Topic-1 MAIN DIMENSIONS

Basic design of the Ship

The main dimensions of the barge influence many of the ship’s characteristics such as stability, carrying capacity, power requirements and its economic efficiency. So, they should be coordinated such that the vessel satisfies the design conditions as well as the characteristics desired by the shipping companies with various combinations of dimensions. The owner requires a vessel which will give him the best possible returns for his initial investment and operating costs. Basic design includes selection of main dimensions, hull form, power, and type of generator, preliminary arrangement of tanks and machinery, and major structural arrangements. Proper selections assure the attainment of the mission requirements such as carrying capacity and deadweight. It includes checks and modifications for achievement of required carrying capacity, subdivision of tanks and stability standards, freeboard and tonnage measurement. 

    Length (L)

The length of the ship is measured from the extreme forward end to the aftermost point of the stern. The length, L, shall be taken as 96 percent of the total length, in meters (feet), on a waterline at 85 percent of the least molded depth, D. In barges designed with a rake of keel, the waterline on which this length is measured shall be parallel to the designed waterline.

 Breadth (B)

The breadth of a ship is its width at the widest point as measured at the ship's nominal waterline. It is measured in meters.

    Depth (D)

Depth is defined as the height of the ship at the midship section from the base line to the molded line of the deck at side.

      Draught (T)

The draught of a ship's hull is the vertical distance between the waterline and the bottom of the hull (keel), with the thickness of the hull included. Draught determines the minimum depth of water a ship or boat can safely navigate. The draught, T, is the molded draught, in meters (feet), from the molded baseline to the summer load line.

Topic-2 COEFFICIENT OF FORM

    Block Coefficient (C_B)

Block coefficient of fineness is the ratio of the volume of displacement (∇) of the molded form up to any waterline to the volume of a circumscribing solid with length, breadth, and depth equal to the length, breadth and draught of that waterline. 

The Block Coefficient (C_B) is given by,

C_B = ∇ /L×B×T

       Midship section area coefficient (C_M)

The fullness of the midship section is expressed by the midship section area coefficient. It is the ratio of the midship section area to the circumscribing rectangle, the width of which is equal to the molded beam at the load waterline and the depth of which is equal to the molded draught at that waterline.

The midship section area coefficient is given by,

C_M = A_M / B×T

       Water plane area coefficient (C_W)

The Water plane area coefficient influences the resistance and stability considerably. It is geometrically related to shape of cross-sections. It is the ratio of Water plane area to the circumscribing rectangle, the length of which is equal to the length of the LWL and width of which is equal to the breadth at that waterline. The value of C_W is largely a function of C_B and sectional shape.

The Water plane area coefficient is given by,

C_W = A_W / L×B

      Longitudinal Prismatic coefficient (C_PL)

The longitudinal prismatic coefficient is the ratio of molded volume of the ship up to the designed waterline to the volume of prism having length equal to the waterline length and cross-sectional area equal to the midship section area. It is the ratio of C_B to C_M.

The longitudinal prismatic coefficient is given by, 

C_PL = C_B / C_M

        Vertical Prismatic coefficient (C_PV)

The vertical prismatic coefficient is the ratio of molded volume of ship up to the designed load waterline to volume obtained by the product of Water plane area with the draught. It is the ratio of C_B to C_W.

The vertical prismatic coefficient is given by,

                                                                   C_PV = C_B / C_W

Topic-3 HULL FORM (LINES PLAN)

The lines plan (lines drawing) consist of projections of the intersection of the hull with a series of planes. The planes are equally spaced in each of the three dimensions. These set of planes are mutually perpendicular or orthogonal in nature.

   Description

The point of intersection of these planes with the hull results in a series of lines that are projected onto a single plane located on the front, top, or side of the ship. These results in three separate projections, or views, called the Body Plan, the Half-Breadth Plan, and the Sheer Plan.

To visualize, place the ship in an imaginary rectangular box whose sides touch the keel and sides of the ship. The bottom, side and front of the box will serve as the basis for three orthogonal projection screens on which lines will be projected onto. The lines to be projected result from the intersection of the hull with planes that are parallel to each of the three orthogonal planes mentioned.

       Body plan

Planes parallel to the front and back of the imaginary box are called stations. There are three important stations. The intersection of the stem of the ship at the design water line is called Forward Perpendicular (FP). The intersection of the stern at design waterline (immersed transom) or the rudder stock is called the Aft Perpendicular (AP). The station midway between the perpendiculars is called the midship stations.

