<p>In this study, we conducted turning tests with rudder angles <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="773_2024_1047_Article_IEq1.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="39" /> </InlineMediaObject> <EquationSource Format="TEX">\(\pm 35^\circ\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>±</mo> <msup> <mn>35</mn> <mo>∘</mo> </msup> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="773_2024_1047_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="70" /> </InlineMediaObject> <EquationSource Format="TEX">\(\pm 20^\circ /20^\circ\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>±</mo> <msup> <mn>20</mn> <mo>∘</mo> </msup> <mo stretchy="false">/</mo> <msup> <mn>20</mn> <mo>∘</mo> </msup> </mrow> </math></EquationSource> </InlineEquation> zig-zag maneuver tests in deep and shallow water using a model of a 3,600 TEU container ship called KCS. Through the comparison of these test results with the free-running test results of three other ships, the shallow-water effect on the maneuverability was investigated. The shallow-water effects obtained during the turning and zig-zag maneuvers are as follows: Turning: The advance (<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="773_2024_1047_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="26" /> </InlineMediaObject> <EquationSource Format="TEX">\(A_D\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>A</mi> <mi>D</mi> </msub> </math></EquationSource> </InlineEquation>) decreases slightly when the water depth-to-ship draft ratio (<i>h</i>/<i>d</i>) is approximately 2.0 and increases significantly as the water depth decreases. The tactical diameter (<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="773_2024_1047_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">\(D_T\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>D</mi> <mi>T</mi> </msub> </math></EquationSource> </InlineEquation>) (up to <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="773_2024_1047_Article_IEq5.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="71" /> </InlineMediaObject> <EquationSource Format="TEX">\(h/d = 2.0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>h</mi> <mo stretchy="false">/</mo> <mi>d</mi> <mo>=</mo> <mn>2.0</mn> </mrow> </math></EquationSource> </InlineEquation>) is approximately the same as that in deep water and becomes significantly larger when <i>h</i>/<i>d</i> becomes smaller than 2.0. Thus, there is a slight difference in the appearance of the shallow-water effects in <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="773_2024_1047_Article_IEq6.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="26" /> </InlineMediaObject> <EquationSource Format="TEX">\(A_D\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>A</mi> <mi>D</mi> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="773_2024_1047_Article_IEq7.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">\(D_T\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>D</mi> <mi>T</mi> </msub> </math></EquationSource> </InlineEquation>. Zig-zag maneuvers: The overshoot angle increases slightly near <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="773_2024_1047_Article_IEq8.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="71" /> </InlineMediaObject> <EquationSource Format="TEX">\(h/d = 2.0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>h</mi> <mo stretchy="false">/</mo> <mi>d</mi> <mo>=</mo> <mn>2.0</mn> </mrow> </math></EquationSource> </InlineEquation> compared with that in deep water and becomes significantly smaller as the water depth becomes shallower. The forward distance (<InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="773_2024_1047_Article_IEq9.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(l_{20}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>l</mi> <mn>20</mn> </msub> </math></EquationSource> </InlineEquation>), until reaching the heading <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="773_2024_1047_Article_IEq10.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="89" /> </InlineMediaObject> <EquationSource Format="TEX">\(+20^\circ /-20^\circ\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>+</mo> <msup> <mn>20</mn> <mo>∘</mo> </msup> <mo stretchy="false">/</mo> <mo>-</mo> <msup> <mn>20</mn> <mo>∘</mo> </msup> </mrow> </math></EquationSource> </InlineEquation> after steering, was approximately the same as that in deep water or decreased slightly, until approximately <InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="773_2024_1047_Article_IEq11.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="71" /> </InlineMediaObject> <EquationSource Format="TEX">\(h/d = 2.0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>h</mi> <mo stretchy="false">/</mo> <mi>d</mi> <mo>=</mo> <mn>2.0</mn> </mrow> </math></EquationSource> </InlineEquation>. Furthermore, it increased as the water depth decreased. This is because the course stability of the ship deteriorated at approximately <InlineEquation ID="IEq12"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="773_2024_1047_Article_IEq12.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="71" /> </InlineMediaObject> <EquationSource Format="TEX">\(h/d = 2.0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>h</mi> <mo stretchy="false">/</mo> <mi>d</mi> <mo>=</mo> <mn>2.0</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Study of shallow-water effects on ship maneuverability using free-running model tests

  • R. Okuda,
  • H. Yasukawa,
  • M. Sano,
  • A. Matsuda

摘要

In this study, we conducted turning tests with rudder angles \(\pm 35^\circ\) ± 35 and \(\pm 20^\circ /20^\circ\) ± 20 / 20 zig-zag maneuver tests in deep and shallow water using a model of a 3,600 TEU container ship called KCS. Through the comparison of these test results with the free-running test results of three other ships, the shallow-water effect on the maneuverability was investigated. The shallow-water effects obtained during the turning and zig-zag maneuvers are as follows: Turning: The advance ( \(A_D\) A D ) decreases slightly when the water depth-to-ship draft ratio (h/d) is approximately 2.0 and increases significantly as the water depth decreases. The tactical diameter ( \(D_T\) D T ) (up to \(h/d = 2.0\) h / d = 2.0 ) is approximately the same as that in deep water and becomes significantly larger when h/d becomes smaller than 2.0. Thus, there is a slight difference in the appearance of the shallow-water effects in \(A_D\) A D and \(D_T\) D T . Zig-zag maneuvers: The overshoot angle increases slightly near \(h/d = 2.0\) h / d = 2.0 compared with that in deep water and becomes significantly smaller as the water depth becomes shallower. The forward distance ( \(l_{20}\) l 20 ), until reaching the heading \(+20^\circ /-20^\circ\) + 20 / - 20 after steering, was approximately the same as that in deep water or decreased slightly, until approximately \(h/d = 2.0\) h / d = 2.0 . Furthermore, it increased as the water depth decreased. This is because the course stability of the ship deteriorated at approximately \(h/d = 2.0\) h / d = 2.0 .