Stability and trim during Dry docking and Grounding

Stability and trim during Dry - docking and Grounding Stability and trim during Dry- docking and Grounding - Capt. S. Nathan 1

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Stability and trim during Dry- docking and Grounding - Capt. S. Nathan 3

Sequence of Events During Dry-Docking 1. When a ship enters a drydock she must have a positive initial GM, be upright, and trimmed slightly by the stern. On entering the drydock the ship is lined up with her centreline vertically over the centreline of the keel blocks and the shores are placed loosely in position. The dock gates are then closed and pumping out water commences. The rate of pumping is reduced as the ship's stern post nears the blocks. 2. After the stern lands on the blocks the draft will decrease and the trim will change by the head. The ship will be trimming by the head as the overall true mean draught reduces. The aft draught will be reducing at a greater rate than what the forward draught is increasing, 3. As more water is pumped out of the dock the true mean draught will start to reduce as the ship experiences more and more support at the stern. The interval of time between the stern post landing on the blocks and the ship taking the blocks overall is referred to as the critical period. During this period part of the weight of the ship is being borne by the blocks, and this creates an upthrust at the stern which increases as the water level falls in the drydock. The upthrust afforded by the blocks at the stern is termed the ‘P force’, this continues to increase as the buoyancy force reduces. Stability and trim during Dry- docking and Grounding - Capt. S. Nathan 4

4. Throughout the docking process the ship will displace a progressively lessening volume of water as the true mean draught reduces and the P force increases to provide more support for the ship (in effect, the P force takes over supporting the ship and the role of the buoyancy force in supporting the ship reduces). 5. Once the ship takes the blocks overall throughout her length, the rate of pumping is increased to empty the dock quickly; the draft will then reduces at the same rate forward and aft. The upthrust P becomes uniformly distributed along the ship’s length and continues to increase as the effective buoyancy force reduces. 6. When the dock becomes nearly empty and the ship is fully dry the upthrust P will be equal to the ship's displacement having now replaced all the upthrust afforded by the buoyancy force. Stability and trim during Dry- docking and Grounding - Capt. S. Nathan 5

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Loss of Stability when Dry-Docking • Loss of stability commences as soon as the ship touches the blocks aft and continues to worsen as the value of the P force increases. The maximum loss of GM of concern occurs at the instant immediately prior to the ship settling on the blocks forward and aft - this time being termed the critical instant. • Once the ship is flat on the blocks it will be in a safe condition as the risk of heeling over as a result of becoming unstable will have passed (most ship’s having a substantial area of flat bottom). • For ships those have a relatively small percentage of flat bottom area additional measures must also be taken such as using side shores to support the ship in the upright condition when in the dry dock. • Either of two methods of calculation of the loss of GM may be used. Stability and trim during Dry- docking and Grounding - Capt. S. Nathan 8

• When a vessel is floating, the weight of the vessel is balanced by the buoyancy provided by the underwater volume. • This is true until when one end of the ship touches the blocks. If the water level false thereafter, a part of the weight of the ship rests on the blocks and remainder is being provided by the reduced underwater volume. • Thus at any instant the total weight of the ship is by: 1) The upward reaction from the blocks on the keel and 2) The buoyancy provided by reduced underwater volume Stability and trim during Dry- docking and Grounding - Capt. S. Nathan 9

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• The effect on the ship’s stability is made clearer if the available righting moment at a particular angle of heel is considered. Figure shows a ship during the critical period where it has taken the blocks at the aft end only. During docking the ship becomes heeled to a small angle of inclination by an external force such as the wind. • The forces acting are as follows: • Wf is the total weight force acting downwards through the centre of gravity at G; • (W- P) is the remaining, or residual, buoyancy force acting upwards through the geometric centre of the underwater volume at B 1. • P is the upthrust of the blocks exerted at the keel aft. • (W - P) x GZ represents a righting moment, • Px. GZ 1 represents a capsizing moment. • Therefore the available righting moment = [(W - P) x GZ] - (P x GZ 1) • It is essential that the righting moment afforded by the upward acting (remaining) buoyancy force remains greater than the capsizing moment afforded by the upthrust of the P force acting at the keel at all times prior to the ship touching the blocks forward and aft. • If the ship should become unstable during the critical period it will slip off the blocks to one side resulting in structural damage to the ship, movement of the blocks and great embarrassment. Stability and trim during Dry- docking and Grounding - • It is for this reason that the loss of GM is calculated for the critical instant (when the ship touches the blocks 11 Capt. S. Nathan forward and aft) to ensure that adequate stability is maintained prior to the ship taking the blocks overall.

