Ship Stability - Movement of the Ce

Ship Stability - Movement of the Centre of Gravity

Centre of gravity
It is the point of a body at which all the mass of the body may be assumed to be concentrated.

The force of gravity acts vertically downwards from this point with a force equal to the weight of the body.

Basically the body would balance around this point.

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

Effect of removing or discharging mass

shifting cargo1shifting cargo12

Consider a rectangular plank as shown. The effects of adding or removing weights would be as shown:

Now cut the length of plank of mass ‘w’ kg whose CG is ‘d’ mtrs away from CG of the plank.

Note that a resultant moment of ‘w x d’ kg m has been created in an anti-clockwise direction about ‘G’.

The CG of the new plank shifts from ‘G’ to ‘G1’.

The new mass (W-w) kg now creates a tilting moment of (W-w) x GG1 about G.

Since both are referring to the same moment,

(W-w) x GG1 = w x d

GG1 = (w x d)/(W-w)

CONCLUSION: When a weight is removed from a body, the CG shifts directly away from the CG of the mass removed, and the distance it moves is given by:

GG1 = (w x d)/Final mass metres

Where, GG1 is the shift of CG

w is the mass removed

d is the distance between the CG of the mass removed and the CG of the body.

Effect of adding or loading mass

Equating the tilting moments created due to the added weight, which must again be equal:

(W + w) x GG1 = w x d

GG1 = (w x d)/(W + w)

GG1 = (w x d)/ (Final mass) metres



Application to ships

DISCHARGING WEIGHTS:

GG1 = (w x d) / (Final displacement) metres



LOADING WEIGHTS

GG1 = (w x d) / (Final displacement) metres



Shifting Weights

GG2 = (w x d) / (Displacement) metres



Vertical Weight Shifts

Shifting weight vertically, no matter where onboard it is, will always cause the ship’s center of gravity to move in the same direction as the weight shift.

shifting cargo2

To calculate the height of the ship’s center of gravity after a vertical weight shift, the following equation is used:

KG1 = ((W0 x KG0) +/- (w x kg)) / ΔF

KGO = The original height of the ship’s center of gravity (M)

Δo = The ship’s displacement prior to shifting weight (MT)

w = The amount of weight shifted (MT)

kg = The vertical distance the weight was shifted (M)

ΔF = The ship’s displacement after shifting the weight (MT)

(+) When the weight is shifted up use (+)

(-) When the weight is shifted down use (-)

Example Problem

10 MT of cargo is shifted up 3 M. ΔO is 3500 MT and KGo is 6 M. What is the new height of the ship’s center of gravity (KG1)?

KG1 = ((Δo x KGo) +/- (w x kg)) / ΔF

KG1 = ((3500 x 6) + (10 x 3)) / 3500

KG1 = 6.009 M



Vertical Weight Additions/Removals

When weight is added or removed to/from a ship, the vertical shift in the center of gravity is found using the same equation.

shifting cargo3

KG1 = ((Δo x KGo) +/- (w x kg)) / ΔF

KGO = The original height of the ship’s center of gravity (M)

ΔO = Ship’s displacement prior to adding/removing weight (MT)

w = The amount of weight added or removed (MT)

kg = The height of the center of gravity of the added/removed weight above the keel (M)

ΔF = The ship’s displacement after adding/removing the weight

(+) When the weight is added use (+)

(-) When the weight is removed use (-)

Example Problem

A 30 MT crate is added 10 M above the keel. Δo is 3500 MT and KG0 is 6 M. What is the new height of the ship’s center of gravity (KG1)?

KG1 = ((Δo x KGo) +/- (w x kg)) / ΔF

KG1 = ((3500 x 6) + (30 x 10)) / 3530

KG1 = 6.034 M

Horizontal Weight Shifts

Shifting weight horizontally, no matter where onboard it is, will always cause the ship’s center of gravity to move in the same direction as the weight shift.

NOTE: A weight shift causing the ship’s center of gravity to move off centerline will always reduce the stability of the ship.

shifting cargo4

To calculate the horizontal movement of the ship’s center of gravity, the following equation is used:

GG2 = (w x d) / ΔF

w = The amount of weight shifted (MT)

d = The horizontal distance the weight is shifted (M)

ΔF = The ship’s displacement after the weight is shifted (MT)

Example Problem

A 50 MT weight is shifted 10 M to starboard. ΔO is 32000 MT.

What is the change in the center of gravity (GG2)?

GG2 = (w x d) / ΔF

GG2 = (50 x 10) / 32000

GG2 = 0.01562 M



Horizontal Weight Additions/Removals

When an off-center weight is added or removed to/from a ship, the ship’s center of gravity will move off centerline, the ship will develop a list.

shifting cargo5

To calculate the horizontal movement of the ship’s center of

ผลลัพธ์ (ไทย) 2:

Ship Stability - Movement of the Centre of Gravity

Centre of Gravity
It is the Point of a Body at which all the mass of the Body May be assumed to be Concentrated.

