航海技术专业精品毕业论文--航行船舶在浅水中的纵倾变化研究

航海技术专业精品毕业论文--航行船舶在浅水中的纵倾变化研究 目 录 ,引言 ............................................................................................................................................................ 1 ,浅水域的概况............................................................................................................................................. 2 1.1浅水区界定....................................................................................................................................... 2 1.2浅水效应产生的原因 ....................................................................................................................... 2 1.3浅水效应产生的现象 ....................................................................................................................... 2 ,船舶纵倾变化的影响因素 ......................................................................................................................... 3 2.1船舶排水量及排水体积变化的影响 ............................................................................................... 3 2.2船体的线型(船舶的方形系数)的影响 ....................................................................................... 3 2.3舷外水密度变化的影响 ................................................................................................................... 4 2.4船速大小的影响............................................................................................................................... 4 3船体下沉量的估计...................................................................................................................................... 5 3.1基于傅汝德数的船体升沉和纵倾变化 ........................................................................................... 6 3.2船首下沉量的定量计算 ................................................................................................................... 6 ,利用纵倾变化提高船舶载货量 ................................................................................................................. 7 4.1通过实例计算船舶可加载的载货量 ............................................................................................... 7 4.2提高载货量的具体建议 ................................................................................................................... 8 5结束语 ....................................................................................................................................................... 10 致谢 ...............................................................................................................................................................11 参考文献 ...................................................................................................................................................... 12 附录 .............................................................................................................................................................. 