Each station plane will intersect the ship's hull and form a curved line at the points of intersection. These lines are called sectional lines and are all projected onto a single plane called the Body Plan.

The body plan takes advantage of the ship's symmetry. Hence only half the section is shown; the sections forward of amidships are drawn on the right side, and the sections aft of the amidships are drawn on the left side. The amidships section is generally shown on both sides of the body plan. The vertical line in the center separating the left and right half of the ship is called the centerline.

      Half-breadth plan

The bottom of the box is a reference plane called the base plane. The base plane is usually level with the keel. A series of planes parallel and above the base plan are imagined at regular intervals, usually at every meter. Each plane will intersect the ship's hull and form a line at the points of intersection. These lines are called waterlines and are all projected onto a single plane called the Half-Breadth Plan.

Each waterline shows the true shape of the hull from the top view for some elevation above the base plane.

The water lines referred to here has nothing to do with where the ship actually floats. There waterlines are the intersection of the ship's hull with some imaginary plane above the base plane.

Since ships are symmetric about their centerline they only need be drawn for the starboard or port side, thus the name Half-Breadth Plan.

    Sheer plan

A plane that runs from bow to stern directly through the center of the ship and parallel to the sides of the imaginary box is called the centerline plane. A series of planes parallel to one side of the centerline plane are imagined at regular intervals from the centerline. Each plane will intersect the ship's hull and form a curved line at the points of intersection. These lines are called buttock or butt lines and are projected onto a single plane called the Sheer Plan.

Each buttock line shows the true shape of the hull from the side view for some distance from the centerline of the ship. The centerline plane shows a special butt line called the profile of the ship. 

Topic-4 Drafting of hull form

The length between perpendiculars is divided into equal divisions to draw a section at each of these divisions. These sections are numbered from AP  to FP . Quarter and half stations are also taken at the ends to define the hull form more accurately. Using the offset table obtained at C_B, a preliminary half breadth is prepared. By fairing the lines in the half breadth plan, a preliminary body plan is prepared. A half transverse section only is drawn since the vessel is symmetrical about the centerline plane. The forward half sections are drawn to the right of the centerline with the aft sections to the left. The outreaches of the stem and stern profiles are drawn in the elevation.

It is essential when designing the hull form of the ship that all the three sets of curves should be fair and coincident with each other and their interdependence becomes important in the fairing process. At the end of the fairing process, lines are faired in all three views and final lines plan is prepared.

Topic-5 SECTIONAL AREAS AND VERTICAL MOMENTS

One of the fundamental hull form characteristics required to prepare the hydrostatic curves are the immersed sectional areas at ordinate stations. The cross-sectional area of each ordinate station shown in the body plan up to the waterline in question is determined which is the input into the calculation of the volume of displacement; this set of curves is known as the Bonjean curves. A typical plot of the bonjean curves is as shown in figure below. When plotted against the ship length, the immersed areas at the ordinate stations form a sectional area curve, whose shape represents the fullness or fineness of the ship form, an important consideration in ship resistance and towing power.

The bonjean curves are used:

• Bonjean curves are drawn on the profile of the vessel. With these curves, we can find the distribution of buoyancy for any waterline (any draft, any trim).
• To find out the volume of displacement and LCB at a trimmed waterline at which the ship is floating due to distribution of cargo or when the ship is floating on even keel.
• In subdivision of ships from the safety point of view so that when the ship is flooded due to accident or damaged, the ship does not sink beyond the margin line.
• In launching calculations, to determine the buoyancy and centre of buoyancy.

Topic - 6 HYDROSTATIC PROPERTIES - 1

Introduction

Throughout its life a ship changes its weight, draught, trim and freeboard. The density of water in which the ship floats varies. Its stability also changes. If its condition at any stated set of circumstances to be estimated, its condition in a precise state must be known so that the effect of changes from that state can be calculated. This precise condition is known as the design condition. For this, changes from the design and properties of underwater form are calculated for a complete range of waterlines. This information is known as hydrostatic data and it plotted against draughts. Draughts are spaced 1 m apart. These curves are drawn on displacement sheet.

The following properties are plotted against draught to form hydrostatic curves.    

