SHIP HYDROSTATICS AND STABILITY

Size: px
Start display at page:

Download "SHIP HYDROSTATICS AND STABILITY"

Transcription

1 [Type text] SHIP HYDROSTATICS AND STABILITY A SYSTEMATIC APPROACH Omar bin Yaakob

2 A systematic Approach Table of Content Table of Content... ii Preface... iv Chapter 1 Ship Types, Basic Terms, Terminologies and Symbols Introduction Types of ships Basic Terms, Terminologies and Symbols Reference positions: Linear Dimensions Size of Ships Form Coefficients Centroids Ship Lines Plan The importance of Ship Lines Plan Body Plan Half Breadth Plan Profile / Sheer Plan Offsets Data Ship Geometry Coordinate System Chapter 2 Hydrostatics and Floatation Archimedes Principles of Floatation Reduction of Weight of Immersed Objects What makes a ship float? Effect of Density Some Simple Problems Tonne per centimeter immersion (TPC) Hydrostatics Particulars Hydrostatic Particulars of a Ship Using Hydrostatic Curves and Tables Bonjean Curves Cross Sectional Area Curve Second Moments of Areas Exercises Chapter 3 Basic Stability Consideration Introduction What is stability? Universiti Teknologi Malaysia, August 2012 ii

3 A systematic Approach 3.3 Longitudinal and Transverse Stability Basic Initial Stability: The role of GM Determining the Centre of Gravity of ships after loading Effect of movement or addition of weights on centre of gravity Hanging Weights, The Use Of Derricks And Cranes Free Surface Correction The Effect of Free Surface on Ship Stability Calculating Second Moment of Area Exercises Chapter 4 Transverse Stability List due to movement of weights onboard Finding list after loading and unloading Correcting Lists by moving or adding weight Exercises Universiti Teknologi Malaysia, August 2012 iii

4 A systematic Approach Preface Man has benefited from the sea in various ways. The sea has been the source of food, ornaments as well as provided means of transportation. Conquests and defences have been carried out on water. Water-based leisure activities are becoming more common and varied. Lately, man has innovated the use of the sea beyond those traditional applications. The sea has now become a primary source of petroleum, gas and lately marine renewable energy. To carry out various activities at sea, rivers and lakes, man uses various types of marine structures, fixed and floating. The structures normally provide safe and stable platforms upon which the activities are carried out. They must be designed and built in various sizes, shapes and sophistication. Some of them are small and simple such as a canoe or a raft while others are large and complicated such as an aircraft carrier or a semi-submersible oil drilling platform. Naval architecture is an engineering field covering the technology in design of ships and floating structures ensuring that they can perform their stipulated functions and missions effectively and safely. The persons having this expertise are called naval architects. To build these structures, shipbuilders requires design plans and guidelines prepared by naval architects. Knowledge in naval architecture is used to carry out design calculation and to produce plans which can be used by the shipyards. Although man has been using marine transport for a long time, not all these vehicles are designed and constructed using naval architecture knowledge. In fact the discipline of knowledge on ship design and naval architecture only appeared in the seventeenth century. Prior to that, shipbuilding is not based on science and technology but rather on the skills of the master craftsmen. This dependence on master craftsmen for shipbuilding can be traced back to the earliest civilization of Egypt, Greek and China. Similarly the warships and exploration vessels built by the Romans, Muslims as well as the European colonial powers were not built using scientific methods. By the seventeenth century a number of scientists and engineers tried to apply science and mathematical methods in ship design. Among the earliest was Sir Anthony Deane who wrote Doctrine of Naval Architecture in Among others, he put forward a method to determine the draught of the ship before it was built, a technique which formed the basis of we now understand as hydrostatics. Since then, a number of scientists and engineers continued to study and document various fields of naval architecture. In 1860, a professional body comprising of naval architects was formed under the name Institution of Naval Architects. A hundred years later the name was changed to Royal Institution of Naval Architects. Universiti Teknologi Malaysia, August 2012 iv

5 A systematic Approach A naval architect works to determine the size and shape of a ship tailored to its intended use. In addition, he estimates its stability, propulsive power as well as calculates the size and strength of its structure and the impact of waves on the vessel. The types of machinery and equipment to be installed, materials to be used and layout of ship are also determined based on naval architectural knowledge. This book will cover only one aspect of naval architecture, that is ship hydrostatics and stability since it is one of the most important subject in naval architecture. The safety of ships, crew, passengers and cargo will be jeopardised if ships are not stable. This book is written to enable readers to appreciate the basic terminologies, carry out simple hydrostatics calculations and to equip them with basic tools to assess stability of vessels. Many books have been written on naval architecture, ship hydrostatics and stability. Most books however are difficult to follow, due to the unsystematic way the materials are presented. This book differs from the rest in the sense that the content is not presented as discrete topics, unrelated to each other. Instead, it is presented in a systematic and logical manner. It introduces the basic concepts and develops the understanding in a continuous progression of knowledge acquisition as well as confidence building through handson calculations examples and exercises. The Chapters are interrelated, as do the Sections. Readers can easily see the relationships between each Chapters and Sections. Materials which are important but not fit to be in the logical flow of the content are put in the appendices. This book is also designed to be a self-teaching and self-explanatory book. Knowledge is built in an incremental manner. Readers can read and understand the step by step explanation and solutions to the problems and able to apply their knowledge by solving the exercises provided. In writing this book, I have depended on many persons. In particular I am thankful to Ir Dr Mohamad Pauzi, Dr. Koh Kho King and Haji Yahya Samian who have contributed to some of the sections. There are many others who have assisted in various ways. Universiti Teknologi Malaysia, August 2012 v

6 A systematic Approach Chapter 1 Ship Types, Basic Terms, Terminologies and Symbols 1.1 Introduction 1.2 Types of ships There are various ways of categorizing ships. Ship types can be classed according to a number of criteria such as the number of hulls, hull form shapes, the way it is supported in water, and its mission/function. 1. Number of Hulls Ships can be categorized in terms of the number of hulls. Most ships have only a single hull; these are called mono-hulls. Some ships have multiple hulls such as catamaran and trimaran. Figure 1 A mono hull Fishing Boat Universiti Teknologi Malaysia, August

7 A systematic Approach Figure 2 A Catamaran 2. Shape of hull form The shape of the hull are different from one ship and the other. Most large slow ships have round-bilge hull form while smaller faster boats normally have chine hulls. The fishing boat in Figure 1 has a round-bilge while the Catamaran in Figure 2 has chine hull form. Chine hulls consists of two or more almost flat surfaces, the line connecting the surfaces is called the chine line. When the hull is made up of two surfaces, then there is a single chine. Double chine vessels have three surfaces. Chine hulls are also called V-shaped hulls while round-bilge hulls are called U-shaped hulls. Figure 3 Mono hull planing craft with single chine 3. How the body is supported in water When a ship is in water, the total weight of the ship is being supported by various forces, depending on the types of hullform. Round-bilge hull forms are normally supported hydrostatically, i.e. all the weight of the vessel is supported by buoyancy forces which equals the total weight of water displaced by the vessel. These are also called displacement hull. Universiti Teknologi Malaysia, August

8 A systematic Approach Figure 4 Marine Craft Support Triangle Volker Bertram, Overview of High-Performance Marine Vehicles as Naval Platforms, Volume 38, Number 2 - Summer 2008 Hydrofoils are an examples of vessels supported by the dynamic lift due to its flat lower foils. At high speeds, the lift forces provided by the foils is enough to support the ship, lifting it out of water. At these speeds, the hydrostatic buoyancy forces are insignificant. By lifting the body above the water surface, the drag of water on the hull is reduced and the vessel can travel at high speeds. Universiti Teknologi Malaysia, August

9 A systematic Approach Figure 5 High speed Hydrofoil Ferry Another kind of ships are the hovercrafts, which operates above the water surface. Air cushion is provided by large fans which pump air to lift the vessel above the water surface. The total weight of the vessel is supported by the air cushion, sometimes referred to as aeropowered lift forces. Figure 6 A Hovercraft Passenger Ferry Many vesssels have combinations of support. For example, when a chine hull vessel is stationary, it is hydrostatically supported. However, when it starts to move and reaches a certain speed, water moving along the lower hull will lift the vessel, reducing the hydrostatic buoyancy forces. In this case, at the cruising speeds the vessel is supported both by a combination of hydrostatics and hydrodynamic forces. Chine-hull vessels which operate at high speeds using partial hydrodynamic support are called planing hull vessels, see Figure 3. Universiti Teknologi Malaysia, August

10 A systematic Approach 4. Its function/mission Ships can also be categorized according to their functions i.e. how they are used for the benefit of mankind. For example, some ships are meant for transport such as crude oil tankers, bulk carriers, containerships, passenger ships, general cargo ships, liquefied natural gas (LNG) carriers. The ships used in the navy may take various size, dimensions and functions such as aircraft carrier, submarine, frigate, destroyer, patrol craft, and minesweeper. Some ships are not meant to carry cargo but to carry out certain service at sea. Examples of work or service vessels include tugs, supply boats, crew boats, heavy lift, crane ships, fishing boats and rescue boats. Some other boats are used for recreational purpose such as luxury yacht, cruise ships, tourists boats. Figure 7 This 396m long containership is one of the largest ship in the world Universiti Teknologi Malaysia, August

11 A systematic Approach Figure 8 A crude oil tanker Universiti Teknologi Malaysia, August

12 A systematic Approach 1.3 Basic Terms, Terminologies and Symbols The terms and terminologies used in naval architecture are unique. Proper and uniform understanding is important since these terms and symbols will be used not only in hydrostatics and stability calculations but also in various other naval architecture calculations such as ship resistance and propulsion, ship structure and ship hydrodynamics. These symbols and terms are used by those in the academic world as well as by the practioners in the industry. Therefore proper understanding is important to ensure smooth and efficient communications Reference positions: Distances and relative locations are measured from certain reference positions on ships. Design Waterline (DWL) Waterlines are lines of the water surface at which the ship is expected to float at. DWL is the waterline at which the ship is expected to float at its fully loaded or operational condition. After perpendicular(ap) AP is the line which is perpendicular to the intersection of the after side of the rudder-post with the DWL. For some ships without rudder-post, the AP is taken as the centre-line of the rudder stock or the intersection of the DWL with the transom. Forward perpendicular (FP) A line drawn perpendicular to the intersection of the DWL with the forward side of the stem. Amidships or Midships ( ) The point midway between the forward and after perpendiculars. Base line The lowest part of the ship, normally the underside of keel where a horizontal line is drawn. This becomes a reference line for measurements in the vertical direction. Universiti Teknologi Malaysia, August

13 A systematic Approach Linear Dimensions Important linear dimensions of the ship are shown in Figure 9. Figure 9 Linear Dimensions Length between perpendiculars (LBP or LPP) The horizontal distance between AP and FP. This is the most important length measurement during ship design development stages. Most calculations such as stability, propulsion, maneuvering use LBP. Universiti Teknologi Malaysia, August

14 A systematic Approach Length on the design load water-line (LWL) The length on the water-line of the ship when floating in still water at DWL. In many cases, this is similar to LBP and also important during calculations in the deisgn stages. Length overall (LOA) The length measured from the extreme point forward to the extreme point aft. This length is an important measure during operational stage of the ship. Breadth or Beam (B) The maximum breadth or beam of the ship is usually measured at amidships. Some ships have the largest breadth not at amidships. Depth (D) The vertical height of the uppermost continuous deck measured at the side amidships from the base line. Draught or Draft (T) The depth of immersion from baseline to any waterline. Freeboard The height of the deck at side above the LWL. It is equal to the difference between the depth and the load draught. Trim The difference between the draughts at AP and FP. If the draught forward is greater than the draught aft it is called trim forward, by the head, or by bow. If the draught aft is greater, it is called trim aft, by stern. Ships without trim are said to be level keel or even keel. Trim are sometimes stated as trim angles, θ. Moulded, Extreme and Displacement Dimensions Moulded linear dimensions refer to measurements of inner dimensions of the ship, i.e. the measurements neglect the thickness of plating. Subscripts mld are used. Moulded breadth for example (Bmld) is the breadth measured between the inside plating on the two sides of the ship, moulded depth (Dmld) and draughts (Tmld) are measured from the top of the keel plate. Moulded dimensions are normally used during ship construction process, especially when lofting is carried out. In hydrostatics and stability calculations, the outer or extreme dimensions are used. These are given the subscript ext, for example Text. These dimensions consider the Universiti Teknologi Malaysia, August