13 附录一、文献综述....................................................................................................................................... 13 附录二、外文翻译....................................................................................................................................... 15 摘 要 基于航行船舶在浅水中的纵倾变化研究，首先当然是确定何为浅水区，然后通过对浅水效应产生的条件、原因和现象的分析来引出船舶在浅水中的纵倾变化。对于船舶的纵倾变化，主要考虑了几个比较重要的影响因素，例如船舶的排水量，船型系数，船体舷外的水密度变化，船舶速度大小等，从而对船舶的纵倾变化有了定性的认识。接着，根据现有的理论和经验公式对船舶的下沉量和纵倾变化进行定量的计算，最后利用计算结果来分析船舶因纵倾变化而可加载的载货量，并用实例进行了论证。在此基础上，再给出具体的建议，希望通过船舶浅水中的纵倾变化能够充分利用船舶的载货量从而提高船舶营运的效益，最终能为船公司带来一定的效益增长。 关键词:航行船舶;浅水效应;纵倾变化;傅汝德数。 Analysis of the navigating ships’change of trim in shallow water Abstract The reseatch of the trim change in shallow water. of course, where is the shallow water should be defined first, and then through the analysis of the conditions, reasons and phenomenon of the shallow water effect leads to the ships’ trim change in shaollow water. For the change of the ship’s trim, we mainly congsider several of the more important factors , such as, displacement tonnage of the ship, ship’s coefficient, the change of water density outboard, ship’s speed, thus we can have a qualitative understanding of the ships’ trim. Then we use the existing theory and empirical formula to calculate the amount of quantitative changes of the ship’s sinking and trimming, and then analyze the results of the calculation to decide the amount of cargo can be loaded due to the trim change and use the example to demonstrate the results. On this basis, and with the specific suggestions, we hope to use the changes of ship’s trim in shallow water to take full advantage of the ship’s cargo capacity and then improve the efficiency of the ship and finally it can bring some efficiency gains to the shipping companies. Keywords: navigating ship; shollow water effect; the change of ship’s trim; Froude coefficient. ,引言 1987年，渡轮”Herald of Free Enterptis”在Zeebrugge倾覆，导致近200人死亡。相关人员对船舶及自然环境等进行了全面的调查后发现，由于船舶在浅水域中高速航行时，船体下沉导致船首 【,】首尖舱进水，淹没了汽车甲板，最终导致了船舶稳性丧失而倾覆。随着航运的发展，此类事件发生的频率日渐增大。究其原因，则归咎于船舶在浅水域航行时所受的影响越来越大。 我国是一个航运大国。近年来，国内航运业得到迅猛发展，随之便带动了我国造船业的发展。为了满足航运市场的需求，新造的船舶便逐渐朝着大型化发展，吃水越来越深。于是，可航水域的水深相对于船舶的吃水就越来越小，相对的浅水域也就越来越多了。因相对水深减小而引起的船舶的浅水效应也越来越显著，出现船体下沉量增加，船舶摇晃剧烈，船舶纵倾变化加剧等现象。而船舶的纵倾变化，不但影响到船舶在浅水域航行时的操纵性能，还对船舶安全和船舶效益等产生一定的影响。虽然国内外有许多专家都对船舶在受限水域的操纵性进行了大量的研究，但有针对性的对浅水中航行船舶的纵倾变化进行研究的却不多。而且与许多年前相比，由船舶纵倾变化带来的各方面影响也越来越大了。本文希望通过对浅水中船舶纵倾变化的研究，探寻船舶纵倾变化的规律及其影响因素，并以此来提高船舶的载货量最终增加船公司的营运效益。毕竟作为一家航运公司，追求的是安全、经济、高效这三者的完美结合，以达到获得高营业额的最终目标。 1 ,浅水域的概况 1.1浅水区界定 虽然人们逐渐认识到相对于船舶的大型化，可航水域的相对水深正在逐渐变小，但怎样去定义浅水区一直没能给出一个明确的方式。 以前，由于船舶小、船速低，浅水效应现象的发生较少，人们就根据水深数值的大小简单的定 【,】义了浅水区，超过某一常量便认为是深水区，而小于此值时则认为是浅水区。然而现在，随着船速的不断提高，船体的不断增大，浅水效应便常有发生，严重的甚至导致船舶毁损。