THE EFFECT OF GM ON LOSS OF CONTROL OF A PLANING MONOHULL IN FOLLOWING SEAS

Transcription

1 THE EFFECT OF GM ON LOSS OF CONTROL OF A PLANING MONOHULL IN FOLLOWING SEAS By: M R Renilson & A J Tuite FOR PRESENTATION AT 5th International Conference on High Speed Marine Craft Safe Design & Operation September 1996 Bergen, Norway REPORT AME, CRC C 96/15 AUSTRALIAN MARITIME ENGINEERING CRC LIMITED ACN

2 The Effect of GM on Loss of Control of a Planing Monohull in Following Seas Martin Renilson* and Andrew Tuite Australian Maritime Engineering CRC Ltd It is well known that When a small vessel travels in a steep following or quartering sea it can suffer from loss of control which may result in broaching-to and possibly a capsize. This is particularly dangerous for high speed vessels which can travel at close to the speed of the waves. Earlier studies by the authors have shown that the destabilising effect caused by the roll/yaw coupling is increased by reducing metacentric height, resulting in an increased tendency to broach when transverse stability is lower. High speed vessels suffer changes in stability when travelling at speed and it is clear that this will further complicate the situation for these vessels in following seas. A four degree of freedom mathematical model which incorporates the effects of heel is described and the coefficients required to simulate the behaviour of a high speed round bilge planing hull, including roll/yaw coupling, are presented. Using the simulation, the effect of varying the vertical position of the centre of gravity on the control of a high speed round bilge planning hull in following seas is investigated. The results of the simulation show how GM can influence control of the vessel at high speeds in these conditions. *Martin ReniLson is on part secondment from the Australian Maritime College -

3 1.0 INTRODUCTION Broaching-to occurs when the vessel's rudder restoring moment cannot counteract a large yawing moment induced by wave forces acting on the vessel. The question of ship safety in regard to broaching has been discussed for many years. Despite an extensive amount of research into the complexities of broaching, no acceptable solution for the problem has been achieved. The reason for this is that in a broach a ship is in a very extreme condition which makes studies of the physics, either theoretical or experimental, difficult. (Vassalos and Maimun 1994) During the onset of a broach a vessel will experience relatively large angles of heel. The modelling of this large amplitude rolling motion requires consideration of the coupling effects with other associated motions. If the amplitude of rolling motions are small, the coupling forces may be neglected which considerably simplifies the modelling of that motion. However, if the amplitude of the rolling motions are large, the coupling effects need to be included. It has been well documented, Thomas and - Renilson(1991), that surf-riding is a prerequisite for broaching. The stability of a planing vessel often varies when travellink at higher speeds (Wakeling et.a1(1984)), such as surf riding. The numerical modelling 'of a planing vessel surf-riding needs to take into account the well known variation of GM with speed for such vessels. By making use of an improved mathematical model which includes the effects of roll and the variation of GM with speed, this work aims to contribute to an increased understanding of the theoretical modelling techniques of broaching. There is a number of methods used to identify unfavourable combinations of ship and wave conditions. An extensive matrix of experiments, both free running and constrained, has proved to be time consuming and rather expensive. A pure analytical approach becomes too difficult as the complexity increases and the statistical approach is not suitable for taking into account the dynamic effects of broaching. For these reasons a time domain numerical simulation approach is the practical tool used to investigate the broaching phenomenon. Time domain simulation allows the vessel's dynamic behaviour to be modelled and the associated forces to be expressed in a non-linear manner obtained from empirical relationships or theoretical computations. 2.0 MATHEMATICAL MODEL As can be seen in Figure 1, two coordinate systems are used: Wave fixed, xo, yo and zo with the origin at a wave crest, with the wave travelling in the direction of the xo axis. Body fixed, x, y and z with the origin at the vessel's LCG, with the x-axis pointing towards the bow, the y-axis to starboard (horizontal) and the z-axis downwards (vertical).

