DRY-DOCKINGSequence of events:

*Ship enters dock trimmed by the stern.*Water pumped out of dock until ship touches blocks aft (start of critical period).*As water is pumped out further the true mean draught starts to reduce as the aft draught reduces more quickly than the forward draught increases (i.e. the ship starts to change trim by the head).*The upthrust at the keel (P) increases to gradually replace the upthrust due to buoyancy force at the centre of buoyancy (caused by the reducing volume of water displaced).*Eventually the ship touches the blocks forward and aft (end of critical period). The ship has now experienced its maximum change of trim.*Water continues to be pumped from the dock and the draught reduces at the same rate forward and aft. The upthrust (P) is now distributed along the length of the ship and continues to increase as the buoyancy force reduces.*When the dock is empty upthrust P equals the ships displacement having replaced all the upthrust due to buoyancy force.

Consider the following diagrams.

Dry Docking (MAR)

1.Ship trimmed by stern.FB2.Touches aft (start of critical period and stability loss).3.True mean draught reduces. Ship changes trim by the head and P increases as Bf reduces, stability loss increases. B moves forward.B1P

Dry Docking (MAR)

4.Ship touches forward and aft. Greatest loss of stability of concern (ship flat on blocks). End of critical period.5.Draught reduces at the same rate forward and aft. Upthrust P increases as Bf decreases.6.Dock empty. Upthrust P distributed across all the blocks.

Dry Docking (MAR)

Calculation of upthrust P

(At any stage in the docking procedure.)

Throughout the docking procedure the true mean draught reduces all the time having the same effect as if the ship were rising out of the water due to weights being discharged.

Consider the formula:Rise (cm) = w TPC

The force P may be considered to be a weight discharged.

Therefore:Rise (cm) = P TPC

or:P (tonnes) = Reduction of true mean draught TPC

This may be used at any stage in the docking procedure.

Dry Docking (MAR)

Calculation of upthrust P

(During the critical period)

In between the time the ship touches the blocks aft and touches forward and aft the ship undergoes a change of trim.

The change of trim at any stage during the critical period may be considered to be the same as that change of trim that would have occurred had a weight w been discharged at the aft perpendicular equivalent to the upthrust P in tonnes.

Consider the formula:COT (cm) = w d MCTC

The force P may be considered to be a weight discharged to cause the change of trim.

Therefore:COT (cm) = P d MCTC

or:P (tonnes) = COT MCTC Distance LCF to AP

This may be used only during the critical period.

Dry Docking (MAR)

G will move directly away from the centre of gravity of the discharged weight (which was at K) to GV.

Loss of GM = GGV where:GGV = w d W - wwhere d is the distance between the the centre of gravity of the ship (G) and the centre of gravity of the discharged weight (in this case K).Therefore:d = Initial KGThe loss of stabilityLoss of stability arises during the critical period and varies directly with the value of P. Maximum loss of GM of concern occurs the instant the ship touches the blocks forward and aft. Two methods of calculation may be considered.

Method 1: Loss of GM as a result of a rise in GConsider the movement of G that will occur if a weight w is discharged from the keel.w

Dry Docking (MAR)

The upthrust P acting at the keel during the critical period will have exactly the same effect as if a weight equal to P had been discharged from the keel. Consider a ship during the critical period being slightly inclined by an external force.Z1 G ZMKB1WP (W-P)The forces acting are as follows:W:the total weight force acing downward through G;(W-P):the force of buoyancy that is remaining (True Mean Draught has reduced).P:The upthrust acting at the keel aft.

Dry Docking (MAR)

[(W-P) GZ] gives a righting moment.[P GZ1] gives a capsizing moment.Therefore: Available righting moment = [(W-P) GZ] - [P GZ1]

If P is considered as a weight discharged from the keel then according to:

GGV = w dLoss of GM = P KG W - w W - P

Dry Docking (MAR)

GMKB1WP (W-P)Method 2: Loss of GM as a result of a fall of MThe total weight force acting down through G is supported by the forces (P) and (W-P). The resultant of these two upward acting forces acts through M1 such that:

P x = (W-P) y

MM1 represents the resulting fall of the transverse metacentre.xyM1Consider the two similar triangles.G

Dry Docking (MAR)

MKWP (W-P)xSine = y y = Sine MM1 MM1

also:Sine = x x = Sine KM1 KM1

(W-P) Sine MM1 = P Sine KM1;

divide both by Sine ;

(W-P) MM1 = P KM1;expanding this;G

Dry Docking (MAR)

(W MM1) - (P MM1) = P KM1

(W MM1) = (P KM1) + (P MM1)

(W MM1) = P (KM1 + MM1)

(W MM1) = P Initial KM

MM1 = P KM W

where MM1 is the loss of GM.

NoteThe KM in the formula is that which is appropriate to the waterline for the time that the loss of GM is being calculated for. It is found by entering the hydrostatic data with either the true mean draught or the effective displacement (W-P).

Dry Docking (MAR)

NOTE : -

Suggested sequence for working out Dry Docking questions.

Calculate Trim

2.Calculate A.M.D.

Calculate T.M.D.

4.Calculate P Force

Calculate Loss of GM due to P Force

6.Recalculate T.M.D. for instant by = P/TPC

7.Interpolate and obtain KM for TMD in no. 6.

8.KM Initial KG = GM

9.GM- GGv (Rise of G) = Effective GM

Dry Docking (MAR)