• Volume of displacement                                                
• Displacement                                                      
• Longitudinal centre of buoyancy from midship                                                          
• Vertical centre of buoyancy above base line                                                    
• Water plane area                                                            
• Longitudinal centre of floatation from midship                                                          
• Tonnes per centimeter immersion                                                        
• Longitudinal moment of inertia about midship                                                           
• Transverse moment of inertia about central line                                                        
•  Longitudinal moment of inertia about axis passing through LCF   
• Transverse meta-centric radius                                                
• Longitudinal meta-centric radius                                                         
• Transverse meta-centre above base line                                                           
• Longitudinal meta-centre above base line                                                        
• Moment to change trim by 1 cm                                                           
• Block coefficient                                                 
• Midship section area coefficient
• Water plane area coefficient                                                     
• Longitudinal prismatic coefficient                                                        
• Vertical prismatic coefficient                                                    
• Wetted surface area of hull              

Topic-7 HYDROSTATIC PROPERTIES - 2 (DEFINITIONS)

Volume of Displacement (∇)

The volume of displacement is the total volume of the fluid displaced by the ship.

Volume of displacement is given by,

∇ = ∆ /ρ

For seawater, ρ = 1.025 ton/m³

Displacement (∆)

Displacement is defined as the total mass of the ship when afloat including everything on board, which is equal to the weight of water displaced.

Displacement is given by,

∆ = Dead wt. + Light ship wt.

Longitudinal centre of buoyancy from midship (LCB)

The centre of volume of fluid displaced by a ship is known as the centre of buoyancy; its projection in the plan is known as longitudinal centre of buoyancy. It is given as distance forward or aft of midship and is represented by the longitudinal centroid of the curve of immersed cross-sectional areas.

Vertical centre of buoyancy above base line (VCB)

The centre of volume of fluid displaced by a ship is known as the centre of buoyancy; its projection in the section is known as vertical centre of buoyancy. It is given as the distance above the keel denoted by KB and is represented by the vertical centroid of the Water plane area curve.

By Morrishes approximate formula;

VCB below the waterline = 1/3(d/2+∇/A_W)

Where, d = draught in m

            ∇ = volume of displacement in m³

               A_W = Water plane area in m²

Water plane area (A_W)

Water plane area is the area of the horizontal plane which passes through a floating ship on a level with the waterline. The water plane area at any draught is calculated by sympsonising the half breadths at ordinate stations.

Longitudinal centre of floatation from midship (LCF)

Longitudinal centre of floatation is the centroid of the water plane and is the axis about which a ship changes trim when a mass is added, removed or moved longitudinally.

Tonne per centimeter immersion (TPC)

The tonne per centimeter immersion of a ship at any given draught is the mass required to increase the mean draught by 1 centimeter.

TPC = (A_W*ρ)/100

For seawater ρ = 1.025 ton/m³

∴TPC in sea water = 0.01025×A_W

Moment of inertia (I)

The second moment of area of a water plane, commonly known as moment of inertia, is a measure of the resistance of a water plane to a change in its state of rest. The moment of inertia is found by putting the cube of the half breadths through Simpson’s multipliers. The sum of these products is multiplied by h/3, by two for both sides and by 1/3 which is a factor in water plane inertia.

Moment of inertia is the mass property of a rigid body that defines the torque needed for a desired angular acceleration about an axis of rotation. Moment of inertia depends on the shape of the body and may be different around different axes of rotation. A larger moment of inertia around a given axis requires more torque to increase the rotation, or to stop the rotation, of a body about that axis. Moment of inertia depends on the amount and distribution of its mass, and can be found through the sum of moments of inertia of the masses making up the whole object, under the same conditions.

Moment to change trim by 1 cm (MCTI)

Moment to change trim by 1 cm is the change of trim in inches, caused by the application of a moment.

MCT1 cm = (∆*GM_L )/12L

Metacentre (M)

The metacentre is the point of intersection of the normal to a slightly inclined water plane of a body, rotated without change of displacement, through the centre of buoyancy pertaining to that water plane through the center of buoyancy pertaining to the upright condition.

Its projection in plan and section are known as longitudinal and transverse metacentre respectively.

Meta-centric height (GM)

The meta-centric height (GM) is a measurement of the initial static stability of a floating body. It is calculated as the distance between the centre of gravity of a ship and its metacentre. A larger meta-centric height implies greater initial stability against overturning. Meta-centric height also has implication on the natural period of rolling of a hull, with very large meta-centric heights being associated with shorter periods of roll.

