RESULTS AND DISCUSSION
7.1. Introduction
Based on the proposed ship resistance prediction formulae that were discussed in previous chapter and the calculation tools which is based on Microsoft Excel and FORTRAN, the output results are calculated and analyzed. In this chapter, it presents and discusses in more detail and wider about the results obtained. Data of related results are presented effectively in tables and several necessary graphs are produced to illustrated clearly about the results and related analysis. In this study, the analysis and discussion also remarks about two case of study as highlighted earlier.
7.2. CASE 1: Severe Drift Effect on the Total Ship Resistance, RTOTAL
As discussed in the earlier chapter, it clearly highlighted that the assumption of this lateral drift with severe effect are due to two separate elements, wind and current (maintaining the calm water condition). First effect of lateral drift which
caused by wind is considerably limited up to 10 degrees drift angle, β, assuming relatively wind effect is small comparing to the forward speed of the ship. However, as severe lateral drift effect is concerned, it is incorporated with the current cause.
This current is said could give a severe drift effect due to the current velocity (as set earlier) acts on the moving ship, which considerably gives more severe lateral drift effect. In measuring wider about this lateral drift effect, the current velocity acting on the moving ship, especially at river mouth area is varied in term of direction angle.
The current direction angle (with fixed velocity) is represented by α and varies from 0o (also known as heading current) up to 360o, with 10o intervals.
As results, it can be summarized that this lateral drift investigation on the ship resistance is influenced by two types of variables with fixed values of current velocity, VC. Consideration is given on the variables from range of drift angles, β, as well as range of current direction angles, α. The calculated result of the lateral drift effect on the ship total resistance, RTOTAL is shown in Table 7.1. According to this result, the total ship resistance is calculated at various drift angles incorporating with the various current direction angles. The ship’s velocity, VS is set at 25 knots (service speed) and current velocity, VC is assumed 4 knots (considerably the typical maximum value). The mathematical calculation for this total ship resistance, RTOTAL
is executed by solving the proposed ship resistance prediction formulae separately into two components of total ship resistance, namely longitudinally (RT(longitudinal)) and laterally (RT(lateral)). Both values are then combined by applying the trigonometric solution as described in previous chapter. These results are plotted and visualized in Figure 7.1
Table 7.1: CASE 1: Result of Ship Total Resistance with Lateral Drift Effect at Various Drift and Current Direction Angles
Drift angle, β(deg)
0 1824.859 0.000 1824.859 1822.333 2.510 1822.334 1814.751 9.250 1814.774 10 1823.946 1.081 1823.946 1821.420 3.760 1821.424 1813.838 10.499 1813.868 20 1821.308 3.797 1821.311 1818.781 6.900 1818.794 1811.199 13.640 1811.251 30 1817.232 7.692 1817.248 1814.706 11.404 1814.742 1807.124 18.144 1807.215 40 1812.168 12.279 1812.209 1809.642 16.710 1809.719 1802.060 23.449 1802.212 50 1806.675 17.029 1806.755 1804.149 22.203 1804.285 1796.567 28.942 1796.800 60 1801.370 21.408 1801.497 1798.844 27.266 1799.051 1791.262 34.006 1791.585 70 1796.867 24.931 1797.040 1794.341 31.340 1794.615 1786.759 38.080 1787.165 80 1793.728 27.211 1793.935 1791.202 33.977 1791.524 1783.620 40.716 1784.085 90 1792.481 27.998 1792.700 1789.955 34.887 1790.295 1782.373 41.627 1782.859 100 1791.229 27.207 1791.436 1788.703 33.972 1789.025 1781.121 40.712 1781.586 110 1788.086 24.924 1788.260 1785.560 31.332 1785.835 1777.978 38.072 1778.386 120 1783.581 21.399 1783.709 1781.055 27.255 1781.263 1773.473 33.995 1773.799 130 1778.275 17.018 1778.357 1775.749 22.190 1775.888 1768.167 28.930 1768.404 140 1772.782 12.268 1772.825 1770.256 16.697 1770.335 1762.674 23.437 1762.830 150 1767.720 7.681 1767.736 1765.194 11.393 1765.230 1757.612 18.132 1757.705 160 1763.647 