Lesson s Ship brium, stability and trim The basis for ship equilibrium Consider a ship floating upright on the surface of motionless water. In order to be equilibrium, there must be no unbalanced forces or moments acting on it. There are two forces that maintain this equilibrium(1)the force of gravity, and(2)the force of buoyancy. When the ship is at rest, these two forces are acting in the same perpendicular line, and, in order for the ship to float in equilibrium, they must be exactly equal numerically as well as opposite in direction The force of gravity acts at a point or center where all of the weights of the ship may be said be concentrated: i.e. the center of gravity. Gravity always acts vertically downward The force of buoyancy acts through the center of buoyancy, where the resultant, of all of the buoyant forces is considered to be acting. This force al ways acts vertically upward. when the ship is heeled, the shape of the underwater body is changed, thus moving the position of the center of buoyancy Now, when the ship is heeled by an external inclining force and the center of buoyancy has been moved from the centerline plane of the ship, there will usually be a separation between the lines of action of the force of gravity and the force of buoyancy. This separation of the lines of action of the two equal forces, which act in opposite directions, forms a couple whose magnitude is equal to the product of one of these forces(i.e. displacement) and the distance separating them In figure 1(a), where this moment tends to restore the ship to the upright position, the moment is called the righting moment, and the perpendicular distance between the two lines of action is the righting arm(Gz) Suppose now that the center of gravity is moved upward to such a position that when the ship s heeled slightly, the buoyant force acts in a line through the center of gravity. In the new position there are no unbalanced forces. or in other words. a zero moment arm and a zero moment I figure 1(b), the ship is in neutral equilibrium, and further inclination would eventually bring about of the state ofequilibrium If we move the center of gravity still higher, as in figure 1(c), the separation between the lines of action of the two forces as the ship is inclined slightly is in the opposite direction from that of figure 1(a). In this case, the moment does not act in the direction that will restore the ship to the upright but will cause it to incline further. In such a situation, the ship has a negative ighting moment or an upsetting moment. The arm is an upsetting arm, or negative righting arm These three cases illustrate the forces and relative position of their lines of action in the three fundamental states of equilibrium
Lesson Seven Ship Equilibrium, Stability and Trim The basis for ship equilibrium Consider a ship floating upright on the surface of motionless water. In order to be at rest or in equilibrium, there must be no unbalanced forces or moments acting on it. There are two forces that maintain this equilibrium (1) the force of gravity, and (2) the force of buoyancy. When the ship is at rest, these two forces are acting in the same perpendicular line, and , in order for the ship to float in equilibrium, they must be exactly equal numerically as well as opposite in direction. The force of gravity acts at a point or center where all of the weights of the ship may be said to be concentrated: i.e. the center of gravity. Gravity always acts vertically downward. The force of buoyancy acts through the center of buoyancy, where the resultant, of all of the buoyant forces is considered to be acting. This force always acts vertically upward. When the ship is heeled, the shape of the underwater body is changed, thus moving the position of the center of buoyancy. Now, when the ship is heeled by an external inclining force and the center of buoyancy has been moved from the centerline plane of the ship, there will usually be a separation between the lines of action of the force of gravity and the force of buoyancy. This separation of the lines of action of the two equal forces, which act in opposite directions, forms a couple whose magnitude is equal to the product of one of these forces (i.e. displacement) and the distance separating them. In figure 1(a) ,where this moment tends to restore the ship to the upright position, the moment is called the righting moment, and the perpendicular distance between the two lines of action is the righting arm (GZ). Suppose now that the center of gravity is moved upward to such a position that when the ship is heeled slightly, the buoyant force acts in a line through the center of gravity. In the new position, there are no unbalanced forces, or, in other words, a zero moment arm and a zero moment. In figure 1 (b) ,the ship is in neutral equilibrium, and further inclination would eventually bring about a change of the state of equilibrium. If we move the center of gravity still higher, as in figure 1 (c) ,the separation between the lines of action of the two forces as the ship is inclined slightly is in the opposite direction from that of figure 1 (a) .In this case, the moment does not act in the direction that will restore the ship to the upright but will cause it to incline further. In such a situation, the ship has a negative righting moment or an upsetting moment. The arm is an upsetting arm, or negative righting arm (GZ). These three cases illustrate the forces and relative position of their lines of action in the three fundamental states of equilibrium
