Institute of Ship Design and Ship Safety

Institute of Ship Design and Ship Safety Exercise Ship Design EEDI, Damage Stability Calculation for Cargo Ships Prof. Dr.-Ing. Stefan Krüger Dipl.-Ing. Philip Augener Dipl.-Ing. Arne Falkenhorst

Exercise Ship Design 17. November 2014 Exercise 5 1 Exercise regarding the EEDI An existing design of a ConRo vessel has to be examined regarding the Energy Efficiency Design Index (EEDI). Tabelle 1: Data of the vessel Quantity Unit Value v Design (SM15 %, EM 15 %) kn 22,5 dw/ 0,43 c p 1, 872 10 3 k 0 c f g CO2 /g fuel 3,1144 sfoc ME g/kwh 190 1. Sketch the curve for the maximum acceptable main engine power following from the EEDI over the deadweight for the mentioned ship type. Please look at the ship type as a container vessel in one case and as an RoRo vessel in the second case. You should concentrate on a scope of the dw from 5.000 t until 25.000 t and please keep the dw/ -ratio constant. 2. Explain the meaning of the diagram! Philip Augener/Arne Falkenhorst Ship Design falkenhorst@tu-harburg.de 1/38

Exercise Ship Design 17. November 2014 2 Questions Regarding the Damage Stability Calculations of Cargo Ships 1. For which kind of vessel is it mandatory to execute a damage stability calculation? 2. Which damage stability calculation is valid for cargo ships currently build? 3. What is the attained index? 4. What is the required index? 5. Explain the relation of A and R? 6. Why should you execute damage stability calculations for both sides of a a RoRo vessel? 7. Which damage stability regulation is valid for cargo vessels built before 2009? 8. What are the major differences between the old and new damage stability regulations for cargo vessels? 9. What is meant by permeability of a room? Please state the permeability according SOLAS 2009 for an engine room! 3 Exercise Damage Stability 1. Please determine the GM min -Curve for the container vessel resulting from the damage stability calculations. The results of the damage stability calculation can be found in Tab. 2. Following from the mean values of the indices A j results the attained index to A = 0, 745. This value corresponds to the required index R = 0, 745, which is determined with a length of L s = 348, 99 m. Because of A = R in this case, the damage stability regulation is fully utilized, which leads to an maximum flexibility of the vessel. 2. Please sketch into the above developed diagram the GM min -curve, which comes from the intact stability regulations concerning the initial stability of the vessel. 3. Find the resulting V CG max -curve resulting from the damage stability calculations! Tabelle 2: Results of the Damage Stability Calculations of a Container Ship j Side Displacement d j KM GM min A j = Σ p i s i Permeability [t] [m] [m] [m] l PS 53154,4 6,45 25,35 3,20 0,820 0,9 l SB 53154,4 6,45 25,35 3,20 0,820 0,9 p PS 108595,5 11,6 20,92 0,80 0,921 0,8 p SB 108595,5 11,6 20,92 0,80 0,917 0,8 s PS 151349,4 15 20,6 0,55 0,536 0,7 s SB 151349,4 15 20,6 0,55 0,534 0,7 Philip Augener/Arne Falkenhorst Ship Design falkenhorst@tu-harburg.de 2/38

Exercise Ship Design 17. November 2014 +-----------------------------------------------------------------------+ HYDROSTATIC TABLES +-----------------------------------------------------------------------+ T AP Dis.SW Dis.FW LCB TCB VCB LCF KM.T T FP Metre Ton Ton m.f.ap m.f.cl m.a.bl m.f.ap m.a.bl Metre +------+--------+--------+-------+-------+-------+-------+-------+------+ 6.000 48733.9 47545.2 165.708 4.7E-18 3.259 166.838 26.387 6.000 6.050 49221.7 48021.2 165.719-1.E-17 3.286 166.814 26.263 6.050 6.100 49710.4 48497.9 165.730-1.E-18 3.314 166.789 26.142 6.100 6.150 50199.9 48975.5 165.740 9.0E-18 3.341 166.762 26.022 6.150 6.200 50690.3 49453.9 165.750 4.1E-17 3.369 166.733 25.905 6.200 6.250 51181.5 49933.1 165.759 7.5E-17 3.396 166.703 25.790 6.250 6.300 51673.5 50413.1 165.768-1.E-17 3.424 166.672 25.677 6.300 6.350 52166.3 50893.9 165.776 1.8E-17 3.451 166.639 25.566 6.350 6.400 52659.9 51375.6 165.784 5.7E-17 3.478 166.604 25.458 6.400 6.450 53154.4 51858.0 165.792 1.9E-17 3.506 166.569 25.353 6.450 6.500 53649.7 52341.2 165.799 4.0E-17 3.533 166.532 25.249 6.500 6.550 54145.8 52825.2 165.805 6.7E-17 3.561 166.493 25.147 6.550 6.600 54642.8 53310.0 165.811 2.1E-17 3.588 166.453 25.047 6.600 6.650 55140.5 53795.6 165.817 3.7E-17 3.615 166.413 24.949 6.650 6.700 55639.1 54282.0 165.822 1.4E-17 3.643 166.375 24.852 6.700 6.750 56138.5 54769.2 165.827-1.E-19 3.670 166.334 24.758 6.750 6.800 56638.7 55257.2 165.831 2.1E-17 3.698 166.292 24.666 6.800 6.850 57139.7 55746.1 165.835 7.2E-17 3.725 166.246 24.577 6.850 6.900 57641.6 56235.7 165.838 6.2E-17 3.752 166.199 24.489 6.900 6.950 58144.3 56726.1 165.841 7.4E-17 3.780 166.150 24.403 6.950 7.000 58647.8 57217.3 165.844-7.E-18 3.807 166.098 24.319 7.000 7.050 59152.1 57709.4 165.846 2.7E-17 3.835 166.045 24.238 7.050 7.100 59657.3 58202.2 165.847 4.2E-17 3.862 165.991 24.159 7.100 7.150 60163.3 58695.9 165.848 3.2E-18 3.890 165.935 24.080 7.150 7.200 60670.1 59190.4 165.849 5.2E-17 3.917 165.878 24.004 7.200 7.250 61177.8 59685.6 165.849 3.7E-17 3.945 165.818 23.929 7.250 7.300 61686.3 60181.7 165.848 4.3E-17 3.972 165.758 23.856 7.300 7.350 62195.6 60678.6 165.847 6.1E-17 3.999 165.697 23.784 7.350 7.400 62705.7 61176.3 165.846 6.0E-17 4.027 165.634 23.712 7.400 7.450 63216.6 61674.8 165.844 7.6E-17 4.054 165.570 23.642 7.450 7.500 63728.4 62174.0 165.841 4.0E-17 4.082 165.504 23.573 7.500 7.550 64240.9 62674.1 165.838-6.E-18 4.109 165.436 23.506 7.550 7.600 64754.3 63174.9 165.835 3.4E-17 4.137 165.367 23.441 7.600 7.650 65268.5 63676.6 165.831 4.0E-17 4.164 165.295 23.377 7.650 7.700 65783.5 64179.0 165.826 3.8E-17 4.192 165.223 23.314 7.700 7.750 66299.3 64682.3 165.821 6.5E-17 4.219 165.149 23.254 7.750 7.800 66816.0 65186.3 165.816 8.0E-18 4.247 165.082 23.188 7.800 7.850 67333.4 65691.1 165.810 2.1E-17 4.274 165.018 23.121 7.850 7.900 67851.5 66196.6 165.804 2.9E-17 4.302 164.952 23.055 7.900 7.950 68370.4 66702.8 165.797-1.E-18 4.329 164.885 22.990 7.950 8.000 68890.0 67209.7 165.790 8.4E-18 4.357 164.816 22.927 8.000 8.050 69410.3 67717.4 165.782 3.6E-17 4.384 164.746 22.864 8.050 8.100 69931.5 68225.8 165.774 5.6E-18 4.412 164.675 22.803 8.100 Philip Augener/Arne Falkenhorst Ship Design falkenhorst@tu-harburg.de 3/38