15 A systematic Approach surfaces which are in contact with water. Unless otherwise stated, all dimensions without subscripts are normally referred to extreme dimensions Size of Ships The size of ships are normally stated in terms of displacement, deadweight or gross registered ton (GRT). Some ships such are measured in terms of their carrying capacity, for example TEUs (Twenty feet Equivalent Units) for containerships, the number of cars for car carriers or the number of heads for livestock carriers. In ship design and operation field, the term weight and mass are used interchangeably and units of mass (tonnes/tons/pounds/kilograms) are normally used. Although this is not strictly correct, the net impact is the same and as long as consistency is maintained, there should not be any problem. Volume Displacement ( ) A floating ship displaces water. The volume of water being displaced is the amount of water pushed aside by the ship. The volume of water is called the volume displacement of the ship usually expressed in m 3. Mass Displacement ( ) When a ship is floating, it is displacing the volume of water whose weight or mass is equivalent to its own weight or mass. The total weight of the vessel is the same as the weight of water being displaced. So the term mass displacement is the same as the total weight or mass of the ship in sea water, normally expressed in units of tonnes or kilogram. This weight of water equals the volume displacement multiplied by the density of water, In fresh water = x 1000 kg/m³ In sea water = x 1025 kg/m³ Most of the time, the term displacement refers to mass displacement. Mass displacement or weight of the ship is equal to the sum of lightship weight and deadweight. The operational displacement of the ship or its total weight will actually vary from time to time. While the lightship weight is constant, the deadweight and hence the displacement will vary from time to time during operation depending on the loading conditions of the ship. Universiti Teknologi Malaysia, August

16 A systematic Approach Lightship Lightship weight is the weight of an empty ship, without cargo, crew, water, fuel and other payload components. It is normally associated with a ship that has just been built and ready to sail. It is the non-variable component of the mass displacement. Deadweight The difference between the mass displacement and the lightship weight is called the deadweight. This is the variable component of displacement and includes cargo, fuel, crew, passengers, stores, etc, expressed in tonnes. The sizes of tankers and bulk carriers are often quoted in terms of the deadweight tonnage, which is the maximum deadweight the ship is designed to carry. Since the weight of the cargo make up most of the deadweight, the deadweight tonnage is a good measure of the cargo carrying capacity of the tankers and bulk carriers. Displacement tonnage The designed total weight of the ship is called ship displacement tonnage and this is normally stated in the ship particulars. The sizes of non-cargo carrying ships such as ships belonging to government agencies are normally stated in terms of displacement tonnage. Gross tonnage (GRT) Although the terms tonnage and tons are used, GRT is not a measure of weight. Instead, gross tonnage is the total volume of enclosed spaces in a ship including the under-deck and the enclosed space in the superstructure of the ships. Due to its history of its use, although its unit is tons, it is a measure of volume, not weight where 1 ton is equivalent to 100 ft3. The sizes of most commercial vessels are stated in terms of gross tonnage. Net or register tonnage GRT is the total volume of enclosed spaces onboard a ship, NRT is the net volume after deductions of non-freight earning spaces such as engine room and crew accommodation. Net tonnage are used when charges are levied for services are provided for the commercial ship, for example for pilotage and port charges. Universiti Teknologi Malaysia, August

17 A systematic Approach Form Coefficients When comparing one ship's form with another, the naval architect makes use of a number of coefficients. These coefficients of forms are used as a general term to describe the fullness or the fineness of the ship hulls. These coefficients are important and used in power, stability, strength and design calculations. Coefficient of forms are stated in terms ratios between the actual area or volumes divided the are or volume of the circumscribing box. The higher the value, the fuller the ship form. However the values do not exceed 1. Block coefficient (CB) This is a measure of the fullness of the form of the ship and is the ratio of the volume of displacement to a given water-line, and the volume of the circumscribing box having the same length, breadth and draught as the ship. ie: CB = (L x B x T) CB varies between ships. Typically slimmer, faster ships such as frigates and patrol crafts have CB between while slower full form ships such as tankers and bulk carriers have CB 0f around Midship section area coefficient(cm) This is the ratio of the midship section area to the area of the circumscribing rectangle having a breadth equal to the breadth of the ship and a depth equal to the draught. ie: CM = AM (B x T) Water-plane area coefficient(cwp) This is the ratio of the area of the water-plane to the area of the circumscribing rectangle having a length equal to the LPP and a breadth equal to B. ie: CWP = AW (L x B) Prismatic coefficient (CP) The ratio of the volume of displacement of the ship to the volume of the circumscribing box having a constant section equal to the immersed midship section area AM, and a length equal to the LwL i.e. CP = (AM x L) Universiti Teknologi Malaysia, August

18 A systematic Approach The above is the most typical prismatic coefficient, sometimes called longitudinal prismatic coefficient, because it is a measure of the longitudinal distribution of displacement of the ship. In certain cases, vertical prismatic coefficient CPV is calculated CPV = Awp x L Centroids The location of centroids of areas, volumes and weights are important in hydrostatics and stability calculations. Centre of flotation (F) When a ship trims at small angles of trim, the ship is pivoting about a transverse axis passing through the centre of floatation, F. When viewed from the side, consecutive water-lines are assumed to be passing through the centre of floatation. The centre of floatation coincides with the centre of the waterplane area at that draught. The location of F is measured longitudinally from the references axes, either amidships, AP or FP. This distance is called longitudinal centre of floation (LCF). Centre of buoyancy (B) The single buoyancy force representing the summation of all hydrostatic forces acting on a ship is considered to act upwards through a single point called the centre of buoyancy (B). This coincides with the centroid of the underwater volume of a ship. Its position is defined by: (a) Vertical centre of buoyancy (VCB) which indicates the location in the vertical direction. The reference line must be stated. In normal practice, the keel line is used as the reference line and in this case, this height is stated as KB which is the vertical distance above keel. (b) The longitudinal distance measured either from amidships or AP or FP is called the longitudinal centre of buoyancy (LCB). Centre of gravity (G) This is the point through which the total weight of the ship may be assumed to act. Similar to the centre of buoyancy, the location of centre of gavity also is defined by: (a) Vertical centre of gravity (VCG) which indicates the location in the vertical direction. In normal practice, KG is used where the keel line is used as the reference line. Universiti Teknologi Malaysia, August

19 A systematic Approach (b) Longitudinal centre of gravity (LCG) which is measured either from amidships or AP or FP. the longitudinal distance 1.4 Ship Lines Plan The importance of Ship Lines Plan Ship has a complex and unique hull shape due to its double curvature and nonhomogeneous cross sections. Unlike simple object like cylinder, box, and cone which can be represented in simple orthographic drawing, ship hull require special way of representing its unique and complex shape. Not only it require to be shown in three different orthogonal views, more lines are also needed in order to represents its shape at different cross sections or planes. For this reason, the ship hull drawing is always called as Lines Plan Drawing. Lines Plan Drawing is a lines drawing that represent the shape of the ship hull looking from three orthogonal (perpendicular to each other) views i.e. front, side and top views. The front view is termed as Body Plan, the side view is the Sheer Plan and the top view is the Half Breadth Plan. Since all of these views represent the same hull, they are interrelated to each other, thus the preparation of lines plan drawing must follow certain standard procedure. Lines plan drawing has always regarded by the naval architects as the most important piece of information about the ship. This is due to two reasons i.e. the ship performance and ship design process. On the performance of the ship, the shape of the hull form determines the power required to drive the ship, thus reflect the ship speed, its also determine the amount of pay load (capacity), comfort, habitability, etc. On the ship design process, lines plan drawing is the first information that needs to be made available. Without lines plan drawing, no calculation, design and analysis works can be performed. Construction process also can only be commenced after the lines plan drawing is completed. Some samples of the various hull form are shown in Figure 10 to 12. Universiti Teknologi Malaysia, August

20 A systematic Approach Figure 10: Body plan of a displacement hull (Container Ship) Figure 11: Body plan of a planning hull (Vee hull with hard chine) Universiti Teknologi Malaysia, August

21 A systematic Approach Figure 12: Body plan of a catamaran Body Plan Body Plan represents the shape of the ship hull when viewing from the front or rear of the ship at every ship stations as shown in Figure 10 and 13. Station is a transverse cross-section along the ship length which normally equally spaced. The body plan concept can be better understood by referring to Figure 14. A ship is normally divided into 11 or 21 stations from after perpendicular, AP (Sometimes noted as station 0) until forward perpendicular, FP (or noted as station 10 0r 20). Half or even quarter station may also be used especially at the region with high curvature. Body plan is normally placed at the top right hand side of the drawing although it can also be placed at the middle or on top of the sheer plan drawing depending on the size and type of ship. Since most ships have symmetrical shape for both port (left side looking from rear) and starboard (right) sides, only one side is shown in the drawing. Therefore, it is almost a standard practice to show the stations of the rear region of the ship at the left side of body plan while the right hand side of the body plan represents the stations at the forward region of the ship. The curve on the body plan is also call station curve. The centre line of the body plan represents the centre line of the ship. Apart from showing the station curves, the body plan also shows the waterlines and the buttock lines grid. These grid lines are essential not only for reference lines but also used for transferring and checking data from one plan to another. Universiti Teknologi Malaysia, August

22 A systematic Approach Figure 13: Body plan Figure 14: 3-Dimensional body plan Universiti Teknologi Malaysia, August

23 A systematic Approach Half Breadth Plan The same hull form if it is viewed from top will produce the plan view of the ship. However since the hull shape is complex and unique, the plan view must be made at several waterline planes. Thus Half Breadth Plan is a lines drawing that represents the shape of the ship hull looking from top view at every waterlines of the ship. Waterline is the horizontal plane that cut the ship along its vertical axis, thus creating the waterlines curves as shown in Figure 15. Waterline is normally equally spaced, although half waterline may also be used at the lower region of the ship. Since the hull is symmetry about its centre line, only half of the hull is shown in this plan as shown in Figure 16. Apart from waterline curves, the deck line curve needs to be drawn on this plan. If the ship has bulwark, chines or / and knuckles lines, these curves have also to be shown in the drawing. In this plan, the grid lines shown are the stations and buttock lines of the ship. Universiti Teknologi Malaysia, August

24 A systematic Approach Figure 15: 3-Dimensional half-breadth plan Figure 16: Half breadth plan Universiti Teknologi Malaysia, August

25 A systematic Approach Profile / Sheer Plan Sheer Plan which is usually placed at the top left hand side of the lines plan drawing represent the shape of the ship hull looking from the side of ship at several buttock lines. Buttock line is the vertical plane that cuts the ship along its length, creating the buttock line curves as indicated in Figure 17. The middle buttock line (normally labeled as BL 0) is the plane that cuts the ship along its centre line which creates the profile curve of the ship. Other buttock lines are drawn outward (offsets) of ship s centre line and normally at equally spaced distance. The stations and waterlines grids are shown in this sheer plan drawing. A typical sheer plan drawing is shown in Figure 18. Plan B = Plan C Figure 17: 3-Dimensional sheer plan Universiti Teknologi Malaysia, August

26 A systematic Approach Figure 18: Profile / Sheer Plan Offsets Data Offsets data is the data that is extracted (measured) from the lines plan drawing and considered the most important data for the design, calculation, analysis and construction of the ship. As the name implied, Offset Data is the distance measured from the centre line of the ship to the specific point on the curves (station or waterline curves). The offset data must be measured at every intersection points on each stations and waterlines including deck line, chines, knuckles and bulwarks (if any). Offset data also called as half breadth data, because it represents the half breadth of the ship at every station and waterlines. A typical example of offsets data is shown in Table 1 and the measurement of offsets data is illustrated in Figure 19. In the offsets Table, it is also a standard practice to indicate the data of height above based for deck, chine, bulwark, and knuckles lines. The height above base of buttock lines may also be included whenever necessary. A sample of the complete lines plan drawing containing the body plan, profile, halfbreadth plan and offset are shown in Figure 20. Table 1: Offsets table Universiti Teknologi Malaysia, August

27 Figure 20: Offset data relation to lines plan

28 1.5 Ship Geometry Coordinate System Sometimes, there is a need to define the locations and positions on the ship hull using coordinates. In such cases, the following system is used: Z axis for vertical direction, positive upwards X axis for longitudinal direction, positive forward Y axis in the transverse direction, positive to starboard. See Figure 21. Y The origin (x=0, y=0, z=0) is normally taken at amidships, the centre line and the baseline. Sometimes, the origin in the longitudinal direction i.e. x = 0 is taken at AP or FP.

