2017-01-24 Lecture Note of Naval Architectural Calculation Ship Stability Ch. 1 Introduction to Ship Stability Spring 2016 Myung-Il Roh Department of Naval Architecture and Ocean Engineering Seoul National University 1 Naval Architectural Calculation, Spring 2016, Myung-Il Roh Contents Ch. 1 Introduction to Ship Stability Ch. 2 Review of Fluid Mechanics Ch. 3 Transverse Stability Due to Cargo Movement Ch. 4 Initial Transverse Stability Ch. 5 Initial Longitudinal Stability Ch. 6 Free Surface Effect Ch. 7 Inclining Test Ch. 8 Curves of Stability and Stability Criteria Ch. 9 Numerical Integration Method in Naval Architecture Ch. 10 Hydrostatic Values and Curves Ch. 11 Static Equilibrium State after Flooding Due to Damage Ch. 12 Deterministic Damage Stability Ch. 13 Probabilistic Damage Stability 2 Naval Architectural Calculation, Spring 2016, Myung-Il Roh 1 2017-01-24 Ch. 1 Introduction to Ship Stability 1. Generals 2. Static Equilibrium 3. Restoring Moment and Restoring Arm 4. Ship Stability 5. Examples for Ship Stability 3 Naval Architectural Calculation, Spring 2016, Myung-Il Roh 1. Generals 4 Naval Architectural Calculation, Spring 2016, Myung-Il Roh 2 2017-01-24 How does a ship float? (1/3) The force that enables a ship to float “Buoyant Force” It is directed upward. It has a magnitude equal to the weight of the fluid which is displaced by the ship. Ship Ship Water tank Water 5 Naval Architectural Calculation, Spring 2016, Myung-Il Roh How does a ship float? (2/3) Archimedes’ Principle The magnitude of the buoyant force acting on a floating body in the fluid is equal to the weight of the fluid which is displaced by the floating body. The direction of the buoyant force is opposite to the gravitational force. Buoyant force of a floating body = the weight of the fluid which is displaced by the floating body (“Displacement”) Archimedes’ Principle Equilibrium State (“Floating Condition”) Buoyant force of the floating body W = -W = -gV = Weight of the floating body G Displacement = Weight G: Center of gravity B: Center of buoyancy B W: Weight, : Displacement : Density of fluid V: Submerged volume of the floating body (Displacement volume, ) 6 Naval Architectural Calculation, Spring 2016, Myung-Il Roh 3 2017-01-24 How does a ship float? (3/3) Displacement() = Buoyant Force = Weight(W) L B T C T: Draft B CB: Block coefficient : Density of sea water W LWT DWT LWT: Lightweight DWT: Deadweight Weight = Ship weight (Lightweight) + Cargo weight(Deadweight) Ship Ship Water 7 Naval Architectural Calculation, Spring 2016, Myung-Il Roh What is “Stability”? FG G B Capsizing ℄ B1 FB FG FG Inclining W L WL(Heeling) 1 1 G G B B B1 Restoring FB ℄ ℄ FB Stability = Stable + Ability 8 Naval Architectural Calculation, Spring 2016, Myung-Il Roh 4 2017-01-24 What is a “Hull form”? Hull form Outer shape of the hull that is streamlined in order to satisfy requirements of a ship owner such as a deadweight, ship speed, and so on Like a skin of human Hull form design Design task that designs the hull form Hull form of the VLCC(Very Large Crude oil Carrier) Wireframe model Surface model 9 Naval Architectural Calculation, Spring 2016, Myung-Il Roh What is a “Compartment”? Compartment Space to load cargos in the ship It is divided by a bulkhead which is a diaphragm or peritoneum of human. Compartment design (General arrangement design) Compartment modeling + Ship calculation Compartment modeling Design task that divides the interior parts of a hull form into a number of compartments Ship calculation (Naval architecture calculation) Design task that evaluates whether the ship satisfies the required cargo capacity by a ship owner and, at the same time, the international regulations related to stability, such as MARPOL and SOLAS, or not Compartment of the VLCC 10 Naval Architectural Calculation, Spring 2016, Myung-Il Roh 5 2017-01-24 What is a “Hull structure”? Hull structure Frame of a ship comprising of a number of hull structural parts such as plates, stiffeners, brackets, and so on Like a skeleton of human Hull structural design Design task that determines the specifications of the hull structural parts such as the size, material, and so on Hull structure of the VLCC 11 Naval Architectural Calculation, Spring 2016, Myung-Il Roh Principal Characteristics (1/2) Loa W.L. W.L. B.L. B.L. A.P. Lbp F.P. Lwl LOA (Length Over All) [m]: Maximum Length of Ship LBP (Length Between Perpendiculars (A.P. ~ F.P.)) [m] A.P.: After perpendicular (normally, center line of the rudder stock) F.P.: Inter-section line between designed draft and fore side of the stem, which is perpendicular to the baseline Lf (Freeboard Length) [m]: Basis of freeboard assignment, damage stability calculation 96% of Lwl at 0.85D or Lbp at 0.85D, whichever is greater Rule Length (Scantling Length) [m]: Basis of structural design and equipment selection Intermediate one among (0.96 Lwl at Ts, 0.97 