Exercise Ship Design 17. November 2014 8.150 70453.3 68734.9 165.766-9.E-18 4.439 164.601 22.743 8.150 8.200 70976.0 69244.8 165.757 1.5E-17 4.467 164.524 22.686 8.200 8.250 71499.4 69755.5 165.748 1.5E-18 4.494 164.448 22.629 8.250 +-----------------------------------------------------------------------+ T AP Dis.SW Dis.FW LCB TCB VCB LCF KM.T T FP Metre Ton Ton m.f.ap m.f.cl m.a.bl m.f.ap m.a.bl Metre +------+--------+--------+-------+-------+-------+-------+-------+------+ 8.300 72023.5 70266.9 165.738 2.2E-17 4.522 164.368 22.574 8.300 8.350 72548.5 70779.0 165.728 4.7E-17 4.549 164.287 22.520 8.350 8.400 73074.2 71291.9 165.717-2.E-17 4.577 164.206 22.467 8.400 8.450 73600.7 71805.6 165.706 2.8E-17 4.604 164.123 22.416 8.450 8.500 74128.0 72320.0 165.695 1.9E-17 4.632 164.040 22.365 8.500 8.550 74656.1 72835.2 165.683 1.0E-18 4.659 163.957 22.316 8.550 8.600 75185.0 73351.2 165.670 3.8E-17 4.687 163.873 22.268 8.600 8.650 75714.6 73867.9 165.657 4.5E-19 4.715 163.788 22.221 8.650 8.700 76245.0 74385.4 165.644-5.E-18 4.742 163.701 22.175 8.700 8.750 76776.3 74903.7 165.630 1.4E-17 4.770 163.611 22.131 8.750 8.800 77308.3 75422.7 165.616-2.E-18 4.797 163.519 22.088 8.800 8.850 77841.2 75942.6 165.601 1.9E-17 4.825 163.424 22.047 8.850 8.900 78374.8 76463.3 165.586-9.E-18 4.852 163.328 22.007 8.900 8.950 78909.3 76984.7 165.571 1.5E-17 4.880 163.227 21.968 8.950 9.000 79444.7 77507.0 165.554 1.6E-17 4.908 163.124 21.931 9.000 9.050 79981.0 78030.2 165.538-2.E-17 4.935 163.018 21.896 9.050 9.100 80518.1 78554.2 165.521 1.5E-17 4.963 162.908 21.862 9.100 9.150 81056.0 79079.1 165.503 9.1E-18 4.990 162.798 21.830 9.150 9.200 81594.9 79604.8 165.485-3.E-17 5.018 162.687 21.798 9.200 9.250 82134.7 80131.4 165.466 3.8E-17 5.046 162.573 21.768 9.250 9.300 82675.4 80658.9 165.447-1.E-17 5.073 162.454 21.740 9.300 9.350 83217.0 81187.3 165.427-5.E-18 5.101 162.340 21.711 9.350 9.400 83759.5 81716.5 165.406 5.3E-17 5.129 162.228 21.681 9.400 9.450 84302.8 82246.7 165.386-2.E-17 5.156 162.113 21.652 9.450 9.500 84847.1 82777.7 165.364 2.5E-17 5.184 161.999 21.623 9.500 9.550 85392.3 83309.5 165.342 3.0E-17 5.212 161.881 21.595 9.550 9.600 85938.3 83842.3 165.320-2.E-17 5.240 161.764 21.568 9.600 9.650 86485.3 84375.9 165.297 3.4E-17 5.267 161.645 21.541 9.650 9.700 87033.2 84910.5 165.274 1.5E-17 5.295 161.517 21.516 9.700 9.750 87582.1 85445.9 165.250-3.E-17 5.323 161.391 21.492 9.750 9.800 88131.9 85982.3 165.225 7.4E-17 5.351 161.265 21.469 9.800 9.850 88682.6 86519.6 165.200-1.E-17 5.378 161.134 21.448 9.850 9.900 89234.3 87057.9 165.175-4.E-17 5.406 160.989 21.428 9.900 9.950 89787.1 87597.2 165.149 5.4E-17 5.434 160.842 21.410 9.950 10.000 90340.9 88137.5 165.122-2.E-17 5.462 160.695 21.393 10.000 10.050 90895.7 88678.7 165.094-6.E-17 5.490 160.547 21.374 10.050 10.100 91451.5 89221.0 165.066 2.3E-17 5.518 160.404 21.355 10.100 10.150 92008.3 89764.2 165.038-2.E-17 5.545 160.270 21.334 10.150 10.200 92566.1 90308.4 165.009 1.6E-17 5.573 160.146 21.313 10.200 10.250 93124.8 90853.5 164.979 6.0E-18 5.601 159.998 21.295 10.250 10.300 93684.5 91399.5 164.949 3.0E-17 5.629 159.841 21.278 10.300 10.350 94245.3 91946.6 164.918 6.5E-17 5.657 159.708 21.259 10.350 Philip Augener/Arne Falkenhorst Ship Design falkenhorst@tu-harburg.de 4/38