29 A Systematic Approach Chapter 2 Hydrostatics and Floatation 2.1 Archimedes Principles of Floatation Archimedes principle states that An object immersed in a fluid experiences a lift equivalent to the mass of fluid the object displaces. It means that when an object is inside a fluid, there is a force acting vertically upwards upon it, the magnitude of which is equivalent to the mass of fluid displaced by the object. This force is called buoyancy. A man immersed in water for example will feel a weight reduction because part of his weight is supported by buoyancy. This buoyancy is equal to the weight of water displaced by the immersed parts of his body. 2.2 Reduction of Weight of Immersed Objects The maximum buoyancy force exist when the object is fully immersed and this equals the weight of the fluid being displaced. This in turn equals the total volume of the space occupied by the object multiplied by the density of the fluid. If the weight of the immersed object is less that the weight of fluid being displaced, the object experience a net positive force upwards i.e. lift. For example, a helium balloon is lifted up by the buoyancy force equivalent to the displaced mass of air. Although the volume of helium in the balloon is similar to the volume of air that the balloon displaces (disregarding the thin skin of the balloon), the weight of helium in the balloon is less than the weight of air being displaced due to the lower density of helium. Therefore, the net force is positively up, i.e. the balloon floats up in the air. This also explains the strong force required to keep a ball to stay underwater. The weight of water being displaced by the ball is more than the weight of the ball itself, and hence the ball will experience a strong net buoyancy force upwards. Omar bin Yaakob and Mohamad Pauzi Abdul Ghani, July

30 A Systematic Approach W Δ> W, giving net lift pushing the ball upwards Δ1> W, ball floats in equilibirum If the ball is slowly brought to the surface, the ball will be pushed upwards until an equilibrium is reached such that the ball floats with only a certain portion of it being immersed in water. In this case, the smaller weight of water being displaced now equals to the weight of the ball. When maximum available buoyancy is less than the weight of the object, the object will sink. That is why an anchor will sink to the bottom. However the object will still feel the effect of weight reduction. Omar bin Yaakob and Mohamad Pauzi Abdul Ghani, July

31 A Systematic Approach Example 2.1: Consider a cuboid having dimensions 1m x 1m x 2m in Figure 3.1. If it weighs 3 tonnes in air, what is its apparent weight in water density 1000 kg/m 3? If the object is immersed in liquid, it will displace liquid around it equivalent to its external volume. In this case, displaced volume = 1 x 1 x 2 = 2 m 3 This is the volume of liquid displaced or pushed aside by the cuboid. According to Archimedes Principle, the weight of this object in liquid is reduced due to the support given by the liquid on the object. The apparent weight is equal to the weight in air minus the reduction in weight of the object or the buoyancy i.e. Buoyancy = weight of fluid displaced = volume displacement x density of liquid = 2m 3 x 1000 kg/m 3 = 2000 kg = 2 tonnes = reduction in weight Apparent weight = weight in air buoyancy Since the object weighs 3 tonne in air, it will apparently weigh only 1 tonne in water. Omar bin Yaakob and Mohamad Pauzi Abdul Ghani, July

32 A Systematic Approach Exercise 2.1 Do similar calculations to find out the apparent weight in oil (density 0.85 tonne/m 3 ) and muddy water (density 1.3 tonne/m 3 ) and mercury (density 13,000 kg/m 3 ) Fluid Oil Density ( ) Fluid Support ( ) Apparent Weight ( ) Fresh Water Muddy Water Mercury What can be concluded about relationships between buoyancy of objects and the densities of fluids in which they are immersed? 2.3 What makes a ship float? As can be seen in Section 3.1, when the maximum available buoyancy is more than the weight of the object, the object will rise to the surface. It will rise to the surface until the weight of the object is equal to the buoyancy provided by its immersed portions. When the object is floating, its buoyancy is just enough to support its weight. At that point: Total weight W = Buoyancy = Displaced volume x liquid This principle explains why a steel or concrete ship can float. As long as the outer shell of the ship can provide enough volume to displace the surrounding water exceeding the actual weight of the ship, the ship will float. A floating ship is such that the total weight of its hull, machinery and deadweight equals to the weight of water displaced by its outer shell. If, while it is floating weights are added until the total weight exceeds the maximum buoyancy That can be provided by the outer shell of the ship, the ship will sink. 2.4 Effect of Density An object experiences buoyancy force equivalent to the weight of fluid it displaces. As seen in Example 3.1, for a particular object, the buoyancy force will depend on the density of the fluid, since its volume is constant. The basic relationship can be written as follows: Total weight W = Buoyancy = Displaced volume x liquid (3.1) Omar bin Yaakob and Mohamad Pauzi Abdul Ghani, July

33 A Systematic Approach From Equation (3.1), the displaced volume is inversely proportional to the density of fluid. For a floating object, this will determine its level of sinkage or draught. This explains for example why a bather will feel more buoyant while swimming at sea compared to the river or lake. Also, a floating object of constant weight will sink at a deeper draught in freshwater compared to in seawater. Consider a boat moving from the sea to a river. There is a change of density from the more dense seawater to freshwater which has a lower density. Since the weight of the boat does not change, the buoyancy force to support the boat is also constant. With the lower density of fluid, the boat need to increase its displaced volume. To ensure this, the boat will need to sink deeper i.e. increase its draught Some Simple Problems The fact that a floating object displaces fluid equivalent to its weight as shown in Equation 3.1 can be used to solve a number of problems. From this equation, we can obtain the weight of the object if we know the volume of water displaced. On the other hand, if we know its weight, we can work out its displaced volume. To illustrate the concept, consider a floating box of dimension L x B x D, floating at a draught T, shown in Figure 3.2. CASE 1: If we know its weight, we can find its draught In this case, we know the weight of the object, so we can find the displaced volume: Displaced volume, = W water Since it is a box-shaped vessel: Displaced volume = L x B x T Hence draught T of the cuboid can be found. Omar bin Yaakob and Mohamad Pauzi Abdul Ghani, July

34 Example 2.2 A Systematic Approach A cuboid shaped wooden block (L x B x D) 1.45m x 0.5m x 0.25m floats in water. If the block weighs tonnes, find its draught if it floats in freshwater density 1.00 tonne/m 3. Solution: The weight of the block of tonnes must be supported by displaced water i.e. the block must displace tonnes of water: In fresh water, Volume of displaced water = L x B x T Weight of displaced water = x FW = 1.45 x 0.5 x T x FW This must equal tonne 1.45 x 0.5 x T x fw = tonnes T = m Exercise 2.2 Do similar calculations for salt water (density 1025 kg/m 3 and oil density 0.85 tonne/m 3 ) CASE 2: If we know its draught, we can know its volume displacement and we can find its weight If we know the draught of the cuboid, we can find its volume displacement and hence the weight of the object; Say if we know its draught T, volume displacement = L x B x T Weight = Buoyancy = Volume Displacement x water Weight = L x B x T x water Example 2.3 A box barge length 100m breadth 20m floats at a draught of 5m in sea water tonne/m 3. Find its weight. Solution While floating in sea water density tonne/m 3 : Volume Displacement = = L x B x T Weight of barge = Weight displacement, W = = x salt water Omar bin Yaakob and Mohamad Pauzi Abdul Ghani, July

35 = 100 x 20 x 5 x = tonnes A Systematic Approach Exercise 2.3 A block of wood length 5m, breadth 0.5m and depth 0.2m is floating in seawater at a draught of 0.1m. Find the weight of the block. Exercise 2.4 Find the new draught of the box in example 3.3 when it goes into river, water density tonne/m 3. Also find a new draught if it is in sea water with density tonne/m 3. Exercise m A cylindrical container weighing 5 tonne floats with its axis vertical. If the diameter is 1.0m, find its draught in: i. sea water ii. oil of density 870 kg/ m 3. Exercise 2.6 A cylindrical tank diameter 0.6m and mass 200kg floats with its axis vertical. Find its present draught in oil ( = 0.95 tonne/m 3 ). Find the weight of cargo to be added to ensure it will float at a draught of 0.85m. Omar bin Yaakob and Mohamad Pauzi Abdul Ghani, July

36 Exercise 2.7 A Systematic Approach A boat with constant triangular crossection is floating with its apex down. Its LBP is 10m, breadth 2m and depth 0.7m. If it floats in sea water ( = 1025 kg/m 3 ). at a draught of 0.5m, what is its weight? 2.6 Tonne per centimeter immersion (TPC) The weight required to increase or reduce trim by one centimeter ia called Tonne per centimeter immersion (TPC) For the ship having area of waterplane Awp, an increase in draught of one centimeter will require an addition of weight equivalent to the additional volume of displacement multiplied by the density. Example 2.4 Additional weight = Awp x 1cm 100 A ship with TPC of 30 floats at a draught of 6.5m. What is the new mean draught ahen 150 tonne is unloaded from the ship. Omar bin Yaakob and Mohamad Pauzi Abdul Ghani, July

37 2.7 Hydrostatics Particulars A Systematic Approach A floating object will be floating at a certain draught depending on the total weight of the object, the density of water and the shape of the object. For a ship, the shape of the object has a strong influence on the draught of the ship; the shape and draught have to provide enough buoyancy to support the ship. When a ship is floating at a certain draught, we can find the mass displacement and weight of the ship if we can find its displaced volume. Also we can know its waterplane area, calculate its TPC, KB, C b etc. These particulars which are properties of the immersed part of the ship are called hydrostatic particulars. Examples of hydrostatic particulars are:,, KB, LCB, A w, BM T, BM L, TPC, C B, C P, C M, C W, LCF, MCTC These particulars describe the characteristics of the underwater portion of ship at a particular draught. It is related to volumes, areas, centroids of volumes and areas and moments of volumes and areas of the immersed portion. If the ship is taken out of water, and draught becomes zero, the particulars ceased to exist. As long as draught and trim are maintained, the size and shape of the underwater immersed parts of the ship remains the same. The volumes, areas and moments of areas and volumes remain the same and consequently, the hydrostatics particulars do not change. Once draught or trim changes, the particulars will also change. These changes in draught and trim will normally occur due to changes in the total weight of the ship, movement of weights onboard or if external forces are applied. Exercise 2.8 A box 2m x 1m (LxB) is floating in sea water. Calculate its,, C B, C WP and TPC at draughts of 0.3 and 0.5m Omar bin Yaakob and Mohamad Pauzi Abdul Ghani, July

38 A Systematic Approach Exercise 2.9 Find hydrostatic particulars in sea water (,,Awp,LCB, LCF,TPC) of a box barge with dimension L=100m, B=20m, at draughts of 1.0m, 3.0m, 5.0m, 7.0m, 9.0m. If the barge weighs 2,300 tonne, what is its draught? If the barge is floating at a draught of 4m, what is its C B? Exercise 2.10 Calculate,, KB, LCB, A w, TPC, C B, C P, C M, C W, LCF of a cylinder radius 1m floating with axis vertical at draughts of 1.0, 1.5, 2.0 and 2.5m. It can be seen from Exercise 2.9 and 2.10 that for cuboids or cylinders, the waterplane areas are constant at different draughts. Hence, many hydrostatics particulars which depend on waterplane areas also remain constant. Exercise 2.11 An empty cylindrical shaped tank is floating in sea water (density t/m 3 ) at a draught of 8.0 m with its axis vertical. The external diameter of the tank is 12.0 m, internal diameter 11.0 m, thickness of base 1.0 m and the overall height is 16.0 meter. Its centre of gravity is 6 meter above its inner base. Calculate:. i. Find Hydrostatic particulars, Awp, LCB, Cb, Cp, TPC, WSA at T=1, 2, 4, 6, 8m. ii. Plot hydrostatic curves similar to page 19 showing all data. ii. Final draught of the tank after 500 m 3 diesel oil (density 850 kg/m 3 ) is poured into the tank. The second moment of area of a circle about its diameter is D Omar bin Yaakob and Mohamad Pauzi Abdul Ghani, July

