Ship Stability for Masters and Mates 5 Episode 12 pps

Maximum kg  Deadweight Moment Deadweight  10 260 2000  5X13 m Example 1 Using the Simpli®ed Stability Data shown in Diagram 3 (Figure 44.1), estimate the amount of cargo (kg 3 m) which can be loaded so that after completion of loading the ship does not have de®cient stability. Prior to loading the cargo the following weights were already on board: 250 t fuel oil kg 0.5 m Free Surface Moment 1400 t m 50 t fresh water kg 5.0 m Free Surface Moment 500 t m 2000 t cargo kg 4.0 m The light displacement is 1000 t, and the loaded Summer displacement is 3500 t Since 10 875 tonnes metres is less than the maximum permissible deadweight moment at a displacement of 3500 tonnes, the ship will not have de®cient stability and may load 200 tonnes of cargo. Ans. Load 200 tonnes. Example 2 Using the Maximum Permiss ible Deadweight Moment diagram 3 (Figure 44.1) and the information given below, ®nd the quantity of timber deck cargo (Kg 8.0 m) which can be loaded, allowing 15 per cent for water absorption during the voyage. 374 Ship Stability for Masters and Mates Item Weight Kg Deadweight Moment Light disp. 1000 t ± ± Fuel oil 250 t 0.5 m 125 t m Free surface ± ± 1400 t m Fresh water 50 t 5.0 m 250 t m Free surface ± ± 500 t m Cargo 2000 t 4.0 m 8000 t m Present cond. 3300 t 10 275 t m À Point 2 (Satisfactory) Maximum balance 200 t 3.0 m 600 t m Summer displ. 3500 10 875 t m À Point 3 (Satisfactory) Simpli®ed stability information 375 Fig. 44.1 Summer displacement 4000 tonnes, Light Displacement 1000 tonnes. Weights alre ady on board: Fuel oil 200 tonnes, Kg 0.5 m, free surface moment 1400 t m Fresh water 40 tonnes, Kg 5.0 m, free surface moment 600 t m Cargo 2000 tonnes, Kg 4.0 m Ballast 350 tonnes, Kg 0.5 m The following weights will be consumed durin g the voyage: Fuel oil 150 tonnes, Kg 0.5 m. Free surface moment will be reduced by 800 t m Fresh water 30 tonnes, Kg 5.0 m. Free surface moment will be by 200 t m Departure Condition From diagram 3, where the line joining points 4 and 5 cuts the curve of Maximum Permissible Deadweight Moments (point 6), the displacement is 3920 tonnes. Total departure displacement 3920 tonnes Departure displacement without deck cargo 3590 tonnes ; Max deck cargo to load 330 tonnes Absorption during voyage  15 100  330  49X5 tonnes 376 Ship Stability for Masters and Mates Item Weight Kg Deadweight Moment Light ship 1000 ± ± Fuel oil 200 0.5 100 Free surface 1400 Fresh water 40 5.0 200 Free surface 600 Cargo 2000 4.0 8000 Ballast 350 0.5 175 Departure Disp. (without deck cargo) 3590 10 475 ± Point 4 (Satisfactory) Maximum deck cargo 410 8.0 3280 Summer disp. 4000 13 755 ± Point 5 (De®cient Stability) Arrival Condition Ans. Load 330 tonnes of deck cargo. Simpli®ed stability information 377 Item Weight Kg Deadweight Moment Departure disp. without deck cargo 3590 10 475 Fuel oil À 150 0.5 À75 Free Surface À800 Fresh water À30 5.0 À150 Free surface À200 Arrival disp. without deck cargo 3410 9250 Deck cargo 330 8.0 2640 Absorption 49.5 8.0 396 Total arrival disp. 3789.5 12 286 ± Point 7 (Satisfactory Stability) Exercise 44 1 Using the Maximum Permissible Deadweight Moment diagram 3, ®nd the amount of deck cargo (kg 8.0 m) which can be loaded allowing 15 per cent for water absoption during the voyage given the following data: Light displacement 1000 tonnes, Loaded