Exercise Ship Design 17. November 2014 10.400 94806.9 92494.6 164.887 7.9E-18 5.685 159.586 21.239 10.400 10.450 95369.6 93043.5 164.855 4.2E-17 5.713 159.422 21.225 10.450 10.500 95933.2 93593.4 164.823 3.9E-17 5.741 159.286 21.208 10.500 10.550 96497.8 94144.2 164.790 9.8E-17 5.769 159.155 21.191 10.550 10.600 97063.6 94696.1 164.756 7.9E-17 5.797 158.958 21.183 10.600 10.650 97630.3 95249.1 164.722-6.E-17 5.825 158.841 21.166 10.650 10.700 98197.9 95802.8 164.688 6.1E-17 5.853 158.722 21.147 10.700 10.750 98766.5 96357.6 164.653 7.0E-17 5.881 158.531 21.136 10.750 10.800 99336.3 96913.4 164.618-6.E-17 5.909 158.369 21.122 10.800 10.850 99907.0 97470.2 164.582 6.2E-17 5.937 158.244 21.104 10.850 10.900 100478.8 98028.1 164.545 5.1E-17 5.965 158.023 21.094 10.900 10.950 101051.7 98587.0 164.508-5.E-17 5.993 157.908 21.076 10.950 11.000 101625.4 99146.8 164.470 7.2E-17 6.022 157.765 21.061 11.000 11.050 102200.4 99707.7 164.432 3.5E-17 6.050 157.505 21.054 11.050 +-----------------------------------------------------------------------+ T AP Dis.SW Dis.FW LCB TCB VCB LCF KM.T T FP Metre Ton Ton m.f.ap m.f.cl m.a.bl m.f.ap m.a.bl Metre +------+--------+--------+-------+-------+-------+-------+-------+------+ 11.100 102776.5 100269.8 164.392-1.E-17 6.078 157.390 21.037 11.100 11.150 103353.5 100832.6 164.353-9.E-18 6.106 157.264 21.021 11.150 11.200 103931.4 101396.5 164.313 7.5E-17 6.134 157.088 21.009 11.200 11.250 104510.4 101961.4 164.273-5.E-18 6.162 156.915 20.997 11.250 11.300 105090.7 102527.5 164.231-2.E-17 6.191 156.657 20.988 11.300 11.350 105672.0 103094.7 164.189 5.0E-17 6.219 156.490 20.976 11.350 11.400 106254.5 103663.0 164.146 3.0E-17 6.247 156.308 20.965 11.400 11.450 106838.0 104232.2 164.103-2.E-17 6.275 156.117 20.956 11.450 11.500 107422.7 104802.7 164.059 1.1E-17 6.304 155.872 20.946 11.500 11.550 108008.6 105374.3 164.014 6.5E-17 6.332 155.726 20.932 11.550 11.600 108595.5 105946.8 163.969-8.E-17 6.360 155.560 20.920 11.600 11.650 109183.6 106520.6 163.923 9.5E-18 6.389 155.311 20.911 11.650 11.700 109773.0 107095.5 163.876 1.2E-17 6.417 155.129 20.899 11.700 11.750 110363.3 107671.5 163.829-7.E-17 6.446 154.931 20.886 11.750 11.800 110954.7 108248.5 163.781 4.3E-17 6.474 154.785 20.871 11.800 11.850 111547.3 108826.6 163.733-2.E-17 6.502 154.509 20.862 11.850 11.900 112141.2 109406.0 163.684-4.E-17 6.531 154.302 20.852 11.900 11.950 112736.0 109986.5 163.633 2.7E-17 6.559 154.117 20.838 11.950 12.000 113332.2 110568.0 163.583-3.E-17 6.588 153.852 20.829 12.000 12.050 113929.7 111151.0 163.531-1.E-17 6.616 153.559 20.820 12.050 12.100 114528.5 111735.0 163.478 6.0E-17 6.645 153.231 20.815 12.100 12.150 115128.9 112320.9 163.424-3.E-17 6.673 153.020 20.808 12.150 12.200 115730.5 112907.8 163.369-5.E-18 6.702 152.749 20.805 12.200 12.250 116333.7 113496.3 163.314-9.E-17 6.731 152.481 20.804 12.250 12.300 116938.2 114086.0 163.257-1.E-17 6.759 152.270 20.803 12.300 12.350 117543.8 114676.9 163.200 5.1E-17 6.788 152.117 20.794 12.350 12.400 118150.5 115268.8 163.143-6.E-17 6.817 151.929 20.786 12.400 12.450 118759.2 115862.7 163.084-1.E-17 6.845 151.479 20.788 12.450 12.500 119369.7 116458.2 163.024 5.2E-17 6.874 151.318 20.786 12.500 12.550 119981.0 117054.7 162.964-8.E-17 6.903 151.237 20.779 12.550 12.600 120593.4 117652.0 162.904-1.E-17 6.932 151.169 20.771 12.600 Philip Augener/Arne Falkenhorst Ship Design falkenhorst@tu-harburg.de 5/38

