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					                                                    Sheet1



      Economical speed based on fuel oil price and market      $/day

                                                 Variables
      Input in yellow area according to ship and voyage            60,000

       TC equivalent at service speed*                 22,000
       Bunker price                                       700
       Distance return                                 22,653
                                                                   48,000
      Assumption:
      Operation costs                                  12,500
      Emission factor HFO to CO2                           3.1
       Bunker consumption at 14.5 knots* - laden            92     36,000
       Bunker Fuel consumption ballast knot - 15.5 knots    85
       Cargo size - tonnes                            280,000
      Emission factor HFO to CO2                           3.1
      Calculated economical speed                                  24,000
      Economical speed laden                               9.7
      Economical speed ballast knots                     10.5
      Economical speed capital costs
                                                                   12,000
      TC equivanlent laden                             38,495
      TC equivanlent laden -charterers' cap costs      30,652
      Economical speed ballast knots                   36,713
       Increase TC result per day          53%       11,683             0
       Speed basis at 90%MCR laden                       14.5             7.0

      Speed basis at 90%MCR ballast                      15.5
      Oil price                                      120
       Capital costs                                 5%




                            TC equivalent    Bunker consumption
                                      TCE
       Speed             TCE Laden Ballast             Laden      Ballast




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                                          Sheet1


           7.0           34465    31326        719    544
           7.5           35778    32695        827    625
          8.0            36853    33884        942     713
          8.5            37675    34881       1,066    806
          9.0            38228    35675       1,198    906
          9.5            38495    36252       1,337   1,011
          10.0           38462    36603       1,485   1,123
          10.5           38112    36713       1,640   1,240
          11.0           37428    36572       1,804   1,364
          11.5           36397    36167       1,975   1,494
          12.0           35001    35487       2,155   1,630
          12.5           33224    34519       2,343   1,772
          13.0           31052    33251       2,539   1,921
          13.5           28468    31672       2,744   2,076
          14.0           25456    29769       2,957   2,237
          14.5           22000    27531       3,178   2,404
          15.0           18085    24945       3,408   2,578
          15.5           13694    21838       3,646   2,758
          16.0            8813    18683       3,893   2,945
          16.5            3424    14983       4,148   3,138
          17.0            -2487   10887       4,412   3,337
          17.5            -8937   6384        4,685   3,544
          18.0           -15942   1462        4,966   3,756
          18.5




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                                                      Sheet1


 $/day                                     TC Equivalent, Emission and Operation costs
         60,000




         48,000




         36,000




         24,000




                                                                          CO2 emission
         12,000
                                                                          TCE laden reduced by cap costs

                                                                          TCE Ballast

                                                                          TCE Laden

                   0
                       7.0        8.0           9.0            10.0      11.0         12.0           13.0        14.0



                   Reduction CO2 emission per tonne-mile 12 versus 14 knots - %*
                                                                               - 27%




       Bunker cost                      Net freight             Days             Emission Tonne miles

  Laden             Ballast       Laden           Ballast      Laden   Ballast            Tonne miles




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                                                       Sheet1


 502,989           380,451       2,895,517 2,4622,555,091       69.4   69.4   3,927    3,171,420,000
 578,599           437,641       2,901,476 2,2982,560,349       64.9   64.9   4,517    3,171,420,000
 659,669           498,960       2,907,434   2,1342,565,607     61.0   61.0   5,150    3,171,420,000
 746,231           564,434       2,913,393   1,9702,570,865     57.5   57.5   5,826    3,171,420,000
 838,316           634,085       2,919,352   1,8062,576,123     54.4   54.4   6,545    3,171,420,000
 935,956           707,938       2,925,310   1,6412,581,381     51.7   51.7   7,307    3,171,420,000
1,039,182          786,017       2,931,269   1,4772,586,639     49.2   49.2   8,113    3,171,420,000
1,148,028          868,345       2,937,228   1,3132,591,897     46.9   46.9   8,962    3,171,420,000
1,262,523          954,947       2,943,186   1,1492,597,155     44.9   44.9   9,856    3,171,420,000
1,382,700         1,045,846      2,949,145    985 2,602,413     43.0   43.0   10,795   3,171,420,000
1,508,590         1,141,067      2,955,103    821 2,607,671     41.3   41.3   11,777   3,171,420,000
1,640,226         1,240,634      2,961,062    657 2,612,929     39.8   39.8   12,805   3,171,420,000
1,777,638         1,344,570      2,967,021    492 2,618,188     38.3   38.3   13,878   3,171,420,000
1,920,859         1,452,899      2,972,979    328 2,623,446     37.0   37.0   14,996   3,171,420,000
2,069,920         1,565,646      2,978,938    164 2,628,704     35.7   35.7   16,160   3,171,420,000
2,224,853         1,682,835      2,984,897     0 2,633,962      34.5   34.5   17,369   3,171,420,000
2,385,690         1,804,488      2,990,855    164 2,639,220     33.5   33.5   18,625   3,171,420,000
2,552,462         1,930,631      2,996,814    328 2,644,478     32.4   32.4   19,927   3,171,420,000
2,725,201         2,061,287      3,002,772    492 2,649,736     31.5   31.5   21,275   3,171,420,000
2,903,938         2,196,481      3,008,731    657 2,654,994     30.6   30.6   22,671   3,171,420,000
3,088,706         2,336,235      3,014,690    821 2,660,252     29.8   29.8   24,113   3,171,420,000
3,279,536         2,480,575      3,020,648    985 2,665,510     29.0   29.0   25,603   3,171,420,000
3,476,459         2,629,524      3,026,607   1,1492,670,768     28.2   28.2   27,140   3,171,420,000
                                                                27.5   27.5