disp lacement 4000 tonnes. Weights already on board: During the voyage the following will be consumed (tonnes and kg): Fuel oil 250 0.5 Reduction in free surface moment 850 t m. Fresh water 40 5.0 Reduction in free surface moment 400 t m. Item Weight Kg Free Surface Moment Cargo 1800 4.0 ± Fuel oil 350 0.5 1200 Fresh water 50 5.0 600 Ballast 250 0.5 ± Appendix I Standard abbreviations and symbols K The keel. B The centre of buoyancy when the ship is upright. B 1 The centre of buoyancy when the ship is inclined. BM The height of the transverse metacentre above the centre of buoyancy. BM L The height of the longitudinal metacentre above the centre of buoyancy. CB Centre of buoyancy. G The original position of the centre of gravity. G 1 The new position of the centre of gravity. M The original position of the transve rse metacentre. M 1 The new position of the transverse metacentre. M L The longitudinal metacentre. KB The height of the centre of buoyancy above the keel. KG The height of the centre of gravity above the keel. Kg The height of the centre of gravity of an item above keel. KM The height of the transverse metacentre above the keel. GM Initial transverse metacentric height. CF Centre of Flotation. GZ The length of the righting lever about centre of gravity. KN The length of the righting lever about keel. Vorj The ship's volume of displacement. Wori The ship's weight of displacement. w A weight to be loaded, discharged, or shifted.  e  Amidships. (The symbol  e  is shown on trim diagrams). L The ship's length. D The ship's depth. B The ship's maximum beam. d The ship's draft. F Forward, or centre of ¯otation. A Aft. M or m Metres. C w The water-plane coef®cient. C b Block coef®cient. C m Coef®cient of midships area. C p Prismatic coef®cient. I or i Second moment of an area. l The distance of the centre of ¯otation from aft. P The upthrust on the keel blocks when drydocking. m The permeability of a compartment. WL The original waterline. W 1 L 1 The new waterline. G v The virtual centre of gravity. t The trim. MCTC or MCT 1 cm The moment to change the trim by 1 cm. TPC The tonnes per centimetre immersion. GM L The longitudinal metacentric height. SG Speci®c gravity. y An angle of list or heel. WPA Area of a water-plane. FWA Fresh water allowance. FW Fresh water. SW Salt water. CDB Cellular double-bottom tank. CI or h The common interval used in Simpson's Rules. E Young's Modulus. y Depth from the neutral layer. f Stress. q Shearing stress. r Density in tonnes/m 3 . r FW Fresh water density @ 1.000 t/m 3 . r SW Salt water density @ 1.025 t/m 3 . r DW Dock water density as given in t/m 3 . d max Maximum squat. S Blockage factor. y Static underkeel clearance. y 2 Dynamical underkeel clearance. H Water depth relating to squat. T Ship's mean draft relating to squat. V k Speed of ship relative to the water. Standard abbreviations and symbols 379 Appendix II Summary of stability formulae* Form Coef®cients Area of waterplane  L  B  C w Area of amidships  B Âd  C m Volume of displacement  L  B  d  C b C b  C m  C p Drafts When displacement is constant: (For box-shapes): New draft Old draft  Old density New density When draft is constant: New displacement Old displacement  New density Old density TPC  WPA 97X56 FWA  W 4  TPC Change of draft or  FWA 1025 À r DW  25 Dock Water Allowance Homogeneous log: draft depth  relative