Definitions

Question 1

Law of Floation

Answer 1

A floating body displaces its own weight of the fluid in which it floats

Question 2

Centre of Gravity (G)

Answer 2

The point in a body where the total weight of the body may be considered to be acting vertically downwards

Question 3

Centre of Buoyancy (B)

Answer 3

The point in a body where the total force of buoyancy may be considered to be acting vertically upwards

Question 4

Transverse Metacentre (M)

Answer 4

The point where the verticals through the Centre of Buoyancy at two consecutive angles of heel intersect

Question 5

Longitudinal Metacentre (M_L)

Answer 5

The point of intersection of the verticals through the Centre of Buoyancy when on an even keel and when trimmed

Question 6

KN

Answer 6

Is a parallel line to that of GZ, drawn from K, then the point of intersection of this line with the vertical line of action of buoyancy, is represented by a N

Question 7

Transverse Metacentric Height (GM)

Answer 7

The distance in metres between’G’ and ‘M’ measured on the Centreline

The relative positions of ‘G’ and ‘M’ indicates the vessel’s initial stability and it is therefore essential that their position is known. This will be ‘stable’, ‘unstable’ or ‘neutral’ equilibrium, and also if stable whether the vessel will be ‘stiff’ or ‘tender’ (GM can be seen to be an indication of a v/l’s stability)

Question 8

Righting Lever / Arm (GZ)

Answer 8

The perpendicular (horizontal) distance between ’G’ and the vertical line (buoyancy force) acting through B/B₁

Question 9

Angle of Loll

Answer 9

Is the angle of heel (to port or stbd), at which a v/l comes to rest when she is in an unstable equilibrium when upright (negative GM)

Question 10

KM

Answer 10

This is the height of ‘M’ above the keel measured in metres
‘KM’ is NOT called the metacentric height
‘KM’ is calculated by the naval architects for the various drafts and then supplied to the ship in tabular form

Question 11

Stable Equilibrium

Answer 11

A v/l is said to be in stable equilibrium if she returns to her initial position after being inclined by an external force
- ‘G’ must be below ’M’
- the v/l is said to have positive stability
- Δ x GZ is a righting moment

Question 12

Neutral Equilibrium

Answer 12

A v/l is said to be in neutral equilibrium if after being inclined by some external force she tends to remain in the inclined position
- ‘G’ must coincide with ’M’
- GZ = 0, and therefore Δ x GZ = 0

Question 13

Unstable Equilibrium

Answer 13

A v/l is said to be in unstable equilibrium if after being inclined by an external force, she tends to heel further
- ‘G’ must be above ’M’
- the v/l is said to have negative stability
- Δx GZ is a capsizing moment

Question 14

List ( ° / θ / φ )

Answer 14

A v/l is said to be listed when she is inclined due to ’G’ being off the centreline

Question 15

Trim

Answer 15

The difference between the forward and after drafts

Question 16

Change of Trim

Answer 16

The difference between the original trim and the final trim

Question 17

Centre of Floatation (CF)

Answer 17

The geometric centre of the v/l’s water-plane
The ‘CF’ is the point about which the v/l trims and it is sometimes called the ‘tipping centre’
In box-shaped c/l’s the ‘CF’ is amidships, but in ship shapes the position will vary with trim and draft
To find the change of trim, moments are taken about the ‘CF’ or large about the AP (After Perp)
Change of Trim = Resultant Trimming Mom (tm) / MCTC

Question 18

Tender Vessel

Answer 18

A v/l is said to be tender when she has a small moment of statically stability at small angles of heel. In general, a tender v/l will have a small ‘’GM’. When a tender v/l is inclined by external forces, she will tend to return to the upright slowly, and the result is a slow easy roll
- long roll period
- slow
- small righting moment (RM)

Question 19

Stiff Vessel

Answer 19

A v/l is said to be stiff when she has a large moment of statically stability at small angles of heel. In general, a stiff v/l will have a large ‘’GM’. When a stiff v/l is inclined by external forces, she will tend to return to the upright quickly
- short roll period
- snappy
- large righting moment (RM)

Question 20

Statical Stability

Answer 20

Is the ability of a v/l to return to her initial position after being forcibly inclined

Question 21

Dynamical Stability

Answer 21

Is the measure of the work done when the v/l is inclined by external forces

Question 22

Moment of Statical Stability (MSS) aka Righting Moment (RM)

Answer 22

The measure of the v/l’s ability to return to her initial position after being inclined by some external force such as wind or waves
Mom (MSS) = Δ x GZ
Where ‘M’ is considered fixed ∴ GZ = GM Sinθ
Mom (MSS) = Δ x GM Sinθ

Question 23

TPC

Answer 23

TPC is the number of tonnes to add or remove from a v/l to change the TMD by 1cm
For a v/l’s draft to increase by 1cm then the Δ of the v/l has increased
The increase in Δ equals change (increase in) ▽ x ρ of the fluid in which the v/l is floating (Δ = ▽ x ρ)
- The TPC is directly proportional to the WPA
- the greater the WPA the greater the TPC
For a v/l at any draft, Δ = ▽ x ρ, the greater the density then the greater the TPC
To increase the v/l’s draft by 1cm will take a greater mass in saltwater compared with freshwater
- the TPC is directly proportional to the density (ρ)

Question 24

Free Surface Effect (FSE)

Answer 24

1. FSE is independent of the actual weight of the liquid in the tank, provided the area of free surface in the tank is unchanged
2. FSE is independent of the position of the tank in the v/l
3. FSE can be reduced to 1/ n² of its original undivided value by fitting longitudinal divisions in the tank, n = number of spaces
4. Moment of Inertia (I) of a rectangular free surface is equal to LB³/12
5. If it is decided to improve stability by filling a DB tank, FSE will initially worsen the situation before the increased weight at the bottom is sufficient to bring ‘G’ down

Question 25

Movement of ‘G’ - Loading a weight ‘W’ at a distance ‘S’ from the v/l’s Centre of Gravity ‘G’

Answer 25

‘G’ moves directly towards the loaded weight
GG_H/V = w x s / Δ + w

Question 26

Movement of ‘G’ - Discharging a weight ‘W’ at a distance ‘S’ from the v/l’s Centre of Gravity ‘G’

Answer 26

‘G’ moves directly away from the discharged weight
GGH/V = w x s / Δ - w

Question 27

Movement of ‘G’ - Shifting a weight ‘W’ already onboard

Answer 27

‘G’ moves parallel to and in the same direction as the shifted weight

GGH/V = w x s / Δ

Question 28

What is List φ_F

Answer 28

It is the angel of heel at which openings in the hull, superstructure or deck-house, which cannot be closed weathertight, immerse

Question 29

Reasons for a vertical rise in ‘G’

Question 30

State the immediate effect on a v/l’s stability on the commencing bunkering/ballasting a tank

Answer 30

It will introduce a free surface moment, which results in a reduction of the v/l’s stability
- Virtual rise in ‘G’
- effective GM reduces
- GZ lever reduces
- Righting moment reduces
- Dynamic stability reduces

Question 31

LL’s - The general principles behind the 1966 Loadline Convention

Answer 31

1 - Adequate reserve buoyancy under normal service conditions
2 - Hull girder strength
3 - Protection of the crew
4 - Subdivision and stability (intact & damaged)
5 - Watertight enclosures of all exposed parts of the ship
6 - Limited deck wetness