4 Figure 1: Coordinate system A complete simulation of a vessel operating in a following sea is a very complex problem in comparison to a vessel operating in calm water. The vessel is subjected to two different hydrodynamic forces simultaneously, namely lifting forces in the horizontal plane acting on the vessel due to plane manoeuvring motion and the forces acting on the vessel arising from the incident wave. The four degrees of freedom model is based on Newton's 2nd law of motion: X = nz(zivvi)1 Y = kir-fuvi) N=1 (1) K = 1.r(1). Surge m(1 Sway If\ X, pi. X Prop + X nut X IVaVe (2) m(1y, )0=Yu+Y,p+Y,nd+Y (3) Yaw mr(1.n,)i=nw+ni-nnd+n. (4) Roll mil(11, K0115. = Kh,, cd K.8 K Invit (5) Xhuib Yhuib Nhull arid Khuu are, the hull hydrodynamic manoeuvring forces and moments. The hull forces and moments can be written as follows:

5 = m(1+ X')vr+ X ulul+ Xhull Luu /I X' uuthi " MU Y,, = m Dur+ Ty:July + kilo Y, U u 114+ x ii11211/1+ X:* th L2 uwv Urn (6) Nho, = mln1u1r+ mnuv + N uomu+ N. Khull = caljulvm K.,u,, lulmi+ Ku, uom.l+ Ki010ImE + K0 0mLg Empirical, theoretical and experimental methods are employed to determine the hull force manoeuvring coefficients used in the mathematical model. The wave induced force and moment coefficients, Xwave, 'wave' Nwave and Kwave are based on slender body theory with some simplifications. (Umeda and Renilson, 1992) The wave induced surge forces, Xwave, are calculated using the Froude-Krylov component of the force. The wave induced sway force, Ywave, yaw moment, - Nwave, and roll moment, Kwave, are calculated using both the Froude-Krylov and diffraction components of the force. The Froude-Krylov forces arise from the undisturbed pressure field acting on the submerged hull surface. The total pressure field is the sum of the hydrostatic and hydrodynamic pressure due to the velocity potential of the incident wave. The diffraction forces are a function of the velocity potential of the diffracted waves due to the presence of the ship hull in an incident wave. The wave forces and moments can be calculated as follows (Renilson and Tuite, 1995): = pgak cosv4e- s (x) cos k( + x)dx 7) The pressure at any point in the wave, either side of the ship is given by: ppw, Apge'cosx0+ pgz psiartuard = Apge-k cosx, + pgz The water particle acceleration and velocity is given by (2gg in ty 10) yacre, = -- AAe-k' sinkr, = 1-2 Ae-' cos kx, jsin yr 11) (y yvave(c.v) =It, a{ (f 0, p dz t, 1-Y(rei--,,,,,dz)+( y,a1-1m dahm Dx v, ) dr 12)

6 N.(4.v)= P((1) P dz dz)x,c, + fp. port Dt board (Ywort dahni All41) ±(Y v (13) Dx Kw..,(4.w) (10 JD: P tanoy dz f Dt P starboard tan OYYdwicsdz)+ (t Pponz icizt, pstathoardzdimaz) 111) ±(Y vet daiim (14) DX cg Rudder effectiveness can be significantly reduced when positioned in certain parts of the wave. The rudder forces within the model have been modified to take into account the change in fluid flow over the surface of the rudder due to the presence of the wave. In order to calculate the change in rudder effectiveness it was necessary to calculate the heave and trim angle of the vessel as a function of the non-dimensional position in the wave. The rudder effectiveness, heave and trim calculations were validated by a series of model experiments. (Mak,1995) The model also takes into account the change in GM relative to the longitudinal position in the wave and the variation in GM at differing speeds in calm water. 3.0 STABILITY IN CALM WATER Research carried out (Wakeling etal, 1984), on similar types of high speed craft, have shown a reduction in transverse stability at the higher speed range. In order to investigate the change in GM -in Calm Water; a captive model experimental study was undertaken in the Australian Maritime College, AMC, towing tank. The model used for the investigation was a 1/20 scale model of a 31m round bilge planing vessel. The vessel's body plan and particulars are outlined below. Figure 2: Hull Body plan 31m Planin vessel 31m Particulars Length Beam (W.L.) 3.76m Draught 1.8m Displacement 100.5t L.C.B. (%aft) 5A6 Crn Cb Table 1: Full Scale Vessel Particulars

