Ship Stability, Statical Stability, Free Surface Effect ,Correction of and Angle of Loll.

HNC NAUTICAL SCIENCE Group Award Code: G8F5 15

Unit Code: F0LD 34 Ship Stability Outcome 3 – Statical Stability

3.5 Free Surface Effect & Correction of and Angle of Loll

Aims To give the student an understanding of: 

the creation of Free Surface Effect (FSE);



the effects of FSE on the vessel‟s stability;

Aims To give the student an understanding of:



how FSE can be reduced/eliminated;



the correction of an angle of loll,

Objectives The Student will be able to: 

Describe with the aid of sketches the effects of FSE in part filled compartments containing fluids;



calculate the reduction in GM caused by FSE, as an adjustment to KG/GM (Single Weights), or by the inclusion of FSM‟s into the Moment about the Keel table (Multiple Weights);

Objectives The Student will be able to: 

Calculate the new FSE if a compartment is subdivided.



Describe the correct procedures required to carry out the correction of and angle of loll without putting the vessel in further danger.

Free Surface Effect M

W

G B

K

L

Showing the vessel at rest with a part filled undivided double bottom tank. The GM shown is the GMSOLID, all of which are on the centreline of the vessel.

Free Surface Effect Δ M

W b W1

L1 G

Z

b1

L

B B1 K Δ

When the vessel in stable equilibrium is inclined by an external force, buoyancy is lost on the raised side and an equal amount created on the submerged side. This creates a shift of buoyancy from b to b1 in the vessel, moving the overall buoyancy of the vessel along a parallel line from B to B1. This creates a righting lever of GZ.

Free Surface Effect M

W

W1

L1 G G1

Z Z1

L

B

g

B1 K

g1

As the ballast moves to the low side this causes a shift of weight of g to g1 This causes a shift of the overall centre of gravity of the vessel G along a parallel line to a new position of G1. This reduces the righting lever to G1Z1.

Free Surface Effect M

G2

Z2

Vi r tua

lL

os

so

fG M

(FS

E)

θ°

G

Z G1

Z1

If a perpendicular line is drawn upwards through G1 to the centreline of the vessel, the GZ can be redrawn between the centreline and the BM line. This gives G2Z2 which is equal to G1Z1. The distance along the centreline measured between G and G2 is the “virtual loss of GM”. This is also known as the Free Surface Effect (FSE).

Calculating FSE 





The stability information required by law to be supplied to a vessel must include information on the effect of free surface of liquid in the tanks and also how to correct the GM for this effect. Information is usually supplied for each tank in the form of "Free Surface Moments". FSE = Free surface moment or FSM Displacement Δ

Calculating FSE 

If there are several Free Surface Moments involved, then they should all be added, then divided by the displacement.



FSE = Σ Free surface moments Displacement

Key Points 

  



FSE does not depend upon the weight of liquid in the tank, providing the area of the free surface remains unchanged. FSE does not depend upon the position of the tank within the ship. FSE is zero if a tank is full or empty Every slack tank contributes it‟s own FSE to the total FSE for the ship therefore to reduce FSE keep the number of slack tanks to a minimum. If it is decided to improve stability by filling a DB tank then FSE will worsen the situation before the increased bottom weight is sufficient to bring G down. If at an angle of loll then fill the smallest tank, on the lowest side first.

Execise 1 A vessel has a KM of 5.13m, KG = 4.82m and the FSE = 0.11m. Calculate the effective (fluid) GM. KM KG GMSOLID FSE GMFLUID

5.13 m - 4.82 m 0.31 m - 0.11 m 0.20 m

The Fluid GM is 0.20 m

(FSE is always negative) GMFLUID is the effective GM

Subdivisions 

FSM and therefore FSE can be reduced to the fitting of equally spaced longitudinal divisions in the tank.



To Calculate the subdivided value the FSM or FSE is divided by the new number of compartments (n) squared



So:



FSMSUB = FSM n2

or

FSESUB = FSE n2

Example 1 A tank has a FSM of 3586 tm. Calculate the FSM if the tank is fitted with: (i) (ii)

A single longitudinal bulkhead, A further two longitudinal bulkheads.

(i) FSMSUB = FSM = 3586 = 396.50 tm n2 22

(ii)FSMSUB = FSM = 3586 = 224.13 tm n2 42

2

1

1

2

3

4

Example 2 A tank has a FSE of 0.26 m. Calculate the FSE if the tank is fitted with: (i) (ii)

A single longitudinal bulkhead, A further two longitudinal bulkheads.

(i) FSESUB = FSE = 0.26 = 0.065m n2 22

(ii)FSESUB = FSE = 0.26 = 0.016 tm n2 42

2

1

1

2

3

4

Subdivisions FSESUB = FSE n2

Can be combined with

FSE

or

ƩFSM Δ

or

ƩFSM (Δ x n2)

= FSM Δ

To give FSESUB =

FSM (Δ x n2)

Example 3 A vessel displacing 8000 tonne has a DB tank half full, it has a free surface moment 2880 tm. Calculate the free surface effect if:i) the tank is undivided ii) there is a centreline division iii) there is a centreline division and two equally spaced longitudinal bulkheads.