The Force of Gravity ACTS Vertically downwards from this Point with a Force Equal to the. Body of the weight.

Basically the Body would balance Around this Point.

The COG is at ITS Body of a homogeneous geometrical Centre.

Effect of removing or discharging mass

shifting Cargo1shifting Cargo12

Consider a rectangular plank as shown. The effects of adding or removing Weights would be as shown:

Now Cut the Length of plank of mass 'W' kg whose CG is 'D' mtrs Away from CG of the plank.

Note that a resultant Moment of 'WX D' kg M. has been Created in an Anti-clockwise direction About 'G'.

The CG of the New plank shifts from 'G' to 'G1'.

The New mass (Ww) kg now creates a tilting Moment of (Ww) x GG1 About G. .

Since both are referring to the Same Moment,

(Ww) x GG1 = Wxd

GG1 = (Wxd) / (Ww)

conclusion: When a weight is removed from a Body, the CG shifts directly Away from the CG of the mass removed,. and the Distance it Moves is GIVEN by:

GG1 = (Wxd) / Final mass METRES

Where, GG1 is the Shift of CG

W is the mass removed

D is the Distance between the CG of the mass removed and the CG of the Body.

Effect. of adding or loading mass

Equating the tilting moments Created Due to the added weight, which must Again be Equal:

(W + W) x GG1 = Wxd

GG1 = (Wxd) / (W + W)

GG1 = (Wxd) / (Final. mass) METRES Application to Ships Discharging WEIGHTS: GG1 = (Wxd) / (Final displacement) METRES LOADING WEIGHTS GG1 = (Wxd) / (Final displacement) METRES Shifting Weights GG2 = (Wxd) / (displacement) METRES Vertical weight Shifts Shifting weight. Vertically, no Matter where onboard it is, Will always Cause the Ship's Center of Gravity to Move in the Same direction as the weight Shift. shifting Cargo2 to Calculate the height of the Ship's Center of Gravity after a Vertical weight Shift, the following Equation is. used: KG1 = ((W0 x KG0) +/- (WX kg)) / ΔF KGO = The Original height of the Ship's Center of Gravity (M) Δo = The Ship's displacement prior to shifting weight (MT) W = The amount. of weight shifted (MT) kg = The Vertical Distance the weight was shifted (M) ΔF = The Ship's displacement after shifting the weight (MT) (+) When the weight is shifted up use (+) (-) When the weight is. use shifted down (-) Example Problem 10 MT of Cargo is shifted up 3 M. ΔO is 3500 MT and KGO is 6 M. What is the height of the New Center of Gravity Ship's (KG1)? KG1 = ((x Δo KGO. ) +/- (WX kg)) / ΔF KG1 = ((3500 x 6) + (10 x 3)) / 3500 = 6.009 M KG1 Vertical weight Additions / Removals When weight is added or removed to / from a Ship, the. Vertical Shift in the Center of Gravity is using the Same Found Equation. Cargo3 shifting KG1 = ((x Δo KGO) +/- (WX kg)) / ΔF KGO = The Original height of the Ship's Center of Gravity (M) = ΔO. Ship's displacement prior to adding / removing weight (MT) W = The amount of weight added or removed (MT) kg = The height of the Center of Gravity of the added / removed weight above the keel (M) ΔF = The Ship's displacement after. adding / removing the weight (+) When the weight is added use (+) (-) When the weight is removed use (-) Example Problem A 30 MT Crate M 10 is added above the keel. Δo is 3500 MT and KG0 is 6 M. What is the height of the New Center of Gravity Ship's (KG1)? KG1 = ((x Δo KGO) +/- (WX kg)) / ΔF KG1 = ((6 x 3500. ) + (30 x 10)) / 3530 KG1 = 6.034 M Horizontal weight Shifts Shifting weight horizontally, no Matter where onboard it is, Will always Cause the Ship's Center of Gravity to Move in the Same direction as the weight Shift. NOTE: A. weight Shift causing the Ship's Center of Gravity to Move off centerline Will always Reduce the stability of the Ship. shifting Cargo4 to Calculate the horizontal Movement of the Ship's Center of Gravity, the following Equation is used: GG2 = (Wxd) / ΔF W =. the amount of weight shifted (MT) D = The weight is shifted the horizontal Distance (M) = ΔF The Ship's displacement after the weight is shifted (MT) Example Problem A 50 MT weight is shifted 10 M to starboard. ΔO is 32000 MT. What is the Change in the Center of Gravity (GG2)? GG2 = (Wxd) / ΔF GG2 = (50 x 10) / 32000 GG2 = .01562 M Horizontal Weight Additions / Removals When an off-Center weight is. added or removed to / from a Ship, the Ship's Center of Gravity Will Move off centerline, the Ship Will Develop a list. Cargo5 shifting to Calculate the horizontal of the Movement of Ship's Center.