Force的單位是newton (N) or Kg

Force除了強度,還有方向性

兩股或以上的forces打在同一個point, forces’ magnitude and direction不同, 會互相影響, 最後形成一股resultant force.

這個計算resultant force的過程叫resolution of forces.

Like parallel forces

Force P and W act through A and B

Resultant force W+P acts through C

W is greater than P, so C is nearer to B than A

Py=Wx

Unlike parallel force

W is greater than P

Wx=Py

Moments of forces

Is a measure of turning effect of force about a point

一股force令東西旋轉的強度

有方向性

Moment = force 乘 length of lever

單位 Nm or Kgm

多股forces形成的moment叫resultant moment

計算resultant moment的過程叫resolution of component moments

Moment: 500N乘2米,再乘4個

Moment=4000Nm anti-clockwise

Moment 除圈的半徑= 繩的strain

4000除圈的半徑(1米)＝繩的受力strain =4000N

圈愈細,繩愈受力

Moment的單位有分clockwise or anti-clockwise, 唔知就寫晒

1.      A uniform plank is 6 metres long and is supported at a point under its mid-length. A weight of 10 kg  is placed on the plank at a distance of 0.5 metres from one end and a weight of 20 kg is placed on the plank 2 metres from the other end. Find the resultant moment about the centre of the plank.

搖搖板,兩邊放野,moment相減

長度是由支撐點開始計

10kg乘2.5米 減 20kg乘1米 = 5kgm clockwise/anti-clockwise

Centre of gravity

·         The centre of gravity of a body is the point at which all the mass of the body may be assumed to be concentrated.

·         It is the point through which the force of gravity is considered to act vertically downwards, with a force equal to the weight of the body.

·         It is also the point about which the body would balance.

The centre of gravity of a homogeneous body is at its geometrical centre.

重心移動的距離GG1=d x w 除final mas(W-w)

w is the mass removed; 重量單位是kg or tonnes, W和w單位要統一

d is the distance between the centre of gravity of the mass removed and the centre of gravity of the body. 單位是m

GG1單位是m

如果SHIFT CARGO, 成隻船的final mass or displacement 就不變.

a)      重心以下卸了貨,重心向上移

b)      重心以上卸了貨,重心向下移

c)      重心右邊卸了貨,重心向左移

d)     重心左下角卸了貨,重心向右上角移

The centre of gravity of the body will always move parallel to the shift of the centre of gravity of any weight moved within the body.

KG 即是keel到center of gravity的距離,單位是m

the centre of gravity of a suspended weight is considered to be at the point of suspension.

不管舉起幾多, 只要一離地,cargo的重心就提升到derrick的高度.gg1

成隻船的重心就會上升GG1

density is mass per unit volume

Density = mass over volume

Density of fresh water 1000 kg/m³

Density of salt water 1025 kg/m³

1 tonne = 1000kg

Relative density of a substance = density of substance除 density of fresh water

冇單位

如果volume一樣,可以約簡.

Relative density of a substance= mass of substance除mass of fresh water

Ullage: top of tank to surface of liquid

Sounding: surface of liquid to base of tank

Relative density 0.9

即係density 900kg/m3

1.      A tank will hold 100 tonnes when full of fresh water. Find how many tonnes of oil of relative density 0.880 may be loaded if 2% of the volume of the oil loaded is to be allowed for expansion.

Tank的volume是100m3, 100 m3 乘 oil density 0.88tonnes/m3

再乘100/102

D油會expand, 不可以裝滿成個tank.

將tank分成102份,裝100份. 100over102.

當100over102 expand 2%, 即是乘1.02, 就=102over102, 剛剛滿晒.
如果98over100, 再expand 2%即是乘1.02, 不是100%, tank裝唔滿,就浪費了

Archimedes’ Principle states that when a body is wholly or partially immersed in a fluid it appears to suffer a loss in mass equal to the mass of the fluid it displaces.

Density of fresh water 是 1000kg/m3

呢個cargo mass是4000kg, volume是1m3

在空中重4000kg, 放在水中, displace 1m3, 變成3000kg重

Cargo的mass沒變,但重量輕了,因為有force of buoyancy.

Center of buoyancy 在center of underwater volume.

Box shaped ship的KB 是draft除2

Force of Buoyancy的單位是kg or tonnes

Force of buoyancy= mass of water being displaced

呢個cargo 重4000kg, volume 8m3

用力壓進水裡, displace 8m3,就產生8000kg force of buoyancy

Cargo 重4000kg, 現在不equilibrium.

放手,cargo會浮起. 只displace 4m3, resultant force zero

在4000kg的cargo上放一個1000kg的小cargo.

兩個加埋5000kg.

會displace 5m3.

結論是東西會displace its own weight of water.

在fresh water displace 1m3有1000kg force of buoyancy

在sea water displace 1m3 有1025kg force of buoyancy.

Volume of enclosed spaces above waterline does not provide buoyancy but is being held in reserve.