The hull is shown inclined by an outside force to demonstrate the tendency in each cas From "Modern Ship Design"Second Edition, by Thomas. C Gillmer, 1975) Stability and trim Figure 2 shows a transverse section of a ship floating at a waterline Wl displaced from its AI d keel (k) Weight of ship Fig. 2 Stability shown in a transverse section of a floating ship(see text) original waterline WL. One condition of equilibrium has been defined above. A second condition is that the centre of gravity of a ship must be in such a position that, if the vessel is inclined, the forces of weight and buoyancy tend to restore the vessel to its former position of rest. At small angles, vertical lines through B, the centre of buoyancy when the vessel is
Fig. 1 Stable (a), Neutral (b), and Unstable (c) Equilibrium in the upright position The hull is shown inclined by an outside force to demonstrate the tendency in each case (From “Modern Ship Design ” Second Edition, by Thomas. C. Gillmer, 1975 ) Stability and trim Figure 2 shows a transverse section of a ship floating at a waterline WL displaced from its Fig. 2 Stability shown in a transverse section of a floating ship (see text) original waterline WL. One condition of equilibrium has been defined above. A second condition is that the centre of gravity of a ship must be in such a position that, if the vessel is inclined, the forces of weight and buoyancy tend to restore the vessel to its former position of rest. At small angles, vertical lines through B, the centre of buoyancy when the vessel is buoyancy Weight of ship
inclined to an angle 0, intersect the center line at m, the metacentre which means"change point". If M is above G(the centre of gravity of the ship and its contents), the vessel is in stable equilibrium, When M concides with G, there is neutral equilibrium. When M is below G, the forces of weight and buoyancy tend to increase the angle of inclination, and the equilibrium is unstable The distance Gm is termed the metacentric height and the distance gz. measured from g perpendicular to the vertical through B, is termed the righting level or Gz value. Weight and buoyancy are equal and act through and B, respectively, to produce a moment(tendency to produce a heeling motion )AGZ, where A is the displacement or weight in tons Stability at small angles, known as initial stability, depends upon the metacentric height GM. At large angle, the value of Gz affords a direct measure of stability, and it is common practice to prepare cross-curves of stability, from which a curve of Gz can be obtained for any particular draft and displacement Transverse stability should be adequate to cover possible losses in stability that may arise from flooding, partially filled tanks, and the upward thrust of the ground or from the keelblock when the vessel touches the bottom on being dry-docked The case of longitudinal stability, or trim, is illustrated in Figure3. There is a direct analogy ith the case of transverse stability. When a weight originally on board at position A is moved a distance d, to position B, the new waterline WILI intersects the original waterline WL at center of flotation(the centre of gravity of the water plane area WL), the new centre of buoyancy is B, and the new centre of gravity is G For a small angle of trim, signified by the greek letter theta( e) (a+f)/L wd=△GM1(a+f)/L nolton B tin i y M hostile trin Isx ++1 Changes in stern trim is x-y Fig 3 Longitudinal section of float ship showing change in stern trim as deck load w was shifted from position A to position B(see text Thus if (a+f)=l inch=1/12 foot, wd=AGM/12L and this presents the moment to change trim one inch The inclining experiment A simple test called the inkling experiment provides a direct method of determining GM, the metacentric height, in any particular condition of loading from which the designer can deduce