3.789 1763.651 1761.121 6.891 1761.135 1753.539 13.631 1753.592 170 1761.013 1.076 1761.013 1758.486 3.754 1758.490 1750.904 10.494 1750.936 180 1760.104 0.000 1760.104 1757.578 2.510 1757.580 1749.996 9.250 1750.020 190 1761.021 1.085 1761.021 1758.495 1.255 1758.495 1750.913 7.995 1750.931 200 1763.663 3.805 1763.667 1761.137 -1.890 1761.138 1753.555 4.850 1753.562 210 1767.741 7.702 1767.758 1765.215 -6.396 1765.227 1757.633 0.343 1757.633 220 1772.807 12.290 1772.850 1770.281 -11.703 1770.320 1762.699 -4.963 1762.706 230 1778.301 17.040 1778.382 1775.775 -17.195 1775.858 1768.193 -10.456 1768.224 240 1783.604 21.417 1783.733 1781.078 -22.257 1781.217 1773.496 -15.518 1773.564 250 1788.105 24.938 1788.278 1785.578 -26.328 1785.773 1777.996 -19.589 1778.104 260 1791.240 27.214 1791.446 1788.714 -28.961 1788.948 1781.132 -22.221 1781.270 270 1792.481 27.998 1792.700 1789.955 -29.867 1790.204 1782.373 -23.128 1782.523 280 1793.739 27.204 1793.945 1791.213 -28.948 1791.447 1783.631 -22.209 1783.769 290 1796.885 24.917 1797.058 1794.359 -26.304 1794.552 1786.777 -19.565 1786.884 300 1801.393 21.389 1801.520 1798.867 -22.225 1799.005 1791.285 -15.485 1791.352 310 1806.700 17.007 1806.780 1804.174 -17.158 1804.256 1796.592 -10.418 1796.622 320 1812.193 12.257 1812.234 1809.667 -11.664 1809.704 1802.085 -4.924 1802.091 330 1817.254 7.671 1817.270 1814.728 -6.361 1814.739 1807.146 0.378 1807.146 340 1821.323 3.781 1821.327 1818.797 -1.862 1818.798 1811.215 4.877 1811.222 350 1823.954 1.071 1823.955 1821.428 1.271 1821.429 1813.846 8.011 1813.864 360 1824.859 0.000 1824.859 1822.333 2.510 1822.334 1814.751 9.250 1814.774
0 1802.097 19.808 1802.206 1784.332 33.924 1784.655 1761.371 51.370 1762.120 10 1801.184 21.058 1801.307 1783.419 35.173 1783.766 1760.459 52.620 1761.245 20 1798.546 24.198 1798.709 1780.781 38.314 1781.193 1757.820 55.760 1758.704 30 1794.471 28.702 1794.700 1776.706 42.818 1777.222 1753.745 60.264 1754.780 40 1789.406 34.008 1789.729 1771.641 48.123 1772.295 1748.680 65.570 1749.909 50 1783.913 39.501 1784.350 1766.148 53.616 1766.962 1743.187 71.062 1744.635 60 1778.608 44.564 1779.167 1760.843 58.680 1761.821 1737.883 76.126 1739.549 70 1774.106 48.638 1774.772 1756.341 62.754 1757.461 1733.380 80.200 1735.234 80 1770.967 51.275 1771.709 1753.202 65.390 1754.421 1730.241 82.837 1732.223 90 1769.720 52.185 1770.489 1751.955 66.301 1753.209 1728.994 83.747 1731.021 100 1768.467 51.270 1769.210 1750.702 65.386 1751.923 1727.742 82.832 1729.726 110 1765.325 48.630 1765.994 1747.560 62.746 1748.686 1724.599 80.192 1726.462 120 1760.819 44.553 1761.383 1743.054 58.669 1744.042 1720.094 76.115 1721.777 130 1755.514 39.488 1755.958 1737.749 53.604 1738.575 1714.788 71.050 1716.259 140 1750.021 33.995 1750.351 1732.256 48.110 1732.924 1709.295 65.557 1710.552 150 1744.958 28.691 1745.194 1727.193 42.806 1727.723 1704.232 60.253 1705.297 160 1740.886 24.189 1741.054 1723.121 38.305 1723.546 1700.160 55.751 1701.074 170 1738.251 21.052 1738.378 1720.486 35.168 1720.845 1697.525 52.614 1698.340 180 1737.342 19.808 1737.455 1719.577 33.924 1719.912 1696.617 51.370 1697.394 190 1738.259 18.553 1738.358 1720.494 32.668 1720.805 1697.534 50.115 1698.273 200 1740.902 15.408 1740.970 1723.137 29.524 1723.390 1700.176 46.970 1700.824 210 1744.980 10.902 1745.014 1727.215 25.017 1727.396 1704.254 42.464 1704.783 220 1750.046 5.595 1750.055 1732.281 19.711 1732.393 1709.320 37.157 1709.724 230 1755.539 0.103 1755.539 1737.774 14.218 1737.832 1714.813 31.665 1715.106 240 1760.843 -4.959 1760.850 1743.078 9.156 1743.102 1720.117 26.603 1720.323 250 1765.343 -9.030 1765.366 1747.578 5.085 1747.585 1724.617 22.532 1724.764 260 1768.478 -11.663 1768.517 1750.713 2.453 1750.715 1727.752 19.899 1727.867 270 1769.720 -12.569 1769.764 1751.955 1.546 1751.955 1728.994 18.993 1729.098 280 1770.977 -11.650 1771.016 1753.213 2.465 1753.214 1730.252 19.912 1730.366 290 1774.124 -9.006 1774.147 1756.359 5.109 1756.366 1733.398 22.556 1733.545 300 1778.632 -4.927 1778.639 1760.867 9.189 1760.891 1737.906 26.635 1738.110 310 1783.939 0.140 1783.939 1766.174 14.256 1766.231 1743.213 31.702 1743.501 320 1789.431 5.634 1789.440 1771.666 19.749 1771.776 1748.705 37.196 1749.101 330 1794.492 10.937 1794.526 1776.727 25.052 1776.904 1753.766 42.499 1754.281 340 1798.562 15.436 1798.628 1780.797 29.551 1781.042 1757.836 46.998 1758.464 350 1801.193 18.569 1801.289 1783.428 32.684 1783.727 1760.467 50.131 1761.181 360 1802.097 19.808 1802.206 1784.332 33.923 1784.655 1761.371 51.370 1762.120