Exercise Ship Design 17. November 2014 12.650 121206.5 118250.3 162.845-1.E-17 6.961 151.090 20.763 12.650 12.700 121820.6 118849.4 162.785-5.E-17 6.989 150.958 20.756 12.700 12.750 122436.6 119450.3 162.725-8.E-18 7.018 150.425 20.761 12.750 12.800 123054.5 120053.2 162.663-2.E-17 7.047 150.344 20.755 12.800 12.850 123673.4 120657.0 162.601-4.E-17 7.076 150.267 20.750 12.850 12.900 124293.0 121261.5 162.539 2.9E-18 7.105 150.195 20.745 12.900 12.950 124913.7 121867.0 162.478-6.E-17 7.134 150.089 20.741 12.950 13.000 125536.5 122474.7 162.414 1.1E-17 7.163 149.575 20.747 13.000 13.050 126161.0 123083.8 162.351 1.7E-17 7.192 149.483 20.745 13.050 13.100 126786.3 123694.0 162.287-6.E-17 7.221 149.399 20.743 13.100 13.150 127412.6 124305.0 162.224-5.E-17 7.250 149.344 20.739 13.150 13.200 128039.9 124917.0 162.160 2.8E-17 7.279 149.105 20.743 13.200 13.250 128669.6 125531.3 162.095-1.E-17 7.308 148.609 20.745 13.250 13.300 129301.0 126147.4 162.029-1.E-17 7.337 148.507 20.745 13.300 13.350 129933.6 126764.5 161.963-5.E-17 7.366 148.464 20.740 13.350 13.400 130566.8 127382.3 161.897-1.E-17 7.396 148.434 20.734 13.400 13.450 131200.8 128000.8 161.832-8.E-18 7.425 148.408 20.728 13.450 13.500 131835.5 128620.0 161.767-4.E-17 7.454 148.385 20.722 13.500 13.550 132471.5 129240.5 161.703-2.E-17 7.483 148.066 20.731 13.550 13.600 133109.4 129862.8 161.637-1.E-17 7.512 147.836 20.734 13.600 13.650 133749.5 130487.3 161.570-6.E-17 7.541 147.465 20.732 13.650 13.700 134390.8 131113.0 161.502-1.E-17 7.571 147.430 20.729 13.700 13.750 135033.0 131739.5 161.435 2.8E-18 7.600 147.401 20.725 13.750 13.800 135676.0 132366.8 161.369-4.E-17 7.629 147.394 20.720 13.800 13.850 136319.7 132994.8 161.302-2.E-17 7.658 147.246 20.723 13.850 +-----------------------------------------------------------------------+ HYDROSTATIC TABLES +-----------------------------------------------------------------------+ T AP Dis.SW Dis.FW LCB TCB VCB LCF KM.T T FP Metre Ton Ton m.f.ap m.f.cl m.a.bl m.f.ap m.a.bl Metre +------+--------+--------+-------+-------+-------+-------+-------+------+ 13.900 136964.8 133624.0 161.236-7.E-18 7.688 147.181 20.721 13.900 13.950 137610.8 134254.4 161.170-4.E-19 7.717 147.116 20.719 13.950 14.000 138257.9 134885.7 161.104-1.E-17 7.746 146.916 20.717 14.000 14.050 138906.3 135518.3 161.038-3.E-17 7.776 146.911 20.713 14.050 14.100 139555.4 136151.7 160.972-4.E-17 7.805 146.911 20.709 14.100 14.150 140205.3 136785.7 160.907-9.E-18 7.834 146.911 20.705 14.150 14.200 140855.9 137420.4 160.842 1.3E-17 7.863 146.917 20.700 14.200 14.250 141507.0 138055.7 160.778 1.2E-17 7.893 146.933 20.694 14.250 14.300 142159.0 138691.7 160.715-5.E-17 7.922 146.952 20.687 14.300 14.350 142811.5 139328.3 160.652 3.5E-17 7.951 146.974 20.680 14.350 14.400 143464.7 139965.5 160.590-1.E-17 7.981 146.997 20.673 14.400 14.450 144118.4 140603.3 160.528-3.E-17 8.010 147.021 20.667 14.450 14.500 144772.8 141241.8 160.467 8.5E-18 8.039 147.051 20.660 14.500 14.550 145427.8 141880.8 160.407 5.3E-18 8.068 147.082 20.653 14.550 14.600 146083.4 142520.4 160.347-3.E-17 8.097 147.116 20.646 14.600 14.650 146739.6 143160.5 160.288-1.E-17 8.127 147.151 20.640 14.650 14.700 147396.4 143801.3 160.229 2.1E-17 8.156 147.187 20.633 14.700 14.750 148053.7 144442.7 160.172-7.E-18 8.185 147.224 20.627 14.750 Philip Augener/Arne Falkenhorst Ship Design falkenhorst@tu-harburg.de 6/38

Exercise Ship Design 17. November 2014 14.800 148711.7 145084.6 160.114-6.E-19 8.214 147.263 20.621 14.800 14.850 149370.3 145727.0 160.058 2.4E-17 8.243 147.302 20.615 14.850 14.900 150029.4 146370.0 160.002 1.8E-17 8.272 147.344 20.609 14.900 14.950 150689.0 147013.8 159.947-5.E-17 8.302 147.388 20.603 14.950 15.000 151349.4 147658.0 159.892 3.4E-18 8.331 147.432 20.597 15.000 15.050 152010.3 148302.7 159.838 2.3E-17 8.360 147.479 20.592 15.050 15.100 152671.7 148948.0 159.784-4.E-17 8.389 147.529 20.586 15.100 15.150 153333.8 149594.0 159.732-2.E-17 8.418 147.580 20.581 15.150 15.200 153996.4 150240.4 159.679 8.8E-18 8.447 147.632 20.576 15.200 15.250 154659.6 150887.4 159.628-2.E-17 8.476 147.684 20.571 15.250 15.300 155323.3 151535.0 159.577-2.E-17 8.505 147.739 20.565 15.300 15.350 155987.6 152183.0 159.527-2.E-18 8.534 147.795 20.560 15.350 15.400 156652.5 152831.6 159.477-4.E-18 8.563 147.852 20.555 15.400 15.450 157317.9 153480.8 159.428-2.E-17 8.592 147.911 20.551 15.450 15.500 157983.8 154130.6 159.380-7.E-18 8.621 147.972 20.546 15.500 15.550 158650.4 154780.8 159.332-9.E-18 8.650 148.034 20.542 15.550 15.600 159317.5 155431.7 159.285-3.E-17 8.679 148.096 20.537 15.600 15.650 159985.0 156083.0 159.238 2.8E-17 8.708 148.159 20.533 15.650 15.700 160653.3 156735.0 159.192-5.E-19 8.737 148.223 20.529 15.700 15.750 161322.0 157387.4 159.147-2.E-17 8.766 148.289 20.525 15.750 15.800 161991.4 158040.3 159.102 1.8E-17 8.795 148.357 20.521 15.800 15.850 162661.2 158693.9 159.058 2.8E-17 8.824 148.426 20.518 15.850 15.900 163331.6 159348.0 159.014-4.E-17 8.853 148.495 20.514 15.900 15.950 164002.6 160002.5 158.971 4.6E-17 8.882 148.565 20.510 15.950 16.000 164674.0 160657.6 158.929 2.4E-17 8.911 148.636 20.506 16.000 +------+--------+--------+-------+-------+-------+-------+-------+------+ Philip Augener/Arne Falkenhorst Ship Design falkenhorst@tu-harburg.de 7/38

Page 12 AMENDMENTS TO THE INTERNATIONAL CONVENTION FOR THE SAFETY OF LIFE AT SEA, 1974, AS AMENDED CHAPTER II-1 CONSTRUCTION - STRUCTURE, SUBDIVISION AND STABILITY, MACHINERY AND ELECTRICAL INSTALLATIONS 1 The existing text of parts A, B and B-1 of the chapter is replaced by the following: PART A GENERAL Regulation 1 Application 1.1 Unless expressly provided otherwise, this chapter shall apply to ships the keels of which are laid or which are at a similar stage of construction on or after 1 January 2009. 1.2 For the purpose of this chapter, the term a similar stage of construction means the stage at which:.1 construction identifiable with a specific ship begins; and.2 assembly of that ship has commenced comprising at least 50 tonnes or one per cent of the estimated mass of all structural material, whichever is less. 1.3 For the purpose of this chapter:.1 the expression ships constructed means ships the keels of which are laid or which are at a similar stage of construction;.2 the expression all ships means ships constructed before, on or after 1 January 2009;.3 a cargo ship, whenever built, which is converted to a passenger ship shall be treated as a passenger ship constructed on the date on which such a conversion commences;.4 the expression alterations and modifications of a major character means, in the context of cargo ship subdivision and stability, any modification to the construction which affects the level of subdivision of that ship. Where a cargo ship is subject to such modification, it shall be demonstrated that the A/R ratio calculated for the ship after such modifications is not less than the A/R ratio calculated for the ship before the modification. However, in those cases where the ship s A/R ratio before modification is equal to or greater than unity, it is only necessary that the ship after modification has an A value which is not less than R, calculated for the modified ship.

