STABILITY SEMINAR (2-5 July, 2012 Briese Swallow Co

STABILITY SEMINAR (2-5 July, 2012 Briese Swallow Co )

Basic Information of A Ship Stability (Основные понятия об остойчивости судна) Stability is a property of a ship disturbed by an external inclining moment of force that changes a ship angular attitude, to return to its original position if this moment removes. Остойчивость – это способность судна, наклоненного на некоторый угол крена (дифферента) внешней силой (моментом), возвращаться в исходное положение после прекращения действия этой силы (момента).

Basic Information of A Ship Stability Criterion: metacentric height (GM) Stability of Ship Static Stability (Heeling rate is small) Dynamic Stability (Heeling rate is large) Manifests: at rolling in waves, at the gust wind action , or so Criteria: 1)the Weather criterion 2) Upsetting angle 3) Area under the GZ curve Initial Stability (Heeling angle is small: not more than 5-8 degrees) General Stability (Heeling angle is large ) Manifests: in still water (loading/unloading, shifting a weight, or so) Criterion: the biggest righting lever and heeling angle at which it takes place

Fundamentals of mechanics for stability calculation. Понятие силы Сила – это нечто, что воздействует на данное материальное тело, вызывая изменение его скорости или деформацию этого тела. Сила – величина векторная, поэтому как всякий вектор она характеризуется, в общем случае, своим численным значением (длиной вектора или его модулем), направлением в пространстве и точкой приложения . Concept of Force Force is what that acts at the material body and causes its velocity alteration (acceleration) or deformation. A force is a vector; therefore, as any other vector, it can be defined by such parameters as: the magnitude of the force, the direction in which the force acts, and the point at which this force is applied (point of application).

Момент силы Моментом силы относительно некоторой точки О называют величину, равную произведению модуля этой силы и длины перпендикуляра, опущенного из точки O на линию действия силы. Длину этого перпендикуляра называют плечом. Предположим, сила F действует на стержень. Стержень и линия действия силы находятся в плоскости XОY при этом один конец стержня находится в начале координат. Вектор, имеющий начало в центре О и конец в точке приложения силы F называют радиусом-вектором r. Тогда момент силы при вращении стержня вокруг точки О (оси OZ) будет равен Moment of Force A moment of force about some point O is called the value equaled to the product of the force magnitude and length of perpendicular that goes from point O to the line of the force action. The length of this perpendicular is called lever (or arm). Let suppose, force F is applied at the rod. The rod and the force action line are in the same plane XOY, and one end of the rod is at the coordinates’ origin.

Момент пары сил Парой сил называют два параллельных вектора, имеющих равные модули и действующих в противоположных направлениях. Примерами пары сил могут служить сила тяжести и выталкивающая сила, действующие на судно при его наклонении, сила постоянного ветра, приложенная в надводной части судна, и сила сопротивления воды, возникшая в подводной части, как реакция на боковое смещение (дрейф) судна под действием этого ветра, и.т.д. Если в кусок пенопласта, спокойно плавающего в воде, забить два гвоздика, привязать к ним нити и потянуть за них (как показано на рис.1.6), то возникнет пара сил, которая начнет вращать кусок пенопласта. При этом интенсивность вращения (вращательный эффект) будет тем больше, чем больше приложенные силы натяжения нитей и больше расстояние между линиями действия этих сил. Moment of Couple A couple is called a pair of collinear forces of equal magnitude acting in parallel but opposite directions. l M F2 F1 A BA

Basic Information of A Ship Stability Archimedes’ Principle (закон Архимеда) : Each body floating freely in a fluid is undertaken by an upward force (buoyant force) that equals the weight of the displaced fluid . This force always is applied at the centroid (centre of buoyancy) of the fluid volume displaced by the body. На каждое тело, свободно погруженное в жидкость, действует направленная вверх сила (сила плавучести), равная весу вытесненной жидкости. Эта сила всегда приложена к геометрическому центру (центру величины) объема жидкости, вытесненного телом. Buoyant force Centre of buoyancy Waterline (WL) B Floating body