所以人们不得不重新考虑浅水效应并进行深入的研究。那么，首先当然是给浅水域划个界限，在什么条件下可不考虑浅水效应，而在什么条件时则必须重视其带来的影响。目前，对于浅水区这个概念并没有给出一个定量的定义，因为出现浅水效应的水域跟船舶尺度、船速大小、船舶形状、航区水深等都存在 【,】着直接的关系。在航区水深较浅时，如果船舶吃水较小，航速较低并不一定出现浅水效应，相反的在航区水深较深而船速较高，吃水又较大时也是可能出现浅水效应的。于是，人们便想到了水深吃水比(h/d)这么一个相对概念。国际上也根据水深对于船舶操纵性的影响程度将水深划分为深水、 【,】中等水深、浅水(1.2 计算公式 六西格玛计算公式下载结构力学静力计算公式下载重复性计算公式下载六西格玛计算公式下载年假计算公式 : 22FF??nnS,C，Δt,C (3-1) mZΘ2222LL1,F1,FPPPPnn LS式中:为船体平均下沉量，Δt为吃水差的改变量，为船舶垂线间长，?为船舶排水体积，FPPmn F,VghmsCC水深傅汝德数，，V为船速()，h为水深(m)，为平均下沉量系数，为nΘZ 【,】吃水差变化量系数。 随后在此基础上衍生出了许多的解析式或一些经验公式，如Hooft(1974)公式、Huuska(1976)公式、Eryuzlu和Hausser(1978)公式、Barrass(1981)公式、Romisch(1989)公式、Millward(1990) 5 公式、Millward(1992)公式、Eryuzlu(1994)公式、Ankudinov(1996)公式等。而不同的公式有其不同的适用条件，对于不同的水域、不同的船型误差大小也不尽相同，所以在估算下沉量时应视具体情况而定。 3.1基于傅汝德数的船体升沉和纵倾变化 在无限深水域，船体的升沉和纵倾变化主要取决于船型和船速，而其改变量则可以用傅汝德数F,VgLms(其中，为船速()，为船长())来衡量。随着船速的提高，逐渐增VLmFnn大，在不同的区间，船舶表现出不同的浮态。 (,)0.1<<0.25时，船体开始出现下沉，船尾吃水基本不变，主要表现为首下沉。 Fn (,)0.25<<0.3时，船尾开始下沉，但其下沉量小于首下沉量，即船舶在该速度区间主要表现Fn 为船体下沉和首倾。而一般的船舶其<0.3，所以在船舶航行过程中，原来平吃水的船舶状态将变Fn 为首倾状态。 (,)=0.3时，是一个过渡状态，此时船首停止下沉，而船尾下沉则继续增大。 Fn (,)0.30.6时，船尾因已降至最低点而开始上浮，而船首则继续上升。随船速提高，船首上升至n 一定程度便开始下沉。总体上，船舶浮态表现为尾倾并上浮，当达到某一程度将保持某一浮态不变 【,】而处于水面滑行状态。 而在浅水区航行时，由于船舶周围水流态势由三维空间流动变为二维平面流动而导致船体周围水动力的分布和大小的改变，船底水流速度的变大使得船体的下沉量比深水中大。长期的实践也表明，浅水区航行，船底富余水深变小，不但船舶操纵性能降低，严重时船舶因下沉和纵倾变化加剧而触底甚至搁浅以致造成财产损失和人员伤亡。 3.2船首下沉量的定量计算 在一般商船速度范围内，船首的下沉量往往要大于船尾下沉量。所以，在计算船舶浅水中航行时的最大下沉量，一般就计算船首下沉量。 CC1974年Hooft利用Tuck在1970提出的计算公式，将取1.4~1.53，取1.0，给出以下开敞ΘZ 水域浅水中船首下沉量的计算公式: 22FF??nnS,，L1.460.5sin() (3-2) bpp2322LL,F,F11PPPPnn 式中: ——船首下沉量 Sb ? ——船舶排水体积 6 ——船长(垂线间长) Lpp 【,】 ——水深傅汝德数，F,Vgh，为船速(m/s)， 为水深(m)VhFnn 对于长江口航行的船舶，我们可以运用此公式进行首下沉量的计算，但考虑到长江口航道的宽度有限，因此受其航道宽度影响，首下沉量将受到影响，大小视航道宽度而定。但总体上航行在宽度受限的航道中，船体的下沉量比无限水域中要大。如图3-1表示船舶在宽度受限的航道中航行时，船体下沉量和与在无限水域中相比吃水差变化的增加率。 图3-1航行船体下沉量和吃水差变化的增加率 ,利用纵倾变化提高船舶载货量 4.1通过实例计算船舶可加载的载货量 长江口地跨江苏省和上海市，有着优越的地理位置，做为长江沿线港口和上海港的唯一通道有着举足轻重的作用。据不完全统计，我国华东地区的煤、油和其他一些原料等有将近百分之八十是由船舶乘潮过长江口来完成的，因此长江口航道的深浅便制约着船舶运输。 自改革开放以来，长江三角洲地区社会经济得到飞快的发展，沿岸重要建筑的不断增多，使得长江口的治理越来越迫切。经过三期治理，长江口的水深由原来的6米多增加到了现今的12.5米，可以靠离的船舶吨数也增加到近10万吨。 然而，长江口虽经治理，航道加深，但对于大型船舶来讲，航经此处时仍旧将产生浅水效应，使船体下沉，首尾吃水改变，纵倾变化加剧。为安全起见，大型船舶都要等涨潮时才能过长江口， 【,,】以防触底搁浅。为此，当船舶抵达长江口时若还没涨潮，则既延误了船期，又降低了船舶的经营效益，这对于船公司来讲是最不愿意发生的事。那么，既然如此，我们除了在船期安排上做工作外，还可以考虑船舶因纵倾变化而损失的载货量，使船舶在这个问题上能多争取一些主动。 下面将通过实例来进行计算船舶因纵倾变化而损失的载货量。 (,)设散货船,轮，船长200米，垂线间长为190米，型宽32米，型深18米，吃水11米，载重 kn55000吨。进港船速12。 7 由3.1船舶深水中的升沉变化可知，当,0.3时，船体下沉，但总体上表现为首倾。而多数商Fn 船船速在该速度范围内，所以静水中平吃水的船舶，在深水中将表现为平均吃水增加，并出现首倾。 mF,VgL由变化得。而一般出于燃料消V,F*gL,0.3*9.8*200,13.3(),26.6knnns 耗的考虑，航行中船速基本都在26以内，再加上长江口船舶密度变大，为了安全，进出长江口的kn 船舶速度将进一步减小，一般都在12左右。所以根据的变化规律，航行在长江口的船舶远knFFnn小于0.3，基本上都将出现船首下沉的情况。于是，我们可以利用船舶首倾，再结合船舶吃水和船舶的初始浮态来增加载货量。由水深傅汝德数可知， F,Vgh,6/9.8*12.5,0.54 nh 根据公式(3-2)可得船首下沉量: S,0.78mb 因为此公式适用于开敞水域，故当船舶进入长江口时还需考虑航道宽度受限带来的影响。 根据公式(3-1)得吃水差变化量 Δt,0.53m 又由图3-1可知，当船舶下沉量为0.78时，船舶吃水差变化的增加率为7.5%，即船舶吃水差变化m ,增加了0.04，则变为0.57，S,0.84m，即相对于开敞水域，船首下沉量增加了0.06。 