Page 13 2 Unless expressly provided otherwise, for ships constructed before 1 January 2009, the Administration shall ensure that the requirements which are applicable under chapter II-1 of the International Convention for the Safety of Life at Sea, 1974, as amended by resolutions MSC.1(XLV), MSC.6(48), MSC.11(55), MSC.12(56), MSC.13(57), MSC.19(58), MSC.26(60), MSC.27(61), Resolution 1 of the 1995 SOLAS Conference, MSC.47(66), MSC.57(67), MSC.65(68), MSC.69(69), MSC.99(73), MSC.134(76), MSC.151(78) and MSC.170(79) are complied with. 3 All ships which undergo repairs, alterations, modifications and outfitting related thereto shall continue to comply with at least the requirements previously applicable to these ships. Such ships, if constructed before the date on which any relevant amendments enter into force, shall, as a rule, comply with the requirements for ships constructed on or after that date to at least the same extent as they did before undergoing such repairs, alterations, modifications or outfitting. Repairs, alterations and modifications of a major character and outfitting related thereto shall meet the requirements for ships constructed on or after the date on which any relevant amendments enter into force, in so far as the Administration deems reasonable and practicable. 4 The Administration of a State may, if it considers that the sheltered nature and conditions of the voyage are such as to render the application of any specific requirements of this chapter unreasonable or unnecessary, exempt from those requirements individual ships or classes of ships entitled to fly the flag of that State which, in the course of their voyage, do not proceed more than 20 miles from the nearest land. 5 In the case of passenger ships which are employed in special trades for the carriage of large numbers of special trade passengers, such as the pilgrim trade, the Administration of the State whose flag such ships are entitled to fly, if satisfied that it is impracticable to enforce compliance with the requirements of this chapter, may exempt such ships from those requirements, provided that they comply fully with the provisions of:.1 the rules annexed to the Special Trade Passenger Ships Agreement, 1971; and.2 the rules annexed to the Protocol on Space Requirements for Special Trade Passenger Ships, 1973. Regulation 2 Definitions For the purpose of this chapter, unless expressly provided otherwise: 1 Subdivision length (L s ) of the ship is the greatest projected moulded length of that part of the ship at or below deck or decks limiting the vertical extent of flooding with the ship at the deepest subdivision draught. 2 Mid-length is the mid-point of the subdivision length of the ship. 3 Aft terminal is the aft limit of the subdivision length. 4 Forward terminal is the forward limit of the subdivision length.

Page 14 5 Length (L) is the length as defined in the International Convention on Load Lines in force. 6 Freeboard deck is the deck as defined in the International Convention on Load Lines in force. 7 Forward perpendicular is the forward perpendicular as defined in the International Convention on Load Lines in force. 8 Breadth (B) is the greatest moulded breadth of the ship at or below the deepest subdivision draught. 9 Draught (d) is the vertical distance from the keel line at mid-length to the waterline in question. 10 Deepest subdivision draught (d s ) is the waterline which corresponds to the summer load line draught of the ship. 11 Light service draught (d l ) is the service draught corresponding to the lightest anticipated loading and associated tankage, including, however, such ballast as may be necessary for stability and/or immersion. Passenger ships should include the full complement of passengers and crew on board. 12 Partial subdivision draught (d p ) is the light service draught plus 60% of the difference between the light service draught and the deepest subdivision draught. 13 Trim is the difference between the draught forward and the draught aft, where the draughts are measured at the forward and aft terminals respectively, disregarding any rake of keel. 14 Permeability (µ) of a space is the proportion of the immersed volume of that space which can be occupied by water. 15 Machinery spaces are spaces between the watertight boundaries of a space containing the main and auxiliary propulsion machinery, including boilers, generators and electric motors primarily intended for propulsion. In the case of unusual arrangements, the Administration may define the limits of the machinery spaces. 16 Weathertight means that in any sea conditions water will not penetrate into the ship. 17 Watertight means having scantlings and arrangements capable of preventing the passage of water in any direction under the head of water likely to occur in intact and damaged conditions. In the damaged condition, the head of water is to be considered in the worst situation at equilibrium, including intermediate stages of flooding. 18 Design pressure means the hydrostatic pressure for which each structure or appliance assumed watertight in the intact and damage stability calculations is designed to withstand.

Page 15 19 Bulkhead deck in a passenger ship means the uppermost deck at any point in the subdivision length (L s ) to which the main bulkheads and the ship s shell are carried watertight and the lowermost deck from which passenger and crew evacuation will not be impeded by water in any stage of flooding for damage cases defined in regulation 8 and in part B-2 of this chapter. The bulkhead deck may be a stepped deck. In a cargo ship the freeboard deck may be taken as the bulkhead deck. 20 Deadweight is the difference in tonnes between the displacement of a ship in water of a specific gravity of 1.025 at the draught corresponding to the assigned summer freeboard and the lightweight of the ship. 21 Lightweight is the displacement of a ship in tonnes without cargo, fuel, lubricating oil, ballast water, fresh water and feedwater in tanks, consumable stores, and passengers and crew and their effects. 22 Oil tanker is the oil tanker defined in regulation 1 of Annex I of the Protocol of 1978 relating to the International Convention for the Prevention of Pollution from Ships, 1973. 23 Ro-ro passenger ship means a passenger ship with ro-ro spaces or special category spaces as defined in regulation II-2/3. 24 Bulk carrier means a bulk carrier as defined in regulation XII/1.1. 25 Keel line is a line parallel to the slope of the keel passing amidships through:.1 the top of the keel at centreline or line of intersection of the inside of shell plating with the keel if a bar keel extends below that line, on a ship with a metal shell; or.2 in wood and composite ships, the distance is measured from the lower edge of the keel rabbet. When the form at the lower part of the midship section is of a hollow character, or where thick garboards are fitted, the distance is measured from the point where the line of the flat of the bottom continued inward intersects the centreline amidships. 26 Amidship is at the middle of the length (L). Regulation 3 Definitions relating to parts C, D and E For the purpose of parts C, D and E, unless expressly provided otherwise: 1 Steering gear control system is the equipment by which orders are transmitted from the navigating bridge to the steering gear power units. Steering gear control systems comprise transmitters, receivers, hydraulic control pumps and their associated motors, motor controllers, piping and cables.