有reserve buoyancy代表可以再裝多一些貨, 再沉一點

Volume of enclosed space above waterline除total volume of vessel 乘100%

Reserve buoyancy的單位是幾多%

將所有reserve buoyancy消滅就會沉

1 liter (1L) = 1000 cm3 = 0.001 m3

圓的面積是半徑二次乘3.14

Lightweight/ light ship:

Weight of ship when completely empty

Deadweight:

The weight that a ship carries.

Eg: fuel, fresh water, stores, lubricating oil, ballast water, crew, cargo, passengers.

Displacement:

Weight of water that the ship displaces.

Displacement = lightweight + deadweight

Water draft:

Vertical distance from waterline down to keel

Draft moulded:

waterline to top of keel

建船者才有用

draft extreme/ draft:

from waterline to bottom of keel

air draft:

vertical distance from waterline to highest point of ship when at zero forward speed.

過橋用

TPC : tonnes per centimeter immersion

要load幾多tonnes貨才可以令船沉1cm

或者相反, 升1cm要discharge 幾多貨

TPC= water-plane area 除100 乘 density of water

Water-plane area 單位m2

Density 單位 tonnes/m3

根據比例,

TPC dock water over TPC salt water = density of dock water over density of salt water

適用於同一隻船, water plane area不變, 所以可以約簡.

For同一隻船, 船的mass不變, 船的length, breadth 也不變

只有density of water 變, 然後draft跟住變.

New Density of water乘 new draft = old density of water 乘old draft

因為length 和 breadth 要固定,所以只適用於box shaped ship

FWA fresh water allowance

由density 1025 kg/m3 的sea water 去到 fresh water, 船會沉幾多mm.

FWA的單位是mm

1cm=10mm

FWA= displacement in tonnes 除 ( 4乘TPC)

TPC裡面的density是salt water的density

Loadline的厚度是25mm

DWA dock water allowance

由density 1025kg/m3 的sea water 去到某density的dock water, 船會沉幾多mm

根據比例計算:

DWA over FWA = 1025 – density of dock water over 1025-1000

經過不同density的水域, 為了維持draft 一樣, 要改變船的displacement. 例如運用ballast water.

New volume = old volume

Then

New displacement over new density = old displacement over old density.

Bunkers 燃料

Load displacement in salt water 即在salt water 最大可以達到的displacement.超過就犯法

Load mark 就是最盡可以去到的loadline

船左右傾斜, 有兩個字

Heel:

Inclined by an external force. 例如waves, wind

List:

Inclined by forces within the ship. 例如船上的cargo放得唔好.

K : keel

B: center of buoyancy

G: center of gravity

M: metacenter

b: force of buoyancy

w: ship weight

b和w 數值相同,方向相反, 是一對,叫righting couple.

Inclined by an external force to a small angle of heel.

船的mass不變, 所以G不變.

船底浸水的部份由wedge WOW1轉到LOL1

B轉去B1, parallel to gg1

BB1= v 乘gg1 除 V

v是volume of wedge

V是船的volume of displacement

當heel angle is 15 degree, 在B1 拉條直線上去, 找到M, 叫做initial metacenter

KM 叫 height of initial metacenter above keel

GM 叫 metacentric height

Positive metacentric height: G在M 下面

Negative metacentric height: G在M 上面

GZ是righting lever.

Stable equilibrium:

When inclined, she returns to initial position.

G要在M下面,即係有positive metacentric height.

這種令船回到initial position的moment叫做moment of statical stability.

Moment of statical stability = W 乘 GZ

W是force,即是船的displacement, 單位是tonnes

GZ是righting lever, 單位是m

Moment of statical stability的單位是tonnes metres.

GZ = GM × sinθ

Unstable equilibrium:

When a ship is inclined to a small angle, tends to heel over still further.

Negative GM. G is above M

W × GZ 令船繼續傾斜, 所以叫做capsizing moment.

Neutral equilibrium:

G coincides with M

When inclined to a small angle, she remains at that angle, until another external force is applied.

Moment of Statical Stability = W × GZ

但GZ是0, 所以Moment of Statical Stability是0

沒有moment去令船作出回應.

Correcting unstable and neutral equilibrium:

將G下降,

Lower weights in ship

Load weights below G

Discharge weights above G

Remove free surfaces in ship.

當GM很大, 大約2-3m, righting moment都會很大,

船就需要很大的moment才會傾斜,

一旦傾斜,有很大的righting moment去令船回到原位,

這個過程很快,大約8秒, roll quickly and violently.

這個情況叫stiff, 是令人不舒服的,應該令GM縮小一點

當GM很小, 大約0.16-0.2m, righting moment很小

船很容易就傾斜, 但不容易回到原處

需要長時間才回到原處, 大約25-35秒

這個情況叫tender, 這個情況也不好

最佳的時間是15-25秒

IMO要求GM一定不能少於0.15m

呢隻船有negative GM.

傾斜了少少, 有capsizing moment GZ.

船會繼續傾斜. B會繼續向右移動

當B向右移動, 直到跟G在同一直線, 船會變穩定

GZ capsizing moment disappears.

這個角度叫做angle of loll.看圖c

如果船受到外力,又再向右傾斜, 即是圖d

B向右移,所以有righting lever GZ令船回到angle of loll.

The ship will oscillate about the angle of loll.