7 A series of experiments was performed to examine how the vessel's GM varies with velocity in calm water. The experiments were carried out over a Froude number range from 0.5 to 1.0. Dynamic inclining experiments were conducted on the model to determine, the effect of forward velocity. Three static GM conditions were investigated. The spline plot in figure 3 represents the 'line of best fit' through the experimental data. Figure 3: Change in stability (calm water) experiment results. 4.0 STABILITY IN THE WAVE When a small vessel is operating in a seaway, the waterplane area, the centre of buoyancy and displaced volume distribution vary causing a change in the vessel's metacentric height. The following seaway causes the vessel to spend extended periods of time in certain positions in the wave, accentuating the effect of this change in GM, which may lead to the loss of stability and possibly capsize. The quasi-steady state assumption is used to predict the vessel's GM as a function of its relative longitudinal position in the wave. The calculation for metacentre height (KM) follows the method proposed by Burcher(1980). KM=.12 A. Z. dx I V V KB + BM (15) A is the sectional area, I is the centroid of the section and V is the underwater volume of the vessel. It is the second moment of area of the waterplane taking into account the vessel's relative longitudinal and vertical position in the wave. In order to validate the proposed theory captive model tests in regular following waves were carried out in the AMC towing tank. Experiments were tarried out using a 1/15 scale model of a 25m Success Class stern trawler. The vessel's body plan, profile general arrangement and particulars are outlined in figures 13 and 14 in the appendix. The theorectical and experimental results are compared in figure 4. As can be seen, agreement is not good but for the current investigation the method employed was considered adequate. Consequently this theorectical method was used to determine the effect of the wave on the stability of the planning vessel.

8 g C I 0.Vn AV Non-CI IND W Figure 4: Change in GM relative to non-d position in the wave (H/X=0.049, X/L = 1.36) 5.0 ROLL COUPLING The effect of roll on the yaw and sway motions of the 31m planing vessel was investigated experimentally. The model used for the investigation was a 1/20 scale model of a 31m round bilge planning vessel. The vessel's body plan and particulars are outlined in section 3.0. The roll coupling experiments were carried out over a Froude number range Figure 5: Non-d sway induced by heel Figure 6: Non-d yaw induced by heel As can be seen, the roll induced sway force and yaw moment can be approximated by linear functions. The sway force coupling, being an even function of forward speed, u, is represented as Ywoluio, whilst the yaw moment coupling, which is an odd function, is represented as Nou0. Plots of Kis, and IS1.0 against Froude number are given in figures 7 and 8. omits arm : Rar Figure 7. Y1.10 as a function of Fn :030 4= ; acolo 4( imp.. limo. o- 0.3 as Figure 8. Nu, as a function of