It should be noted that KM also changes as a result of a reduction in the ship’s draught. Loss of GM as a Result of a Fall in M (Decrease in KM) Figure shows a ship heeled by an external force such as the wind during the critical period where the ship has taken the blocks at the aft end only. • The total weight force of the ship acts downwards through G. Counteracting this are the two upward forces; the P force acting upwards at the keel and the residual buoyancy force (W - P) acting upwards through the centre of buoyancy (B 1). The resultant of the two upward acting forces acts through the new metacentre (M 1) such that: capsizing moment = righting moment • Note: In this formula the KM value is that which corresponds to the true mean draught for the instant that the loss of GM is being calculated and not that for the initial true mean draught that the ship has prior to docking. It is found by entering the hydrostatic data with a displacement value that corresponds to that given by (W - P). W in this formula is the ship’s initial displacement. Stability and trim during Dry- docking and Grounding - [This formula assumes that P is a transfer of buoyancy to the keel blocks resulting in a decrease of KM while the weight and 12 KG Capt. S. Nathan remains constant]

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Which formula to use? • Though the loss in GM and therefore the residual GM calculated separately using the two expression would give slightly different results, it should not be inferred that the slight difference of answer does not mean one answer is more accurate than the other. • This is due to the fact the criterion for ship’s stability is the righting moment she has at any angle of heel and not just the initial GM. • The righting moment obtained for any small angle is W x GM sinƟ would be nearly same. This is because in one case virtual displacement is taken as W and in the other it is taken as W-P. • Therefore it is advised to know both methods, as sometimes the information given in the question is sufficient for one of the methods only; but follow any one method throughout the problem. Stability and trim during Dry- docking and Grounding - Capt. S. Nathan 14

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• Prior to entering dry dock M. V. AMET has draughts F 4. 86 m A 5. 24 m and an effective KG of 9. 16 m. • Calculate • (a) the GM when the ship takes the blocks forward and aft (at the critical instant), • (b) the draughts at the same instant; Stability and trim during Dry- docking and Grounding - Capt. S. Nathan 16

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• KM at critical instant 10. 698 m • KG 9. 160 m • Initial GM 1. 538 m • Loss of GM 0. 083 m • GM at critical instant 1. 455 m Virtual loss of GM = • Both answers for ‘GM at critical instant’ are different Initial GM= but are both valid since a true measure of a ship’s stability is it's righting moment value at any given GM at critical angle of heel. • Within small angles of heel the righting moment is given by: instant= 0. 083 m 0. 096 m 1. 538 m 1. 455 m 1. 442 m 22009. 203 x. SinƟ tm 22010. 668 SinƟ tm • Righting moment (t-m) = Displacement x GMx SineƟ RM @ Ɵ° = Stability and trim during Dry- docking and Grounding - Capt. S. Nathan 18

• • During the docking operation it is essential that the ‘critical instant’ draught is determined as both draughts forward and aft will be constantly being read. • As the ship’s draught approaches that as calculated for the critical instant, also evidenced by the fact that the ship will be in a near even keel condition at that time, the rate at which the water is pumped out of the dock will be slowed down to allow final adjustment of the ship’s fore and aft alignment prior to the ship taking the blocks overall. • Once on the blocks the rate of pumping will be increased again. Stability and trim during Dry- docking and Grounding - Capt. S. Nathan 19

• M. V. VIJAY enters a SW drydock drawing 3 m fwd & 5. 2 m aft. KG 9 m, FSM 1200 tm. Calculate the virtual GM & the moment of statical stability at 0. 5° heel, when she is just about to take to blocks fwd. Stability and trim during Dry- docking and Grounding - Capt. S. Nathan 20

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• Virtual loss of GM = 0. 590 m 0. 608 m Initial GM fluid = 0. 724 m Virtual GM = 0. 134 m 0. 116 m RM @ 0. 5° = W. GM. Sin Ɵ = 7853. 1 x 0. 116 x Sin 0. 5° 8. 618 tm Stability and trim during Dry- docking and Grounding - Capt. S. Nathan 7. 950 tm 22