1500 1550 1600 1650 1700 1750 1800 1850
0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360
Current Angle, a (deg)
Total Resistance,RTOTAL (kN)
R(t) with 0 deg drift R(t) with 2 deg drift R(t) with 4 deg drift R(t) with 6 deg drift R(t) with 8 deg drift R(t) with 10 deg drift
Figure 7.1: CASE 1: Result of Total Ship Resistance with Lateral Drift Effect at Various Drift and Current Direction Angles
Referring to the calculated and analyzed result in Table 7.1 and Figure 7.1, it is showed that the total ship resistance, RTOTAL incorporating with the effect of lateral drift decreased with increase of drift angle, β. However, the values of total ship resistance incorporating with severe drift effect showed decrease trend with the increase of current direction angle until α = 180o. After 180o, total resistance starts to increase until current direction angle, α= 360o. From β=0o to 10o and from α=0o to 180o shows that the values of total ship resistance linearly decrease. Must be borne in mind that this severe drift effect is caused by combination of two types of sources;
due to wind, which produces drift angle, β and due to current, which at its speed of 4 knots (max.) acts at various current direction angle, α.
In discussing more about this effect, we might view the effect of both causes of severe drift effect separately. In other words, first, we possibly discuss the effect of lateral drift due wind which causes drift angle, β.
7.2.1 Ship Total Resistance, RTOTAL with the Drift Effect (due to wind)
Appendix B1 shows that the trend of total ship resistance is decrease with the increase of drift angle, β. The total ship resistance determination at this case is made by solving it in separate components; longitudinally and laterally. As a result, total ship resistance is calculated as Longitudinal Total Ship Resistance, RT (L) and Lateral Total Ship Resistance, RT (T) as shown in Table 7.1. From there, as a resultant of total ship resistance, it is combined and solved by applying a trigonometric solution.
As indicated in Table 7.2, the total resistance with lateral drift effect due to drift angle is influenced by component of ship’s velocity parameter, which is ship longitudinal velocity, VS (L) and ship lateral velocity, VS (T). Due to that, ship resistance determination is made by breaking down into longitudinal and lateral component as well, where all the component of resistances, coefficients and functions are solved separately in longitudinal and lateral direction (as per discussed in Chapter V). As the result, from the table, it shows that longitudinal total resistance of the ship, RT(L) decrease with the increase of drift angle, β, whereas in lateral component, the trend of total resistance, RT(T) is proportionally increase with the increment of drift angle. It explains that with the increase of drift angle, from β = 0o to 10o, the resistance acting longitudinally becomes less, but the magnitude increases in lateral component point of view.
However, we also find out that although the total ship resistance laterally, RT(T) is proportionally increase, the resultant value of total ship resistance, RTOTAL still decrease with the increase of drift angle (refer to Table 7.2). This is due to the increasing values of total resistance in lateral direction, RT (T), which is relatively small comparing the decreasing values of total resistance in longitudinal component with the increase of drift angle. This trend are looked similarly with other range of ship speed values, as shown in Figure 7.2
Table 7.2: Resultant Ship Total Resistance at Speed 25 knots with Various Drift Total Resistance, RT (kN)
Ship speed,v=5 knots ship speed,v=10 knots Ship speed,v=15 knots Ship speed,v=20 knots Ship speed,v=25 knots Ship speed,v=30 knots
Figure 7.2: Total Ship Resistance, RTOTAL at Various Ship Speed, Vs with Lateral
Drift Angles (due to wind).
