Capsizing of Small Vessel Due to Waves and Water Trapped on Deck

Proceedings of the 9 th International Conference on Stability of Ships and Ocean Vehicles 1 Capsizing of small vessel due to waves and water trapped on deck Jan Jankowski, Polish Register of Shipping Andrzej Laskowski , Polish Register of Shipping ABSTRACT The paper presents the phenomenon of small vessel capsizing due to irregular waves and water trapped on deck. The phenomenon is identified by simulating vessel motions in waves based on numerical solution of non-linear equations of motion. The volume of water on deck, varying in time and affecting ship motions, depends on the distance between the wave surface and the upper edge of the bulwark or the lower edges of openings in the bulwark. This paper is a continuation of earlier works on simulation of fishing vessel motions in irregular waves leading to its capsizing (Jankowski & Laskowski, 2005a). Some general conclusions regarding fishing vessel safety have been drawn. Keywords: irregular waves, vessel motion, vessel capsizing, water on deck 1. INTRODUCTION Simplified models regarding forces induced by For the large part, safety initiatives developed water on deck have been applied. The main as- by the maritime industry focus on large seago- sumption, taken from Vassalos et al (Vassalos, ing vessels such as tankers and bulk carriers. 1997), is that the surface of water on deck is However, figures reported by the IMO itself horizontal. This idea was also applied by show that the annual loss of life on world’s (Jankowski & Laskowski, 2005a), where only fishing vessels accounts for the loss of a huge the hydrostatic pressure of water on deck and number of human lives every year, and that the the acceleration of the ship was taken into ac- safety of small vessels is a real global problem. count in determining the forces acting on the deck. One of the important reasons for capsizing of small vessels is water trapped on deck. Theo- This paper presents results based on a more retical models and computer programs enabling sophisticated method regarding the determina- simulation of ship motion in irregular waves tion of the pressure acting on the deck were earlier developed by the authors (Buchner, 2002), based on the evaluation of (Jankowski & Laskowski, 2004), (Jankowski & Newton’s momentum relations for a control Laskowski, 2005b), (Laskowski, 2002) but the mass volume over the deck. Integration of the problem of vessel motion with water flowing pressure over the wetted part of the deck, tak- on and off the deck is more complex. ing into account generalised normal vector to the deck, yields additional forces affecting motions of the vessel. Proceedings of the 9 th International Conference on Stability of Ships and Ocean Vehicles 2 A fishing vessel, which was regarded as having solutions can be applied for determining the good stability, has been used in simulations and diffraction forces during the simulation. the analyses. The results showed essential fea- tures influencing safety of fishing vessels sail- The radiation forces are determined by added ing in irregular waves. masses for infinite frequency and by the so-called memory functions (given in the form of convolution). The memory functions take 2. EQUATION OF VESSEL MOTION, into account the disturbance of water, caused WITH WATER ON DECK IN by the preceding ship motions, affecting the IRREGULAR WAVES motion of the ship in the time instant in which the simulation is calculated. The simulation of vessel motions in waves is based on numerical solutions of non-linear The volume of water on deck, varying in time, equations of motion (non-linear model). The depends on the difference in heights between hydrodynamic forces and moments defining the wave surface and the following edges: the equations are determined in each time step. The accuracy of the simulation depends on the - the upper edge of the bulwark, accuracy of calculating the hydrodynamic forces and moments due to waves. - the lower edges of openings in the bulwark. It is assumed that the hydrodynamic forces act- The inflow and outflow of water on the deck ing on the vessel can be split into Froude- are determined by the hydraulics formulae of Krylov forces, diffraction and radiation forces (Pawłowski, 2002) and depend on the dimen- as well as other forces, such as those induced sions of holes in the bulwark. When the wave by water on deck, rudder forces and non linear profile exceeds the upper bulwark edge, the damping. amount of inflowing water on deck is determined by the