Example 3 (i) The tank is undivided FSE

= FSM = 2880 = 0.36m Δ 8000

Example 3 (i) The tank is undivided FSE

= FSM = 2880 = 0.36m Δ 8000

(ii) There is a centreline division FSESUB =

FSM = 2880 = 0.09 tm (Δ x n2) (8000 x 42) 1

2

Example 3 (iii)

There is a centreline division and two equally spaced longitudinal wash bulkheads

FSESUB =

FSM = 2880 = 0.023 tm (Δ x n2) (8000 x 42)

1

2

3

4

FSE and the Angle of Loll 

FSE causes a virtual rise in G



If the vessel is tender she will have a small GMSOLID.



If the FSE is greater than the GMSOLID then the vessel will have a negative GMFLUID and will be in unstable equilibrium.



An unstable vessel could capsize, but more usually just develops an angle of loll.

FSE and the Angle of Loll 

The best way to avoid this is to keep the number of slack tanks to a minimum during the voyage. Wherever possible tanks should be either empty or pressed up.



Whilst the vessel is on passage she will use FW, DO & FO, so some slack tanks cannot be avoided.



To avoid an angle of loll due to FSE the vessel‟s GMSOLID must be large enough to withstand any anticipated rise in G during the voyage.

List vs Angle of Loll Angle of List 1. +ve GM 2. Stable Equilibrium. 3. G off the Centreline. 4. Corrected by moving G back to the Centreline – by moving/loading weights towards the “high side”.

Angle of Loll 1. -ve GM 2. Unstable Equilibrium. 3. G on the Centreline. 4. Corrected by lowering G below M

Correcting an angle of Loll 

Lowering G below M to make the vessel stable will correct an angle of Loll.



This can be achieved by: 

  



Moving cargo to a lower position; Jettisoning top-weight (in an emergency); Reducing FSE by pressing up/emptying tanks; Filling low ballast spaces such as DB tanks.

Filling an empty tank will introduce FSE causing a further virtual rise of G, so this must be done with caution and adopting the following procedures:

Correcting an angle of Loll 1.

top up tanks that are already slack.

2. calculate the FSE which will arise before pumping into empty tanks. This will ensure that the rise of G during the operation is acceptable. 3. fill empty tanks one at a time.

Correcting an angle of Loll 4. Start with the smallest tank on the LOW side first. (If a tank on the high side is filled first, the ship will start to right herself but will then tend to roll over suddenly in an uncontrolled fashion as she passes through the upright. She will then „whip‟ through to a larger angle of loll on the other side. She may even capsize if the momentum gathered is sufficient.) When the low side is filled first, the angle of list will increase initially, but in a slow and controlled fashion. After some time, the weight of the ballast water added will be sufficient to lower the ship‟s COG (despite the extra FSE), to cause the angle of list to decrease. By this method the inclining motions of the v/l take place in a gradual and controlled manner.

Correcting an angle of Loll 5. now fill the opposite tank on the high side. 6. fill tanks alternately, low side first, until the v/l returns to positive GM. 7. ensure that all tanks are completely filled.

Correcting an angle of Loll

Correcting an angle of Loll

Correcting an angle of Loll

Correcting an angle of Loll

FSM and Moments about the Keel 

Since Moments about the Keel and Free Surface Moments are both Vertical Moments, they can be combined into the same table to calculate KG.



The KG calculated automatically will be the KGFLUID



The FSM can just be added to the Loaded Moments about the Keel column.

Example 1 A vessel of  = 17,922 tonnes is initially upright, KG = 12.66m, KM = 14.24m. The FSM‟s of the various tanks add up to 1225tm. Calculate the GMf after the following cargo operations if KM is constant.

Discharge: Load:

Weight (t) 624 1,296 3,042 312 397

Kg (m) 14.88 8.71 6.69 13.27 14.88

Example 1 Weight (t) Loaded

KG (m)

Discharged

17 922

Moment about the Keel (tm) Loaded

12.66

226 892.52

624

14.88

9 285.12

1 296

8.71

11 288.16

3 042

6.69

20 350.98

312

13.27

4 140.24

397

14.88

5 907.36

FSM

1225.00

21 673 - 1 920 Ʃ19 753

Discharged

1 920

258 516.10 - 20 573.28 Ʃ237 942.82

20 573.28

Example 1 KGf

KGf

KM KGf GMf

=

=

Ʃ Moments about the Keel = Ʃ Weights 12.045m

14 240 m - 12 045 m 2.195 m

The Final GMf is 2.20m

237 942.82 19 753.00