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                                                         Sheet1



s                                                 tonnes emission

                                                                  25,000

                                                                                   A vessels income is calculated base
                                                                                   The net freight is a function of World

                                                                  20,000
                                                                                   Net freight= Grossfreight -commision


                                                                                   The equation can then be written

                                                                  15,000
                                                                                   x   = speed
                                                                                   f(x) = time charter as a function of sp


                                                                  10,000

                                                                                   f(x) = Net freight/days(x)-Bunkercos


                                                                                   The netfreight is based on a basis s
                                                                  5,000
ed by cap costs


                                                                                   Net freight/day(x) = TCbasis*x/vo+B

                                                               0
                                                                  Speed




      13.0                14.0            15.0   16.0      17.0




                          Capital cost
               Emission/                        (Vx/
              Tonne miles Tonne miles Speed % Vbasis)^                     Laden
                                                 3




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                                               Sheet1


      0.0012             1,137,305   48%    0.12        18082     517360
      0.0014              985,664    52%    0.15        20596
      0.0016             852,979      55%   0.18        22868
      0.0018             735,903      59%   0.22        24882
      0.0021             631,836      62%   0.26        26621
      0.0023             538,723      66%   0.30        28071
      0.0026             454,922      69%   0.35        29214
      0.0028             379,102      72%   0.40        30036
      0.0031             310,174      76%   0.45        30521
      0.0034             247,240      79%   0.52        30652
      0.0037             189,551      83%   0.58        30414
      0.0040             136,477      86%   0.65        29791
      0.0044              87,485      90%   0.73        28768
      0.0047              42,122      93%   0.82        27328
      0.0051                 0        97%   0.90        25456
      0.0055              -39,217    100%   1.00        23135   3,054,464
      0.0059              -75,820    103%   1.10        20351
      0.0063             -110,062    107%   1.21        17086
      0.0067             -142,163    110%   1.33        13327
      0.0071             -172,319    114%   1.45        9055
      0.0076             -200,701    117%   1.58        4257
      0.0081             -227,461    121%   1.71        -1085
      0.0086             -252,734    124%   1.86        -6985




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                                                        Sheet1




 ls income is calculated based on WS taking into account cargo, volume, bunker cost, voyage cost , port cost, e
 freight is a function of World scale points and based on a certain speed V0. At that speed the vessel has an e


ght= Grossfreight -commision


 ation can then be written




me charter as a function of speed




 et freight/days(x)-Bunkercost(x)-Voyage cost/day(x)


 reight is based on a basis speed basis consumption and basis voyage cost and can be written as




ght/day(x) = TCbasis*x/vo+BCbasis*BP*x/v0+Voyage cost/day(x)


           where


           v0                       = basis speed should be chosen as the speed at 90 %MCR
           TCbasis = Time charter based on v0
           BCbasis = Bunker consumption based on v0
           BP              = Bunker price
           day(x)          = factor for number of days of voyage

           The bunker consumption is varying as a function of the speed with a exponent of power of 3 and can

           Bunkercost(x)/day(x) = BP*BCbasis*(x/v0)^3




           s:\<alid>\2000.1\<file   >                                                    2/23/2014 6:15 AM
                                           Sheet1


by combining these equation you will get the following equation

f(x) = TCbasis*x/vo+BCbasis*BPx/v0+Voyage cost/day(x)- BP*BCbasis*(x/v0)^3 - Voyage cost/day(
f(x) = TCbasis*x/vo+BCbasis*BP*x/v0- BP*BCbasis*(x/v0)^

The derived function is
f(x)’ = TCbasis/vo+BP*BCbasis/v0- BP*BCbasis*3*x^2/v0^3

By setting this function to zero the theoretical economical speed will be found.
f(x)’= 0
x = SQRT( (TCbasis+BP*BCbasis)/(3* BP*BCbasis)*v0^2)




s:\<alid>\2000.1\<file   >                                                         2/23/2014 6:15 AM
                                                       Sheet1




 t, voyage cost , port cost, etc. Based on the WS for a specific voyage a net freight is calculated. The target with
 speed the vessel has an estimated bunker consumption BCbasis. The actual bunker consumption is will vary w




                                                                               SQRT




n be written as




nent of power of 3 and can be written as :




           s:\<alid>\2000.1\<file   >                                                        2/23/2014 6:15 AM
                                       Sheet1




x/v0)^3 - Voyage cost/day(x)




          s:\<alid>\2000.1\<file   >            2/23/2014 6:15 AM
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calculated. The target with this exercise is to optimise the income per day as a function of speed.
er consumption is will vary with the chosen speed.




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                             Sheet1




s:\<alid>\2000.1\<file   >            2/23/2014 6:15 AM
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tion of speed.




           s:\<alid>\2000.1\<file   >            2/23/2014 6:15 AM
                             Sheet1




s:\<alid>\2000.1\<file   >            2/23/2014 6:15 AM

				
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