4. Initial Stability

Question 1

Define Metacentric Height

Answer 1

The metacentric height (GM) is a measurement of the initial static stability of a floating body. It is calculated as the distance between the centre of gravity of a ship and its metacentre.
The distance between G and M.
Large GM = Positive stability, Stiff Vessel, Positive GZ(righting Lever), meaning large righting Moment.

Question 2

Define Metacentre (aka Transverse Metacentre)

Answer 2

The point of intersection of the vertical through the center of buoyancy of a ship in the position of equilibrium with the vertical through the new center of buoyancy when the ship is slightly heeled.

Simply put it is the Point about which a vessel inclines transversly.

• Position determinded largely by the water plane area. (larger the WPA, the higher the metacentre)
• Varies with displacement, heel and trim.
• is calculated in the hydrostatics for each draft.
• for small angles of inclination(initial stability) remains on Centreline, directly above CoB.
• Calculated by the naval architects and found in ships stability booklet.

Question 3

Define the Height of the Metacentre?

Answer 3

MT Metacentre is the point around which a vessel inclines.

 Position is largely defined by the WPA and varies with displacement, heel and trim.

 Known for each draft.

 For small angles of inclination (< 10°) it remains on the CL and vertically above the Centre of Buoyancy. “Small Angle Stability”.

 naval architect provides the vessel with a table or graph of KM against draft and this is given in the Hydrostatics.

KM Height of the Metacentre above the keel. Calculated by the Naval Architect for different drafts and listed in the Hydrostatics.

GM Metacentric Height, the distance between the Centre of Gravity and the Metacentre.

BM Metacentric Radius, distance Centre of Buoyancy to Metacentre

Question 4

Explain how the beam of a ship has a higher metacentre?

Answer 4

The relationship between BM, which is the distance of the CoB to the Metacentre and the area of the waterplane are fundamental to the stability of a vessel.

The larger the waterplane area, the wider the beam, therefore the higher the metacentre.

Greater Beam = Larger GM (height of metacentre)

Question 5

Explain the term “Initial Transverse Stability”?

Answer 5

Initial = Small angles of inclinatioin usually around 10 degree’s

Question 6

Illustrate the Force of Gravity and force of Bouyancy acting on an upright ship.

Answer 6

See diagram

Question 7

Understanding the Centre of Bouyancy.

Answer 7

See diagram

Question 8

Understanding the centre of gravity of an upright ship.

Answer 8

see diagram

Remember G moves

• towards a weight added
• away from a weight removed
• parallel to a weight shifted.

Question 9

Defintions and forces of an upright vessel at initial stability.

Answer 9

• K The keel (fixed and therefore used as a reference point)
• G Centre of Gravity (sometimes referred to as CoG) is the centre of all downward acting forces.
• KG Distance from the keel to the vertical centre of gravity is known.
• B Centre of Buoyancy (sometimes referred to as CoB) is the centre of all upward acting forces, or the centre of the immersed portion of the vessel.
  
  • This is easily calculated by the Naval Architect.
• KB Distance from the keel to the centre of buoyancy.
• • For the ship to float at rest, the downward force due to gravity must be opposed by an equal but opposite force acting upwards in the same vertical line. The combined forces, due to buoyancy, acting upwards through the Centre of Buoyancy (B) cancel the downward forces due to gravity.

Question 10

Heel Vs List explain the difference.

Answer 10

If a ship is inclined from the upright, this may be due to:

• external forces, such as wind or wave action Ship is said to be Heeled.
• internal forces or an asymmetrical distribution of internal weights Ship is said to be Listed.

Heel:

• G remains in the same position
• A righting lever has been developed known as GZ
• Downward Forces of G are equal to the upward forces of bouyancy.

List:

• G moves off the centre line
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