Page 16 2 Main steering gear is the machinery, rudder actuators, steering gear, power units, if any, and ancillary equipment and the means of applying torque to the rudder stock (e.g. tiller or quadrant) necessary for effecting movement of the rudder for the purpose of steering the ship under normal service conditions. 3 Steering gear power unit is:.1 in the case of electric steering gear, an electric motor and its associated electrical equipment;.2 in the case of electrohydraulic steering gear, an electric motor and its associated electrical equipment and connected pump; or.3 in the case of other hydraulic steering gear, a driving engine and connected pump. 4 Auxiliary steering gear is the equipment other than any part of the main steering gear necessary to steer the ship in the event of failure of the main steering gear but not including the tiller, quadrant or components serving the same purpose. 5 Normal operational and habitable condition is a condition under which the ship as a whole, the machinery, services, means and aids ensuring propulsion, ability to steer, safe navigation, fire and flooding safety, internal and external communications and signals, means of escape, and emergency boat winches, as well as the designed comfortable conditions of habitability are in working order and functioning normally. 6 Emergency condition is a condition under which any services needed for normal operational and habitable conditions are not in working order due to failure of the main source of electrical power. 7 Main source of electrical power is a source intended to supply electrical power to the main switchboard for distribution to all services necessary for maintaining the ship in normal operational and habitable conditions. 8 Dead ship condition is the condition under which the main propulsion plant, boilers and auxiliaries are not in operation due to the absence of power. 9 Main generating station is the space in which the main source of electrical power is situated. 10 Main switchboard is a switchboard which is directly supplied by the main source of electrical power and is intended to distribute electrical energy to the ship's services. 11 Emergency switchboard is a switchboard which in the event of failure of the main electrical power supply system is directly supplied by the emergency source of electrical power or the transitional source of emergency power and is intended to distribute electrical energy to the emergency services. 12 Emergency source of electrical power is a source of electrical power, intended to supply the emergency switchboard in the event of a failure of the supply from the main source of electrical power.

Page 17 13 Power actuating system is the hydraulic equipment provided for supplying power to turn the rudder stock, comprising a steering gear power unit or units, together with the associated pipes and fittings, and a rudder actuator. The power actuating systems may share common mechanical components (i.e. tiller, quadrant and rudder stock) or components serving the same purpose. 14 Maximum ahead service speed is the greatest speed which the ship is designed to maintain in service at sea at the deepest sea-going draught. 15 Maximum astern speed is the speed which it is estimated the ship can attain at the designed maximum astern power at the deepest sea-going draught. 16 Machinery spaces are all machinery spaces of category A and all other spaces containing propelling machinery, boilers, oil fuel units, steam and internal combustion engines, generators and major electrical machinery, oil filling stations, refrigerating, stabilizing, ventilation and air conditioning machinery, and similar spaces, and trunks to such spaces. 17 Machinery spaces of category A are those spaces and trunks to such spaces which contain:.1 internal combustion machinery used for main propulsion;.2 internal combustion machinery used for purposes other than main propulsion where such machinery has in the aggregate a total power output of not less than 375 kw; or.3 any oil-fired boiler or oil fuel unit. 18 Control stations are those spaces in which the ship's radio or main navigating equipment or the emergency source of power is located or where the fire recording or fire control equipment is centralized. 19 Chemical tanker is a cargo ship constructed or adapted and used for the carriage in bulk of any liquid product listed in either:.1 chapter 17 of the International Code for the Construction and Equipment of Ships Carrying Dangerous Chemicals in Bulk adopted by the Maritime Safety Committee by resolution MSC.4(48), hereinafter referred to as the International Bulk Chemical Code, as may be amended by the Organization; or.2 chapter VI of the Code for the Construction and Equipment of Ships Carrying Dangerous Chemicals in Bulk adopted by the Assembly of the Organization by resolution A.212(VII), hereinafter referred to as the Bulk Chemical Code, as has been or may be amended by the Organization, whichever is applicable.

Page 18 20 Gas carrier is a cargo ship constructed or adapted and used for the carriage in bulk of any liquefied gas or other products listed in either:.1 chapter 19 of the International Code for the Construction and Equipment of Ships Carrying Liquefied Gases in Bulk adopted by the Maritime Safety Committee by resolution MSC.5(48), hereinafter referred to as the International Gas Carrier Code, as may be amended by the Organization; or.2 chapter XIX of the Code for the Construction and Equipment of Ships Carrying Liquefied Gases in Bulk adopted by the Organization by resolution A.328(IX), hereinafter referred to as the Gas Carrier Code, as has been or may be amended by the Organization, whichever is applicable. PART B SUBDIVISION AND STABILITY Regulation 4 General 1 The damage stability requirements in parts B-1 through B-4 shall apply to cargo ships of 80 m in length (L) and upwards and to all passenger ships regardless of length but shall exclude those cargo ships which are shown to comply with subdivision and damage stability regulations in other instruments developed by the Organization. 2 The Administration may, for a particular ship or group of ships, accept alternative methodologies if it is satisfied that at least the same degree of safety as represented by these regulations is achieved. Any Administration which allows such alternative methodologies shall communicate to the Organization particulars thereof. 3 Ships shall be as efficiently subdivided as is possible having regard to the nature of the service for which they are intended. The degree of subdivision shall vary with the Cargo ships shown to comply with the following regulations may be excluded from the application of part B-1:.1 Annex I to MARPOL 73/78, except OBO ships with type B freeboards are not excluded;.2 International Bulk Chemical Code;.3 International Gas Carrier Code;.4 Guidelines for the design and construction of offshore supply vessels (resolution A.469(XII));.5 Code of Safety for Special Purpose Ships (resolution A.534(13), as amended);.6 Damage stability requirements of regulation 27 of the 1966 Load Lines Convention as applied in compliance with resolutions A.320(IX) and A.514(13), provided that in the case of cargo ships to which regulation 27(9) applies, main transverse watertight bulkheads, to be considered effective, are spaced according to paragraph (12)(f) of resolution A.320(IX), except ships intended for the carriage of deck cargo; and.7 Damage stability requirements of regulation 27 of the 1988 Load Lines Protocol, except ships intended for the carriage of deck cargo.

