The Issues of Ship's Transverse Stability while Dry-Docking - Math Problem Example

The Issues of Transverse Stability while Dry-docking Ships are often needed to be dry-docked in order to perform the repairing and maintenance related works that are constrained due to its connection with water. Necessarily the maintenance, refurbishing, repair, renovation of the underwater hull, the outer surface, the major portion of the exterior and mainly those parts that remain in constant contact with the sea water are performed in a dry-dock. Even the total construction of a ship is to be carried out in a dry dock. The key-factor to dry-dock a ship is to support it avoiding the possible and potential hazard, while it is taken out of the water. Both with the moments of the dry-docking and re-launching a ship several issues of transverse stability are to be tackled in order to ensure the safety of the ship and to avoid any damage. The issues are as following: 1. Positive Initial GM 2. Lining up Vertically with the Center-line 3. Lining up Vertically over the Center-line of the Keel Blocks 4. Managing the Critical Period When the ship is fully waterborne, it is complete stable enough to avoid any major collision. But as soon as its stern touches the blocks due to the fall of the water level when the water is pumped out, the draft aft will decrease (Docking and Launching). The water will be pumped out, till the ship will fully land on the blocks throughout its length. During the critical period between the landings of the stern and the other end of the ship, most of the issues of transverse stability need to be addressed. At the beginning of the critical period when the stern touches the blocks, they are to bear a part of the weight of the ship and an up-thrust is created at the stern. Consequently metacentric height of the ship decreases due to the up-thrust of the blocks at the stern. During the critical period, an effective and positive GM (metacentric height) is to be maintained. (Best 167) Effective Metacentric Height for Transverse Stability While docking a ship, an Effective Metacentric Height (GM) is necessary for Transverse Stability of the ship. At the beginning of the critical period when the ship touches the blocks, its stability depends on two supports: one by the blocks and the other by its buoyancy at the other end. The situation increases the virtual center of gravity and decreases the metacentric height. Determining an Effective Metacentric Height for Transverse Stability necessarily involves measuring the positive metacentric height for any instant while dry-docking. If the metacentric height is excessively decreased and the buoyancy is not more than the inclined weight of the ship, its stability will be affected. So for the stability of the ship, an effective Metacentric Height can be maintained during the dry-docking process in the following ways: 1. Maintaining the inclination or slope of the blocks 2. Using external forces as supplementary to the buoyancy 3. Avoiding any angle heel caused by wind, wave, etc. Now if the weight of a ship is W and its center of gravity is G­­0, the weight W acts downward through G0. The up-thrust of the blocks P acts through the Keel K. The equilibrium will be maintained, if (W­ – P) is equal to FB (buoyancy). Now if the initial metacenter of (W – P) force is M and the virtual Gravity is Gv, then Gv will be as following: And the virtual metacentric height is: As the ship looses stability during the critical period due to up-thrust at the keel, the “righting moment at inclination ‘’ before the application of ‘P’ is (). After application, the righting moment is,.” (Launching and Docking) Transverse Stability at the Angle of Heel When Launching Source: Launching and Docking Right at the moment the stern of the ship touches the bocks and until its other end lands, the transverse stability of the ship may be affected by the external heeling forces like the beam wind, wave, grounding on uneven blocks, towline pull of tug, entrapped water on deck, etc. The more the weight of the ship is borne by the blocks, the more the buoyancy of the ship decreases. Consequently the risk of transverse stability increases. Such instability can be tackled by the sufficient support of tugs, dockside lines, workboats etc. The same risk of transverse stability affected by the external forces may cause hazards during the launching of the ship. During the re-launching or the docking of the ship, both when for the first time the stern lands in water or on the block, the weight of the ship shift either from the keel blocks to the buoyancy of the ship or from buoyancy to the keel blocks. While re-launching and docking the ship, a tug pull Ft is necessary to let the ship fully being water-borne in order to avoid the abrupt up-thrust of water generated by the buoyancy Fb. The way that is used to slide the ship to the sea is greased thoroughly. When the ship enters the water, the force of buoyancy rises up to a certain value, which is enough to pivot the ship around the fore poppet (Launching and Docking). At this moment, the force generated by the weight of the ship grew and reaches the critical stage. The factors that may