**Q1. A vessel of length 142m, displacement 16130t, KM 8.24m, KG 7.26m MCTC 192 mt, TPC 23.4t, LCF 71m, FSM 1372 mt, at a draft of F 6.70m, A 8.86m, ground on a rock. The draft then F 5.90m, A 9.30m.**

** Calculate :**

**Q1. A vessel of length 142m, displacement 16130t, KM 8.24m, KG 7.26m MCTC 192 mt, TPC 23.4t, LCF 71m, FSM 1372 mt, at a draft of F 6.70m, A 8.86m, ground on a rock. The draft then F 5.90m, A 9.30m.**

**Calculate :**

**The upthrust provided by the rock.****The position with respect to AP where the grounding occurred.****Her virtual GM (FI.) then****The rise of tide required for her to refloat.**

**Solution –**

**Solution –**

**Draft before Grounding = 6.70m, Aft = 8.86m**

**Trim = 2.16m**

** Correction to aft draft = 2.16 ⨯ 71/142**

** = 1.08m**

** ∴ Hydrostatic draft = 7.78m**

**Draft after grounding = 5.90 m fwd**

**Trim = 3.4m**

** Correction to aft draft = 3.4 ⨯ 71/142**

** ∴ Hydrostatic draft = 7.60m**

** Rise = P/ TPC ⨯ 100**

** P = (0.18 ⨯ 23.4 ⨯ 100)**

** = 421.2 tonnes**

**Trim before grounding = 2.16m,**

**Trim after grounding = 3.40m**

** Change in trim = 1.24m**

** 1.24 = 421.2 ⨯ d/192 ⨯ 100**

** d = 56.52 m from COF**

**From AP distance = 71.00 + 56.52 = 127.52m**

**GG**_{1}= (P ⨯ KM)/W

**= 421.2 ⨯ 8.24/16130**

** = 0.215m**

**New GM = 0.765m **

**FSC = 1372/(16130 – 421.2)**

** = 0.0873m**

**GM (fluid) = 0.678m**

**Rise of tide required = P/ TPC + P ⨯ d/ MCTC ⨯ d/ LBP**

**= 421.2/23.4 + 421.2 ⨯ 56.52 ⨯ 56.52/192 ⨯ 142**

** = 18 + 49.35**

**= 67.35cm**

**Q2. A vessel of length 140m is floating at draft forward 5.23m Aft 5.74m runs aground lightly on a rock 12m abaft the stern. The tide falls by 80cms. Given the following data estimate the virtual GM of the vessel and her draft forward and aft after the fall of tide. KG 5.80m, KM 6.40m, MCTC 130tm, TPC 18t, AF 73m, Displacement 18500t.**

**Q2. A vessel of length 140m is floating at draft forward 5.23m Aft 5.74m runs aground lightly on a rock 12m abaft the stern. The tide falls by 80cms. Given the following data estimate the virtual GM of the vessel and her draft forward and aft after the fall of tide. KG 5.80m, KM 6.40m, MCTC 130tm, TPC 18t, AF 73m, Displacement 18500t.**

**Solution –**

**Solution –**

**Distance of grounding point from COF = 55m**

** We have P = trim ⨯ MCTC/d**

** Change in draft = P/TPC + P ⨯ d/MCTC ⨯ d/LBP**

** So, 80 = P/18 + P ⨯ 55/130 ⨯ 55/140**

**Or, P = 360.74**

**GG _{1} = (P ⨯ KM)/ W**

**= 0.125m****Virtual GM = GM – Virtual loss of GM( GG1) **

** = 0.475m**

**Also,**

** Trim caused = Tc = (P ⨯ d)/ MCTC ⨯ 100**

** = 1.526m**

**Ta = 0.796m,**

** Tf = 0.730m**

**Rise = P/ TPC ⨯ 100**

** = 0.200 tonnes**

| Fwd | Aft |

Draft | 5.23m | 5.74m |

Rise | -0.200m | -.200m |

| -0.730m | +0.796m |

| 4.300m | 6.336m |

**Q3. A vessel of displacement 7200 tonnes. Length 120m, MCTC 110tm, KG 6.0m, TPC 16 tonnes, center of floatation 2 mts forward of midship ground on a rock 10mts. Abaft her forward perpendicular. Given initial draft F : 4.2m, A : 5.1m.**

**Q3. A vessel of displacement 7200 tonnes. Length 120m, MCTC 110tm, KG 6.0m, TPC 16 tonnes, center of floatation 2 mts forward of midship ground on a rock 10mts. Abaft her forward perpendicular. Given initial draft F : 4.2m, A : 5.1m.**