inclined to an angle 0,intersect the center line at M, the metacentre, which means “change point”. If M is above G (the centre of gravity of the ship and its contents),the vessel is in stable equilibrium, When M concides with G, there is neutral equilibrium. When M is below G, the forces of weight and buoyancy tend to increase the angle of inclination, and the equilibrium is unstable. The distance GM is termed the metacentric height and the distance GZ, measured from G perpendicular to the vertical through B, is termed the righting level or GZ value. Weight and buoyancy are equal and act through G and B, respectively, to produce a moment (tendency to produce a heeling motion) △GZ, where △ is the displacement or weight in tons. Stability at small angles, known as initial stability, depends upon the metacentric height GM. At large angle, the value of GZ affords a direct measure of stability, and it is common practice to prepare cross-curves of stability, from which a curve of GZ can be obtained for any particular draft and displacement. Transverse stability should be adequate to cover possible losses in stability that may arise from flooding, partially filled tanks, and the upward thrust of the ground or from the keelblocks when the vessel touches the bottom on being dry-docked. The case of longitudinal stability, or trim, is illustrated in Figure3.There is a direct analogy with the case of transverse stability. When a weight originally on board at position A is moved a distance d, to position B, the new waterline W1L1 intersects the original waterline WL at center of flotation (the centre of gravity of the water plane area WL),the new centre of buoyancy is B, and the new centre of gravity is G. For a small angle of trim, signified by the Greek letter theta(θ), θ=(a+f)/L wd=△GMl(a+f)/L Fig. 3 Longitudinal section of float ship showing change in stern trim as deck load w was shifted from position A to position B (see text ) Thus if （a+f）=1 inch =1/12 foot, wd =△GM/12L and this presents the moment to change trim one inch. The inclining experiment A simple test called the inkling experiment provides a direct method of determining GM, the metacentric height, in any particular condition of loading, from which the designer can deduce Changes in stern trim is x-y
the position of G, the ship's centre of gravity. If a weight w(ton) is transferred a distance d (feet) from one side of the ship to the other and thereby causes an angle of heel theta( e)degrees measured by means of a pendulum or otherwise, then Gm=wd/Atan 0(see Figure 2) For any particular condition, KB and BM can be calculated, GM is found by the inclining experiment, whence KG=KM-GM. It is simple to calcul ate the position of G for any other condition of loading From"Encyclopedia Britannica", Vol. 16, 1980) Technical Terms 1. equini uin 15. stable equilibrium稳定平衡 2. stability and trim稳性与纵倾 16. netural equilibrium中性平衡 3. floating upright 17. metacenter height稳心高 4. force of gravity重力 l8. righting level复原力臂 5. resultant合力 19. initial stability初稳性 6. center of buoyancy浮力 20. cross-curves of stability稳性横截曲线 7. couple力偶 21. flooding进水 8. magnitude数值(大小) 22. thrust推力 9. displacement排水量,位移,置换 23. keelblock龙骨墩 10. righting moment复原力矩 24. dry dock干船坞 1l. righting arm复原力臂 enter of floatation漂心 12. upsetting moment倾复力矩 26. Greek letter希腊字母 13. upsetting arm倾复力臂 27. inclining experiment倾斜试验 14. metacentre稳心 8. pendulum铅锤,摆 Additional Terms and expressions 1. lost buoyancy损失浮力 9. stability at large angles大倾角稳性 2. reserve buoyancy储备浮力 10. dynamical stability动稳性 3. locus of centers of buoyancy浮心轨迹1 damaged stability破舱稳性 4. Bonjean' s curves邦戎曲线 12. stability criterion numeral稳性衡准书 5.Ⅵ laso' s curves符拉索夫曲线 13. lever of form stability形状稳性臂 6. Firsov' s diagram菲尔索夫图谱 14. locus of metacenter稳心曲线 7. Simpson' s rules辛浦生法 15. angle of vanishing stability稳性消失角 8. trapezoidal rule梯形法 16. free surface correction自由液面修正 1. When the ship is at rest, these two forces are acting in same perpendicular line, and, in order for the ship to float in equilibrium, they must be exactly equal numerically as well as opposite
the position of G, the ship’s centre of gravity. If a weight w (ton) is transferred a distance d (feet) from one side of the ship to the other and thereby causes an angle of heel theta(θ) degrees, measured by means of a pendulum or otherwise, then GM=wd/△tanθ(see Figure 2). For any particular condition, KB and BM can be calculated, GM is found by the inclining experiment, whence KG=KM-GM. It is simple to calculate the position of G for any other condition of loading. (From “Encyclopedia Britannica”, Vo1. 