### Theory

1. During dry docking the ship shall be in as light a condition as possible.

2. It shall be trimmed by the stern.

3. Minimum trim required for safe and convenient docking is prescribed by the dock authorities.

4. Chief Officer shall ensure that during the docking process the ship continues to have sufficient positive stability till it is fully sitting on the keel blocks and it is fully supported and secured by the side shores and bilge blocks. Once it is so secured the stability problem ceases to exist.

5. After the ship enters the dry dock and water is being pumped out, first the stern will touch the blocks at the aft perpendicular (AP).

6. Because the stern cannot go down any further, the aft draft will start reducing.

7. This in effect means that the underwater volume of the ship will start reducing.

8. As the ship is still floating, the reduction in underwater volume means that the ship’s displacement and the hydrostatic draft would reduce. In other words we can say that some part of the ship’s weight is transferred to the land with which it is in contact, or that there is a virtual discharge of weight from the ship.

9. This discharge of weight will occur from the point of contact with the land or keel blocks i.e. the position from where the weight is discharged will be the intersection of AP and the keel.

10. Any discharge of weight from ship causes the ship’s COG to shift away from the weight discharged.

11. This means that during dry docking the ship’s COG will shift forward and upwards.

12. Upward shift of COG would mean an increase in the KG, or a virtual loss of ship’s GM.

13. Forward shift of COG would mean change of trim forward, or reduction of ship’s original trim.

14. Hence, as the pumping out of water continues, the ship’s displacement, aft draft, hydrostatic draft, GM and trim will keep on reducing. Once the bow of the ship touches the keel blocks, it would be fully resting on the blocks, i.e. it would be on even keel. This condition will not change any further, but the other parameters will continue to reduce.

15. It will be observed that during the above process, the forward draft will steadily increase till the ship reaches even keel, after which it will also reduce along with the aft draft.

16. Once the bow touches the blocks, the dock authorities will place the side shores and bilge blocks in position to fully support the ship. Hence any subsequent loss of GM has no significance because now the ship cannot capsize.

17. It has to be ensured that from the time the ship’s stern touches the keel blocks and till the bow touches the blocks, the loss of GM should not result in the ship developing a negative GM because if it happens then the ship will capsize as the shores are not there to support it.

18. Due to this stability aspect, the time interval stated above is called the “Critical period” and the time when the bow touches the blocks is called the “Critical instant”.

19. Hence the Chief Officer should ensure that before entering the dry dock, the ship has sufficiently low KG and minimum FSM so that during the critical period, and at the critical instant, the GM(F) does not become negative.

20. Once the critical instant is reached he should ensure that the dock authorities promptly place the shores in position to fully support the ship. If for any reason it does not happen then the pumping out of the water should be immediately stopped to prevent any further loss of GM.

21. To ascertain the value of the initial GM(F) before entering dry dock, he should calculate the amount of loss of GM during the critical period.

## Dry docking Numericals

#### How to solve??

**ABBREVIATIONS USED**

**DF & DA :**– Drafts forward and aft.

**Drop **:- Fall in water level during dry docking after the stern has touched the blocks.

**Hyd **:-Hydrostatic draft.

**P :**-Loss of weight of ship during dry docking, after stern has touched the blocks.

**T :-**Initial or final trim of the ship as stated.

**TF & TA:**-Trim forward and aft.

**TC :-**Change of trim during dry docking, after the stern has touched the blocks.

**FORMULAE APPLICABLE**

a) TC (cm.)= (P ´ LCF) / MCTC

b) Loss of GM = (P ´ KG) / (W – P)

c) GM(F) = KM – KG – Loss of GM – FSC

d) Drop (cm.) = (P / TPC) + (P ´ LCF2) / (MCTC ´ LBP)

*(This formula is to be used only if the other formulae cannot be used.)*

**CALCULATION OF INITIAL DATA REQUIRED FOR FURTHER CALCULATION**

**CASE 1**** — **Data given : DF and DA.

Calculate Trim and mean draft. Using mean draft calculate *LCF* from hydrostatic tables.

Calculate Correction = (T ´ *LCF*) / LBP

*(This LCF will not be used again in any calculation.)*

Calculate Hyd = DA – Correction

Using Hyd calculate W, MCTC and LCF from the tables.

**CASE 2** — Data given : W and LCG.

Using W calculate Hyd, MCTC, LCB and LCF from the tables.

Calculate the DF and DA as follows :

BG = LCB – LCG ; T = (W ´ BG) / MCTC

TA = (T ´ LCF) / LBP ; TF = T – TA

DF = Hyd – TF ; DA = Hyd + TA

**CASE 3** — Data given : W and T.

Using W calculate Hyd, MCTC and LCF from the tables.

Calculate the DF and DA as follows :

TA = (T ´ LCF) / LBP ; TF = T – TA

DF = Hyd – TF ; DA = Hyd + TA

In addition to the above data, KG and FSM will also be given.

**CALCULATION OF FINAL GM(F), DRAFTS AND DROP IN WATER LEVEL AT THE CRITICAL INSTANT (C.I.)**

**STEP 1**** — CALCULATE THE LOSS OF WEIGHT (P) AT THE C.I.**

At C.I. the ship is on even keel, hence Initial T = TC

Formula **I** : P = (TC ´ MCTC) / LCF

**STEP 2**** — CALCULATE THE FINAL GM(F)**

W1 = W – P ; Using W1 calculate KM1 from the tables.