39 2.8 Hydrostatic Particulars of a Ship A Systematic Approach The objects considered in the previous sections are simple, uniform objects such as cuboids, cylinders and prisms. The formulae involved in these cases are simple and familiar. In some cases, the particulars such as block coefficient and waterplane areas remain constant at various draughts. By using these objects, the calculations are simplified and can be used to show the main concepts. Those formulae used for the simple objects are no longer applicable for real ships, although the concepts remain relevant. Unlike those simple objects considered earlier, real ships rarely have uniform cross sectional areas or waterplane areas. The waterplanes are no longer made up of straight lines. Therefore, there is no simple formulae to calculate their areas, volumes and moments and hence hydrostatic particulars. Consider the ship whose lines plan is shown in Figure 3.2. At different draughts, the ship will have different waterplane areas, sectional areas, volumes and centroids. Hence, the hydrostatic particulars will also vary as the draught changes. The methods to calculate areas, volumes, moments, centroids of the waterplanes and sections of ships will be covered in Chapter 3. If areas, volumes, moments, centroids of the waterplanes and sections of the ships can be calculated, hydrostatic particulars of a ship can be obtained. These are calculated at the design stage, once the shape and size of the ship has been decided. The particulars can be presented in two forms, either as a set of curves or in tabular format. Table 2.1 shows a typical table of hydrostatic particulars while an example of hydrostatic curves is shown on Figure 2.3. Omar bin Yaakob and Mohamad Pauzi Abdul Ghani, July

40 A Systematic Approach Table 2.1 Hydrostatic Particulars of Bunga Kintan LBP 100m Draught (m) Displacement (tones) Cb KB (m) BM T (m) BM L (m) MCTC (tonne-m) LCB (m from ) LCF (m from ) Exercise 2.12 A ship with length 100m, breadth 22m has the following volumes and areas at different waterlines. Calculate its, C B, C W and TPC in saltwater density 1.025tonnes/m 3. Draught (m) Aw (m 2 ) (m 3 ) (tonnes) x Cb Cw TPC LBT Aw (LB) Aw x 100 Omar bin Yaakob and Mohamad Pauzi Abdul Ghani, July

41 A Systematic Approach 2.9 Using Hydrostatic Curves and Tables Hydrostatic curves and tables can be used to obtain all hydrostatic particulars of a ship once the draught or any one of the particulars is known. Example 2.5 From MV Bulker hydrostatic Curves (Figure 3.3 ) at a draught of 7m, we can obtain displacement = 31,000 tonnes, LCF = 2.0m forward of amidships and MCTC = 465 tonne-m etc. Also if we know the ship weighs 40,000 tonnes, its draught, TPC, MCTC, LCF and LCB can be obtained. Exercise 2.13 Using MV Bulker Hydrostatic Curves, find displacement, LCB, LCF, TPC at draught of 9.5m. If 1500 tonnes is added to the ship, what is its new draught? Omar bin Yaakob and Mohamad Pauzi Abdul Ghani, July

42 A Systematic Approach Hydrostatic tables can be used in a similar manner to obtain hydrostatic particulars once draught is known or to obtain draught and other particulars once the displacement or another particular is known. There is however a need to interpolate the table to obtain intermediate values. Exercise 2.14 By using the hydrostatic particulars of Bunga Kintan shown in Table 3.1: i. Draw full hydrostatic curves of the ship ii. Find values of displacement, KB, LCB, BM T, BM L, MCTC, C B, LCF of the ship if it is floating at a draught of 6.75m. iii. Find values of T, KB, LCB, BM T, BM L, MCTC, C B, LCF of ship if the ship weighs 11,480 tonnes. iv. When the ship is floating at a draught of 5.5m, 3000 tonne cargo was added. What is its new draught? 2.10 Bonjean Curves One important hydrostatic particular is the area of a section. For a particular transverse section, the sectional area can be calculated up to a particular waterline. This can be done for all waterlines at each station. If these areas are plotted against draughts at all station positions along the ship, the resulting diagram is called Bonjean Curves. The curves are frequently drawn on the ships profile at the displacement stations or on a centre line with those for stations in the fore body on the right hand side and for the after body on the left hand side. They enable the displacement and LCB to be calculated for any waterline, trimmed or even keel. Omar bin Yaakob and Mohamad Pauzi Abdul Ghani, July

43 A Systematic Approach The plot for every stations are superimposed on the profile of the ship as follows: 2.11 Cross Sectional Area Curve The shape of the hull can be defined by a curve representing the distribution of the crosssectional area (CSA) of each section at the respective stations up to a particular waterline, normally DWL. The curve is called Sectional Area curve Second Moments of Areas The Basic Formulae The second moment of area or moment of inertia are used in the calculations of metacentric heights. Therefore is important to have a firm understanding of this important quantity. By definition, second moment of area is the product of area multiplied by square of the distance of the centre of that area to the reference axis. The second moment of an element of an area about an axis is equal to the product of the area and the square of its distance from the axis Omar bin Yaakob and Mohamad Pauzi Abdul Ghani, July

44 A Systematic Approach Consider the rectangle length l and breadth b. A small segment area length I and breadth dy will have an area l x dy. The second moment of the rectangle about an axis parallel to one of its sides and passing through the centroid (XX) is Ixx = Area x y 2 Ixx = l x y2 x dy = Consider the elementary strip which is shown shaded in the figure. The second moment (i) of the strip about the axis AB is given by the equation:- i= l dx x x 2 Let I AB be the second moment of the whole rectangle about the axis AB then:- IXX b/2 -b/2 l. y 2. dy b/2 1 l y 2. dy XX -b/2 3 y l 3 b / 2 b / 2 1 XX 3 lb 12 1 AB 3 lb 12 The second moment of a rectangle about one of its sides ( axis AB):- b 1 x 2 AB l.. dx O Omar bin Yaakob and Mohamad Pauzi Abdul Ghani, July

45 x 3 l 3 b O A Systematic Approach 1 AB 3 lb 3 According to the Theorem of Parallel Axes the second moment of an area about an axis through the centroid is equal to the second moment about any other parallel axis minus by the product of the area and the square of the perpendicular distance between the two axes. Thus, in Figure A.4, 2 I I - Area y XX AB Fig. A.4 Omar bin Yaakob and Mohamad Pauzi Abdul Ghani, July

46 A Systematic Approach Second moment of area of a circle X Fig. A.5 X For circle, the second moment of area about an axis AB. I AB D 64 4 Exercise Determine what is IXX? Calculations of Metacentric Heights Second moment of areas are used in calculations of the distances from ship centre of buoyancy to the longitudinal and transverse metacentres, BML and BMT respectively: BM L I F and BM T I T Where I F is longitudinal second moment of area of the waterplane about the centre of floatation, I T is transverse second moment of area about the centreline and is volume displacement. Omar bin Yaakob and Mohamad Pauzi Abdul Ghani, July

47 A Systematic Approach In hydrostatic calculations, the longitudinal second moment of area is initially calculated about amidships. To obtain IF, theorem of parallel must be used: I F I WPA LCF 2 Where WPA is the waterplane area and LCF is the centre of floatation measured from amidship. BML and BMT are important hydrostatic particulars which are required in the calculations of ship stability. a) Calculations of Moment to Change Trim one Centimeter (MCTC) MCTC is the moment required to change trim one centimeter. `````` The actual formula for MCTC is MCTC GM 100 L L tonne-m Where GM L is the distance from the centre of gravity to longitudinal metacentre and L is LBP. Usually, GM L is large and can be approximated by BML. Therefore the formula becomes: MCTC IF 100 L tonne-m Since MCTC IF 100 L Omar bin Yaakob and Mohamad Pauzi Abdul Ghani, July

48 A Systematic Approach Exercises 1. Find BM L and BM T of a box shaped barge 120m x 20m x 10m floating at a draught of 7m. 2. A cylinder of radius r = 10m is floating upright at draught of 6m in fresh water. Find its KM L and KM T. 3. A fish cage consists of a wooden platform placed on used oil drums with the following dimensions. If the total weight of the structure is 3 tonnes, floating in sea water calculate: i) draught ii) KMT iii) KML 4. A catamaran consists of two box-shaped hulls spaced 5m apart, centreline to centreline. Each hull measures (L x B x D) 10m x 0.5m x 1m. If its draught is 0.3m, find its : i) and ii) KB iii) BMT iv) Maximum allowable KG if GM minimum is 0.2m Omar bin Yaakob and Mohamad Pauzi Abdul Ghani, July

49 A Systematic Approach 5. A ship has the following characteristics at a draught of 2m: LBP = 220m Displacement = 153 tonnes BML = 24.3 m LCF = 0.97m aft of amidships Calculate: i. MCTC in sea water density tonne/m 3. ii. longitudinal second moment of area of the waterplane about the centre of floatation iii. longitudinal second moment of area of the waterplane about the centre of amidships Omar bin Yaakob and Mohamad Pauzi Abdul Ghani, July

50 A Systematic Approach Chapter 3 Basic Stability Consideration 3.1 Introduction One of the factor threatening the safety of the ship, cargo and crew is the lost or lack of stability of the vessel. Stability calculation is an important step in the design of the ship and during its operation. While designing the ship, the designers must be able to estimate or calculate to check whether the ship will be stable when constructed and ready to operate. During operation, the ship's officers must be able to load and stow cargo and handle the ship while ensuring that the ship will be stable and safe. 3.2 What is stability? Stability is the tendency or ability of a system to return to its original condition when disturbed or displaced from its normal equilibrium condition. Ship stability is the tendency or ability of the ship to return to upright when displaced from the upright position. A ship with a strong tendency to return to upright is regarded as a stable vessel. On the other hand, a vessel is said to be not stable when it has little or no ability to return to the upright condition. In fact, an unstable ship may require just a small external force or moment to cause it to capsize. A ship is normally stable to a certain degree of heel, after which it will capsize. Some have a large or strong tendency to return to upright while others have a smaller returning or righting moment. Some ships have a large range of stability, up to 90 degrees and beyond while others capsize when heeled beyond small angles of say, 20 degrees. An analogy for stability is often given of the marble. In Figure 3.1 (a), the marble in the bowl will return to its original position at the bottom of the bowl if it is moved to the left or to the right. This marble is in a condition called positively stable. Figure 3.1 Omar bin Yaakob and Mohamad Pauzi Abdul Ghani, July

51 A Systematic Approach A slight push on the marble which is put on an upside down bowl as in Figure 3.1 (b) will cause it to roll off, a condition equivalent to instability. A neutrally stable ship is analogous to a marble put on a flat surface, it will neither return nor roll any further. It can also be seen there are various degrees of stability. For example a bowl with very steep sides will have larger stability than a bowl with less sloping sides. As we will see later, there are also varying degrees of ship stability, from ships with a highly positive stability to those having negative stability. 3.3 Longitudinal and Transverse Stability Ship initial stability can be seen from two aspects, longitudinally and transversely. From longitudinal viewpoint, the effect of application internal and external moments on ship's trim is considered. Examples of application of moment is the movement of weights on board in the forward-aft direction or the addition or removal of weights to/from the ship. Important parameters to be calculated are trim and the final draughts at the perpendiculars of the ship. In any state, there is a definite relationship between trim, draughts and the respective locations of the centres of buoyancy and centre of gravity. Sometimes, the trim angle is also calculated. Transverse stability calculation considers the ship stability in the port and starboard direction. We are interested in the behaviour of the ship when external moments are applied such as due to wind, waves or a fishing net hanging from the side. The effect of internally generated moments such as movement of weights on-board transversely is also studied. This includes the shifting of weights or crowding of passengers on one side of the boat. Important relationships considered are those between heeling, listing and righting moments, as well as the resulting angle of heel or list and its consequence on the safety of the boat. Note that the words list and heel have similar meanings. However, heel has a more general meaning and normally used for effects of outside moments which are temporary such as due to wind, while list is normally used for the effects of internally generated moment, such as movement of weights on-board. This Chapter will focus on basic transverse stability particularly the relationship between the metacentre and the centre of gravity and its effect on ship stability. Further transverse stability calculation will be dealt with in the next Chapter while the details regarding longitudinal stability will be covered in the Chapter 7. Omar bin Yaakob and Mohamad Pauzi Abdul Ghani, July