**Find the fall in tide in cm, that will make the vessel unstable, given KM at that moment equal to 6.4 mts.****What will be the drafts forward and aft at that moment.**

**Solution –**

**Solution –**

**For vessel to unstable GM should be zero.**

**GG _{1} = 0.4m **

**So,**

**0.4 = P ⨯ 6.4/ 7200**

**P = 450 tonnes****We can calculate fall in tide – **

** Fall in tide = P/ TPC + ( P x AL / MCTC) + AL/ LBP **

** = 450/16 + 450 ⨯ 48/110 ⨯ 48/120**

** = 1.067m**

**Trim caused = 450 ⨯ 48/110 ⨯ 100****= 1.964m**

**Ta = 1.014,**

** Tf = ( Tc – Ta)**

** = 0.95m**

**Rise = 450/1600 **

** = 0.281m**

| Fwd | Aft |

Draft | 4.200m | 5.100m |

-0.281m | -0.281m | |

3.919m | 4.819m | |

-0.950m | +1.014m | |

2.969m | 5.833m |

**Q4. A vessel of length 120m, Displacement 6400 tonnes, TPC 15 tonnes, MCTC 110tm, Km 6.4m, KG 5.1m, CF 2m for’ d of the midlength grounds on a rock 45m for’d of midlength the tide then by 80 cm. Calculate the residual GM then.**

**Q4. A vessel of length 120m, Displacement 6400 tonnes, TPC 15 tonnes, MCTC 110tm, Km 6.4m, KG 5.1m, CF 2m for’ d of the midlength grounds on a rock 45m for’d of midlength the tide then by 80 cm. Calculate the residual GM then.**

**Solution –**

**Solution –**

**We can calculate fall in tide – **

**Fall in tide = P/ TPC + ( P x AL / MCTC) + AL/ LBP **

** 80 = P/15 + P ⨯ 43/110 ⨯ 43/120**

** So, P = 386.95 cm.**

** GG1 = 386.95 ⨯ 6.4/ 6400**

** = 0.3869m**

**Residual GM = 0.91m**

**Q5. A vessel of L = 140m, CF = 2m FWd of midship, KM = 6.1m, KG = 5.5m, MCTC = 130 mt, w = 5700t at a draft of F = 4.15m, grounds on a rpck 10 mts for’d of her stern. The tide then falls 80cm. Calculate her virtual GM then and her draft f & A, TPC = 16.**

**Q5. A vessel of L = 140m, CF = 2m FWd of midship, KM = 6.1m, KG = 5.5m, MCTC = 130 mt, w = 5700t at a draft of F = 4.15m, grounds on a rpck 10 mts for’d of her stern. The tide then falls 80cm. Calculate her virtual GM then and her draft f & A, TPC = 16.**

**Solution –**

**Solution –**

**We can calculate fall in tide – **

**Fall in tide = P/ TPC + ( P x AL / MCTC) + AL/ LBP **

** 80 =P/15 + P ⨯ 58/130 ⨯ 58/140**

** P = 323.44 tonnes**

** GG _{1} = 0.346m**

**GM = 0.254m****Rise = P/ TPC ⨯ 100**

** = 0.202m**

**Trim caused = 323.44 ⨯ 58/130 ⨯ 100**

** = 144m**

**Ta = 0.701m,**

** Tf = ( Tc – Ta)**

** = 0.739m**

| Fwd | Aft |

Draft | 4.15m | 4.851m |

Rise | -0.202m | -0.202m |

| +0.739m | -0.701m |

| 4.687m | 3.948m |

**Q6. Vessel of length 120m, LCF = 2m, Aft of midship, Draft = 4.70m. For’d = 5.20 m, Aft TPC = 15 t, MCTC = 110 tm, KM = 5.9, KG = 5.1 m. Grounds on a rock 10 meters abaft her stern. The tide then falls 80cm. Calculate the drafts F & A then and state whether she would remain upright.**

**Q6. Vessel of length 120m, LCF = 2m, Aft of midship, Draft = 4.70m. For’d = 5.20 m, Aft TPC = 15 t, MCTC = 110 tm, KM = 5.9, KG = 5.1 m. Grounds on a rock 10 meters abaft her stern. The tide then falls 80cm. Calculate the drafts F & A then and state whether she would remain upright.**