9 yi, 6.0 BEHAVIOUR IN FOLLOWING SEAS A vessel's dynamic behaviour in a following seaway can be predicted using the Numerical Following Sea Simulation (NFSS) model which solves equations 2-5 in the time domain (Tuite and Renilson, 1995). The program is primarily a practical engineering tool designed not only to investigate the mechanisms of broaching but to derive guidelines for operators and designers. Such guidelines require an extensive number of simulations. For this practical reason, NFSS has been designed to run quickly on a PC. 6.1 Simulation An advantage of time domain simulation of ship motions is the possibility to provide detailed information about the processes in terms of how the forces and motions interact and result in the dynamic behaviour associated with a vessel broaching. A disadvantage is the sensitivity of initial conditions of the dynamic system. There is no dispute that the broaching of a vessel is a non-linear problem. Thus, when modelling this non-linear behaviour, the irregular and unpredictable time evolution of the system needs to be investigated. The numerical model is dependent upon prescribed initial conditions, therefore deciding on suitable initial conditions becomes a major problem. Throughollt all simulations the heading phase trajectories were plotted. A range of realistic initial conditions were selected and simulation solutions were only obtained when the initial transients, due to the initial conditions, died out and a steady state solution was obtained. That is, the phase trajectories reached a realistic periodic attractor. It was noted that for all plausible initial conditions the system reached the same periodic attractor eventually. 6.2 Definition of a broach A series of simulations were then undertaken to identify dangerous operating conditions. Approximately 450 runs of 8 minutes real time duration were performed and in each case the periodic attractor was investigated. The authors concluded that no single variable of the model could be used to define a vessel broaching, so a combination of variables were used as shown in table 2. Broaching: Rudder angle d =±d. a =±d., 1 Yaw velocity > 0 yr 0 Yaw acceleration Iii >0 Heading angle iv yrded Table 2: Definition of broaching for periodic attractor Marginal Broaching: 6.3 Influence of GM Simulations were undertaken to present a clear indication of the effect roll has upon the behaviour of a vessel in following seas. The results for three different metacentric heights are presented in figure 9. Roll can be seen to have a strong influence on the yaw behaviour of the vessel. The coupling between yaw-roll and sway-roll influences the relative motion (yaw and sway) which in turn effects the vessels position in the wave hence dictating the vessels behaviour in following seas. Thus, during following sea simulations, the vessel's metacentric height as well as the corresponding roll period have to be considered carefully.

10 Gil 0.0 OM GM CO er) ao %.,,...ioo 120 o "tso 1ref CC a -/ o > c Time (s) Figure 9: Time domain plots (31m Planing vessel) =25 degs,vl = 2.0 and HA, = 118 Simulations performed by Tuite and Renilson (1995) demonstrated the effect of GM on the calm water manoeuvring behaviour of a high speed ship. The manoeuvring simulations showed that the sway-roll and yaw-roll coupling decreases the directional stability and

11 turning response of the vessel. In the manoeuvres investigated, the effect of roll coupling is emphasised when the metacentric height is small. As can be seen in figure 9, the metacentric height greatly influences the behaviour of a fast planing vessel operating in a following seaway. A large number of simulations covering a matrix of wave conditions was then carried out for three GM values, 0.9m, 1.8m and In each case the phase periodic attractor was analysed to determine a broach or non broach. This analysis allowed the broaching zones to be presented in figure n Owl.; mad u, S Broaching Zones HorlIng. ridallve to wan end.25 dep. Win Broach Zone Figure 10: Broaching zones as a function of static GM (m) The size of the broaching zone is particularly sensitive to the vessel's metacentric height for the longer waves with GM values less then 1.8m. 7.0 VESSEL COMPARISON Wama Length/Ship Length OstaciOnay IMO Figure 15 and 16 represents a comparison between a slow displacement type vessel (25m success class trawler, Tuite and Renilson,1996) and the 31m planing vessel. The comparison in figure 11 was carried out for a wave encounter angle of 15. The speed of both vessels was set at the design service speed. It can be noted that the shift in broaching zone is a function of the wave speed. That is, a broach only occurs when the vessel is travelling at close to the relative speed of the wave. Broaching Zones lbsects 2one I CLOS ( Non Broach Zola Mae encounur is Naga Wait LergasiShip Length Figure 11: Comparison broaching plot Figure 12: Comparison broaching polar plot