16, 1980) Technical Terms 1. equilibrium 平衡 2. stability and trim 稳性与纵倾 3. floating upright 正浮 4. force of gravity 重力 5. resultant 合力 6. center of buoyancy 浮力 7. couple 力偶 8. magnitude 数值（大小） 9. displacement 排水量，位移，置换 10. righting moment 复原力矩 11. righting arm 复原力臂 12. upsetting moment 倾复力矩 13. upsetting arm 倾复力臂 14. metacentre 稳心 15. stable equilibrium 稳定平衡 16. netural equilibrium 中性平衡 17. metacenter height 稳心高 18. righting level 复原力臂 19. initial stability 初稳性 20. cross-curves of stability 稳性横截曲线 21. flooding 进水 22. thrust 推力 23. keelblock 龙骨墩 24. dry dock 干船坞 25. center of floatation 漂心 26. Greek letter 希腊字母 27. inclining experiment 倾斜试验 28. pendulum 铅锤，摆 Additional Terms and Expressions 1. lost buoyancy 损失浮力 2. reserve buoyancy 储备浮力 3. locus of centers of buoyancy 浮心轨迹 4. Bonjean’s curves 邦戎曲线 5. Vlasov’s curves 符拉索夫曲线 6. Firsov’s diagram 菲尔索夫图谱 7. Simpson’s rules 辛浦生法 8. trapezoidal rule 梯形法 9. stability at large angles 大倾角稳性 10. dynamical stability 动稳性 11. damaged stability 破舱稳性 12. stability criterion numeral 稳性衡准书 13. lever of form stability 形状稳性臂 14. locus of metacenters 稳心曲线 15. angle of vanishing stability 稳性消失角 16. free surface correction 自由液面修正 Notes to the Text 1. When the ship is at rest, these two forces are acting in same perpendicular line, and, in order for the ship to float in equilibrium, they must be exactly equal numerically as well as opposite in direction
in order for the ship to float in equilibrium是“ in order带to的不定式“结构,表示目 的状语,其中 for the ship中的 the ship是不定式逻辑主语 As well as是一个词组,可有几种译法,具体译成什么意思应根据上下文加以适当 选择。例如 The captain as well as the passenger was frightened 船长和旅客一样受惊。(和 样) 受惊的既有旅客又有船长。(既.又) 不仅旅客而且船长也受惊了。(不仅…而且) 除旅客外,还有船长也受惊了。(除.外,还) 不管那种译法,强调的都是 as well as前面的那个名次(例句中的 the captain,船长), 因此谓语动词的性、数也由这个名词决定。 2. thus moving the position of the center of buoyancy 由thus引出的现在分词短语用作表示结果的状语。一般来说,如分词短语位于句末 往往有结果、目的等含义 3. suppose now that the center of gravity is moved upward to such a position that when the ship is heeled slightly, the buoyant force acts in a line through the center of gravity pose Suppose now that…与 now let's suppose that..同意,其后t所引出的从句是 的宾语从句 to such a position that.是such.that.引导结果状语从句。但在这个从句中又包含 了一个由关系副词when引导的时间状语从句 4. Figure 2 shows a transverse section of a ship floating at a waterline WL, displaced from its WL floating at a waterline Wl现在分词短语(含有主动态),修饰前面的名词 a ship displaced from its original waterline WL过去分词短语(含有被动态),也是修饰前面 的名词,ship,注意这里的 displaced应选择“移动位置”的词义。 5. At small angles, vertical lines through B, the center of buoyancy when the vessel is inclined an angle 0, intersect the center line at m, the metacenter, which means change point 此句的主要成分为 vertical lines intersect the center line the center of buoyancy是B的同位语。 the metacenter是M的同位语 6. Tranverse stability should be adequate to cover possible losses in stability that may arise from flooding partically filled tanks, and the upwards thrust of the ground or from the keelblock when the vessel touches the bottom on being dry-docked that may arised from. the keelblock是定语从句,修饰 losses when the vessel. on being dry- docked是时间状语从句,修饰 may arise from the keelblock on being dry- docked中的 being dry- docked是动名词的被动态,接在on之后表示 刚)进船坞的时候 7. or otherwise意为“或相反,或其他”。例: It can be verified by trial or otherwise 这可用试验或其他方法加以验证 Fine or otherwise we shall have to do this test 不管天气好不好,我们非做这个试验不可
in order for the ship to float in equilibrium 是“in order 带 to 的不定式“结构，表示目 的状语，其中 for the ship 中的 the ship 是不定式逻辑主语。 As well as 是一个词组，可有几种译法，具体译成什么意思应根据上下文加以适当 选择。例如： The captain as well as the passenger was frightened. 船长和旅客一样受惊。（和……一样） 受惊的既有旅客又有船长。（既……又） 不仅旅客而且船长也受惊了。（不仅……而且） 除旅客外，还有船长也受惊了。（除……外，还） 不管那种译法，强调的都是 as well as 前面的那个名次（例句中的 the captain,船长）， 因此谓语动词的性、数也由这个名词决定。 2. thus moving the position of the center of buoyancy. 由 thus 引出的现在分词短语用作表示结果的状语。一般来说，如分词短语位于句末， 往往有结果、目的等含义。 3. suppose now that the center of gravity is moved upward to such a position that when the ship is heeled slightly, the buoyant force acts in a line through the center of gravity. Suppose now that …与 now let’s suppose that…同意，其后 that 所引出的从句是 suppose 的宾语从句。 to such a position that…是 such…that…引导结果状语从句。但在这个从句中又包含 了一个由关系副词 when 引导的时间状语从句。 4. Figure 2 shows a transverse section of a ship floating at a waterline WL, displaced from its original waterline WL. floating at a waterline WL 现在分词短语（含有主动态），修饰前面的名词 a ship; displaced from its original waterline WL 过去分词短语（含有被动态），也是修饰前面 的名词，ship,注意这里的 displaced 应选择“移动位置”的词义。 5. At small angles, vertical lines through B, the center of buoyancy when the vessel is inclined at an angle θ, intersect the center line at M, the metacenter, which means “change point”. 此句的主要成分为 vertical lines intersect the center line. the center of buoyancy 是 B 的同位语。 the metacenter 是 M 的同位语。 6. Tranverse stability should be adequate to cover possible losses in stability that may arise from flooding ,partically filled tanks, and the upwards thrust of the ground or from the keelblocks when the vessel touches the bottom on being dry-docked. that may arised from…the keelblocks 是定语从句，修饰 losses. when the vessel…on being dry-docked 是时间状语从句，修饰 may arise from the keelblock. on being dry-docked 中的 being dry-docked 是动名词的被动态，接在 on 之后表示 （刚）进船坞的时候。 7. or otherwise 意为“或相反，或其他”。例： It can be verified by trial or otherwise. 这可用试验或其他方法加以验证。 Fine or otherwise,we shall have to do this test. 不管天气好不好，我们非做这个试验不可