52 3.4 Basic Initial Stability: The role of GM A Systematic Approach Figure 3.2 Consider the ship floats upright in equilibrium as in the above Figure 4.2 (a). The weight of the ship equals its displacement and the centre of buoyancy is directly below the centre of gravity. The points B, G and M are centre of buoyancy, centre of gravity and metacentre respectively. When the ship is slightly disturbed from upright for example due to wind blowing from port, the centre of buoyancy (which is also the centre of immersed or displaced volume) moves to the right. The line of action of buoyancy points vertically upward crossing the original centreline at the metacentre, M. Since G does not move, a moment is generated to turn the ship back to its original position. This moment is called the returning or righting moment. In this case, M was originally above G and we can see that the righting moment is positive i.e. the ship is stable. If M was below G i.e. GM negative, the righting moment will be negative hence the ship is unstable. If M is at G, then the ship is neutrally stable. Righting moment is the real indication of stability i.e. the ability of the ship to return to oppose any capsizing moment and return the ship to upright position. The larger the righting moment, the better stability is. Omar bin Yaakob and Mohamad Pauzi Abdul Ghani, July

53 Consider the triangle shown below: A Systematic Approach Righting moment = x GZ and GZ = GMT sin For any displacement, righting moment depends on GZ. And GZ depends on GM. The bigger the value of GZ, the bigger will be the righting moment. Since GZ is a function of GM, then bigger GM will lead to larger GZ, bigger righting moment and hence better stability. It is very essential that ships have large enough GM to ensure that it has enough righting moment to overcome external moments. The relationships between K, B, G and MT are important. The relationships can be used to guide us how to increase GM. KMT = KB + BMT KMT = KG + GMT For any particular draught or displacement at low angle of heel, keel K and metacentre M are fixed. Therefore the values of KB, BM and hence KM are fixed, as can be obtained from hydrostatic particulars and the distance GMT will only depend on the height of the centre of gravity. In other words, if we can control KG, we can also control GM and hence ship stability. The lower the centre of gravity, the larger will be GM, and conversely a high value of KG may lead to small or even negative GM, which means an unstable ship. Omar bin Yaakob and Mohamad Pauzi Abdul Ghani, July

54 A Systematic Approach 3.5 Determining the Centre of Gravity of ships after loading The ability to pin-point the location of the ship s centre of gravity is important because its distance from keel will affect GM and hence the ship s stability. The centre of gravity will remain unchanged except under two conditions: i. Weights are added to or removed from the ship at locations not coinciding with the original centre of gravity. ii. Weights already onboard are shifted, causing changes in moments about the centre of gravity. The effect of addition and removal of weights from ships on the centre of gravity can be calculated by using the fundamental concepts of centroids of composite bodies. The concept is given in Appendix 1. The tabular methods described in Appendix 1 can be applied directly. When considering the net centre of gravity after loading and unloading, three groups of items are normally considered; the original ship. Their respective weights and centres of gravity become the input data from where the final KG is calculated. Example 3.1 A ship originally weighs 2000 tonnes with KG= 5.5m. One cargo of 300 tonne was unloaded from Kg=7.6m and another 500 tonne was loaded at Kg=2.5m. Find the final KG. Item Weight (tonnes) Kg (m above keel) Lightship Unload Cargo Load Cargo TOTAL Moment about keel (tonne-m) KG = Total moment about Keel = Total weight m Omar bin Yaakob and Mohamad Pauzi Abdul Ghani, July

55 Example 3.2 A Systematic Approach A ship of 6,000 tonnes displacement has KG = 6 m and KM = 7.33 m. The following cargo is loaded: 1000 tonnes, Kg 2.5 m 500 tonnes, Kg 3.5 m 750 tonnes, Kg 9.0 m The following cargo is then discharged: 450 tonnes of cargo Kg 0.6 m And 800 tonnes of cargo Kg 3.0 m If KM on completion of loading is 7.3, what is the final GM. Item Weight (tonne) Kg Moment about keel (tonne-m) Ship Loaded Cargo1 Cargo2 Cargo3 Unloaded Cargo 4 Cargo Final moment Final KG = Final displacement = Final KG = m Final KM = m Final KG = m Ans. Final GM = m Omar bin Yaakob and Mohamad Pauzi Abdul Ghani, July

56 Exercise A Systematic Approach A box-shaped barge is floating in sea water at a draught of 5m. The extreme dimensions of the barge (L x B x D) are 12m x 11m x 10m. The wall and floor are 0.5m thick. Its centre of gravity is 4m above keel. Calculate: i. The displacement and GMT of the empty barge. ii. The barge is to be used to carry mud (density1500 kg/m 3 ). If the draught of the barge cannot exceed 7.5m, find the maximum volume of mud that can be loaded into the barge. iii. For the barge loaded as in (ii), find its GMT. 3.6 Effect of movement or addition of weights on centre of gravity When portions of weights or areas or volumes are moved, added or removed the overall centroid of the object will also move. The basic concepts to determine the movement of centroids due to the movement or addition/removal of weights, areas or volumes is described in Appendix 2. The concepts given in Appendix 2 can be directly applied to ships. When weights are shifted transversely on-board a ship, the moments change in the port-starboard direction, causing the centre of gravity to shift. Similarly, when weights are added or removed, the net effect is the centre of gravity will shift. When a weight is added, the centre of gravity will move in the direction towards the point at which added. On the other hand, when a weight is removed, the centre of gravity will shift in the direction away from the point at which the weight is removed. Example 3.3 A boat displacement 150 tonnes has KG of 1.25m, GM 1.7m and floating upright in salt water. A weight of 2 tonne already onboard is moved from port to starboard. Find the shift of the centre of gravity. Omar bin Yaakob and Mohamad Pauzi Abdul Ghani, July

57 Example 3.4 A Systematic Approach A ship weighing 7000 tonnes is floating at the wharf. At that time, KM = 6.5 m and GM 0.5m. A 30 tonnes box is loaded at a distance 10.0m above keel. By considering the shift in the centre of gravity, find new GM. Assume no change in KM. Solution: Find rise in KG Original KG = KM - GM = m Distance 30 tonnes box from original G = GG = 30 x 4.0 = 0.017m 7030 m KG = KG+ GG = m KM does not change, therefore, GM = = m Exercise: Find the new KG and GM of the ship in Example 3.3 using Method 2: Find final KG using table of moment about keel Portion Mass (m) Kg (m) Moment about keel (tonne-m) Ori. Ship Box Total 7030 KG = Sum of moment Sum of weight KG = m GM = KM - KG KM - KG = m Omar bin Yaakob and Mohamad Pauzi Abdul Ghani, July

58 A Systematic Approach 3.7 Hanging Weights, The Use Of Derricks And Cranes The use of cranes and derricks will make the weights suspended. Suspended weights are assumed to act at the point of suspension. Therefore a weight that was initially located on the lower deck for example will instantly be transferred to the point of suspension at the instant the weight is lifted off the deck by the derrick. The centre of gravity KG will suddenly increase and because KM is constant, GM will suddenly reduce. If the rise in KG is more than the original GM, the net GM will be negative, leading to instability. Example 3.5 A ship of 7,500 tonnes displacement is upright and has GM 0.20m and KM 6.5 m. A heavy cargo of 100 tonnes already on the lower deck (kg=2m) is to be unloaded using the ship s crane. When lifting the cargo crane head is 15 m above keel. What is GM during lifting. Comment of the safety of the operation. Treat as if the weight is suddenly transferred from lower deck to the point of suspension, a distance of 15 meters. The KG will rise, and since KM constant, GM will be reduced. Omar bin Yaakob and Mohamad Pauzi Abdul Ghani, July

59 Original KG = KM-GM= = 6.3m A Systematic Approach Rise in KG = 100 x 13 7,500 =0.173m KG during lifting = KG + Rise = 6.473m GM during lifting = KM- Kgnew = = 0.027m 3.8 Free Surface Correction The Effect of Free Surface on Ship Stability When free surface exists on board the ship, stability of ship is affected. The free surface gives rise to free surface moment which in effect reduce GM. The reduction is called Free Surface Correction (F.S.C). FSC is calculated from the second moment of area of the surface of the fluid; FSC = Free surface moment Ship displacement Omar bin Yaakob and Mohamad Pauzi Abdul Ghani, July

Chapter 3 Hydrostatics and Floatation

Chapter 3 Hydrostatics and Floatation Chapter 3 Hydrostatics and Floatation Naval Architecture Notes 3.1 Archimedes Law of Floatation Archimedes (born 287 B.C) Law states that An object immersed in a liquid experience a lift equivalent to

More information

NAVAL ARCHITECTURE 1. Class Notes

NAVAL ARCHITECTURE 1. Class Notes NAVAL ARCHITECTURE 1 Class Notes d G G 1 W tonnes d G 1 G w tonnes d G 1 G w tonnes Omar bin Yaakob Chapter 1 Introduction Naval Architecture Notes Introduction To carry out various activities at sea,

More information

SHIP FORM DEFINITION The Shape of a Ship

SHIP FORM DEFINITION The Shape of a Ship SHIP FORM DEFINITION The Shape of a Ship The Traditional Way to Represent the Hull Form A ship's hull is a very complicated three dimensional shape. With few exceptions an equation cannot be written that

More information

S0300-A6-MAN-010 CHAPTER 2 STABILITY

S0300-A6-MAN-010 CHAPTER 2 STABILITY CHAPTER 2 STABILITY 2-1 INTRODUCTION This chapter discusses the stability of intact ships and how basic stability calculations are made. Definitions of the state of equilibrium and the quality of stability

More information

SECOND ENGINEER REG III/2 NAVAL ARCHITECTURE

SECOND ENGINEER REG III/2 NAVAL ARCHITECTURE SECOND ENGINEER REG III/2 NAVAL ARCHITECTURE LIST OF TOPICS A B C D E F G H I J Hydrostatics Simpson's Rule Ship Stability Ship Resistance Admiralty Coefficients Fuel Consumption Ship Terminology Ship

More information

Hydrostatics and Stability Dr. Hari V Warrior Department of Ocean Engineering and Naval Architecture Indian Institute of Technology, Kharagpur

Hydrostatics and Stability Dr. Hari V Warrior Department of Ocean Engineering and Naval Architecture Indian Institute of Technology, Kharagpur Hydrostatics and Stability Dr. Hari V Warrior Department of Ocean Engineering and Naval Architecture Indian Institute of Technology, Kharagpur Module No.# 01 Lecture No. # 01 Introduction Hello everybody.

More information

Hydrostatics and Stability Prof. Dr. Hari V Warrior Department of Ocean Engineering and Naval Architecture Indian Institute of Technology, Kharagpur

Hydrostatics and Stability Prof. Dr. Hari V Warrior Department of Ocean Engineering and Naval Architecture Indian Institute of Technology, Kharagpur Hydrostatics and Stability Prof. Dr. Hari V Warrior Department of Ocean Engineering and Naval Architecture Indian Institute of Technology, Kharagpur Module No. # 01 Lecture No. # 23 Trim Calculations -

More information

CLASS 1E 8 SMOOTH WATERS OPERATIONS 8

CLASS 1E 8 SMOOTH WATERS OPERATIONS 8 Table of Contents INSTRUCTION TO MASTERS SAFETY INFORMATION 3 STABILITY BOOK TO BE KEPT ON VESSEL 3 LOADING CONDITIONS 3 ASPECTS OF LOADING 3 PASSENGER PARTICULARS 3 HYDROSTATIC AND KN VALUES 4 EXCESS

More information

CERTIFICATES OF COMPETENCY IN THE MERCHANT NAVY MARINE ENGINEER OFFICER

CERTIFICATES OF COMPETENCY IN THE MERCHANT NAVY MARINE ENGINEER OFFICER CERTIFICATES OF COMPETENCY IN THE MERCHANT NAVY MARINE ENGINEER OFFICER EXAMINATIONS ADMINISTERED BY THE SCOTTISH QUALIFICATIONS AUTHORITY ON BEHALF OF THE MARITIME AND COASTGUARD AGENCY STCW 95 CHIEF

More information

Marine Kit 4 Marine Kit 4 Sail Smooth, Sail Safe

Marine Kit 4 Marine Kit 4 Sail Smooth, Sail Safe Marine Kit 4 Marine Kit 4 Sail Smooth, Sail Safe Includes Basic ship Terminologies and Investigation Check list Index 1. Ship Terminology 03 2. Motions of a Floating Body...09 3. Ship Stability.10 4. Free

More information

EN400 LAB #2 PRELAB. ARCHIMEDES & CENTER of FLOTATION

EN400 LAB #2 PRELAB. ARCHIMEDES & CENTER of FLOTATION EN400 LAB #2 PRELAB ARCHIMEDES & CENTER of FLOTATION Instructions: 1. The prelab covers theories that will be examined experimentally in this lab. 2. The prelab is to be completed and handed in to your

More information

Chapter 2 Hydrostatics and Control

Chapter 2 Hydrostatics and Control Chapter 2 Hydrostatics and Control Abstract A submarine must conform to Archimedes Principle, which states that a body immersed in a fluid has an upward force on it (buoyancy) equal to the weight of the

More information

Multihull Preliminary Stability Estimates are Fairly Accurate

Multihull Preliminary Stability Estimates are Fairly Accurate Multihull Design (Rev. A) 45 APPENDIX A ADDITIONAL NOTES ON MULTIHULL DESIGN MULTIHULL STABILITY NOTES Multihull stability is calculated using exactly the same method as described in Westlawn book 106,

More information

Have you seen a truck weighing bridge? Do you know how it works?