12 The comparison in figure 12 covers a range of headings and speeds for three wave steepness conditions. It can be seen for both vessels that the broaching zone decreases with wave steepness. 8.0 CONCLUDING REMARKS From this investigation the following conclusions can be drawn: * The captive model experiments demonstrated a change in stability when travelling at speed in calm water. * The simulations performed confirm that the roll motion has a pronounced influence on the manoeuvring behaviour of fast planing vessels in following seas. * The region of broaching of a fast planing vessel decreases as the vessel's metacentric height is increased. 9.0 ACKNOWLEDGMENT The work described was part funded by an Australian Research Council grant. The authors would like to thank Mr S. Fitzsimmons and other colleagues at the Australian Maritime Engineering CRC Ltd. and the Australian Maritime College for their encouragement and support REFERENCES Burcher, R.K. (1980), The Influence of Hull Shape on Transverse Stability, The Naval Architect Technical Papers, May, pp Mak, T. (1995), Loss of Stability for Small :Vessels in a Regular Following Seaway, undergraduate final year thesis, Australian Maritime college. Norrbin, N. H. (1971), Theory and Observations On the Use of a Mathematical Model for Ship Manoeuvring in Deep and Confined Waters, Elanders Boktryckeri Alciebolag, Publications of the Swedish State Ship building Experimental Tank, Goteborg, Sweden. Oltmann, P. (1993), Roll-An Often Neglected Element of Manoeuvring, Proceedings International Conference of Marine Simulation and Ship Manoeuvrability. Renilson, M.R. and Tuite, A.J. (1995), Broaching simulation of small Vessels in Severe Following Seas, Proceedings International Symposium Ship Safety in a Seaway, Kaliningrad, Russia. Tuite, A.J. and Renilson, M.R. (1995), The effect of GM on the manoeuvring of a high speed container ship, Eleventh International Maritime and Shipping Symposium, Sydney. Umeda, N and ReniLson, M.R. (1993), Broaching in Following Seas - A Comparison of Australian Trawlers and Japanese Trawlers, Bulletin of National Research Institute of Fisheries Engineering, No.14. Umeda, N and ReniLson, M.R. (1994), Broaching of a fishing vessel in following and quartering seas - non linear dynamical systems approach, Fifth International Conference on Stability of Ships and Ocean Vehicles. Wakeling, Sproston, J.L. and Millward A. (1984), Transverse stability of a fast round bilge hull, International Conference on design Consideration for Small Craft, RINA London.

13 11.0 NOMENCLATURE A = wave amplitude AHM = 2-d sectional added horizontal mass g = gravity I = moment of inertia k = wave number Ki,,,,,,,o.0101 = linearised K-component manoeuvring coefficients k wave number Kwind wind external moment Krud rudder external moment Kprop = propeller external moment L = length of ship m = mass of ship Nwind = wind external moment Nrud rudder external moment NAprop = propeller external moment r.urov.01u1 linearised N-component manoeuvring coefficients r = yaw velocity i = yaw acceleration S(x) local wetted surface area of the ship resolved in the x-direction u = velocity in the x-direction i = acceleration in the x-direction velocity in the y-direction f, = acceleration in the y-direction xc x-distance from the centre of the strip to. the wave crest xp = x-distance from the port side of the strip to the wave crest xs x-distance from the starboard side of the strip to the wave crest xlcg x-distance from strip to the longitudinal centre of gravity Xwind wind external forte in the x-direction Xrud rudder external force in the x-direction Xprop = propeller external force in the x-direction X r iiatu,uvvy = linearised X-component manoeuvring coefficients xc = x-distance from the centre of the strip to the wave crest xp = x-distance from the port side of the strip to the wave crest xs = x-distance from the starboard side of the strip to the wave crest xlcg x-distance from strip to the longitudinal centre of gravity xrudlcg = x-distance from the rudder to amidships xproplcg = x-distance from the propeller to amidships v,vr,sw,01.1 linearised Y-component manoeuvring coefficients 'wind = wind external force in the y-direction Yrud = rudder external force in the y-direction Yprop = propeller external force in the y-direction zcg z-distance from strip to transverse centre of gravity z = z position of the strip A. wave length 0 = heel angle 0 roll velocity i = roll acceleration

14 water density non-dimensional position in the wave heading angle yaw rate volume APPENDIX Figure 13. Hull Body plan Figure 14. Proffie of 25m Success Class Trawler Model scale Length B.P m Beam W.L m Draught 0.200m Displacement 58.9kg L.C.B. 3.1% Cm Cb Table 3: Vessel particulars