**Solution –**

**Solution –**

**Not possible to calculate displacement not given.**

**Q7. A vessel of displacement 12200 t, MCTC = 200 tm, COF = 3 m, for’d of midship, length 152 m, KG = 7.2 m, KM = 8.1 m has draft for’d 5.1m, A 5.2 m. This vessel runs aground on an isolated rock 11.5 m aft of for’d perpendicular. Find the virtual Gm and Draft for’d and Aft. Given TPC = 25t, fall in tide 1 meter.**

**Q7. A vessel of displacement 12200 t, MCTC = 200 tm, COF = 3 m, for’d of midship, length 152 m, KG = 7.2 m, KM = 8.1 m has draft for’d 5.1m, A 5.2 m. This vessel runs aground on an isolated rock 11.5 m aft of for’d perpendicular. Find the virtual Gm and Draft for’d and Aft. Given TPC = 25t, fall in tide 1 meter.**

**Solution –**

**Solution –**

**W = 12200, distance from COF of grounding location = 61.5m**

**We can calculate fall in tide – **

**Fall in tide = P/ TPC + ( P x AL / MCTC) + AL/ LBP **

** 100 = P/25 + P ⨯ 58/200 ⨯ 58/152**

** P = 608.21 tonnes.**

** GG _{1} = (P ⨯ KM)/W**

**GG1 = 0.404**

**Virtual GM = 0.495m.****Rise = P/ TPC ⨯ 100**

** Rise = 0.243m**

**T _{C }= (P x D)/ MCTC**

**= (608.21x 58) /200**

**Tc = 1.870m,****We know that –**

** Ta = 0.972m,**

** Tf = ( Tc – Ta)**

** = 0.898m**

| Fwd | Aft |

Draft | 5.1m | 5.2m |

| -0.243m | -0.243m |

| -0.898m | +0.972m |

| 3.959m | 5.929m |

**Q8. A vessel of displacement 15185t, MCTC = 378 tm, TPC = 36.9t, Draft for’d 4.4m, AFT = 4.7 m, Length 180m, runs lightly aground on an isolated wok 7.5m, abaft for’d end. Find the virtual GM and draft for’d and aft COF 4.06m for’d of midship. Given KG = 8.0m, KM = 8.5m, fall in tide 80cm.**

**Q8. A vessel of displacement 15185t, MCTC = 378 tm, TPC = 36.9t, Draft for’d 4.4m, AFT = 4.7 m, Length 180m, runs lightly aground on an isolated wok 7.5m, abaft for’d end. Find the virtual GM and draft for’d and aft COF 4.06m for’d of midship. Given KG = 8.0m, KM = 8.5m, fall in tide 80cm.**

**Solution –**

**Solution –**

**Distance from COF = 78.44m**

** We can calculate fall in tide – **

**Fall in tide = P/ TPC + ( P x AL / MCTC) + AL/ LBP **

** 80 = P/36.9 + P ⨯ 78.44/378 ⨯ 78.44/180**

** P = 680.67 tonnes**

** GG _{1} = (P ⨯ KM)/W**

**= 0.381m**

**Virtual GM = 0.119m****Rise = P/ TPC ⨯ 100**

** Rise = 0.184m**

**T _{C }= (P x D)/ MCTC **

**= (680.67 x 78.44) / 378**

**Tc = 1.412m,****We know that –**

** Ta = ( Tc x AL ) / LBP**

** = (1.412 x**

** Ta = 0.674m,**

**Tf = ( Tc – Ta)**

** = 0.737m**

| Fwd | Aft |

Draft | 4.4m | 4.7m |

| -0.184m | -0.184m |

| -0.674m | +0.737m |

| 3.542m | 5.253m |

**Q9. A vessel of Length L = 150 mtrs, CF = 2.5m forward of midship, KM = 6.0M, KG = 5.4m, MCTC = 120, W = 6000t, TPC = 15, ata draft of F : 4.25m, A : 5.00m ground on a rock at midship. The Tide then falls and draft at midship is observed to be 4.46m. Calculate her virtual GM then and her drafts forward and aft.**

**Q9. A vessel of Length L = 150 mtrs, CF = 2.5m forward of midship, KM = 6.0M, KG = 5.4m, MCTC = 120, W = 6000t, TPC = 15, ata draft of F : 4.25m, A : 5.00m ground on a rock at midship. The Tide then falls and draft at midship is observed to be 4.46m. Calculate her virtual GM then and her drafts forward and aft.**

**Solution –**

**Solution –**

**Correction to aft draft = 0.75 ⨯ 75/150**

** = 0.375**

**Midship draft = 4.625**

** Fall in water at midship = (4.625 – 4.46)**

** = 0.165**

**16.5 = P/15 + P⨯ 75/120 ⨯75/150**

** P = 43.51 tonnes**