Have you seen a truck weighing bridge? Do you know how it works? Have you seen a truck weighing bridge? Do you know how it works? Weigh bridge It weighs the empty weight of the truck and then the loaded weight. The difference is the weight of the cargo on that truck.

More information

Ship Stability. Ch. 8 Curves of Stability and Stability Criteria. Spring Myung-Il Roh

Ship Stability. Ch. 8 Curves of Stability and Stability Criteria. Spring Myung-Il Roh Lecture Note of Naval Architectural Calculation Ship Stability Ch. 8 Curves of Stability and Stability Criteria Spring 2016 Myung-Il Roh Department of Naval Architecture and Ocean Engineering Seoul National

More information

Final KG plus twenty reasons for a rise in G

Final KG plus twenty reasons for a rise in G Chapter 3 Final KG plus twenty reasons for a rise in G hen a ship is completed by the builders, certain written stability information must be handed over to the shipowner with the ship. Details of the

More information

This lesson will be confined to the special case of ships at rest in still water. Questions of motions resulting from waves are not considered at

This lesson will be confined to the special case of ships at rest in still water. Questions of motions resulting from waves are not considered at STATIC STABILITY When we say a boat is stable we mean it will (a) float upright when at rest in still water and (b) return to its initial upright position if given a slight, temporary deflection to either

More information

Irrigation &Hydraulics Department lb / ft to kg/lit.

Irrigation &Hydraulics Department lb / ft to kg/lit. CAIRO UNIVERSITY FLUID MECHANICS Faculty of Engineering nd Year CIVIL ENG. Irrigation &Hydraulics Department 010-011 1. FLUID PROPERTIES 1. Identify the dimensions and units for the following engineering

More information

COURSE OBJECTIVES CHAPTER 2

COURSE OBJECTIVES CHAPTER 2 COURSE OBJECTIVES CHAPTER 2 2. HULL FORM AND GEOMETRY 1. Be familiar with ship classifications 2. Explain the difference between aerostatic, hydrostatic, and hydrodynamic support 3. Be familiar with the

More information

Chapter 5 Transverse Stability

Chapter 5 Transverse Stability Chapter 5 Transverse Stability Naval Architecture Notes Consider a ship floating upright as shown in Figure 5.1. The centres of gravity and buoyancy are on the centre line. The resultant force acting on

More information

PHYS 101 Previous Exam Problems

PHYS 101 Previous Exam Problems PHYS 101 Previous Exam Problems CHAPTER 14 Fluids Fluids at rest pressure vs. depth Pascal s principle Archimedes s principle Buoynat forces Fluids in motion: Continuity & Bernoulli equations 1. How deep

More information

Fluid Mechanics. Liquids and gases have the ability to flow They are called fluids There are a variety of LAWS that fluids obey

Fluid Mechanics. Liquids and gases have the ability to flow They are called fluids There are a variety of LAWS that fluids obey Fluid Mechanics Fluid Mechanics Liquids and gases have the ability to flow They are called fluids There are a variety of LAWS that fluids obey Density Regardless of form (solid, liquid, gas) we can define

More information

Hydrostatics and Stability Dr. Hari V Warrior Department of Ocean Engineering and Naval Architecture Indian Institute of Technology, Kharagpur

Hydrostatics and Stability Dr. Hari V Warrior Department of Ocean Engineering and Naval Architecture Indian Institute of Technology, Kharagpur Hydrostatics and Stability Dr. Hari V Warrior Department of Ocean Engineering and Naval Architecture Indian Institute of Technology, Kharagpur Module No. # 01 Lecture No. # 22 Righting Stability II We

More information

In the liquid phase, molecules can flow freely from position to position by sliding over one another. A liquid takes the shape of its container.

In the liquid phase, molecules can flow freely from position to position by sliding over one another. A liquid takes the shape of its container. In the liquid phase, molecules can flow freely from position to position by sliding over one another. A liquid takes the shape of its container. In the liquid phase, molecules can flow freely from position

More information

In the liquid phase, molecules can flow freely from position. another. A liquid takes the shape of its container. 19.

In the liquid phase, molecules can flow freely from position. another. A liquid takes the shape of its container. 19. In the liquid phase, molecules can flow freely from position to position by sliding over one another. A liquid takes the shape of its container. In the liquid phase, molecules can flow freely from position

More information

STABILITY OF MULTIHULLS Author: Jean Sans

STABILITY OF MULTIHULLS Author: Jean Sans STABILITY OF MULTIHULLS Author: Jean Sans (Translation of a paper dated 10/05/2006 by Simon Forbes) Introduction: The capsize of Multihulls requires a more exhaustive analysis than monohulls, even those

More information

Exam Question 9: Hydrostatics. March 6, Applied Mathematics: Lecture 8. Brendan Williamson. Introduction. Density, Weight and Volume

Exam Question 9: Hydrostatics. March 6, Applied Mathematics: Lecture 8. Brendan Williamson. Introduction. Density, Weight and Volume Exam Question 9: Hydrostatics March 6, 2017 This lecture is on hydrostatics, which is question 9 of the exam paper. Most of the situations we will study will relate to objects partly or fully submerged

More information

Understanding How Excessive Loading Lead to a Capsize with Loss of Life Can Help Avoid Future Tragedies

Understanding How Excessive Loading Lead to a Capsize with Loss of Life Can Help Avoid Future Tragedies Understanding How Excessive Loading Lead to a Capsize with Loss of Life Can Help Avoid Future Tragedies By Dave Gerr, CEng FRINA 2012 Dave Gerr fter sailing out to watch the fireworks on July 4th, 2012,

More information

ANNEX 5 IMO MARINE CASULATY AND INCIDENT REPORT DAMAGE CARDS* AND INTACT STABILITY CASUALTY RECORDS

ANNEX 5 IMO MARINE CASULATY AND INCIDENT REPORT DAMAGE CARDS* AND INTACT STABILITY CASUALTY RECORDS ANNEX 5 IMO MARINE CASUATY AND INCIDENT REPORT DAMAGE CARDS* AND INTACT STABIITY CASUATY RECORDS Statistics of damaged ships and of intact stability casualties are important to the work of the Organization

More information

WATERTIGHT INTEGRITY. Ship is divided into watertight compartments by means of transverse and longitudinal bulkheads bulkheads.

WATERTIGHT INTEGRITY. Ship is divided into watertight compartments by means of transverse and longitudinal bulkheads bulkheads. Damage Stability WATERTIGHT INTEGRITY Ship is divided into watertight compartments by means of transverse and longitudinal bulkheads bulkheads. When a watertight compartment (or a group of compartments)

More information

MSC Guidelines for the Submission of Stability Test (Deadweight Survey or Inclining Experiment) Results

MSC Guidelines for the Submission of Stability Test (Deadweight Survey or Inclining Experiment) Results S. E. HEMANN, CDR, Chief, Hull Division References a. 46 CFR 170, Subpart F Determination of Lightweight Displacement and Centers of Gravity b. NVIC 17-91 Guidelines for Conducting Stability Tests c. ASTM

More information

OPERATIONS SEAFARER CERTIFICATION GUIDANCE NOTE SA MARITIME QUALIFICATIONS CODE

OPERATIONS SEAFARER CERTIFICATION GUIDANCE NOTE SA MARITIME QUALIFICATIONS CODE Page 1 of 8 Compiled by Chief Examiner Approved by Qualifications Committee: 27 September 2013 OPERATIONS SEAFARER CERTIFICATION GUIDANCE NOTE SA MARITIME QUALIFICATIONS CODE Page 2 of 8 KNOWLEDGE, UNDERSTANDING

More information

Stability Information Booklet. Priority Pontoon

Stability Information Booklet. Priority Pontoon Stability Information Booklet Priority Pontoon Lightship Index General Particulars...3 General Details...4 Plan - GA...5 Plan - Frames...6 General Precautions against capsizing...7 Special Notes Regarding

More information

A Guide to the Influence of Ground Reaction on Ship Stability

A Guide to the Influence of Ground Reaction on Ship Stability Journal of Shipping and Ocean Engineering 6 (2017) 262-273 doi 10.17265/2159-5879/2017.06.004 D DAVID PUBLISHING A Guide to the Influence of Ground Reaction on Ship Stability Ahmed Helmy Abouelfadl and

More information

Report on inclining test and light ship survey

Report on inclining test and light ship survey Report 79 Report on inclining test and light ship survey Nae of ship (Yard no. and yard): Signal letters: Carried out, place and date: Suary of results: Light ship weight: tonnes Vertical centre of gravity,

More information

Trim and Stability Report for M.V. Storm Warning

Trim and Stability Report for M.V. Storm Warning Pacific Motor Boat Design/R. W. Etsell, P.E. Naval Architecture and Marine Engineering Trim and Stability Report for M.V. Storm Warning for Kimberlin s Water Taxi Valdez, Alaska Prepared by Richard W.

More information

RESCUE BOAT DESIGN UTILIZING REUSED PLASTIC BOTTLES FOR ACCIDENT PREVENTATION

RESCUE BOAT DESIGN UTILIZING REUSED PLASTIC BOTTLES FOR ACCIDENT PREVENTATION RESCUE BOAT DESIGN UTILIZING REUSED PLASTIC BOTTLES FOR ACCIDENT PREVENTATION Abstract- Fiberglass layer of rescue boat has tendency to crack when hit by a heavy wave or involves in accident. As an alternative

More information

COURSE NUMBER: ME 321 Fluid Mechanics I Fluid statics. Course teacher Dr. M. Mahbubur Razzaque Professor Department of Mechanical Engineering BUET

COURSE NUMBER: ME 321 Fluid Mechanics I Fluid statics. Course teacher Dr. M. Mahbubur Razzaque Professor Department of Mechanical Engineering BUET COURSE NUMBER: ME 321 Fluid Mechanics I Fluid statics Course teacher Dr. M. Mahbubur Razzaque Professor Department of Mechanical Engineering BUET 1 Fluid statics Fluid statics is the study of fluids in

More information

FLUID MECHANICS. Fluid Statics BUOYANCY. Fig. Buoyancy CENTER OF BUOYANCY

FLUID MECHANICS. Fluid Statics BUOYANCY. Fig. Buoyancy CENTER OF BUOYANCY FLUID MECHANICS Fluid Statics BUOYANCY When a body is either wholly or partially immersed in a fluid, the hydrostatic lift due to the net vertical component of the hydrostatic pressure forces experienced

More information

2 Available: 1390/08/02 Date of returning: 1390/08/17 1. A suction cup is used to support a plate of weight as shown in below Figure. For the conditio

2 Available: 1390/08/02 Date of returning: 1390/08/17 1. A suction cup is used to support a plate of weight as shown in below Figure. For the conditio 1. A suction cup is used to support a plate of weight as shown in below Figure. For the conditions shown, determine. 2. A tanker truck carries water, and the cross section of the truck s tank is shown

More information

. In an elevator accelerating upward (A) both the elevator accelerating upward (B) the first is equations are valid

. In an elevator accelerating upward (A) both the elevator accelerating upward (B) the first is equations are valid IIT JEE Achiever 2014 Ist Year Physics-2: Worksheet-1 Date: 2014-06-26 Hydrostatics 1. A liquid can easily change its shape but a solid cannot because (A) the density of a liquid is smaller than that of

More information

Lab test 4 Seakeeping test with a model of an oil tanker

Lab test 4 Seakeeping test with a model of an oil tanker Lab test 4 Seakeeping test with a model of an oil tanker The response amplitude operators (RAO) in head seas of a 1:100 scale model of a 257 m long oil tanker shall be determined by model testing in the

More information

Ship Stability September 2013 Myung-Il Roh Department of Naval Architecture and Ocean Engineering Seoul National University

Ship Stability September 2013 Myung-Il Roh Department of Naval Architecture and Ocean Engineering Seoul National University Planning Procedure of Naval Architecture and Ocean Engineering Ship Stability September 2013 Myung-Il Roh Department of Naval Architecture and Ocean Engineering Seoul National University 1 Ship Stability

More information

FC-CIV HIDRCANA: Channel Hydraulics Flow Mechanics Review Fluid Statics

FC-CIV HIDRCANA: Channel Hydraulics Flow Mechanics Review Fluid Statics FC-CIV HIDRCANA: Channel Hydraulics Flow Mechanics Review Fluid Statics Civil Engineering Program, San Ignacio de Loyola University Objective Calculate the forces exerted by a fluid at rest on plane or

More information

RULES PUBLICATION NO. 86/P EXPLANATORY NOTES TO SOLAS CONVENTION AND DIRECTIVE 2003/25/EC STABILITY AND SUBDIVISION REQUIREMENTS

RULES PUBLICATION NO. 86/P EXPLANATORY NOTES TO SOLAS CONVENTION AND DIRECTIVE 2003/25/EC STABILITY AND SUBDIVISION REQUIREMENTS RULES PUBLICATION NO. 86/P EXPLANATORY NOTES TO SOLAS CONVENTION AND DIRECTIVE 2003/25/EC STABILITY AND SUBDIVISION REQUIREMENTS 2011 Publications P (Additional Rule Requirements) issued by Polski Rejestr

More information

Dec 6 3:08 PM. Density. Over the last two periods we discussed/observed the concept of density. What have we learned?