Δtmmmb (,)已知下沉量求吃水的改变 假定,轮入长江口前处于尾倾，则当进入长江口航道时，由于船速的降低，使得船舶的0.84m 傅汝德数F<0.3，于是，船舶表现为首下沉量大于尾下沉量，而后逐渐变为平吃水。由上面的计算n 可知，在船舶变为平吃水时相对于船舶平吃水进入长江口而后变为首倾，船舶的吃水减少了0.84m 0.42，因此，船舶在进入长江口前还可以适当的增加一定的货物。 m (,)根据吃水变化量求可增加的载货量 tcm根据静水力曲线图，我们可以查得55000吨的散货船，其厘米吃水吨数约为41.00那TPC么由公式P,TPC*Δd得可以增加的货物量约为1722吨。 从计算结果我们可以看出，利用船舶进入浅水区前后纵倾的变化可以给船舶适当增加一部分载货量。而这只是一个航次的增加量。如果从船舶一年的载运量考虑的话，不同的季节都尽量将船舶配至满载，在长江口涨潮时就有足够的富余水深可以安全的通过了，再在进入长江口前配载好货物使船舶具有一定量的尾倾，进入长江口航道时则刚好变为平吃水。这样，对于55000吨的散货船而言，每个航次都可以考虑增加载货1722吨左右。而以上海和秦皇岛之间的航线为例，由于航线较短，一般船舶每月可跑四个航次，考虑到气象原因，此航线一年可跑十个月左右。于是，对于55000吨的散货船来讲，正常情况下一年可以跑40个航次，按照每个航次增加1722吨货物，则一年下来可以增加近68880吨货物。而如果忽视掉这部分载货量，在进长江口前就已经调成平吃水的话，进入长江口航道则将受浅水效应影响，船速降低，船体下沉，出现首倾。这样，为了船舶安全，不得不用压载水来调整船舶纵倾，在无形中便损失了一部分的载货量。由此可见，利用好船舶的纵倾变化是可以给船舶营运带来一定的效益的。 4.2提高载货量的具体建议 作为一家航运公司，实现利润最大化当然是所追求的最终目标。而利润要由支出和收入来衡量，对于支出，船公司需考虑除了正常的船员工资，船舶各项开销外还应尽量减少不必要的消耗，这主要是船公司方面要解决的问题。而对于收入，除了船公司考虑货物的运输价格外，对于船舶本身来讲，当然是尽量达到满舱满载，使得船舶的利用率达到最大。 那么作为船舶本身要怎样才能实现对船舶舱容的充分利用。 8 首先，当然是开航前的货物配积载问题。大副应充分的考虑船舶将要航经的水域的密度，船舶所装货物的积载因素。在尽量多装货的前提下，使船舶具有一定的尾倾。这样不但使改善了船舶的操纵性，还能够充分利用舱容。 其次，便是确定船舶的初始尾倾量。过大，在浅水区航行时由于纵倾的变化，虽然尾倾现象减轻但船舶的吃水相对于平吃水将增大，甚至超过规定的载重线;过小，则浅水区航行中可能出现一定的首倾，不但船舶操纵性变差，而且将损失一部分舱容。那么，在计算船舶的尾倾量时，我们应根据船舶的具体参数，通过对船舶的船型系数、船速等进行分析，再结合航经浅水域的情况，开敞或宽度受限等条件选择合适的下沉量计算公式。最后再以经验公式作为参考，确定最终的一个结果。 最后，便是准确的把握船期。以长江口为例，由于其涨潮的时间不一定跟人们的生物钟吻合，那么船长应根据长江口潮汐的规律确定好航行过程中船舶的行驶速度，使得船舶抵达长江口外时刚好涨潮，这样就避免了候潮而浪费时间，于是，在有足够的富余水深的前提下，船舶按时乘潮过长江口，其浮态也有初始的尾倾变为平吃水，使船舶的舱容得到了充分利用。 9 5结束语 船舶的大型化使得相对的浅水区越来越多，当船舶航经此处时，受浅水效应影响将产生各种影响。本文主要针对船舶航行于浅水区时其纵倾的变化，通过对船舶载重量、船型系数、船舶舷外水密度的变化和船速的大小等因素的分析，了解了纵倾变化的影响因素。又从数学计算的角度，利用现有的理论和经验公式进行了定量的计算，从计算结果来推导出船舶可以利用纵倾变化而增加的载货量。通过航行于长江口的船舶的实例分析可以看出，原先尾倾的船舶进入长江口后变为平吃水，因船舶纵倾变化而可增加的载货量是非常可观的。因此，充分的利用好船舶在浅水中航行时的纵倾变化对于提高船舶的营运效益是有一定的现实意义的。 10 致 谢 感谢。。。。。。。。。 11 参考文献 [1] 雷涛，郭国平(浅水航行船舶下沉量的确定[J](航海技术，2002:2~4( [2]周华兴，郑宝友(关于深水、浅水与限制性航道界定的探讨[J](水运工程，2006:54~58( [3] 朱伟(浅谈浅水道航行对船舶工况的影响[J](天津航海，2007:1，31( [4] 洪碧光(船舶操纵原理与技术[M](大连:大连海事大学出版社，2007.5:192~198，210~223( [5] 招定友(船舶浅水效应的研究[J](天津航海，2009(2):4~6( [6] 陈哲，谢世平(浅析浅水对船舶操纵的影响[N](重庆交通学院学报，2002(12):119~122( [7] 乔归民(一种不可忽视的纵倾变化[J](中国航海，2004(1):59~61( [8] 洪碧光，于洋(船舶在浅水中航行下沉量的计算方法[N](大连海事大学学报，2003:1~5( [9] 沈玉如(船舶货运[M](大连，大连海事大学出版社，1998:68~77( [10] 朱红波，邱云明(浅水航行船舶限速的探讨[J](天津航海，2005:1~2，6( [11] 吴明，庄毅，代亮，杨波，石爱国，杨宝章(试论纵倾对舰船操纵性能的影响[C](船舶航泊安全的新经验新技术论文集(下册)，2007:369~379( [12] 董存义，吴东江(浅论船体下沉量与富余水深的确定[C](海洋船舶安全理论与实践论文集，2008:218~223( [13] 闫伟(大型船舶在浅水域操纵性能的探讨[J](航海技术，2008:4~6( [14] 张大有，李绍波(关于浅水影响及其改善技术[J](船还工程，2006:1~4( [15] 俞嘉虎(船舶进入限制航道后的操纵性变化和安全防范[J](航海技术，2005:28~29( [16] 潘浩(关于船舶航行中的船体下坐[J](航海技术，1996:27~28( [17] T.P.Gourlay and E.O.Tuck(The Maximum Sinkage of a ship[J](Jourmal of Ship Research，2001:50~58( [18]Dr C.B.Barrass(Ship Design and Performance for Masters and Mates[M](Butterworth-Heinemann，2004:148~179( 12 附录 附录一、文献综述 一( 材料来源 通过学校的图书馆中西文数据库及互联网，阅读了期刊、学报、著作 上的相关文章二十余篇，直接参考文献十八篇，其中外文文献两篇。