所以negative GM都不一定會翻船, 可能會停留在angle of loll

但如果G實在太高, B未移到跟G同一直線, 船已經翻了

free surface effect:

double bottom tank 裝滿了liquid.

當船傾斜時, liquid的center of gravity g 冇改變.

所以成隻船的center of gravity G都冇改變

這種liquid叫做static weight

Double bottom tank is partially filled.

當船傾斜時, liquid的g 移到g1

船的G移到G1, parallel to gg1

想知道free surface effect令metacentric height GM減少多少,

就把G1向上拉, 找到Gv

Metacentric height由GM減少到GvM.

Righting lever也由GZ減到GvZv

GM減少即是stability減少

如果本來的GM已經很少,有free surface effect可能令GM變negative

船傾斜了,又不回到原處.

有兩個原因, 可能是uneven distribution of weights on board, 可能是negative GM造成angle of loll.

首先把重量都平均分佈,如果船仍然傾斜, 就可以假設是有angle of loll.

要把船的G降低, 可以lower the weights within the ship.例如搬貨,例如lower derricks, 可以top up slack tanks to eliminate free surface effect.

Slack tanks即是半滿的tank

做了以上的動作, 船仍然傾斜, 就要加ballast water去empty double bottom tanks.

要知道, 只要一加少少水, 加上船搖擺, 立即就會有free surface effect

所以同一時間, 只能加水到一個tank

要選擇smallest surface area的tank去加水先, 即係比較細的tank.

假設船傾斜向starboard side.

現在有port和starboard side的tank可以選擇, 要首先加水到哪一邊呢

加水到port side的tank, 即係在高處的tank.

會將G下降, 但因為port tank在高處, G下降的效果不佳

但同時加水會有free surface effect.

船會稍稍向port side傾斜一點, 然後一野反彈去starboard side, 可能會反船.

If the high side is filled first the ship will start to right herself but will then roll suddenly over to take up a larger angle of loll on the other side, or perhaps even capsize.

所以答案是要加水到starboard side的tank.

加水會造成free surface effect, 船會更加向starboard side傾斜,

但加水同時令船的G下降.

船會首先向starboard side傾斜, 慢慢就受到控制, 回到原處,

Starboard side完成, 就加水到port side

為什麼G會上升?

1.       有partially filled tanks, 有free surface effect

2.       有污水bilge積聚, 造成free surface effect

3.       Deck面有結冰

4.       Deck面有積水,造成重量

5.       打開左derrick

6.       Raise weights in ship

7.       Passengers 聚在高處

8.       Upper deck排水管scuppers blocked

9.       Load貨在高處

10.   Timber deck cargo 吸了水

11.   Discharge貨在低處

12.   如果Hatch不防水,比水入了hold, flooding在tween deck

13.    

Moment是什麼?

Moment是一條lever, 被一股force打,

成隻船的lever就是KG,即是keel到center of gravity, KG是成隻船受力的地方.

那股力就是船的重量, displacement.

Moment= KG 乘 displacement

KG單位是m, 重量單位是tonnes, moment單位是tonnes m

船本來的displacement乘KG 就是本來的moment.

如果有cargo loading, 就加入cargo的moment (cargo的KG乘cargo的重量)

如果有cargo discharge,就減cargo的moment.

有了最後的moment, 除最後船連貨的displacement.

就找到最後的KG

KG, KM, GM 的關係都是加加減減

當船上的weights 不平均, 造成port or starboard side moment.

船就會list.

船的G移到G1. 船會傾斜, 然後B移到B1,

G1和B1在同一直線, 船才會穩定下來

為了不要頭已側, 用下圖去計數就OK

有GM, 有GG1 , 用tan θ 就計到 List的角度, 單位是degree and minutes.

List要寫埋to starboard or port.

GG1 就是 moment to port or starboard 除 displacement.

GM就要首先找到KG,  KM- KG=GM

不要攪亂GG1和GZ.

GG1是船的重心的移動, 計算方法是shifted cargo weight乘shifted distance. 再除成隻船的displacement.

GZ不是重心的移動, 而是righting lever, GZ出現是因為船比浪或風吹歪了, 船的重心沒有改變, 因為船歪了, 出現GZ去令船回到原位, Moment of statical stability=W乘GZ

GG1的出現因為list, GZ的出現因為heel.

small angle of heel, 細過15度,B1跟M成一直線

  

這個是heel. Heel的圖要將船畫傾斜, GZ是一條橫線.

而list的圖就不用把船畫側, 方便自己睇

Moment of statical stability = W乘 GZ

W是船的displacement

GZ可以再拆為 GM乘sin θ°

Moment的單位是tonnes m

當angle of heel超過15°

B移到B1, 而B1已經超過M, 不再跟M成一直線,

所以計法不同了,

Moment of statical stability = W乘GZ

GZ不再等於GM sin θº

就用 wall-sided formula

GZ= (GM+ 1/2 BM tan² θ) sin θ

Note: tan² θ = tan θ × tan θ = (tan θ)² ≠ tan θ²

BM =B2次方 除12d    where B is the breadth, d the draft.

其實這條formula在small angle of heel都可以用.