roll Angle

φ = Tank Roll Angle

ε = Ship-Tank Phase Difference

ψ = Wave Slope

ω = Wave Frequency

JS = Ship Second Moment of Inertia

BS = Ship Roll Damping Coefficient

CS = Ship Roll Righting Coefficient

JT = Equivalent Tank Inertia

BT = Tank Damping Coefficient

JST, CST = Ship-Tank Coupling Coefficients

MW = Wave Moment

∆ = Ship Displacement

δ = Added Mass Fraction

k = Radius of Gyration

η = Damping Ratio

G’ = Centre of Gravity of Ship & Empty Tank G = Centre of Gravity of Ship & Filled Tank GM = Metacentric Height

X,Y,Z = External Tank Dimensions

W = U-Tube Column Width

h = U-Tube Duct Height

D = Centre of Duct

H = Tank Filling Depth

m = Mass of Water in Tank

O = Centre of Mass of Water in Tank q = Flow Resistance Coefficient

S T A N D I N G W A V E H Y D R A U L I C J U M P

C O M B I N A T I O N W A V E T R A V E L I N G W A V E

Figure 1: Free surface waves types

Figure 2: Fishing vessel Forever Grateful

Figure 4: U-Tube Dimensions

Figure 5: Intermittent Flow Control

LC3 : Departure from Port WaveHeight = 4m 0 2 4 6 8 10 12 8 9 10 11 12 13 14 Wave Period A m pl ific ati on Active Closed Open Fixed U-tube

LC13 : Arrival in Port - Medium Catch WaveHeight = 4m 0 2 4 6 8 10 12 8 9 10 11 12 13 14 Wave Period A m pl ific ati on Active Closed Open Fixed U-tube

LC3 : Departure from Port WaveHeight=1m 0 2 4 6 8 10 12 8 9 10 11 12 13 14 Wave Period A m pl ific at io n Active Closed Open Fixed U-tube

LC13 : Arrival in Port - Medium Catch WaveHeight=1m 0 2 4 6 8 10 12 8 9 10 11 12 13 14 Wave Period A m pl ific at io n Active Closed Open Fixed U-tube

Figure 6: Experimental Setup of Barge & Tank Figure 7: Anti-Roll Tank Instrumentation

Figure 8: Partition & Baffles Figure 9: 30º & 60º Baffles

Non Dimensional Roll Response No mass Added

0 0.5 1 1.5 2 2.5 3 3.5 4 0.8 1 1.2 1.4 1.6 1.8 2 Wave Period (s) ND PT P Rol l An gl e (d eg) No Baffle B90 B60 B45 B30 B15

Non Dimensional Roll Reponse 54 kg at keel 0 0.5 1 1.5 2 2.5 3 0.8 1 1.2 1.4 1.6 1.8 2 Wave Period (s) ND P T P Ro ll Angl e (d eg .) B90 B60 B45 B30 B15 No Baffle

Figure 11: Roll response for loading configuration 2

Non dimensional Roll Response 54 kg at Keel 6 litres of water

0 1 2 3 4 5 6 7 0.8 1 1.2 1.4 1.6 1.8 2 wave period (s) ND PT P Ro ll an gl e ( d eg ) No Baffle B90 B60 B45 B30 B15

Non Dimensional Roll Response 10 kg on top of tank 0 1 2 3 4 5 6 0.8 1 1.2 1.4 1.6 1.8 2 Wave Period (s) ND RM S PT P Ro ll An g le b ( d e g ) No Baffle B90 B60 B45 B30 B15

Figure 13: Roll response for loading configuration 4

Table 1: Forever Grateful Main Details

LC Status Delta GM KG _Period Roll

1 Lightship 1715.8 0.605 5.172 10.38

2 Departure from Port (RSW empty) 2189.6 0.637 4.938 10.12

3 Departure from Port (RSW mid & fwd centre) 2698.3 0.763 4.831 9.24 4 Arrival at Grounds (RSW mid & fwd centre) 2679.4 0.754 4.835 9.30 5 Arrival at Grounds (RSW mid & fwd centre) + ½ Icing 2695.0 0.724 4.869 9.49

6 Departure from Grounds: Full Catch 3096.3 0.708 5.026 9.60

7 Departure from Grounds: Full Catch + ½ Icing 3112.0 0.686 5.054 9.75

8 Departure from Grounds: Medium Catch 2663.2 0.525 5.080 11.14

9 Departure from Grounds: Medium Catch + ½ Icing 2678.8 0.496 5.113 11.46

10 Departure from Grounds: Small Catch 2436.4 0.423 5.122 12.41

11 Departure from Grounds: Small Catch + ½ Icing 2452.0 0.389 5.157 12.95

12 Arrival in Port: Full Catch 3071.1 0.681 5.043 9.78

13 Arrival in Port: Medium Catch 2637.9 0.501 5.101 11.41

14 Arrival in Port: Small Catch 2411.1 0.398 5.145 12.80

15 Arrival in Port: Port Discharge 1852.9 0.332 5.399 14.01

16 Extended Trip: Depart from Port 2811.9 0.698 4.925 9.66

17 Extended Trip: Arrival at Grounds 2751.6 0.760 4.845 9.26

18 Extended Trip: Arrival at Grounds + ½ Icing 2767.2 0.732 4.878 9.44 19 Extended Trip: Depart from Grounds Full Catch + ½ Icing 3139.0 0.736 5.016 9.41

Table 2: Forever Grateful Loading Conditions

Length Overall = 55.950 Metres

Length B.P. = 47.400 Metres

Breadth Mld. = 11.500 Metres

Depth Mld. (Main Deck) = 6.000 Metres

Depth Mld. (Shelter Dk) = 8.400 Metres

Configuration Added Weight Tank Filling ∆ (kg) GM (m) Tn (s)

1 None 4 litres 317 0.1038 1.697

2 54kg at keel 4 litres 371 0.1222 1.473

3 54kg at keel 6 litres 373 0.1199 1.498

4 _{10 kg on top of tank}54kg at keel 4 litres 381 0.1045 1.733