Dec 6 3:08 PM. Density. Over the last two periods we discussed/observed the concept of density. What have we learned? Over the last two periods we discussed/observed the concept of density. What have we learned? is a ratio of mass to volume describes how much matter is packed into a space is a property of both solids

More information

Light draught m

Light draught m Tugboats 900hp tugboat 1200hp tugboat 2400hp ABS ocean going tugboat Built in 2010, brand-new LOA 30.00 m Length 27.76 m Length of waterline 28.75 m Breadth 7.50 m Depth 3.20 m Light draught 1.450 m Full-load

More information

From and

From  and From http://www.school-for-champions.com/science/fluidpressure.htm and http://www.school-forchampions.com/science/fluidfloating.htm by Ron Kurtus, School for Champions Pressure in Fluids by Ron Kurtus

More information

1. All fluids are: A. gases B. liquids C. gases or liquids D. non-metallic E. transparent ans: C

1. All fluids are: A. gases B. liquids C. gases or liquids D. non-metallic E. transparent ans: C Chapter 14: FLUIDS 1 All fluids are: A gases B liquids C gases or liquids D non-metallic E transparent 2 Gases may be distinguished from other forms of matter by their: A lack of color B small atomic weights

More information

Ship Resistance and Propulsion Prof. Dr. P. Krishnankutty Ocean Department Indian Institute of Technology, Madras

Ship Resistance and Propulsion Prof. Dr. P. Krishnankutty Ocean Department Indian Institute of Technology, Madras Ship Resistance and Propulsion Prof. Dr. P. Krishnankutty Ocean Department Indian Institute of Technology, Madras Lecture - 7 Air and Wind Resistance Dimensional Analysis I Coming back to the class, we

More information

Numerical Modelling Of Strength For Hull Form Components Of A 700 Tonne Self-Propelled Barge Under Moment And Operational Loading

Numerical Modelling Of Strength For Hull Form Components Of A 700 Tonne Self-Propelled Barge Under Moment And Operational Loading IOSR Journal of Engineering (IOSRJEN) ISSN (e): 2250-3021, ISSN (p): 2278-8719 Vol. 05, Issue 05 (May. 2015), V1 PP 45-55 www.iosrjen.org Numerical Modelling Of Strength For Hull Form Components Of A 700

More information

RULES FOR THE CLASSIFICATION AND CONSTRUCTION OF SEA-GOING SHIPS

RULES FOR THE CLASSIFICATION AND CONSTRUCTION OF SEA-GOING SHIPS RULES FOR THE CLASSIFICATION AND CONSTRUCTION OF SEA-GOING SHIPS PART IV STABILITY AND SUBDIVISION 2015 July GDAŃSK RULES FOR THE CLASSIFICATION AND CONSTRUCTION OF SEA-GOING SHIPS prepared and edited

More information

Science 8 Chapter 9 Section 1

Science 8 Chapter 9 Section 1 Science 8 Chapter 9 Section 1 Forces and Buoyancy (pp. 334-347) Forces Force: anything that causes a change in the motion of an object; a push or pull on an object balanced forces: the condition in which

More information

OFFSHORE RACING CONGRESS World Leader in Rating Technology

OFFSHORE RACING CONGRESS World Leader in Rating Technology OFFSHORE RACING CONGRESS World Leader in Rating Technology ORC SY MEASUREMENT GUIDANCE 2017 1. INTRODUCTION This paper must be taken as guidance for the process of boat measurement to allow for the issuance

More information

Subj: Explanation of Upper Level Capacity and Stability Characteristics for Rolling Boat, Inc. Vessels.

Subj: Explanation of Upper Level Capacity and Stability Characteristics for Rolling Boat, Inc. Vessels. 23 Apr, 2009 From: Tullio Celano III P.E. To: Underwriters of Rolling Boat, Inc. Via: Phil Kazmierowicz, President, Rolling Boat, Inc. Subj: Explanation of Upper Level Capacity and Stability Characteristics

More information

The Physics of Water Ballast

The Physics of Water Ballast The Physics of Water Ballast Nick Newland recently wrote an informative article on water ballast for Water Craft magazine (Newland 2015). Following a discussion on the Swallow Boats Association Forum,

More information

Visit Us:

Visit Us: Visit Us: www.officerofthewatch.co.uk www.officerofthewatch.co.uk JUL-Y 2005 STABILITY AND STRUCTURE Attempt ALL questions Marks for each part question are shown in brackets 1. A vessel is to transit

More information

(Refer Slide Time: 0:25)

(Refer Slide Time: 0:25) Port and Harbour Structures Prof. R. Sundaravadivelu Department of Ocean Engineering Indian Institute of Technology Madras Module 01 Lecture 04 Ships and Size of Ships So in this class we will continue

More information

Page 1

Page 1 Contents: 1. Thrust and Pressure 2. Pressure in Fluids 3. Buoyancy 4. Why objects sink or Float when placed on surface of water? 5. Archimedes Principle 6. Relative Density Learning Objectives: The students

More information

RULES PUBLICATION NO. 20/P SHIP SIDE STRENGTHENING OF FISHING VESSELS MOORING AT SEA ALONGSIDE OTHER VESSELS

RULES PUBLICATION NO. 20/P SHIP SIDE STRENGTHENING OF FISHING VESSELS MOORING AT SEA ALONGSIDE OTHER VESSELS RULES PUBLICATION NO. 20/P SHIP SIDE STRENGTHENING OF FISHING VESSELS MOORING AT SEA ALONGSIDE OTHER VESSELS 1995 Publications P (Additional Rule Requirements), issued by Polski Rejestr Statków, complete

More information

BUOYANCY, FLOATATION AND STABILITY

BUOYANCY, FLOATATION AND STABILITY BUOYANCY, FLOATATION AND STABILITY Archimedes Principle When a stationary body is completely submerged in a fluid, or floating so that it is only partially submerged, the resultant fluid force acting on

More information

Load lines and freeboard marks

Load lines and freeboard marks Chapter 8 Load lines and freeboard marks The link Freeboard and stability curves are inextricably linked. With an increase in the freeboard: Righting levers (GZ) are increased. GM T increases. Range of

More information

ConcepTest PowerPoints

ConcepTest PowerPoints ConcepTest PowerPoints Chapter 10 Physics: Principles with Applications, 6 th edition Giancoli 2005 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for

More information

Ship Resistance and Propulsion Prof. Dr. P. Krishnankutty Ocean Department Indian Institute of Technology, Madras

Ship Resistance and Propulsion Prof. Dr. P. Krishnankutty Ocean Department Indian Institute of Technology, Madras Ship Resistance and Propulsion Prof. Dr. P. Krishnankutty Ocean Department Indian Institute of Technology, Madras Lecture - 6 Bulbous Bow on Ship Resistance Welcome back to the class we have been discussing

More information

Stability Booklet (simplified) M/V Sea Breeze. 1 Ships Particulars Stability KGc-max curves according IMO Resolution A.749(18)...

Stability Booklet (simplified) M/V Sea Breeze. 1 Ships Particulars Stability KGc-max curves according IMO Resolution A.749(18)... Stability Booklet (simplified) M/V Sea Breeze Inhaltsverzeichnis 1 Ships Particulars...3 2 Stability...3 3 KGc-max curves according IMO Resolution A.749(18)...5 4 General Arrangement...6 5 Freeboard Mark...7

More information

The salient features of the 27m Ocean Shuttle Catamaran Hull Designs

The salient features of the 27m Ocean Shuttle Catamaran Hull Designs The salient features of the 27m Ocean Shuttle Catamaran Hull Designs The hull form is a semi-planing type catamaran. It employs a combination of symmetrical and asymmetrical sponson shapes, thereby combining

More information

CERTIFICATES OF COMPETENCY IN THE MERCHANT NAVY MARINE ENGINEER OFFICER

CERTIFICATES OF COMPETENCY IN THE MERCHANT NAVY MARINE ENGINEER OFFICER CERTIFICATES OF COMPETENCY IN THE MERCHANT NAVY MARINE ENGINEER OFFICER EXAMINATIONS ADMINISTERED BY THE SCOTTISH QUALIFICATIONS AUTHORITY ON BEHALF OF THE MARITIME AND COASTGUARD AGENCY STCW 78 as amended

More information

Stability and Computational Flow Analysis on Boat Hull

Stability and Computational Flow Analysis on Boat Hull Vol. 2, Issue. 5, Sept.-Oct. 2012 pp-2975-2980 ISSN: 2249-6645 Stability and Computational Flow Analysis on Boat Hull A. Srinivas 1, V. Chandra sekhar 2, Syed Altaf Hussain 3 *(PG student, School of Mechanical

More information

Chapter 3 PRESSURE AND FLUID STATICS

Chapter 3 PRESSURE AND FLUID STATICS Fluid Mechanics: Fundamentals and Applications, 2nd Edition Yunus A. Cengel, John M. Cimbala McGraw-Hill, 2010 Chapter 3 PRESSURE AND FLUID STATICS Lecture slides by Hasan Hacışevki Copyright The McGraw-Hill

More information

A Study on Roll Damping of Bilge Keels for New Non-Ballast Ship with Rounder Cross Section

A Study on Roll Damping of Bilge Keels for New Non-Ballast Ship with Rounder Cross Section International Ship Stability Workshop 2013 1 A Study on Roll Damping of Bilge Keels for New Non-Ballast Ship with Rounder Cross Section Tatsuya Miyake and Yoshiho Ikeda Department of Marine System Engineering,

More information

RULES FOR THE CONSTRUCTION AND CLASSIFICATION OF SHIPS IDENTIFIED BY THEIR MISSIONS CHAPTERS SCOPE

RULES FOR THE CONSTRUCTION AND CLASSIFICATION OF SHIPS IDENTIFIED BY THEIR MISSIONS CHAPTERS SCOPE PART II RULES FOR THE CONSTRUCTION AND CLASSIFICATION OF SHIPS IDENTIFIED BY THEIR MISSIONS TITLE 12 CONTAINER SHIPS SECTION 1 NAVAL ARCHITECTURE CHAPTERS A SCOPE B DOCUMENTS, REGULATIONS AND STANDARDS

More information

EXPERIMENT (2) BUOYANCY & FLOTATION (METACENTRIC HEIGHT)

EXPERIMENT (2) BUOYANCY & FLOTATION (METACENTRIC HEIGHT) EXPERIMENT (2) BUOYANCY & FLOTATION (METACENTRIC HEIGHT) 1 By: Eng. Motasem M. Abushaban. Eng. Fedaa M. Fayyad. ARCHIMEDES PRINCIPLE Archimedes Principle states that the buoyant force has a magnitude equal

More information

Objectives deals with forces applied by fluids at rest or in rigid-body motion.