Page 19 subdivision length (L s ) of the ship and with the service, in such manner that the highest degree of subdivision corresponds with the ships of greatest subdivision length (L s ), primarily engaged in the carriage of passengers. 4 Where it is proposed to fit decks, inner skins or longitudinal bulkheads of sufficient tightness to seriously restrict the flow of water, the Administration shall be satisfied that proper consideration is given to beneficial or adverse effects of such structures in the calculations. PART B-1 STABILITY Regulation 5 Intact stability information * 1 Every passenger ship regardless of size and every cargo ship having a length (L) of 24 m and upwards, shall be inclined upon its completion and the elements of its stability determined. 2 The Administration may allow the inclining test of an individual cargo ship to be dispensed with provided basic stability data are available from the inclining test of a sister ship and it is shown to the satisfaction of the Administration that reliable stability information for the exempted ship can be obtained from such basic data, as required by regulation 5-1. A weight survey shall be carried out upon completion and the ship shall be inclined whenever in comparison with the data derived from the sister ship, a deviation from the lightship displacement exceeding 1% for ships of 160 m or more in length and 2% for ships of 50 m or less in length and as determined by linear interpolation for intermediate lengths or a deviation from the lightship longitudinal centre of gravity exceeding 0.5% of L s is found. 3 The Administration may also allow the inclining test of an individual ship or class of ships especially designed for the carriage of liquids or ore in bulk to be dispensed with when reference to existing data for similar ships clearly indicates that due to the ship s proportions and arrangements more than sufficient metacentric height will be available in all probable loading conditions. 4 Where any alterations are made to a ship so as to materially affect the stability information supplied to the master, amended stability information shall be provided. If necessary the ship shall be re-inclined. The ship shall be re-inclined if anticipated deviations exceed one of the values specified in paragraph 5. 5 At periodical intervals not exceeding five years, a lightweight survey shall be carried out on all passenger ships to verify any changes in lightship displacement and longitudinal centre of gravity. The ship shall be re-inclined whenever, in comparison with the approved stability information, a deviation from the lightship displacement exceeding 2% or a deviation of the longitudinal centre of gravity exceeding 1% of L s is found or anticipated. * Refer to the Code on Intact Stability for All Types of Ships covered by IMO Instruments, adopted by the Organization by resolution A.749(18).

Page 20 6 Every ship shall have scales of draughts marked clearly at the bow and stern. In the case where the draught marks are not located where they are easily readable, or operational constraints for a particular trade make it difficult to read the draught marks, then the ship shall also be fitted with a reliable draught indicating system by which the bow and stern draughts can be determined. Regulation 5-1 Stability information to be supplied to the master 1 The master shall be supplied with such information satisfactory to the Administration as is necessary to enable him by rapid and simple processes to obtain accurate guidance as to the stability of the ship under varying conditions of service. A copy of the stability information shall be furnished to the Administration. 2 The information should include:.1 curves or tables of minimum operational metacentric height (GM) versus draught which assures compliance with the relevant intact and damage stability requirements, alternatively corresponding curves or tables of the maximum allowable vertical centre of gravity (KG) versus draught, or with the equivalents of either of these curves;.2 instructions concerning the operation of cross-flooding arrangements; and.3 all other data and aids which might be necessary to maintain the required intact stability and stability after damage. 3 The stability information shall show the influence of various trims in cases where the operational trim range exceeds +/- 0.5% of L s. 4 For ships which have to fulfil the stability requirements of part B-1, information referred to in paragraph 2 are determined from considerations related to the subdivision index, in the following manner: Minimum required GM (or maximum permissible vertical position of centre of gravity KG) for the three draughts d s, d p and d l are equal to the GM (or KG values) of corresponding loading cases used for the calculation of survival factor s i. For intermediate draughts, values to be used shall be obtained by linear interpolation applied to the GM value only between the deepest subdivision draught and the partial subdivision draught and between the partial load line and the light service draught respectively. Intact stability criteria will also be taken into account by retaining for each draft the maximum among minimum required GM values or the minimum of maximum permissible KG values for both criteria. If the subdivision index is calculated for different trims, several required GM curves will be established in the same way. 5 When curves or tables of minimum operational metacentric height (GM) versus draught are not appropriate, the master should ensure that the operating condition does Refer also to the Guidelines for the preparation of intact stability information (MSC/Circ.456); Guidance on the intact stability of existing tankers during transfer operations (MSC/Circ.706); and the Revised guidance to the master for avoiding dangerous situations in following and quartering seas (MSC.1/Circ.1228).

Page 21 not deviate from a studied loading condition, or verify by calculation that the stability criteria are satisfied for this loading condition. Regulation 6 Required subdivision index R * 1 The subdivision of a ship is considered sufficient if the attained subdivision index A, determined in accordance with regulation 7, is not less than the required subdivision index R calculated in accordance with this regulation and if, in addition, the partial indices A s, A p and A l are not less than 0.9R for passenger ships and 0.5R for cargo ships. 2 For all ships to which the damage stability requirements of this chapter apply, the degree of subdivision to be provided shall be determined by the required subdivision index R, as follows:.1 In the case of cargo ships greater than 100 m in length (L s ): R = 128 1 Ls + 152.2 In the case of cargo ships not less than 80 m in length (L s ) and not greater than 100 m in length (L s ): Ls Ro R = 1 [1/(1+ )] 100 1 R o where R o is the value R as calculated in accordance with the formula in subparagraph.1..3 In the case of passenger ships: R = where: 1 5,000 L + 2.5N 15,225 s + N = N 1 + 2N 2 N 1 = number of persons for whom lifeboats are provided N 2 = number of persons (including officers and crew) the ship is permitted to carry in excess of N 1..4 Where the conditions of service are such that compliance with paragraph 2.3 of this regulation on the basis of N = N 1 + 2N 2 is impracticable and where the Administration considers that a suitably * The Maritime Safety Committee, in adopting the regulations contained in parts B to B-4, invited Administrations to note that the regulations should be applied in conjunction with the explanatory notes developed by the Organization in order to ensure their uniform application.