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• (4) Calculate the maximum allowed P force and hence the maximum initial trim loss of GM at critical instant 0. 203(23821 -P) = 8. 860 P 4835. 663 - 0. 203 P = 8. 860 P 4835. 663 = 8. 860 P + 0. 203 P 4835. 663 = 9. 063 P P = 534 t P COT (cms) = COT Maximum permissible trim by the stern on Stability and trim during Dry- docking and Grounding - entering the dry Capt. S. Nathan dock = 130 cms =1. 300 m = 126 cms = 1. 26 m 25

• M. V. VIJAY has W = 6849 t in SW, KG = 9. 6 m, FSM = 900 tm. Find the maximum trim with which she may enter a drydock, if the GM at the critical instant is to be not less than 0. 3 metre. Stability and trim during Dry- docking and Grounding - Capt. S. Nathan 26

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• M. V. VIJAY has W = 6849 t in SW, KG = 9. 6 m, FSM = 900 tm. Find the maximum trim with which she may enter a drydock, if the GM at the critical instant is to be not less than 0. 3 metre. • W(t) Draft TPC(t) MCTC (tm) AF (m) KM (m) • 6849 3. 60 21. 36 154. 1 72. 141 10. 274 • Initial GM = 10. 274 - 9. 600= 0. 674 m Total loss of GM • Virtual GM @ critical instant = 0. 300 m Permissible loss of GM • Permissible Loss of GM = 0. 374 m 0. 374 m FSC + dry docking loss 0. 374 P 166. 6 t 159. 6 t 78. 0 cm=0. 78 m 74. 7 cm=0. 747 m COT Maximum trim required Stability and trim during Dry- docking and Grounding - Capt. S. Nathan 28

• MV Hindship at a draft of F 3. 82 m A 5. 46 m, in water of density 1. 015 is being docked. KG 8. 38 m, FSC 0. 12 m. Assuming the KM, MCTC, LCF and FSC remain unchanged over the range of drafts involved, calculate: i. The virtual GM of the vessel on taking blocks all over ii. Her righting movement at a heel of 2°, at the critical instant iii. The fore and aft drafts at which her virtual GM becomes nil. Stability and trim during Dry- docking and Grounding - Capt. S. Nathan 29

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(i) Virtual loss of GM (ii) Virtual loss of GM 0. 359 m 0. 377 m Initial GM 0. 676 m Virtual GM on taking blocks all over 0. 317 m 0. 299 m (W-P) x GM sin Ɵ W x GM sin Ɵ 8510. 3 x 0. 317 sin 2°=94. 1 tm 8875. 1 x 0. 299 sin 2°= 92. 6 tm Righting moment (iii) For virtual GM to become zero, virtual loss of GM must be equal to the Initial GM. Virtual loss of GM 0. 676 = 0. 676 W - 0. 676 P = 8. 38 P 0. 676 P = 0. 676 x 8875. 1 P P Stability and trim during Dry- docking and Grounding - Capt. S. Nathan 662. 5 t 653. 8 t 31

iii Virtual loss of GM Effective displ. when GM becomes zero 8212. 6 t 8221. 3 t 8293. 5 t 8302. 3 t 4. 317 m 4. 321 m 4. 317 m 4. 321 m Equivalent weight in SW TMD for equivalent weight in SW Since she is already taken the blocks forward and aft; TMD = draft F & A draft Stability and trim during Dry- docking and Grounding - Capt. S. Nathan 32

• MV. Hindship' displacing 9540 tonnes and trimmed 0. 78 m by the stern is to be drydocked for bottom inspection. KG 7. 826 m, FSC 0. 164 m. Calculate: i. The GM (Fluid) of the vessel before entering dry dock. ii. The virtual GM of the vessel when her keel takes the blocks all along the length of the vessel. iii. The forward and after draft, at which the virtual GM of the vessel becomes zero. iv. The fall in water level, between the vessel taking blocks all over and her virtual GM becoming zero. Stability and trim during Dry- docking and Grounding - Capt. S. Nathan 33