affect the transverse stability of the ship are as following: a. Damage due to longitudinal weakness b. The Ship might be unstable due to more 100 angle of heel c. Abrupt Plunge into water d. The Collapse of the ground way due to Excessive Pressure generated by the abrupt lifts of the buoyancy. e. Excessive breaking Effect on the ship-structure. Calculation of the transverse stability of a ship has a lot to avoid such damages during the launching of ship. The weight and the center of gravity are measured at the preparatory stage. When the ship enters the water, the bon-jean curves are used to study the immersed sectional areas and the longitudinal center and the buoyancy of the submerged portion of the ship are measured down in a profile. The ship moves downward until the buoyancy increases enough to be equal to the moment of weight around the fore poppet. A series of launching curves are used to present the data gathered from the preparatory stage to the equilibrium between the buoyancy and the moment of weight about the fore poppet. Figure: Ship and ways geometry. Source: Launching and Docking Figure: Bon-jean curves for the immersed sectional areas Source: Launching and Docking Prediction Ship Stability through Launching Curves A set of six curves is prepared in order to predict the behaviour of the ship during the re-launch safely. The important features of the curves are as follows: a. Weight W of the ship, the buoyancy of the submerged part FB.d and the weight around the fore poppet Wa are constant b. The buoyancy FB of the ship raises as it moves downward c. Weight around the fore poppet Wa is constant d. When FB.d and Wa are equal, the stern lifts. e. When the stern raises, force on the fore poppet reaches at the highest level f. FB.d must be higher than the moment of buoyancy about after end of the ways, FB.c (Launching and Docking). Figure: Typical launching curves. Source: Launching and Docking Launching Ways Constructed to Avoid the Angels of Heel and Proper Trim In order to avoid the heel –produced due to the sliding along the ways- affecting the transverse stability of the ship, the launching ways are constructed according to some mathematical instructions. In the following picture, α = The initial slope of the keel. β = Declivity of the ground ways, ie, slope of chord. LBP = Length between perpendicular. e = Distance of the fore poppet abaft the forward perpendicular. h = Initial height of the fore poppet above water. f = Camber of ways of length k. r = Radius of camber. (Launching and Docking) Figure: Construction of launching ways. The camber of an arc of a circle is given by, (Launching and Docking) If the ship moves downward at a distance ‘x’, the forepart of the poppet is elevated at the height ‘y’ above the chord and meanwhile the keel shifts at an angle of ‘x/r’. Now, the height of the fore is: (Launching and Docking) On the other hand, “the height of a point‘t’ above water abaft the fore poppet” (Launching and Docking) is, (Launching and Docking) If the camber of the way is 0, ‘r’ tends to be infinite. If, ‘t’ equivalent to (-e), it will give the height of the keel at the fore poppet above water. When ‘t’ is equivalent to (L-e), it yields the negative draft at the after perpendiculars. For the stability of the ship Wa and FB must be equal. FB and Fb at the fore poppet should be calculated for several trims about the fore poppet. The proper trim is where the curves of moment about fore poppet cut (Launching and Socking). Figure: Trim calculation. Source: Launching and Docking Pressure on the Initial Contact during the Docking When the stern of a ship lands first on the blocks, the force pushed in the contact point needs to be measured properly as it plays a crucial role in determining the pull of the tug and sidelines in order to maintain the stability of the ship on the blocks. Also at the time of re-launching of the ship needs the proper measurement of the force to maintain balance between the buoyancy and the moment of weight about the fore poppet. At any time of docking, the weight of the ship is difference between weight and buoyancy (W- FB). If this weight is divided by the length between the contact point on the block and the center of buoyancy, the mean load per unit length is: Wm = W - FB / lw The mean pressure, where, lw = the length of ways, bw = the width of ways. And, the mean pressure on the keel, (Launching and Docking) When re-launching the ship the maximum pressure is equal to the weight of the ship W. If the stern lift, the pressure on the launching way will be (W- FB). Consequently the moment of this weight about the fore poppet is (W.a-FB.d). Figure: Pressure distribution on the ground ways. If the weight of the ship is distributed unevenly on the launching way, the curve of load per unit length is a trapezoid. If the length is ‘lW’ at any moment, the weight per unit length about the forepart of the poppet and at the end of ways are Pfp and Pap. (Launching and Docking) The Pfp and Pap are as following: The mean pressure on the keel, and also Then, The moment of way load about f.p., Solving the above equations for Pfp and Pap, Or, let be ‘r’ the distance of the center of pressure distribution about fore poppet; And, (Launching and Docking) This is a satisfactory solution while Pfp and Pap are positive and the load per unit length can be represented by a trapezium. When is greater than , Pfp becomes negative and when is less than , Pap becomes negative (Launching and Docking). The Issue of Transverse Stability while Sideway Launching Ships are often launched sideway due to some of its facilities. If the vessel is small or the space of water front is not wide then the three common ways of vessel launching can be applied. The processes of sideway launching are shown below. 