Transverse meta-centric radius (BM_T)                        =                      I_T/∇

                                               

Longitudinal meta-centric radius (BM_L)                     =               I_LCF/∇                                                 

Transverse meta-centre above base line (KM_T)           =                     KB + BM_T

                                                           

Longitudinal meta-centre above base line (KM_L)       =                     KB + BM_L

Wetted surface area of the hull (S)

The wetted surface area of a ship is the area of the ship’s hull which is in contact with water. This area may be found by putting the transverse girths of the ship, from water line to water line, through Simpson’s rule and adding about ½ percent to allow for the longitudinal curvature of the shell.     

Formulae for wetted surface area are;

Denny’s formula:                 

S= (1.7*L*T) + ∇/T

S= c (∇*L)^1/2

Taylor’s formula:                  

Where, S= wetted surface area in m²,   L= length of barge in m, T=draught in m, ∇=volume of displacement in m³, C=coefficient which depends on shape of the ship.

and coefficient of forms which we have discussed in Topic - 2

Topic - 8 GENERAL ARRANGEMENT

The general arrangement of a ship can be defined as the assignment of spaces for all required functions and equipment, properly coordinated for location and access. The general arrangement represents a summary and integration of information from other divisions and specialties in ship design, intended to provide for all the necessary functions of the ship in the most efficient and economical way. This general arrangement of a ship gives a rough idea of how and in what way the arrangement of various decks as well as inside components is made. Generally this arrangement is done in co-ordination with the owner of the ship, and based on what equipment, with which the working personnel of the owner are familiar, based on that this general arrangement is done.

The efficient operation of any ship depends upon the proper arrangement of various components like cargo hold space, engine room, accommodation, ballast tanks, anchoring equipment and bulk heads etc.These bulk heads play an important role in maintaining water tightness and thereby preventing flooding.These also provide additional strength to the main deck or the weatherdeck. The bulk heads are of two types, longitudinal and transverse. Selection of number of these bulk heads must be made carefully. More number of longitudinal bulk heads may result in large amount of additional steel weight, which constitutes the light weight of the ship, thereby increasing the total weight of the ship.More number of transverse bulk heads may cause more stiffening and thus result in loss of strength. So, the number of bulkheads to be placed should be carefully selected.

The general arrangement represents mainly two views; profile view and main deck arrangement.

• Profile view:In profile view, we represent the accommodation area and the anchor handling arrangement, and if at all the ship is going to be located or moved near the yard or jetty, the fenders are also to be represented.These fenders are useful in preventing the direct contact between the ship hull and the yard or jetty wall.In addition to these we represent the tank division and other machinery equipment spacing.This spacing contains winch room, generator set room,pump room and the tank division involves double bottom tanks (ballast &bilge tanks), fuel oil tank etc.
• Main deck arrangement: In this, the arrangement of various deck components is depicted such as placing a crane, hatch door and access door arrangement.Further the arrangement of inside water ballast tanks is shown by a dotted line since these are located inside of the main deck.Arrangement of these water ballast tanks is very important for barges because, these water ballast tanks comes to necessity when to compensate the load acting during the loading and unloading operation of the jack-up structure.
• Sub deck arrangement: The arrangement in the sub deck is also shown. Generally in barges, the sub deck arrangement mainly consists of water ballast tanks, forward and after winch arrangement and the location of generator sets. The proper arrangement of these components ensures proper and desired results.

Topic - 9 STABILITY CALCULATIONS

Introduction

Ship stability is an area of naval architecture and ship design that deals with how a ship behaves at sea, both in still water and in waves. Stability calculations focus on the center of gravity and center of buoyancy of vessels and on how these interact.

Ship stability, as it pertains to naval architecture, has existed for hundreds of years. Historically, ship stability calculations for ships relied on rule of thumb calculations, often tied to a specific system of measurement.

Definitions of related terms 

Centre of gravity (G)

Center of gravity is an imaginary point in the exact middle of a weight where the entire weight may be considered to act. The weight always acts vertically downwards.

Centre of buoyancy (B)

Centre of buoyancy is an imaginary point in the exact middle of the volume of displaced water where the entire buoyancy may be considered to act. (The force of) buoyancy always acts vertically upwards.

Metacentre (M)

Metacentre is a point in space where the vertical line upwards through the centre of buoyancy of the ‘inclined’ vessel cuts through the vertical line upwards through the centre of buoyancy of the ‘upright’ vessel.

Meta-centric height (GM)

Meta-centric height is the vertical distance between the Centre of Gravity (G) and the Metacentre (M). If M is above G the vessel will stay upright and if G is above M the vessel will capsize. i.e., GM positive is Stable, GM negative is Unstable.