阅读的期刊包括航海技术(由上海市航海学会主办的面向海员、面向航海科技、面向航运实践的科技期刊)、中国航海(由中国航海学会主办的专业性刊物，反映我姑航海科技领域的科研成果)、天津航海(由天津航海学会主办)、水运工程(由交通部主管中交水运规划设计院主办)、船舶工程(即中国造船工程学会会刊，国家技术类核心期刊)等;阅读的学报包括重庆交通学院学报等;阅读的著作包括洪碧光(教授、硕士生导师，主要从事船舶操纵，船舶避碰，船舶 安全管理 企业安全管理考核细则加油站安全管理机构环境和安全管理程序安全管理考核细则外来器械及植入物管理 ，港口水域船舶运动安全评估领域的工作)的船舶操纵原理与技术(本书全面、系统地论述了船舶操纵原理和实践的基本内容)及沈玉茹的船舶货运。 二( 研究历史及现状 文献[4]和文献[8]中明确了浅水的定义，浅水只是一个相对概念，同一水深对于小船可能是深水，而对于大船可能是浅水。通常，采用水深吃水比(h/d)来表示水深的深浅。当1.2 ship squat in open water and in confined channels What exactly is ship squat? When a ship proceeds through water, she pushes water ahead of her. In order not to leave a ‘hole’ in the water, this volume of water must return down the sides and under the bottom of the ship. The streamlines of return flow are speeded up under the ship. This causes a drop in pressure, resulting in the ship dropping vertically in the water. As well as dropping vertically, the ship generally trims for’d or aft. Ship squat thus is made up of two components, namely mean bodily sinkage plus a trimming effect. If the ship is on even keel when static, the trimming effect depends on the ship type andbeing considered. Cb The overall decrease in the static underkeel clearance (ukc), for’d or aft, is called ship squat. It is not the difference between the draughts when stationary and the draughts when the ship is moving ahead. If the ship moves forward at too great a speed when she is in shallow water, say where this static even-keel ukc is 1.0–1.5 m, then grounding due to excessive squat could occur at the bow or at the stern. For full-form ships such as Supertankers or OBO vessels, grounding will occur generally at the bow. For fine-form vessels such as Passenger Liners or Container ships the grounding will generally occur at the stern. This is assuming that they are on even keel when stationary. If is >0.700, then maximum squat will occur at the bow. Cb If is <0.700, then maximum squat will occur at the stern. Cb If is very near to 0.700, then maximum squat will occur at the stern, amidships and at the bow. Cb The squat will consist only of mean bodily sinkage, with no trimming effects. It must be generally, because in the last two decades, several ship types have tended to be shorter in length between perpendiculars (LBP) and wider in Breadth Moulded (Br. Mld). This has lead to reported groundings due to ship squat at the bilge strakes at or near to amidships when rolling motions have been present. Why has ship squat become so important in the last 40 years? Ship squat has always existed on smaller and slower vessels when under-way. These squats have only been a matter of centimetres and thus have been inconsequential. However, from the mid-1960s to this new millennium, ship size