1. The process can be applied if the way built under the water and the ship slides down over the way: 2. In this process the ship drops off the end of the launching ways: While sideway re-launching the stability of the ship may be affected because of the violent up-thrust of the water. The transverse stability of the ship may be affected at thirty degree of heel. So stability at large angle is seriously considered during this type of launching. Figure: Effect of Sliding Speed Source: Transverse Stability at Small Angle of Heel Planning Procedure for Dry-Docking Dry-docking involves removing a ship out of water to a place where all of the facilities of repairing and other maintenance are available. A dry-dock is necessarily situated near the sea. It is a tough task to repair a ship when it is still in the water and if the damage is in the exterior part under the ship then it would be a tough task to repair. This is why a ship is necessary to be pulled on over the dry part of the dockyard. When a vessel dry-docked and re-launched there has to face some kind problems, which are available. When a ship is dry-docked we need to be careful about the issues, which are given below. The yard where a vessel is repaired should be well developed. All of the facilities of a modern shipyard should be available there. Proper guiding principles are needed to set up a dockyard. The berthing of vessels should be easy. The owner should ensure that the loading and unloading process of cargos is easy. The access of vessels should be easy and the way of entrance should be wide and deep. Providing more facilities and suitable designed dockyard is desired. The consideration factors are the design of dockyard, winds, currents, deposition of undesired materials, etc. The location of the dockyard is a factor and it should be chosen on the comfortable position. The avoidance of wave agitation is necessary. Dry-docking mainly consists of mainly three different stages: 1. Primary Preparation, 2. Docking, 3. Launching. Any miscalculation or flaw may bring catastrophe and disaster such as life-casualties, ship tilting, structural damage, etc. Primary Preparation: A through preparation is necessary for the success of the total dry-docking of a ship. The dock master will critically examine the ship and note down it weight, volume, size, category, etc. If possible the center of gravity, the center of buoyancy, and other necessary should be gathered. This information will help the dock master to assess the whole plan of dry-docking. Also he should prepare the dry dock by setting the keel blocks into right position. The staffs of the dockyard will take all the preparations: all of physical, mental, instrumental preparations. “A qualified dockmaster supervises the operation. Dock-based winches are usually used to position the ship in the dock” (USDL). The Phase of Docking: Docking is a slow and strenuous process. Using some pulling and pushing forces by tugs, dockside lines, etc. the ship is carefully positioned over the blocks. Once the ship lands properly on the blocks, the water is pumped out of the dock. The most critical task is to make the ship land properly on the keel blocks. Usually the stern of the ship lands first, then the other end of the ship is supported by the buoyancy. “The most dangerous time in drydocking occurs when support for the ship is changing from water buoyancy to dry dock blocks. If the strength of the blocks is insufficient, they can be crushed, overturning the ship” (USDL). When the stern of the ship lands on the blocks, the center of gravity rises and the metacentric height decreases. Undocking Phase: The process of undocking should be performed carefully, because any mistake may cause great damage. While launching a sound idea of the transverse stability and the watertight integrity is very necessary. Re-launching process is same as the basic of the docking, to a great extent. “Careful planning and considerable expertise are required to launch a ship by sliding it into the water. Drag chains of predetermined weights are used to control the ship's entry into the water. Tugs are needed to control the ship after entry into the water” (USDL). Works Cited Best, A.M. "Dry dock operations." Loss Control Engineering Manual, 1975. “Launching and Docking”. 07 March, 2009. Retrieved from “Transverse Stability at Small Angles of Heel”, 07 March, 2009. Retrieved from United States Department of Labour, “Process: Dry Docking and Launching.” Occupational Safety & Health Administrations, Washington DC, 30 January, 2008. 07 March, 2009. from ”Launching and Docking” Read More