INFLUENCE OF DAMPING ON ROLL MOTIONS OF SHIPABSTRACT:This paper presents the effect of damping on roll motions for ship heading in beam seas. The roll motion is very important because when coupled with some other motions it can cause the vessel to capsize. Damping is very important because it controls the magnitude of motion. So it is dealt by many scientists and researchers in different ways. But yet thorough understanding has not been done. The paper introduces non linear terms in the damping and restoring term of the equation. The damping co-efficient is divided into various constituents like eddy making, wave, lift, friction and bilge keel damping.

1.INTRODUCTION:Roll motion is important phenomenon in ships because when coupled with other motions it can make the ship capsize. Damping is most important in case of roll motion as it brings down the peak values. Damping is broken down into various components like wave damping, lift damping, friction damping, eddy damping, bilge keel damping. Therefore it is of complex nature. But Ikeda et al has made an comprehensive study and given empirical formula for evaluation of each of the component. This work uses available methods to solve the non-linear roll equation of motion and uses numerical simulation techniques to apply chosen modal to chosen ship.2.METHODOLOGY:A sample vessel is taken and assuming the non-linear damping and restoring coefficients, the equation for roll motion is analyzed. The damping is broadly divided into linear and non-linear terms. The linear terms are the wave and lift damping, whereas the non-linear terms include the eddy damping, friction damping and appendage damping. Then the influence of various parameter like speed of the vessel, loading of the vessel, stability of the vessel, presence of bilge keel, wave slope on the roll motion are studied and graphically plotted.3.WORKThe details of the model are given belowTYPE OF VESSEL: TWIN SCREW FISHING VESSELLBP = 64.0 m.BREADTH = 11.6 m.DEPTH = 7.32 m.DRAFT = 4.48 m. (loaded) = 1556 tonsGM = 0.78 m.= 0.449= 0.852LCF = 2.02 m. (aft)LCB = 1.17 m. (aft)

Various loading , hydrostatic and hydrodynamic characteristics of the ship have been used in the analysis. The ship is fitted with bilge keels, rudder and fin stabilizers. But the rudder and fin stabilizers were not considered in the analysis because they are control surfaces used to counteract any moment acting in the ship. Other surfaces such as bilge keel act as passive anti rolling devices. Various hydrostatic and stability data of the ship were calculated using software.Non-linear equation of motion:

. The above equation can be expressed as the following in case of regular sea wave:

In the expression the restoring term which is an odd order polynomial is also non-linear in nature. Restoring term may appear as cubic or quintic polynomial depending upon the nature of GZ curve. Sometimes also the restoring term can also be expressed as a higher order polynomial, but it requires bulky manipulations throughout the solution scheme.If we establish the equation of motion basing on the above assumed assumptions we get:

Dividing the above equation with and substituting the values of we get the following expression:

Where

Evaluation of the linear and non-linear terms has been by ikedas and Himeno approach. More detailed evaluation id decided in the following sections.The equation incorporates various effects of ship dynamic and environmental parameters including damping, restoring and wave excitation. The GZ curve is approximated as where the co-efficients are determined by the static and dynamic nature of GZ curve which includes the metacentric height GM, Angle of vanishing stability , Area under the GZ curve as follows:

Solution can be made by perturbation method or by using runge-kutta method.Basically two different displacement values are used in analysis 1556 tons and 1909 tons. However three metacentric values are taken into account : 0.43m, 0.61m, 0.788m. four conditions are taken into consideration:

Vessel is provided with Bilge keel. The geometric details of the bilge keel are:

In order to see the effect of Bilge keel, the damping values and roll amplitudes are calculated with and without Bilge keel. Thus eight different test conditions have been analyzed.As far as experimental conditions are concerned linear sinusoidal waves are generated with no phase lag between the waves and motion. The wave slope plays an very important role on the right hand side of the roll equation. So the experiment is conducted with three wave slopes i.e , , .Finally the speed of the vessel is altered between 0-10 knots to observe the influence of speed on roll damping and hence on the roll amplitudes.Estimation of roll damping co-efficients is ambigious owing to the complex nature of the damping terms. Though extensive research, numerical simulation and experiments have been performed but yet it is not completely understood. Radiation theory can alone not solve for damping terms. Viscousity plays an important role. Haddara and Zhang carried out experiments to prove that speed influences roll motion of the ship. Contributions from many sources and their interaction makes evaluation of the damping terms difficult.Ikeda has broken down the damping into five different parts:1. Wave damping2. Lift damping3. Eddy damping4. Friction damping5. Appendage damping or Bilge keel damping

Furthermore the first two terms come under linear damping co-efficients whereas the other three are non-linear in nature. The effect of each damping co-efficient is studied on the fishing vessel by numerical simulation. Empirical formulaes developed by Ikeda and Himeno have been utilized.The procedure and relavent formulation have been shown in the appendix.

4.RESULT:

Based on the numerical simulation the damping characteristics of the sample ship are shown in figure 2 and figure 3.

The main purpose to estimate the damping co-efficients is to understand their effect on the roll amplitudes. Therefore several parameters, displacement, GM, wave characteristics and wave speed were altered and the equation of motion was solved in time and frequency domain. But in this paper only few of the combinations are discussed due to space constraints. A sample of graph is given for each individual parameter.

Figure 4 depicts the influence of speed on the roll motion for specific condition. 15% increase is observed for knots when compared to 0 knots. So, damping values are susceptible to the velocity variations. Figure 5 compares the roll amplitude with and without the presence of Bilge keel. The Bilge keel reduces the amplitude by 35% at resonant frequency.

Figure 6 depicts the influence of GM on roll amplitudes. Increase in GM not only reduces the peak to a lower value but only increases the frequency at which it occurs.

Wave steepness also has a considerable effect on the roll amplitudes. About 40% reduction in amplitude occurs between slope and .

Effect of increased displacements on roll amplitudes for highest wave slopes is also shown in figure 8.

Furthermore time domain solutions and phase diagrams can be obtained for each case. Figure 9 and Figure 10 are the examples of such specific solution.

5.CONCLUSIONS:

In the paper the effect of damping, waves and stability on the roll motions of ship have been investigated by numerical simulation techniques for sample vessel. It has been shown that wave steepness plays an important role on especially the peak amplitudes regardless of other factors. A change of 25-40% is seen between the lowest and highest wave steepness.

Speed also effects the roll motions. But the effect cannot follow linear trend. A increase of 50% is present with the speed increased from 0 knots to 10 knots.

Stability characteristics can be translated as the different weight and the centers which the ship undergoes during her voyage. A change in the resonant frequency can be observed along with the change in the amplitude.

As expected the Bilge keel is the simplest and most conventional source for roll damping. A 30-40% reduction in roll amplitudes can be seen with the presence of Bilge keel.

Finally the above assessment we understand roll damping is an important parameter in predicting the motions of ship. Therefore meaningful estimation of roll damping is essential for the prediction of roll characteristics for the ship. In principle it may be explained that it is simply an energy balance between damping and excitation forces. Since wave and wind excitation cannot be controlled so one can play with the damping forces to enhance the stability and motion characteristics of the ship.

6.REFERENCES:Influence of damping on roll motions of ship by Emre PESMAN, Deniz BAYRAKTAR and Metin TAYLAN.