dimensions of the cross section of The Froude-Krylov forces are obtained by in- the wave by the extended bulwark surface. tegrating over the actual wetted ship surface the pressure caused by irregular waves undis- The amount of water trapped on deck and its turbed by the presence of the ship. position is determined by the horizontal plane and the actual position of the vessel deck in the The diffraction forces (caused by the presence given time instant. If the plane is higher than of the ship diffracting the waves) are deter- the lowest point of the bulwark above the wave mined as a superposition of diffraction forces surface than the horizontal plane is taken on the caused by the harmonic components of the ir- level of this bulwark point. regular wave. It is assumed that the ship diffracting the waves is in its mean position. This The dynamics of water caused by the motion of is possible under the assumption that the dif- water particles in relation to the deck is ne- fraction phenomenon is described by a linear glected. The forces and moments caused by hydrodynamic problem. The variables of dif- water on deck are obtained by integrating the fraction function are separated into space and hydrostatic pressure determined by water hori- time variables with the space factor of the func- zontal plane above the deck in the vessel’s ac- tion being the solution of the hydrodynamic tual position, vessel’s acceleration and by problem and the known time factor. Such an changing in time heights of the horizontal approach significantly simplifies calculations plane above the deck. because bulky calculations can be performed at the beginning of the simulations and the ready The equations of ship motion in irregular waves are written in the non-inertial reference Proceedings of the 9 th International Conference on Stability of Ships and Ocean Vehicles 3 system. The system Q is fixed to the ship in the where Sd is the wetted surface of the deck, n1, centre of its mass and the equations of ship mo- n2, n3 are components of the normal vector in tion assume the following form (Jankowski, the considered deck point: 2006): = n4 x QP 2n3-x QP 3n2, . + × = + n = x n -x n , m[V Q (t) Ω(t) VQ (t)] FW (t) 5 QP 3 1 QP 1 3 (3) −1 = + + + + + n6 xQP 1n2-x QP 2n1 FD (t) FR (t) FT (t) FA (t) mD G, • + × = + L(t) Ω(t) L(t) M QW (t) (1) and RQP = (x QP1 , x QP2 , x QP3 ) is the position vec- + + + + M QD (t) M QR (t) M QT (t) M QA (t), tor of deck point P in non inertial system Q • (the components of the normal vector are de- = − × RUQ (t) VQ (t) Ω(t) RUQ (t), termined in the reference system fixed to the • • • vessel in its centre of mass). The pressure in ϕ θ ψ T = −1 ( (t), (t), (t)) DΩ Ω(t) this point is equal to: where m is the mass of the vessel, dh p = ρ w + ρ(g + a )h VQ = (V Q1,V Q2,V Q3) is the velocity of the mass dt v (4) centre, Ω = ( ω1, ω2, ω3) is angular velocity, L = (l Q1 , l Q2 , l Q3 ) is the moment of momentum, RUQ = (x UQ1 , x UQ2 , x UQ3 ) is the position vector where of the ship mass centre in relation to the inertial system U, moving with a constant speed equal ϕ θ ψ = + + to the average speed of the vessel, ( , , ) are w d 31 VP1 d 32 VP2 d 33 VP3 , Euler’s angles, FW, FD and FR are a = d A + d A + d A , Froude–Krylov, diffraction and radiation V 31 P1 32 P2 33 P3 V = V + Ω × R , (5) forces, respectively, G = (0, 0, -g), MQW , MQD , P Q QP • • MQR are their moments in relation to the mass A ≈ V Q + Ω× R centre , D is the rotation matrix, and DΩ is the P QP matrix which transforms. Euler. components of rotational velocity (ϕ,θ,ψ) into Ω. The additional forces and moments such as damping d3i , i = 1,2,3 , are components of the matrix D forces or those generated by the rudder are de- and h is the vertical distance of the horizontal noted by FA and MQA . plane from the point of the deck in the inertial coordinate system U. Velocity w and accelera- The ways of solving 3D hydrodynamic prob- tion av are also determined in the system U. lems and determining forces appearing in the equation of motion are presented in This formula has been derived basing on the (Jankowski, 2006). evaluation of Newton’s momentum relation for a control volume on deck in the following way The forces FT, and moments MQT caused by (Buchner, 2002): water on deck, are calculated according to the following formula: d(∆mw ) d(∆m) dw ∆F = = w + ∆m (6) dt dt dt = −ρ ⋅ i = 1,2, .., 6 Fi ∫ p ni ds , (2) Sd where ∆F is the force acting on the area ∆A of the deck containing the point P considered.

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