Ship Velocity= 25 knots Drift angle, β(deg) RTOTAL(L)
(kN)
7.2.2 Ship Total Resistance, RTOTAL with Current Effect
On the other hand, besides drift effect due to wind which produces drift angles, since concerning the severe lateral drift effect at the river mouth, it also is caused by the current acting on the ship. This factor of lateral drift is said to give severe effect to the ship, due to the presence of current velocity itself. The mathematical investigation due to this current speed on the ship resistance is made by approaching the so called a relative solution. With the fixed value of current velocity, VC = 4 knots (approx.), the analysis is made by considering various direction of angles, α. The varying of current direction angles begin at 0o, which also namely as heading current, with 10o of interval up to 180o (following current), then continues until α = 360o (which considerably back to heading current). At these various current direction angles, a wider effect of drift on the ship resistance can be analyzed. For the analysis of total ship resistance with drift effect only caused by current itself, is shown in Appendix B2.
In reviewing the total ship resistance at 25 knots with lateral drift due to 4 knots current from point view of longitudinal and lateral component, it shows that the total ship resistance produced longitudinally, RT(L) decrease with increase of current direction angle until α = 180o. However, the trend then indicates linearly increase from α = 190o until reach up to α = 360o (which considerably back to heading current). There also indicates that the total ship resistance is determined as maximum value at current direction angles, α= 0o or α = 360o with RT (L) is 1824.86 kN. Whilst, the value of total ship resistance laterally, RT (T) at this angle is zero. This situation happened since at α= 0o, the current is said in the position of heading current. Means, the traveled ship at 25 knots is encountered by the current with 4 knots speed completely in longitudinal component and in opposite direction of traveled ship, and there is absence of lateral component at this direction. Relatively, at this condition, ship total resistance is added by the resistance produced due to the heading current at 4 knots and the resistance due to the current is found at highest value at the α= 0o or α = 360o (heading current).
As passed with the increment of current angle, the longitudinal component of total resistance starts decreasing, while in lateral component proportionally increase.
This increasing value of lateral component came to the highest point when the current direction angle, α= 90o, also namely as starboard beam current. The lateral total resistance, RT (T) is determined 28 kN at this angle. This due to the magnitude of lateral velocity component at 90o is the maximum magnitude, since there only has the absolute lateral component, without longitudinal current velocity. This condition also occurs in the case of port beam current. The only difference is that the total resistance laterally, RT (T) produced is in the opposite direction of the case of starboard beam current. After current direction angle passing starboard beam current (90o), both total resistance produced longitudinally and laterally decrease till reaching 180o. This trend can be explained that at this range of angle current, the longitudinal resistance is encountered in opposite direction of current, which is the same direction with traveled ship. As a result, it is found that the longitudinal resistance due to current effect is produced in negative values, hence brought the total ship resistance lesser as compared to the total ship resistance produced in normal condition. These negative reading of resistance can be interpreted and converted into the additional force or thrust in moving the ship forward (longitudinally). The traveled ship is gained a merit in term of powering requirement at this range of current angles. The peak of this merit was achieved when the current angle, α at 180o. At this direction (following current) resistance due to this current produced absolutely in longitudinal component, same direction with the traveled ship direction. In other words, it produced the maximum value of additional force/ thrust (negative resistance) for the traveled ship forward. The comprehension of this various condition of current action in effecting lateral drift is shown in Figure 7.3 below.
Figure 7.3: Schematic Diagram of Lateral Drift Effect Due to Current
7.2.3 Ship Total Resistance, RTOTAL with Lateral Drift Effect Due to Combination of Wind and Current (Severe Case)
In general discussion about total ship resistance produced with the effect of severe drift; these two causes are combined together. The severe lateral drift due to combination of wind (due to drift angle) and current (current direction angle), it can be summarized that the trend is decreased with increase of these angles. In this case, at ship service speed of 25 knots, the maximum value of total ship resistance produced is RTOTAL = 1824.86 kN, at the condition when she is encountered by the heading current (α= 0o or α= 360o) and no drift effect due to wind (β= 0o). Whereas, the lowest value produced is RTOTAL =1697.39 kN when she is drifted by wind at maximum drift angle, β= 10o incorporating with the following current (α= 180o). It is possibly clearer to view the comparison and difference between the total ship resistance calculated using original Holtrop;s and Mennen’s formula (at normal
X Vc Vc(T)
Vc(L)
Y Current direction angle Current velocity, Vc
Ship velocity, Vs
α
Up to 360o
condition), with maximum and minimum total ship resistance produced due to the effect of severe drift (caused by combination of wind and current). The exact values are shown in Table 7.3
Table 7.3: Comparison of differences between total ship resistance produced in normal condition with maximum and minimum total ship resistance produced due to drift effect
Condition at service speed 25 knots Total Resistance, RTOTAL (kN)
Percentage of difference Total ship resistance at normal
condition 1792.48
Maximum of total ship resistance produced due to drift effect (caused by combination of wind and current)
1824.86 1.81 %(added) Minimum of total ship resistance
produced due to drift effect (caused by combination of wind and current)
1697.39 5.31 % (reduced)