density of log relative density of water * See note on page 386. Variable immersion hydrometer: Density  M y M y À x  M y ÀM x L  Trim MCTC  W  GM L 100  L Change of trim  Trimming moment MCTC Change of draft aft  l L  Change of trim Change of draft forward  Change of trim À Change of draft aft Effect of trim on tank soundings: Head when full Length of tank  Trim Length of ship True Mean Draft: Correction FY  Trim Length To Keep the Draft Aft Constant: d  MCTC  L TPC  l To ®nd GM L : GM L GG 1  L t Simpson's Rules 1st Rule: Area  h/3 (a  4b  2c 4d e) or 1 3  CI  S 1 2nd Rule: Area  3h/8 (a  3b  3c 2d  3e  3f  g) or 3 8  CI  S 2 3rd Rule: Area  h/12 (5a  8b À c) or 1 12  CI  S 3 Summary of stability formulae 381 KB and BM Transverse Stability For rectangular waterplanes: I  LB 3 12 BM  I/V For box-shapes: BM  B 2 /12d KB  d/2 KM min  Ba  6 p For triangular prisms: BM  B 2 /6d KB  2d/3 Depth of centre of buoyancy  1 3  d 2  V A  below the waterline Longitudinal Stability For rectangular waterplanes: I L  BL 3 12 BM L  I L V For box-shapes: BM L  L 2 /12d For triangular prisms: BM L  L 2 6d Transverse Statical Stability Moment of Statical Stability  W  GZ At Small Angles of Heel: GZ  GM  sin y 382 Ship Stability for Masters and Mates By Wall-Sided Formula: GZ GM  1 2 BM tan 2 ysin y By Attwood's Formula: GZ  v  hh 1 V À BG sin y Stability Curves: New GZ  Old GZ Æ GG 1 sin Heel or New GZ  KN À KG sin Heel Dynamical Stability  W  Area under stability curve  W v(gh  g 1 h 1 ) V À BG(1 À cos y) ! List Final KG  Final Moment Final Displacement GG 1  w  d Final W tan List  GG 1 GM Increase in draft due to list: New draft  1 2 EbEsin y  (d À rcos y Inclining Experiment: GM GG 1  Length of plumbline Deflection Effect of Free Surface Virtual loss of GM  lb 3 12  r W  1 n 2 Drydocking and Grounding Upthrust at Stern: P  MCTC  t l or P  Old À New displacement Summary of stability formulae 383 [...]... 4.63 4. 65 4.70 4. 75 4.79 4.83 4.91 5. 00 5. 04 5. 10 5. 18 5. 25 5. 35 5. 45 5 .55 5. 65 5.72 5. 79 5. 85 5.90 5. 93 5. 98 6.04 6.10 6. 15 6.18 6.22 6. 25 6.28 6.32 6.36 6.38 6.40 6.43 6.48 6 .53 6 .58 6.48 6 .58 6.68 6.73 6.78 6.83 6.88 6.93 6.98 7.02 7.07 7.11 7.18 7.20 7.22 7.24 7.26 7.27 7.28 7.29 7.30 6.91 6. 95 7.00 7.08 7.14 7.18 7.20 7. 25 7.30 7. 35 7.40 7. 45 7 .50 7 .55 7.60 7. 65 7.70 7.70 7.70 7.68 7.66 7. 05 7.08... KG (m) 19 50 0 19 000 18 50 0 18 000 17 50 0 17 000 16 50 0 16 000 15 500 15 000 14 50 0 14 000 13 50 0 13 000 12 50 0 12 000 11 50 0 11 000 10 50 0 10 000 950 0 9000 850 0 8000 750 0 7000 650 0 6000 55 00 50 00 7. 85 7.93 8.02 8.10 8.17 8.20 8.19 8.18 8.18 8.19 8.20 8.22 8.24 8.28 8.34 8.42 8 .50 8.60 8.71 8. 85 9.03 9.24 9.48 9.73 9.82 9.62 9.43 9.18 8.84 8.40 408 Ship Stability for Masters and Mates SHIP STABILITY. .. 15 000 14 50 0 14 000 13 50 0 13 000 12 50 0 12 000 11 50 0 11 000 10 50 0 10 000 950 0 9000 850 0 8000 750 0 7000 650 0 6000 55 00 50 00 Angle of Heel (Degrees) 12 20 30 40 50 60 75 1.72 1.73 1.74 1. 75 1.77 1.78 1.78 1.80 1.82 1.83 1.86 1.93 2.00 2. 05 2.10 2.17 2.22 2.32 2.42 2 .57 2.72 2.98 2.98 2.98 2.99 3.00 3.03 3. 05 3 .12 3. 15 3.19 3.23 3.28 3.36 3.43 3 .52 3.62 3.70 3. 85 4.00 4. 15 4.32 4.48 4 .51 4 .55 4 .58 ... 7713 750 5 7296 7088 6880 6673 22.21 22. 15 22.10 22. 05 22.00 21. 95 21.90 21. 85 21.80 21. 75 21.70 21. 65 21.60 21 .55 21 .50 21. 45 21.40 21. 