COMPARISON OF STABILITY OF A SHIP IN THE LIGHT AND FULLY LOADED CONDITIONS

Figure 1 shows the metacentric diagram for M.V. Almar. As the ship is progressively loaded from the light condition (draught 2.33 m) to the summer load condition (draught 10.20 m) KM decreases (with a slight increase occurring for draughts 8.60 m upwards).

Fig.1

KM = KB + BM

COMPARISON OF STABILITY OF A SHIP IN THE LIGHT AND FULLY LOADED CONDITIONS 1

M.V. ALMAR METACENTRIC DIAGRAM

0

2

4

6

8

10

12

14

16

3 4 5 6 7 8 9 10 11

Draught (m)

KM, KB & BM (m)

KB BM KM

KB obviously increases with draught whereas BM reduces as explained below.

Fig. 2

The movement of B for any angle of heel could be calculated using:

BB1 = v bb 1

V

where: v is the volume of the transferred wedge; bb1 is the distance through which the centroid of the wedge has moved, and; V is the volume of displacement of the ship.

At the load draught (displacement) the volume of the transferred wedge of buoyancy (v) represents a smaller part of the total volume of displacement of the ship (V) than it would at the light draught (displacement).

Thus: BM decreases as draught increases. For the normal range of operational draughts of a ship KM will generally decrease as draught increases with a slight increase again at the deepest draughts as evidenced by the metacentric diagram for M.V. Almar (figure 1).

Figure 3 makes a comparison of the curves of statical stability for M.V Almar in the light condition and fully loaded condition assuming a constant value of KG. The dotted curve (…….) is for a lesser value of KG that would provide a more suitable condition of loading (as recommended in a loading condition in the stability book on which M.V. Almar was based).

COMPARISON OF STABILITY OF A SHIP IN THE LIGHT AND FULLY LOADED CONDITIONS 2

M

b

bb1

b1

B

B

B1

B1

M

Fig. 3

In terms of GZ values alone, for a given KG value the ship will become less stable the more it is loaded, however:

RIGHTING MOMENT (t-m) = GZ (m) DISPLACEMENT (t)

The righting moment curves show that the extra weight of the loaded ship will require more ‘work’ by the external forces to heel the ship to a particular angle of heel (figure 4).

COMPARISON OF STABILITY OF A SHIP IN THE LIGHT AND FULLY LOADED CONDITIONS 3

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 10 20 30 40 50 60 70 80 90

Light condition (KG 9.00 m) Load condition (KG 9.00 m) Load condition (KG 7.83 m)

Fig. 4

In terms of righting moment, provided that the ship has a suitable value of KG in the loaded condition then in reality the ship will have greater stability as more ‘work’ will be required to heel the vessel to a particular angle of heel as a consequence of the increased displacement.

COMPARISON OF STABILITY OF A SHIP IN THE LIGHT AND FULLY LOADED CONDITIONS 4

-10000

-5000

0

5000

10000

15000

20000

25000

30000

35000

40000

0 10 20 30 40 50 60 70 80 90

Heel (deg.)

Righting moment

(t-m)

Light condition (KG 9.00 m) Load condition (KG 9.00 m) Load (KG 7.83 m)