Buoyancy equilibrium condition of ship Если на судно не действуют внешние силы (волны, ветер, и т.д.), то оно будет неподвижным относительно поверхности воды. При этом, на судно всегда действуют две силы: --сила тяжести (весового водоизмещения), которая направлена вертикально вниз и приложена к точке, называемой центром тяжести; --сила плавучести (выталкивающая сила), направленная вертикально вверх и приложенная к геометрическому центру погруженного объема судна (центру величины). If a ship is not disturbed by an external force (waves, wind, or so), she will float quietly at the surface of water without any motion. And there are always two forces acting on the ship: –the weight force (displacement force), which acts downward from a point called centre of gravity; -the buoyant force, (or buoyancy), which always acts upward from point called centre of buoyancy. B G ZB zG xG xB Z WL1 WL X Angle of trim

Initial Stability of Ship Z B G B1 G B Z Z Y Y WL WL1 Positive Initial Stability (metacentric height GM>0) Heeling moment --righting moment GZ—righting lever (positive) BM—metacentric radius M -- metacentre

Initial Stability of Ship b) Negative Initial Stability (metacentric height GM<0) --righting moment heeling moment-- G Y Y Z Z Z G B1 B WL WL WL1 M B GZ—righting lever (negative) BM—metacentric radius

Initial Stability of Ship c) Neutral Initial Stability (metacentric height GM=0) Heeling moment Y Y Z Z G B1 B WL WL WL1 M B --righting moment because GZ=0 GZ=0 —righting lever BM—metacentric radius G

Z B1 G B Z Y WL1 Heeling moment 1) righting moment: M -- metacentre Initial Stability Criteria (Transversal Inclinations) Metacentric height (is a rate of the righting moment per unit of the ship displacement while the heel is intially growing): 2) Stability coefficient (is a rate of the righting moment while the heel is initially growing : Righting moment

Initial Stability Criteria (Longitudinal inclinations) 1) Longitudinal righting moment: X ZL ML B B1 O G Z WL1 WL Angle of trim 2) Longitudinal stability coefficient: 3) Moment to change the trim by 1 cm :

Initial Stability of Ship (Mutual positions of the basic points) GML—longitudinal metacentric height GM – (transverse) metacentric height F – flotation centre M – metacentre ML – longitudinal metacentre B – centre of buyoancy Z 0 F ML M G B K (keel line) WL X

GZ GZmax 0 WL WL WL WL GZ 57,30 GZmax GZ GZ=0 GZmax and General Stability of Ship -- general stability reserve =GM -- initial stability reserve GM SSC area – dynamical stability reserve Static Stability Curve (Righting Lever Curve) --upsetting angle (angle of vanishing stability)

Stable & Unstable Equilibrium Conditions of Ship C B A Stable equilibrium branch of GZ-curve Unstable equilibrium branch of GZ-curve General Stability of Ship GZ Heel angle Righting lever Heeling lever

Negative Initial Stability & Lolling A2 A1 Lolling range GZ Might be due to: 1—centre of gravity is above a metacentre (GM<0) 2— unfixed cargo on board ship (mostly, free surfaces of liquids or freely suspended weight unit): GMcor=(GM-FSC)<0

Dynamical Stability of Ship 0 0 Heeling lever Time Time Heeling angle --dynamical heeling angle (due to gust wind) --angle of steady heel Heeling lever (dynamically applied) Dynamical stability is defined as the work done by the righting moment in heeling a ship. Dynamical angle of heel is the biggest inclination of ship while a ship is damply rolled due to application of the dynamical heeling moment (lever)

Dynamical Stability of Ship (Calculation of steady and dynamical heeling) D B C E A 0 righting lever (GZ) heeling lever righting lever=heeling lever area AB0=area BCE Dynamical stability is defined as the work done by the righting moment (lever) against a heeling moment (lever) while a ship is damply rolled. --steady heeling angle (under steady wind action or so) --dynamical heeling angle (under a gust wind action or so)

Dynamical Stability of Ship Severe Wind and Rolling Criterion (Weather Criterion) The Weather criterion is an official one established by IMO Resolution A.749(18). B A GZ WL Pw —heeling lever of the steady wind —heeling lever of the gust wind: --heeling angle under steady wind LW1 --angle of roll to windward due to wave --angle of down flooding or or

Shifting A Single Weight A1 A G1 G

Vertical Shifting A Single Weight: At a vertical shift of a single weight upward, the ship stability will be reduced. (If centre of gravity were gotten above a metacentre, the ship would have a negative initial stability, and it would also heeled.) At a vertical shift of a single weight downward, the ship stability will be increased, and its attitude will be never changed.