Lwl at Ts, Lbp at Ts) 12 Naval Architectural Calculation, Spring 2016, Myung-Il Roh 6 2017-01-24 Definitions for the Length of a Ship Structures above main deck Main deck (Main) Hull Wetted line Molded line Length overall(LOA) Length on waterline(LWL) Stem tstem Design waterline Length between perpendiculars(L ) AP BP FP 13 Naval Architectural Calculation, Spring 2016, Myung-Il Roh Principal Characteristics (2/2) B (Breadth) [m]: Maximum breadth of the ship, measured amidships -Bmolded: excluding shell plate thickness -Bextreme: including shell plate thickness Air Draft D (Depth) [m]: Distance from the baseline to the deck side line -Dmolded: excluding keel plate thickness -Dextreme: including keel plate thickness Td (Designed Draft) [m]: Main operating draft Depth - In general, basis of ship’s deadweight and speed/power performance Draft Ts (Scantling Draft) [m]: Basis of structural design B.L. B.L. Breadth Air Draft [m]: Distance (height above waterline only or including operating draft) restricted by the port facilities, navigating route, etc. - Air draft from baseline to the top of the mast - Air draft from waterline to the top of the mast - Air draft from waterline to the top of hatch cover -… 14 Naval Architectural Calculation, Spring 2016, Myung-Il Roh 7 2017-01-24 Definitions for the Breadth and Depth of a Ship 1/2 Molded breadth(B ) ,mld Deck plating Camber Deck beam Freeboard Scantling waterline Molded depth(D,mld) Scantling draft Centerline Dead rise CL Baseline Keel Sheer after Sheer forward Depth 15 Naval Architectural Calculation, Spring 2016, Myung-Il Roh 2. Static Equilibrium 16 Naval Architectural Calculation, Spring 2016, Myung-Il Roh 8 2017-01-24 Center Plane Before defining the coordinate system of a ship, we first introduce three planes, which are all standing perpendicular to each other. Generally, a ship is symmetrical about starboard and port. The first plane is the vertical longitudinal plane of symmetry, or center plane. 17 Naval Architectural Calculation, Spring 2016, Myung-Il Roh Base Plane The second plane is the horizontal plane, containing the bottom of the ship, which is called base plane. 18 Naval Architectural Calculation, Spring 2016, Myung-Il Roh 9 2017-01-24 Midship Section Plane The third plane is the vertical transverse plane through the midship, which is called midship section plane. 19 Naval Architectural Calculation, Spring 2016, Myung-Il Roh Centerline in (a) Elevation view, (b) Plan view, and (c) Section view Centerline: Intersection curve between center plane and hull form Centerline Elevation view Plan view (a) ℄ (c) Section view ℄ ℄: Centerline (b) 20 Naval Architectural Calculation, Spring 2016, Myung-Il Roh 10 2017-01-24 Baseline in (a) Elevation view, (b) Plan view, and (c) Section view Baseline: Intersection curve between base plane and hull form Elevation view BL BL Plan view (a) ℄ (c) Section view Baseline (b) 21 Naval Architectural Calculation, Spring 2016, Myung-Il Roh System of Coordinates zb zn yb O n-frame: Inertial frame xn yn zn or x y z E yn xb Point E: Origin of the inertial frame(n-frame) b-frame: Body fixed frame xb yb zb or x’ y’ z’ Point O: Origin of the body fixed frame(b-frame) xn 1) Body fixed coordinate system The right handed coordinate system with the axis called xb(or x’), yb(or y’), and zb(or z’) is fixed to the object. This coordinate system is called body fixed coordinate system or body fixed reference frame (b-frame). 2) Space fixed coordinate system The right handed coordinate system with the axis called xn(or x), yn(or y) and zn(or z) is fixed to the space. This coordinate system is called space fixed coordinate system or space fixed reference frame or inertial frame (n-frame). In general, a change in the position and orientation of the object is described with respect to the inertial frame. Moreover Newton’s 2nd law is only valid for the inertial frame. 22 Naval Architectural Calculation, Spring 2016, Myung-Il Roh 11 2017-01-24 System of Coordinates for a Ship Body fixed coordinate system (b-frame): Body fixed frame xb yb zb or x’ y’ z’ Space fixed coordinate system (n-frame): Inertial frame xn yn zn or x y z Stem, Bow zb zn zb SLWL yb yn xb x n BL yb AP LBP xb FP AP: aft perpendicular : midship FP: fore perpendicular LBP: length between perpendiculars. Stern BL: baseline (a) SLWL: summer load waterline (b) 23 Naval Architectural Calculation, Spring 2016, Myung-Il Roh K : keel Center of Buoyancy (B) LCB: longitudinal center of buoyancy LCG: longitudinal center of gravity VCB: vertical center of buoyancy VCG : vertical center of gravity and Center of Mass (G) TCB: transverse center of buoyancy TCG : transverse center of gravity z z Elevation view Section view y x x y G LCG VCG B G B LCB VCB K CL Plan view y z TCG z x G B G TCB LCB LCG B K CL ※ In the case that the shape of a ship is asymmetrical Center of buoyancy (B) with respect to the centerline.