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• Virtual loss of GM 0. 148 m 0. 168 m KM for displ. 9362. 5 t 9. 027 m KG 7. 826 m Initial GM(fluid) 1. 034 m Virtual loss of GM 0. 148 m 0. 168 m Residual GM on taking blocks Fore & Aft 0. 886 m 0. 866 m Stability and trim during Dry- docking and Grounding - Capt. S. Nathan 35

(iii) Approximate calculation of force P For Virtual GM to become nil, virtual loss of GM = Initial GM Virtual loss of GM 1. 201 (after the critical period is over, FSE may be ignored) 7. 826 P 1. 201 x 9540 -1. 201 P 9. 027 P 11457. 54/9. 027 P 1269. 252 t Effective disp when GM=0 TMD for disp 1269. 252 t 9540 -1269. 252= 8270. 748 t = 4. 307 m 4. 806 m Fall of water level 0. 499 m Stability and trim during Dry- docking and Grounding - Capt. S. Nathan 36

Stability and trim during Grounding Stability and trim during Dry- docking and Grounding - Capt. S. Nathan 37

• While drawing 3 m fwd and 7 m aft in SW, M. V. VIJAY runs aground lightly on a sandy coast. External soundings indicate that the depth of water near the after perpendicular is 2 m greater than near the fwd perpendicular. If KG is 8. 1 m & FSM is 1200 tm, find; (a) the drop in water level at which the ship would sit overall on the sea-bed; (b) the virtual GM when the ship sits overall on the sea-bed; (c) The drop in water level at which the ship would become unstable. Stability and trim during Dry- docking and Grounding - Capt. S. Nathan 38

• Draft of ship Depth of water aft (m) fwd (m) Initial: 7. 000 3. 000 7. 000 5. 000 Final: 5. 764 3. 764 Final trim by stern = 2 m Bottom slope 2 m higher at fwd end. GM solid @ critical instant = 8. 881 - 8. 100 = 0. 781 m FSC = FSM / (W - P) = 1200/9310. 30 = 0. 129 m Fluid GM when sitting overall = 0. 652 m Stability and trim during Dry- docking and Grounding - Capt. S. Nathan 39

Virtual loss of GM 0. 400 m GM (fluid) 0. 652 m Ans(b) Virtual GM 0. 252 m 0. 418 m 0. 234 m Initial GM = Initial KM - KG = 0. 625 m, The ship will become unstable when its GM is Zero For Virtual GM to become nil: Initial GM (fluid) = virtual loss of GM Total loss of GM = FSC + loss due to P Stability and trim during Dry- docking and Grounding - Capt. S. Nathan 40

Total loss of GM 0. 625 m 0. 625 P 562. 321 t 554. 1 t 9770 -562. 321=9207. 679 t 9770 -554. 1=9215. 9 t W (t) Draft AF (m) 9207. 7 4. 689 71. 994 W (t) Draft AF (m) 9215. 9 4. 693 71. 993 4. 689+1. 028= 5. 717 m 4. 693+1. 028=5. 721 m Draft when GM becomes zero 5. 717 m 5. 721 m Draft when aground lightly 7. 000 m Ans(c) Drop in water level for 0 GM 1. 283 m 1. 279 m When GM becomes zero; displacement =W-P Ta Draft • Note: Due to the nature of the problem, the value of P is available only towards the end of the calculation. Hence the KM used is for the original displacement (W) not for the reduced displacement (W - P). In reality, (for M. V. VIJAY) the KM for (W - P) would be more than the KM used above and hence the maximum safe trim would Stability and trim during Dry- docking and Grounding - 41 Capt. S. Nathan be more than the value calculated here. The error is thus on the safer side.

• M. V. Hindship sailed from port in condition No. 8. soon after departure she grounded on an isolated rock, without damage to the hull. The drafts were then observed to be F 5. 90 m A 9. 30 m. Calculate the following: I. The upthrust provided by the rock II. The position with respect to AP, where the grounding occurred III. The virtual GM of the ship then IV. The angle of heel, if she grounded 2 m to starboard of centerline V. The rise of tide required for the ship to refloat Stability and trim during Dry- docking and Grounding - Capt. S. Nathan 42

• For hydrostatic draft 7. 614 m: Displacement =15725. 8 t MCTC =191. 996 mt LCB =72. 687 m LCF =70. 965 m KM =8. 238 m Stability and trim during Dry- docking and Grounding - Capt. S. Nathan 43

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