Page 22 reduced degree of hazard exists, a lesser value of N may be taken but in no case less than N = N 1 + N 2. Regulation 7 Attained subdivision index A 1 The attained subdivision index A is obtained by the summation of the partial indices A s, A p and A l, (weighted as shown) calculated for the draughts d s, d p and d l defined in regulation 2 in accordance with the following formula: A = 0.4A s + 0.4A p + 0.2A l Each partial index is a summation of contributions from all damage cases taken in consideration, using the following formula: where: A = Σ p i s i i represents each compartment or group of compartments under consideration, p i s i accounts for the probability that only the compartment or group of compartments under consideration may be flooded, disregarding any horizontal subdivision, as defined in regulation 7-1, accounts for the probability of survival after flooding the compartment or group of compartments under consideration, and includes the effect of any horizontal subdivision, as defined in regulation 7-2. 2 In the calculation of A, the level trim shall be used for the deepest subdivision draught and the partial subdivision draught. The actual service trim shall be used for the light service draught. If in any service condition, the trim variation in comparison with the calculated trim is greater than 0.5% of L s, one or more additional calculations of A are to be submitted for the same draughts but different trims so that, for all service conditions, the difference in trim in comparison with the reference trim used for one calculation will be less than 0.5% of L s. 3 When determining the positive righting lever (GZ) of the residual stability curve, the displacement used should be that of the intact condition. That is, the constant displacement method of calculation should be used. 4 The summation indicated by the above formula shall be taken over the ship s subdivision length (L s ) for all cases of flooding in which a single compartment or two or more adjacent compartments are involved. In the case of unsymmetrical arrangements, the calculated A value should be the mean value obtained from calculations involving both sides. Alternatively, it should be taken as that corresponding to the side which evidently gives the least favourable result. 5 Wherever wing compartments are fitted, contribution to the summation indicated by the formula shall be taken for all cases of flooding in which wing compartments are

Page 23 involved. Additionally, cases of simultaneous flooding of a wing compartment or group of compartments and the adjacent inboard compartment or group of compartments, but excluding damage of transverse extent greater than one half of the ship breadth B, may be added. For the purpose of this regulation, transverse extent is measured inboard from ship s side, at right angle to the centreline at the level of the deepest subdivision draught. 6 In the flooding calculations carried out according to the regulations, only one breach of the hull and only one free surface need to be assumed. The assumed vertical extent of damage is to extend from the baseline upwards to any watertight horizontal subdivision above the waterline or higher. However, if a lesser extent of damage will give a more severe result, such extent is to be assumed. 7 If pipes, ducts or tunnels are situated within the assumed extent of damage, arrangements are to be made to ensure that progressive flooding cannot thereby extend to compartments other than those assumed flooded. However, the Administration may permit minor progressive flooding if it is demonstrated that its effects can be easily controlled and the safety of the ship is not impaired. Regulation 7-1 Calculation of the factor p i 1 The factor p i for a compartment or group of compartments shall be calculated in accordance with paragraphs 1.1 and 1.2 using the following notations: j = the aftmost damage zone number involved in the damage starting with No.1 at the stern; n = the number of adjacent damage zones involved in the damage; k = is the number of a particular longitudinal bulkhead as barrier for transverse penetration in a damage zone counted from shell towards the centre line. The shell has k = 0; x1 = the distance from the aft terminal of L s to the aft end of the zone in question; x2 = the distance from the aft terminal of L s to the forward end of the zone in question; b = the mean transverse distance in metres measured at right angles to the centreline at the deepest subdivision loadline between the shell and an assumed vertical plane extended between the longitudinal limits used in calculating the factor p i and which is a tangent to, or common with, all or part of the outermost portion of the longitudinal bulkhead under consideration. This vertical plane shall be so orientated that the mean transverse distance to the shell is a maximum, but not more than twice the least distance between the plane and the shell. If the upper part of a longitudinal bulkhead is below the deepest subdivision loadline the vertical plane used for determination of b is assumed to extend upwards to the deepest subdivision waterline. In any case, b is not to be taken greater than B/2.

Page 24 If the damage involves a single zone only: p i = p(x1 j,x2 j ) [r(x1 j,x2 j,b k ) - r(x1 j,x2 j,b k-1 )] If the damage involves two adjacent zones: p i = p(x1 j,x2 j+1 ) [r(x1 j,x2 j+1,b k ) - r(x1 j,x2 j+1,b k-1 )] - p(x1 j,x2 j ) [r(x1 j,x2 j,b k ) - r(x1 j,x2 j,b k-1 )] - p(x1 j+1,x2 j+1 ) [r(x1 j+1,x2 j+1,b k ) - r(x1 j+1,x2 j+1,b k-1 )] If the damage involves three or more adjacent zones: p i = p(x1 j,x2 j+n-1 ) [r(x1 j,x2 j+n-1,b k ) - r(x1 j,x2 j+n-1,b k-1 )] - p(x1 j,x2 j+n-2 ) [r(x1 j,x2 j+n-2,b k ) - r(x1 j,x2 j+n-2,b k-1 )] - p(x1 j+1,x2 j+n-1 ) [r(x1 j+1,x2 j+n-1,b k ) - r(x1 j+1,x2 j+n-1,b k-1 )] + p(x1 j+1,x2 j+n-2 ) [r(x1 j+1,x2 j+n-2,b k ) - r(x1 j+1,x2 j+n-2,b k-1 )] and where r(x1, x2, b 0 ) = 0 1.1 The factor p(x1, x2) is to be calculated according to the following formulae: Overall normalized max damage length: J max = 10/33 Knuckle point in the distribution: J kn = 5/33 Cumulative probability at J kn : p k = 11/12 Maximum absolute damage length: l max = 60 m Length where normalized distribution ends: L * = 260 m Probability density at J = 0: pk 1 pk b = 0 2 J kn J max J * When L s L : J m = min J max, l max L s kn J k = ( 1 2 p ) 1 1+ k b0 J J m + 2 b 0 m 1 + b 4 2 0 J 2 m b 12 = b 0 * When L s > L : * J m min J max = max, * l L

Page 25 J ( 1 2 p ) 1 b * * 1 1+ k b0 J m + * J m 4 k = + 2 b0 2 0 J * 2 m J m = J * m L s L * J k = J * k L s L * b 12 p = 2 J k k 1 pk J J m k b 1 p k 11 = 4 2 m k k 2 ( J J ) J J p k k b 21 = 2 1 p ( J J ) 2 m k k b22 = b21j m The non-dimensional damage length: J = ( x2 x1) L s The normalized length of a compartment or group of compartments: J n is to be taken as the lesser of J and J m 1.1.1 Where neither limits of the compartment or group of compartments under consideration coincides with the aft or forward terminals: J = J k : 1 p ( x1, x2) = p + 6 ( b J ) 2 1 = J 11 3b12 J>J k : p 1 3 1 2 1 2 2 1 3 3 ( b J b ) J + b JJ b ( J J ) 3 ( x1, x2) = p2 = b11j k + 11 12 k 12 k 21 n k 2 2 ( b J b )( J J ) + b J ( J J ) + 21 22 n k 22 1.1.2 Where the aft limit of the compartment or group of compartments under consideration coincides with the aft terminal or the forward limit of the compartment or group of compartments under consideration coincides with the forward terminal: n 3 k