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.
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 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 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
equilibrium 平衡
stability and trim 稳性与纵倾
floating upright 正浮
force of gravity 重力
resultant 合力
center of buoyancy 浮力
couple 力偶
magnitude 数值（大小）
displacement 排水量，位移，置换
righting moment 复原力矩
righting arm 复原力臂
upsetting moment 倾复力矩
upsetting arm 倾复力臂
metacentre 稳心
stable equilibrium 稳定平衡
netural equilibrium 中性平衡
metacenter height 稳心高
righting level 复原力臂
initial stability 初稳性
cross-curves of stability 稳性横截曲线
flooding 进水
thrust 推力
keelblock 龙骨墩
dry dock 干船坞
center of floatation 漂心
Greek letter 希腊字母
inclining experiment 倾斜试验
pendulum 铅锤，摆
Additional Terms and Expressions
lost buoyancy 损失浮力
reserve buoyancy 储备浮力
locus of centers of buoyancy 浮心轨迹
Bonjean’s curves 邦戎曲线
Vlasov’s curves 符拉索夫曲线
Firsov’s diagram 菲尔索夫图谱
Simpson’s rules 辛浦生法
trapezoidal rule 梯形法
stability at large angles 大倾角稳性
dynamical stability 动稳性
damaged stability 破舱稳性
stability criterion numeral 稳性衡准书
lever of form stability 形状稳性臂
locus of metacenters 稳心曲线
angle of vanishing stability 稳性消失角
free surface correction 自由液面修正
Notes to the Text
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……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。
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。
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。
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。
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。
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。
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。
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.
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 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 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
equilibrium 平衡
stability and trim 稳性与纵倾
floating upright 正浮
force of gravity 重力
resultant 合力
center of buoyancy 浮力
couple 力偶
magnitude 数值（大小）
displacement 排水量，位移，置换
righting moment 复原力矩
righting arm 复原力臂
upsetting moment 倾复力矩
upsetting arm 倾复力臂
metacentre 稳心
stable equilibrium 稳定平衡
netural equilibrium 中性平衡
metacenter height 稳心高
righting level 复原力臂
initial stability 初稳性
cross-curves of stability 稳性横截曲线
flooding 进水
thrust 推力
keelblock 龙骨墩
dry dock 干船坞
center of floatation 漂心
Greek letter 希腊字母
inclining experiment 倾斜试验
pendulum 铅锤，摆
Additional Terms and Expressions
lost buoyancy 损失浮力
reserve buoyancy 储备浮力
locus of centers of buoyancy 浮心轨迹
Bonjean’s curves 邦戎曲线
Vlasov’s curves 符拉索夫曲线
Firsov’s diagram 菲尔索夫图谱
Simpson’s rules 辛浦生法
trapezoidal rule 梯形法
stability at large angles 大倾角稳性
dynamical stability 动稳性
damaged stability 破舱稳性
stability criterion numeral 稳性衡准书
lever of form stability 形状稳性臂
locus of metacenters 稳心曲线
angle of vanishing stability 稳性消失角
free surface correction 自由液面修正
Notes to the Text
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……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。
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。
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。
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。
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。
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。
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。
