2017-01-24 Lecture Note of Naval Architectural Calculation Ship Stability Ch. 6 Free Surface Effect 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. 6 Free Surface Effect 3 Naval Architectural Calculation, Spring 2016, Myung-Il Roh Free Surface Effect G: Center of total mass (gravity) B: Center of buoyancy z z B1: New position of center buoyancy after the ship has been inclined * M(Metacenter): The intersection of a If the cargo in hold is fixed, e.g. a vertical line through the center of buoyancy at initial position(B) with a solid cargo, this keeps its original vertical line through the new M position of the center of position when a ship is inclined. buoyancy(B1) after the ship has been inclined transversally through a small angle y FG If there is a liquid cargo in hold, what will happen when y the ship is inclined? G Z B B 1 FB K * Hold or Cargo Hold: Space for loading the cargo in the ship 4 Naval Architectural Calculation, Spring 2016, Myung-Il Roh 2 2017-01-24 Definition of Free Surface Effect G: Center of total mass (gravity) G1: New position of center of total • When the ship is inclined, the liquid in mass (gravity) z z B: Center of buoyancy the tank is also inclined. And the center B1: New position of center of buoyancy after the ship has been inclined of gravity of the liquid shifts toward the g: Center of the emerged volume M g1: Center of the submerged volume inclined side. b: Center of liquid in tank b1: New position of center of liquid in tank • This causes the ship’s center of gravity to move toward the inclined side, reducing the righting arm. y FG y Z G 1 Definition of Free Surface Effect G1 • The motion of the liquid in a tank that is B B 1 partially full causes the ship’s center of g1 gravity to move. g b • This reduces the righting arm and b 1 FB reduces the ship’s stability. K 5 Naval Architectural Calculation, Spring 2016, Myung-Il Roh Assumption to Evaluate the Effect of Free Surface G: Center of total mass (gravity) G1: New position of center of total The effects of free surface depend on mass (gravity) z z B: Center of buoyancy the dimensions of the surface of the liquid. B1: New position of center of buoyancy after the ship has been inclined g: Center of the emerged volume M What assumption is appropriate g1: Center of the submerged volume b: Center of liquid in tank to evaluate the effect of free b1: New position of center of liquid in tank surface in a ship’s tank? G0: Virtual risen center of gravity y Assumption: Small inclination The metacentric height (GM) provides a y fairly accurate evaluation of the righting G moment up to 7~10 degrees. G1 B B 1 And, surface of the liquid does not reach g1 the top or bottom of the tank during this g inclination. b b 1 K 6 Naval Architectural Calculation, Spring 2016, Myung-Il Roh 3 2017-01-24 Transverse Righting Moment When there is no Effect of Free Surface G: Center of total mass (gravity) B: Center of buoyancy z B1: New position of center of buoyancyz after the ship has been inclined b: Center of liquid in tank Transverse Righting Moment M Righting arm: GZ • Transverse Righting Moment FGZ y righting B GZ GM sin y Z G GM KB BM KG B B 1 b K 7 Naval Architectural Calculation, Spring 2016, Myung-Il Roh GZ F The Influence of Free Surface restoring B GZ GM sin on the Initial Stability at Small Angle (1/5) GM KB BM KG G: Center of total mass (gravity) G1: New position of center of total Evaluation of effect of free surface on mass (gravity) z z B: Center of buoyancy metacentric height B1: New position of center of buoyancy after the ship has been inclined g: Center of the emerged volume M g1: Center of the submerged volume b: Center of liquid in tank If a ship is inclined, the plane of liquid in b1: New position of center of liquid in tank tank is changed to be parallel to water plane. y bb11// gg // GG 1 And the relation between change in total y center of gravity and center of liquid in Z tank is G G w 1 GG bb 11F B G B 1 g1 g b b 1 K 8 Naval Architectural Calculation, Spring 2016, Myung-Il Roh 4 2017-01-24 GZ F The Influence of Free Surface restoring B GZ GM sin on the Initial Stability at Small Angle (2/5) GM KB BM KG z z bb11// gg // GG 1 M Evaluation of effect of free surface on metacentric height From the