Objectives deals with forces applied by fluids at rest or in rigid-body motion. Objectives deals with forces applied by fluids at rest or in rigid-body motion. The fluid property responsible for those forces is pressure, which is a normal force exerted by a fluid per unit area. discussion

More information

MSC Guidelines for Review of Stability for Sailing Catamaran Small Passenger Vessels (T)

MSC Guidelines for Review of Stability for Sailing Catamaran Small Passenger Vessels (T) K.B. FERRIE, CDR, Chief, Hull Division References: a. 46 CFR Subchapter T, Parts 178, 179 b. 46 CFR Subchapter S, Parts 170, 171 c. Marine Safety Manual (MSM), Vol. IV d. Navigation and Vessel Circular

More information

ACTIVITY 1: Buoyancy Problems. OBJECTIVE: Practice and Reinforce concepts related to Fluid Pressure, primarily Buoyancy

ACTIVITY 1: Buoyancy Problems. OBJECTIVE: Practice and Reinforce concepts related to Fluid Pressure, primarily Buoyancy LESSON PLAN: SNAP, CRACKLE, POP: Submarine Buoyancy, Compression, and Rotational Equilibrium DEVELOPED BY: Bill Sanford, Nansemond Suffolk Academy 2012 NAVAL HISTORICAL FOUNDATION TEACHER FELLOWSHIP ACTIVITY

More information

The OTSS System for Drift and Response Prediction of Damaged Ships

The OTSS System for Drift and Response Prediction of Damaged Ships The OTSS System for Drift and Response Prediction of Damaged Ships Shoichi Hara 1, Kunihiro Hoshino 1,Kazuhiro Yukawa 1, Jun Hasegawa 1 Katsuji Tanizawa 1, Michio Ueno 1, Kenji Yamakawa 1 1 National Maritime

More information

Unit 7. Pressure in fluids

Unit 7. Pressure in fluids -- Unit 7. Pressure in fluids Index 1.- Pressure...2 2.- Fluids...2 3.- Pressure in fluids...3 4.- Pascal's principle...5 5.- Archimedes principle...6 6.- Atmospheric pressure...7 6.1.- Torricelli and

More information

Vacuum P=0. h=76 cm A B C. Barometer

Vacuum P=0. h=76 cm A B C. Barometer Recap: Pressure Pressure = Force per unit area (P = F /A; units: Pascals) Density of object = mass / volume (ρ = m /V; units: kg / m 3 ) Pascal s Law:Pressure is transmitted equally in all directions throughout

More information

3. A fluid is forced through a pipe of changing cross section as shown. In which section would the pressure of the fluid be a minimum?

3. A fluid is forced through a pipe of changing cross section as shown. In which section would the pressure of the fluid be a minimum? AP Physics Multiple Choice Practice Fluid Mechanics 1. A cork has weight mg and density 5% of water s density. A string is tied around the cork and attached to the bottom of a water-filled container. The

More information

RESOLUTION MSC.141(76) (adopted on 5 December 2002) REVISED MODEL TEST METHOD UNDER RESOLUTION 14 OF THE 1995 SOLAS CONFERENCE

RESOLUTION MSC.141(76) (adopted on 5 December 2002) REVISED MODEL TEST METHOD UNDER RESOLUTION 14 OF THE 1995 SOLAS CONFERENCE MSC 76/23/Add.1 RESOLUTION MSC.141(76) THE MARITIME SAFETY COMMITTEE, RECALLING Article 38(c) of the Convention on the International Maritime Organization concerning the functions of the Committee, RECALLING

More information

Study on Resistance of Stepped Hull Fitted With Interceptor Plate

Study on Resistance of Stepped Hull Fitted With Interceptor Plate 39 Study on Resistance of Stepped Hull Fitted With Interceptor Plate Muhamad Asyraf bin Abdul Malek, a, and J.Koto, a,b,* a) Department of Aeronautic, Automotive and Ocean Engineering, Faculty of Mechanical

More information

Buoyancy and Density. Buoyant Force and Fluid Pressure. Key Concept Buoyant force and density affect whether an object will float or sink in a fluid.

Buoyancy and Density. Buoyant Force and Fluid Pressure. Key Concept Buoyant force and density affect whether an object will float or sink in a fluid. 2 Buoyancy and Density Key Concept Buoyant force and density affect whether an object will float or sink in a fluid. What You Will Learn All fluids exert an upward buoyant force on objects in the fluid.

More information

Chapter 10 Fluids. Which has a greater density? Ch 10: Problem 5. Ch 10: Problem Phases of Matter Density and Specific Gravity

Chapter 10 Fluids. Which has a greater density? Ch 10: Problem 5. Ch 10: Problem Phases of Matter Density and Specific Gravity Chapter 10 Fluids 10-1 Phases of Matter The three common phases of matter are solid, liquid, and gas. A solid has a definite shape and size. A liquid has a fixed volume but can be any shape. A gas can

More information

RULES PUBLICATION NO. 94/P SUBDIVISION AND DAMAGE STABILITY OF NEW OIL TANKERS, CHEMICAL TANKERS AND GAS CARRIERS January

RULES PUBLICATION NO. 94/P SUBDIVISION AND DAMAGE STABILITY OF NEW OIL TANKERS, CHEMICAL TANKERS AND GAS CARRIERS January RULES PUBLICATION NO. 94/P SUBDIVISION AND DAMAGE STABILITY OF NEW OIL TANKERS, CHEMICAL TANKERS AND GAS CARRIERS 2016 January Publications P (Additional Rule Requirements) issued by Polski Rejestr Statków

More information

APPENDIX IV DEVELOPMENT AND MEASUREMENT RULES OF THE INTERNATIONAL TEN SQUARE METER SAILING CANOE

APPENDIX IV DEVELOPMENT AND MEASUREMENT RULES OF THE INTERNATIONAL TEN SQUARE METER SAILING CANOE APPENDIX IV Development Canoe Rules APPENDIX IV DEVELOPMENT AND MEASUREMENT RULES OF THE INTERNATIONAL TEN SQUARE METER SAILING CANOE 1 GENERAL Class and measurement rules measurement forms may be obtained

More information

CRITERIA OF BOW-DIVING PHENOMENA FOR PLANING CRAFT

CRITERIA OF BOW-DIVING PHENOMENA FOR PLANING CRAFT 531 CRITERIA OF BOW-DIVING PHENOMENA FOR PLANING CRAFT Toru KATAYAMA, Graduate School of Engineering, Osaka Prefecture University (Japan) Kentarou TAMURA, Universal Shipbuilding Corporation (Japan) Yoshiho

More information

MANOEUVRING BOOKLET V1.06

MANOEUVRING BOOKLET V1.06 MANOEUVRING BOOKLET V1.6 Mathematical model of Integrated Tug Barge 45 Version: v9 Dll Version: 2.31.558 According to: Solas II-1, regulation 28.3 St. Petersburg 26 1. GENERAL DESCRIPTION 1.1. Ships particulars

More information

AP Lab 11.3 Archimedes Principle

AP Lab 11.3 Archimedes Principle ame School Date AP Lab 11.3 Archimedes Principle Explore the Apparatus We ll use the Buoyancy Apparatus in this lab activity. Before starting this activity check to see if there is an introductory video

More information

RULES FOR THE CLASSIFICATION AND CONSTRUCTION OF SMALL SEA-GOING SHIPS

RULES FOR THE CLASSIFICATION AND CONSTRUCTION OF SMALL SEA-GOING SHIPS RULES FOR THE CLASSIFICATION AND CONSTRUCTION OF SMALL SEA-GOING SHIPS PART IV STABILITY, SUBDIVISION AND FREEBOARD 2015 January GDAŃSK RULES FOR THE CLASSIFICATION AND CONSTRUCTION OF SMALL SEA-GOING

More information

Additional Information

Additional Information Buoyancy Additional Information Any object, fully or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object. Archimedes of Syracuse Archimedes principle

More information

Ship Resistance and Propulsion Prof. Dr. P. Krishnankutty Ocean Department Indian Institute of Technology, Madras

Ship Resistance and Propulsion Prof. Dr. P. Krishnankutty Ocean Department Indian Institute of Technology, Madras Ship Resistance and Propulsion Prof. Dr. P. Krishnankutty Ocean Department Indian Institute of Technology, Madras Lecture - 17 Resistance of Advanced Marine vehicles - III (Refer Slide Time: 00:10) Now,

More information

Comparative Stability Analysis of a Frigate According to the Different Navy Rules in Waves

Comparative Stability Analysis of a Frigate According to the Different Navy Rules in Waves Comparative Stability Analysis of a Frigate According to the Different Navy Rules in Waves ABSTRACT Emre Kahramano lu, Technical University, emrek@yildiz.edu.tr Hüseyin Y lmaz,, hyilmaz@yildiz.edu.tr Burak

More information

ISO NON-SAILING BOATS OF LENGTH GREATER THAN OR EQUAL TO 6 m CALCULATION WORKSHEET No. 1 Design:

ISO NON-SAILING BOATS OF LENGTH GREATER THAN OR EQUAL TO 6 m CALCULATION WORKSHEET No. 1 Design: ISO 12217-1 NON-SAILING BOATS OF LENGTH GREATER THAN OR EQUAL TO 6 m CALCULATION WORKSHEET No. 1 Design: Design Category intended: Monohull / multihull: Item Symbol Unit Value Ref. Length of hull as in

More information

Fluid Mechanics - Hydrostatics. Sections 11 5 and 6

Fluid Mechanics - Hydrostatics. Sections 11 5 and 6 Fluid Mechanics - Hydrostatics Sections 11 5 and 6 A closed system If you take a liquid and place it in a system that is CLOSED like plumbing for example or a car s brake line, the PRESSURE is the same

More information

STABILITY & TRIM (MT4241)

STABILITY & TRIM (MT4241) MASSACHUSETTS MARITIME ACADEMY DEPARTMENT OF MARINE TRANSPORTATION STABILITY & TRIM (MT4241) I. LEARNING OBJECTIVES FALL 2015 This course is designed to meet all stability, knowledge based assessments,

More information

FLOATING AND SINKING

FLOATING AND SINKING NAME SCHOOL INDEX NUMBER DATE FLOATING AND SINKING 1. 1994 Q5a P2 (a) State Archimedes s principal (1 mark) 2. 1996 Q29 P1 A solid copper sphere will sink in water while a hollow copper sphere of the same

More information

Concept of Fluid. Density. Pressure: Pressure in a Fluid. Pascal s principle. Buoyancy. Archimede s Principle. Forces on submerged surfaces

Concept of Fluid. Density. Pressure: Pressure in a Fluid. Pascal s principle. Buoyancy. Archimede s Principle. Forces on submerged surfaces FLUID MECHANICS The fluid essential to all life has a beauty of its own. It also helps support the weight of this swimmer. (credit: Terren, Wikimedia Commons) Concept of Fluid Density Pressure: Pressure

More information

Static Fluids. **All simulations and videos required for this package can be found on my website, here:

Static Fluids. **All simulations and videos required for this package can be found on my website, here: DP Physics HL Static Fluids **All simulations and videos required for this package can be found on my website, here: http://ismackinsey.weebly.com/fluids-hl.html Fluids are substances that can flow, so

More information

2 Buoyant Force. TAKE A LOOK 2. Identify What produces buoyant force?

2 Buoyant Force. TAKE A LOOK 2. Identify What produces buoyant force? CHAPTER 3 2 Buoyant Force SECTION Forces in Fluids BEFORE YOU READ After you read this section, you should be able to answer these questions: What is buoyant force? What makes objects sink or float? How

More information

APPENDIX IV DEVELOPMENT AND MEASUREMENT RULES OF THE INTERNATIONAL TEN SQUARE METRE SAILING CANOE (JANUARY 2008) 1 GENERAL

APPENDIX IV DEVELOPMENT AND MEASUREMENT RULES OF THE INTERNATIONAL TEN SQUARE METRE SAILING CANOE (JANUARY 2008) 1 GENERAL APPENDIX IV DEVELOPMENT AND MEASUREMENT RULES OF THE INTERNATIONAL TEN SQUARE METRE SAILING CANOE (JANUARY 2008) 1 GENERAL Class and measurement rules measurement forms may be obtained from the I.C.F.

More information