Transversal Shifting A Single Weight: At a small single weight shifting, a ship will be heeled, but its metacentric height will be practically not changed. B1 G B Y WL WL1 M A1 A G1 Z

Longitudinal Shifting A Single Weight At a longitudinal shifting of a single weight, the ship will be trimmed, but its metacentric height will be practically not changed. T1 WL WL1 Z AP FP TA1 TA TF1 TF LBP A A1 F B1 t1 X -- angle of trim ML G G1 B LCF(XF)

General Case of Shifting A Weight Сalculation procedure must include three steps: The first step is a vertical shifting a weight from point A to AZ at which new values of GM and GML are to be determined: The second step is a transversal shifting a wwight from AZ to AY: The third step is a transversal shifting a wwight from AY to A1:

A Freely Suspended Weight At the very moment of suspension of a single weight (by the ship crane), the effect on the ship’s stability is looked like a situation when this weight is immediately lifted up at the point of suspension (point S). Consequently, a subsequent real lifting or lowing of the suspended weight does not affected on the ship stability anymore. Heeling moment due to suspension: Metacentric height (corrected due to suspended weight): Z Y S 0 A WL1 Berth WL A0 G M

Effect of Free Surfaces of Liquids A free surface of a liquid always reduces a ship stability. From each single liquid surface, the GM reduction is proportional to a specific gravity of the liquid and the moment of inertia (mostly the beam of the surface) Z Y WL1 WL g1 g rliq --moment of inertia of the liquid surface

Effect of loading/unloading a single weight A ship will be not trimmed if the loaded single weight is located at the vertical line passed through the flotation centre (CF) of the ship. X For wall-sided ships, equation of the neutral plane of stability: 2. Loading a single weight above the actual WL always causes the ship stability reduction, as long as, loading the weight below the actual WL causes the ship stability increase. Vertical line through Flotation centre

Loading/discharging a large single weight Stability and Trim Calculation (by means of Hydrostatic Data) WL WL1 2) By the use of the Hydrostatic data, let determine: 1) Calculate a new displacement and new gravity centre position: 3) Calculate new trim of the ship:

The Inclining Experiment Before an inclining experiment, the following conditions are necessary: There should be little or no wind. The ship should be floating freely. Any loose weights within the ship should be removed or secured in place. There must be no free surfaces within the ship. (Bilges should be dried. Boilers and tanks should be completely fill or empty.) Any persons not directly concerned should be sent ashore. The ship must be upright. A note of “weights on” and “ weights off” to complete the shipeach with a VCG and LCG. --average heel angle due to shifting the weight (should be measured several times)

Testing due the roll time trial The ship is freely rolling --natural roll period, s --rolling coefficient (0.7-0.9) The first approach: If you know for a specific case values of and , then:

Brief Inclining Experiment (by turning a crane jib of a ship) Should be performed: If а you are not quite sure of the real number of GMcor. Before heavy lift operation. If you you want to check your stability calculation results. G1 G1 G2 G2 Berth WL Jib Crane G1,G2—Centre of gravity of jib --luffing angle --transversal shift of the jib CG, m --length of jib, m --angle of list due to turning the jib at angle 90 degrees (must be accurately measured)

Brief Inclining Experiment Measuring U-tube WL WL1 Water or other liquid Measuring an angle of heel (by means of a U-tube filled by a liquid): Example. After turning the jib: Then: Consequently, the real stability of the ship is less than the calculated one (before the brief inclining experiment):

Heavy Lift Operation (Loading A Weight from A Berth) The most dangerous moment is what at which a heavy single weight has been just hoisted up from a berth and freely suspended by the ship crane. Z Y S1 B1 BII B BI Smax S 0 Stability loss at standard hoisting Stability reserve WL Stability loss if the weight is fixed b) the biggest loss (while point S is the highest): The biggest angle of heel (roughly) : Neutral plane The metacentric height loss : a) at the very moment of suspension: ship displacement and metacentric height (corrected due to free surface) before heavy lift operation weight of a cargo

Heavy Lift Operation (Unloading A Weight from A Ship) WL Z Y S A AI A1 AII Smax S1 0 The biggest stability loss at standard lift operation Stability loss if the weight is fastened Stability reserve The most dangerous moment is what at which a heavy single weight has been just hoisted up and freely suspended by the ship crane. At the very moment of suspension a) the metacentric height loss : b) angle of heel is zero (if ) The biggest GM loss (while point S is in the highest position): If a suspended cargo is transversally fastened then the biggest GM loss: consequently, a stability reserve: The biggest angle of heel (when the cargo is at point A1):