Righting lever (+GZ) or Overturning lever (-GZ)

Righting lever is the (horizontal) distance between the two (vertical) ‘lines of action’ of the buoyancy force (upwards), and the gravity force (downwards). The size of GZ is the measure of how stable or unstable the vessel is at any particular angle of heel. For small angles of heel (less than 15°), the ‘righting’ or ‘overturning lever’ GZ = GM x sinθ (where is the angle of heel, in degrees).

Initial Stability

To be adequately stable, the meta-centric height (GM) of the loaded vessel, floating upright in still water, is required to be above a minimum value.

GM_min = 0.35 meters is a recommended minimum guidance value.

Meta-centric height can be calculated using the formula:

GM = KB + BM – KG

(Where the distances between K, B, G, and M are all in meters, KB is the vertical distance from the keel to the centre of buoyancy, BM is the vertical distance from the centre of buoyancy to the metacentre, and KG is the vertical distance from the keel to the centre of gravity).

The vertical distance between the centre of buoyancy (B) and the metacentre (M), that is

BM =I / V (where I is the inertia of the water plane area, and V is the volume of displacement.)

For a rectangular water plane area, such as that displaced by a pontoon barge, the ‘roll inertia’

I = (l x b3)/12, and for a box shaped barge the ‘displaced volume’ is V = (L x B x T) (where

L is the length, B is the beam, and T is the draught).

In order to more exactly determine the position of the centre of gravity (G) and the meta-centric height (GM) for a particular barge, an inclining experiment needs to be conducted and the results used for a stability analysis. In an inclining experiment weights are moved to the outer edge of the deck of the barge and the heel that results is measured with a pendulum.

Topic - 10 INTACT STABILITY

Intact stability

Illustration of the stability of bottom-heavy (left) and top-heavy (right) ships with respect to the positions of their centers of buoyancy (CB) and gravity (CG)

Intact stability calculations are relatively straightforward and involve taking all the centers of mass of objects on the vessel which are then computed to identify the center of gravity of the vessel, and the center of buoyancy of the hull. Cargo arrangements and loadings, crane operations, and the design sea states are usually taken into account.

GZ = KN - KG×sinθ

Statical Stability

Statical stability is a measure of the tendency of a ship to return to the upright position if inclined by an external force.

For stability to be adequate, the righting lever (GZ) resulting from the heeling of a loaded barge is required to be greater than zero (positive) for all angles of heel up to a certain minimum heel angle. 35° is a recommended minimum heel value.

When the ship is heeled by an external force by an angle θ, the centre of gravity of the ship remains in the same position but the centre of buoyancy moves from B to B₁.

The buoyancy, therefore acts through B₁, while the weight still acts downwards through G, creating a moment ∆g×GZ which tends to return the ship to the upright. ∆g×GZ is known as righting moment and GZ is known as righting lever.

For small angles of heel, (up to about 10°)

GZ = GM×sinθ

Where, GZ is the righting lever, GM is the transverse meta-centric height.

For large angles of heel, (>10°):

When the ship heels to an angle greater than 10^°,the position of centre of gravity of the ship changes.

Let, G is the assumed position of centre of gravity

G₁ is the actual position of centre of gravity

If G₁ lies below G, then the ship is more stable and

G₁Z = GZ+GG₁sinθ

If G₁ lies above G, then the ship is less stable and

G₁Z = GZ-GG₁sinθ

Dynamical Stability

The area under the GZ curve (and above the horizontal (0) axis), is a product of meters and degrees, and is also an important measure of the stability of a vessel. The larger this area the greater the capacity of the vessel to right itself as it rolls from side to side. This is known as righting energy.

A recommended minimum value for the area under the GZ curve is 5.73 meter x degrees.

The size of this area is determined by the initial GM (which gives the starting slope of the curve), the heel angle at which maximum GZ occurs (which gives the height of the curve) and the rangeof heel angles for which GZ is positive (which gives the length of the curve).

The moment of dynamical stability is the work done in heeling the ship to a particular angle.

Dynamical stability = W x A (in t-m-rad)

W = Displacement (in tonnes)

A = area between the curve and the baseline up to the given angle of heel (in metre radians).

Statical stability curve:The righting levers arising from different angles of heel are best understood when plotted on a curve.  Each vessel will have a unique curve depending on displacement, weight distribution and hull shape.