geometric shape, the righting y arm G1Z1 is expressed as follows: GZ11GZG G1 y Z M G G1 GZ(cossin) yGG z B B 1 This term has negative effect to the restoring moment arm. g1 g b : It means that the shift of center of total b 1 gravity GG1 causes reduction of righting K arm. And it causes stability to be worse. G: Center of total mass (gravity) G0 G0: Virtual risen center of gravity : Free Surface Effect (FSE) G1: New position of center of total mass (gravity) G1’: The intersection of the line GZ with G0G1 Reduction of righting arm B: Center of buoyancy (It causes stability to be worse.) B1: New position of center of buoyancy after the ship has been inclined Z g: Center of the emerged volume G g : Center of the submerged volume 1 z sin 1 Z1 G b: Center of liquid in tank G1 ' b1: New position of center of liquid in tank y cos m: Metacenter of cargo hold G G G1 G1 G zG yG GG0 : free surface correction 9 Naval Architectural Calculation, Spring 2016, Myung-Il Roh : free surface correction GG0 GZ F The Influence of Free Surface restoring B GZ GM sin on the Initial Stability at Small Angle (3/5) GM KB BM KG z z bb11// gg // GG 1 M Evaluation of effect of free surface on metacentric height : Free Surface Effect (FSE) y Reduction of righting arm (It causes stability to be worse.) y Z M Assume that 1 , then from the G G1 geometric shape, the righting arm G1Z1 is B expressed as follows: B 1 g 1 GZ GZG G g 11 1 b b 1 GMsin GG0 sin K ()sinGM GG0 G: Center of total mass (gravity) G G : Virtual risen center of gravity 0 0 GM0 sin G1: New position of center of total mass (gravity) G1’: The intersection of the line GZ with G0G1 B: Center of buoyancy It means that the shift of center of total B1: New position of center of buoyancy after gravity GG is considered as the elevation the ship has been inclined Z 1 g: Center of the emerged volume G G G1 of center of total gravity from to 0. g1: Center of the submerged volume Z b: Center of liquid in tank 1 GG : free surface correction b1: New position of center of liquid in tank 0 m: Metacenter of cargo hold G G1 GM KB BM KG KG0 10 Naval Architectural Calculation, Spring 2016, Myung-Il Roh 5 2017-01-24 GZ F The Influence of Free Surface restoring B GZ GM sin on the Initial Stability at Small Angle (4/5) GM KB BM KG z z bb11// gg // GG 1 KG0 M Evaluation of effect of free surface on M righting arm y G0 y GG11// bb , GG0 // bm , GG10// bm 1 Z G G0 G1 m GG G B Triangle 10 is similar to triangle bb 1 m . B 1 g 1 g Z GG w w b G1 1 b 1 Z GG11 bb 1 F G bb1 FG G K G 1 G: Center of total mass (gravity) m G0: Virtual risen center of gravity G1: New position of center of total mass (gravity) G1’: The intersection of the line GZ with G0G1 B: Center of buoyancy B1: New position of center of buoyancy after the ship has been inclined b g: Center of the emerged volume b 1 g1: Center of the submerged volume b: Center of liquid in tank b1: New position of center of liquid in tank m: Metacenter of cargo hold w: Weight of liquid in tank 11 Naval Architectural Calculation, Spring 2016, Myung-Il Roh w restoringGZ F B The Influence of Free Surface GG bb 11F GZ GM sin on the Initial Stability at Small Angle (5/5) G GM KB BM KG z z bb11// gg // GG 1 KG0 M Evaluation of effect of free surface on M righting arm y Because ϕ is small, (small inclination) G 0 GG11 GG , GG10 GG sin , y GG10 GG sin , Z G G0 G1 In the same manner, bb1 bmsin m B B 1 ww g GG10 GGsin bb 1 bm sin 1 FF g Z GG b G1 b 1 Z w 1 GG bm K G1 0 G FG G: Center of total mass (gravity) m w iT F gv iT F iT G0: Virtual risen center of gravity G1: New position of center of total mass (gravity) Fv g v G1’: The intersection of the line GZ with G0G1 G SW SW B: Center of buoyancy B1: New position of center of buoyancy after the ship has been inclined b g: Center of the emerged volume b 1 i : Free Surface Moment g1: Center of the submerged volume F T b: Center of liquid in tank b1: New position of center of liquid in tank The elevation of center of total gravity due to m: Metacenter of cargo hold the shift of center of gravity of liquid in tank is w: Weight of liquid in tank related to the density of liquid in tank and iT: Moment of inertia of liquid plane area in tank about x' axis moment of inertia of liquid plane area in tank.