35 21.30 21.24 21.19 21.66 21.61 21 .56 21 .51 21.46 21.41 21.36 21.32 21.27 21.22 21.17 21 .12 21.07 21.02 20.97 20.93 20.88 20.83 20.78 20.72 20.67 163.9 162.9 161.8 160.8 159 .8 158 .8 157 .9 156 .9 156 .0 155 .1 154 .2 153 .3 152 .4 151 .5 150 .6 149.7 148.7 147.8 146.8 1 45. 9 144.9... 68.39 68.48 68 .57 68. 65 68.73 8.34 8. 35 8.36 8.37 8.38 8.39 8.41 8.43 8.46 8.49 8 .52 8 .55 8 .59 8.63 8.67 5. 50 5. 40 5. 30 5. 20 5. 10 5. 00 4.90 4.80 4.70 4.60 4 .50 4.40 4.30 4.20 4.10 4.00 3.90 3.80 3.70 3.60 3 .50 11 180 10 958 10 737 10 51 6 10 296 10 076 9 857 9638 9420 9202 89 85 8768 855 2 8336 8121 7906 7692 7478 72 65 7 052 6840 10 908 10 691 10 476 10 260 10 0 45 9830 9616 9403 9190 8978 8766 855 4 8344 8133... 13 657 13 429 13 201 12 9 75 12 748 12 52 3 12 297 12 073 11 848 11 6 25 11 402 14 220 13 996 13 771 13 54 8 13 324 13 102 12 879 12 658 12 437 12 217 11 997 11 778 11 55 9 11 342 11 124 TPC t SW RD 1.0 25 23.13 23.06 22.99 22.92 22. 85 22.78 22.72 22.66 22.60 22 .54 22.48 22.43 22.37 22.32 22.26 MCTC tm FW SW RD 1.000 RD 1.0 25 22 .57 22 .50 22.43 22.36 22.29 22.23 22.17 22.11 22. 05 21.99 21.93 21.87 21.82 21.77... 7. 35 7.40 7.41 7.42 7.46 7 .50 7 .51 7 .52 7 .51 7 .50 KN values are for hull and forecastle only DATASHEET Q.2(b) (This Datasheet must be returned with your answer book) Note: `foap' denotes for' d of AP Hydrostatic Particulars Draught m Displacement t SW FW RD 1.0 25 RD 1.000 7.00 6.90 6.80 6.70 6.60 6 .50 6.40 6.30 6.20 6.10 6.00 5. 90 5. 80 5. 70 5. 60 14 57 6 14 3 45 14 1 15 13 886 13 657 13 429 13 201 12 9 75. .. 1 45. 9 144.9 160.0 158 .9 157 .9 156 .9 155 .9 154 .9 154 .0 153 .1 152 .2 151 .3 150 .5 149.6 148.7 147.8 146.9 146.0 1 45. 1 144.2 143.3 142.3 141.3 8.71 8.76 8.81 8.86 8.92 8.98 9.06 9.13 9.22 9.30 9.40 9.49 9.60 9.71 9.83 9.96 10.11 10. 25 10.41 10 .57 10.76 2. 85 2.80 2.74 2.69 2.63 2 .58 2 .53 2.48 2.43 2.38 2.32 2.27 2.22 2.17 2 .12 2.07 2.01 1.96 1.91 1.86 1.81 70.60 70.64 70.68 70.72 70. 75 70.79 70.82 70.86... 179.9 178.3 176.8 1 75. 3 173.9 172 .5 171.1 169.8 168 .5 167.3 166.1 1 65. 0 KMT FW RD 1.000 180.1 178 .5 177.0 1 75. 5 174.0 172 .5 171.0 169.6 168.3 167.0 1 65. 7 164.4 163.2 162.1 161.0 KB LCB foap LCF foap m m m m 3.64 3 .58 3 .53 3.48 3.43 3.38 3.33 3.28 3.22 3.17 3.11 3.06 3.01 2. 95 2.90 70.03 70.08 70 .12 70.16 70.20 70.24 70.28 70.32 70. 35 70.38 70.42 70.46 70 .50 70 .53 70 .57 67. 35 67.46 67 .57 67.68 67.79 67.90... commencement of this 394 Ship Stability for Masters and Mates Act such information in writing about the ship' s stability as is necessary for the guidance of the master in loading and ballasting the ship (2) The said information shall be in such a form as may be approved by the Minister (who may approve the provision of the information in the form of a diagram or drawing only), and shall be based on the . 1964 c. 47. 390 Ship Stability for Masters and Mates SCHEDULE 7 Information as to Stability of Ships (Rule 30) The information relating to the stability of a ship to be provided for the master. allowing 15 per cent for water absorption during the voyage. 374 Ship Stability for Masters and Mates Item Weight Kg Deadweight Moment Light disp. 1000 t ± ± Fuel oil 250 t 0 .5 m 1 25 t m Free. Rule: Area  h /12 (5a  8b À c) or 1 12  CI  S 3 Summary of stability formulae 381 KB and BM Transverse Stability For rectangular waterplanes: I  LB 3 12 BM  I/V For box-shapes: BM  B 2 /12d KB