Formula **II** : Loss of GM = (P ´ KG) / W1 ; FSC = FSM / W1

Formula **III** : GM(F) = KM1 – KG – Loss of GM – FSC

**Note** : FSC is applied because it is assumed that at the C.I. the shores are not yet in position. Once these are in position, then the ship will be fully secured and the FSM will cease to exist. Hence the GM will suddenly increase.

**STEP 3**** — CALCULATE THE FINAL DRAFTS**

Using W1 calculate Hyd1 = Final DF = Final DA , as the ship is on even keel at the C.I.

**STEP 4**** — drop in water level** is the difference between initial DA and final DA.

**CALCULATION OF FINAL DRAFTS AND DROP IN WATER LEVEL WHEN THE GM(F) REDUCES TO ‘X’ m. **

**STEP 1**** — CALCULATE THE GM(F) AT THE** **C.I. AS EXPLAINED ABOVE**

There will be two possibilities as follows :

**Possibility 1 :** If GM(F) @ C.I. > X m. then the final GM(F) will reduce to X m. after C.I.

**Possibility 2 :** If GM(F) @ C.I. < X m. then final GM(F) will reduce to X m. before C.I.

**STEP 2**** — CALCULATE LOSS OF WEIGHT (P1) WHEN FINAL GM(F) = X m.**

Using Hyd calculate KM from the tables.

Calculate P1 by combining Formulae **II & III **as follows :

**Possibility 1 : **X = KM – KG – (P1 ´ KG) / (W – P1)

**Possibility 2 : **X = KM – KG – (P1 ´ KG) / (W – P1) – (FSM) / (W – P1)

**Note : **FSM will not apply in **Possibility 1** because GM(F) of X m. occurs after the C.I. and hence the shores must be in position.

**STEP 3**** — CALCULATE THE FINAL DRAFTS **

W2 = W – P1 ; Using W2 calculate Hyd2 from the tables.

**Possibility 1 : **Hyd2 = Final DF = Final DA , as the ship will be on even keel after the C.I.

**Possibility 2 : **

Using Hyd2 calculate MCTC1 and LCF1 from the tables.

Formula **I : **TC = (P1 ´ LCF1) / MCTC1

Final T = Initial T – TC

TA = (T ´ LCF1) / LBP ; TF = T – TA

Final DF = Hyd2 – TF ; Final DA = Hyd2 + TA

**STEP 4**** — drop in water level** is the difference between initial DA and final DA.

**CALCULATION OF FINAL GM(F) AND DRAFTS** **AFTER THE WATER LEVEL HAS DROPPED BY ‘X’ m.**

**STEP 1**** — CALCULATE THE DROP IN WATER LEVEL AT THE C.I. AS EXPLAINED ABOVE (without calculating GM(F) )**

There will be two possibilities as follows :

**Possibility 1 : **If Drop @ C.I. < X m. then the drop of X m. will occur after the C.I.

**Possibility 2 :** If Drop @ C.I. > X m. then the drop of X m. will occur before the C.I.

**STEP 2**** — CALCULATE THE FINAL DRAFTS **

**Possibility 1 :**

Initial DA – Drop of X m. = Final DA = Final Hyd2 = Final DF , as the ship is on even keel after the C.I.

Using Hyd2 calculate W2 and KM1 from the tables.

**Possibility 2 :**

Using initial Hyd calculate TPC from the tables.

Calculate P1 using Formula **IV : **X = (P1 / TPC) + (P1 ´ LCF2) / (MCTC ´ LBP)

W2 = W – P1 ; Using W2 calculate Hyd2, MCTC1, LCF1 and KM1 from the tables.

Formula **I : **TC = (P1 ´ LCF1) / MCTC1

Final T = Initial T – TC

TA = (T ´ LCF1) / LBP ; TF = T – TA

DF = Hyd2 – TF ; DA = Hyd2 + TA

**STEP 3**** — CALCULATE THE FINAL GM(F)**

Formula **II : **Loss of GM = (P1 ´ KG) / W2 ; FSC = FSM / W2

Formula **III :**

**Possibility 1 : **GM(F) = KM1 – KG – Loss of GM

**Possibility 2 : **GM(F) = KM1 – KG – Loss of GM – FSC

**Note : **FSC will not apply in **Possibility I **because drop of X m. occurs after C.I. and hence the shores must be in position.

**CALCULATION OF DRAFTS AND MAXIMUM INITIAL TRIM TO ENTER THE DRY DOCK SO THAT GM(F) AT THE C.I.** **IS ‘X’ m.**

**STEP 1**** — **Data given : W, KG and FSM.

Using W calculate Hyd, LCF and KM from the tables.

**STEP 2** **— CALCULATE THE LOSS OF WEIGHT (P) AT THE C.I.**

Calculate P using Formula **III : **X = KM – KG – (P ´ KG) / (W – P) – (FSM) / (W – P)

**Note : **FSM is to be applied assuming that at the C.I. the shores are not yet in position.

**STEP 3** **— CALCULATE THE INITIAL DRAFTS**

W1 = W – P ; Using W1 calculate Hyd1, MCTC1 and LCF1 from the tables.

Formula **I : **Initial T = (P ´ LCF1) / MCTC1

TA = (Initial T ´ LCF1) / LBP ; TF = Initial T – TA

DF = Hyd1 – TF ; DA = Hyd1 + TA