steadily has grown until we have Supertankers of the order of 350 000 tonnes dead-weight (dwt) and above. These Supertankers have almost out-grown the Ports they visit, resulting in small static even-keel ukc of only 1.0–1.5 m. Alongside this development in ship size has been an increase in service speed on several ships, e.g. Container ships, where speeds have gradually increased from 16 up to about 25 kt. Ship design has seen tremendous changes in the 1980s and 1990s. In Oil Tanker design we have the ‘Jahre Viking’ with a dwt of 564 739 tonnes and an LBP of 440 m. This is equivalent to the length of five football pitches. In 2002, the biggest Container ship to date, namely the ‘Hong Kong Express’ came into service. She has a dwt of 82 800 tonnes, a service speed of 25.3 kt, an LBP of 304 m, Br. Mld of 42.8 m and a draft moulded of 13 m. As the static ukc have decreased and as the service speeds have increased, ship squats have gradually 15 increased. They can now be of the order of 1.50-1.75m, which are of course by no means inconsequential. Department of Transport ‘M’ notices In the UK, over the last 20 years the UK Department of Transport have shown their concern by issuing four ‘M’ notices concerning the problems of ship squat and accompanying problems in shallow water. These alert all Mariners to the associated dangers. Signs that a ship has entered shallow water conditions can be one or more of the following: 1. Wave-making increases, especially at the forward end of the ship. 2. Ship becomes more sluggish to manoeuvre. A pilot’s quote … ‘almost like being in porridge.’ 3. Draught indicators on the bridge or echo sounders will indicate changes in the end draughts. 4. Propeller rpm indicator will show a decrease. If the ship is in ‘open water’ conditions, i.e. without breadth restrictions, this decrease may be up to 15% of the Service rpm in deep water. If the ship is in a confined channel, this decrease in rpm can be up to 20% of the service rpm. 5. There will be a drop in speed. If the ship is in open water conditions this decrease may be up to 30%. If the ship is in a confined channel such as a river or a canal then this decrease can be up to 60%. 6. The ship may start to vibrate suddenly. This is because of the entrained water effects causing the natural hull frequency to become resonant with another frequency associated with the vessel. 7. Any rolling, pitching and heaving motions will all be reduced as ship moves from deep water to shallow water conditions. This is because of the cushioning effects produced by the narrow layer of water under the bottom shell of the vessel. 8.Turning circle diameter (TCD) increases. TCD in shallow water could increase 100%. 9. Stopping distances and stopping times increase, compared to when a vessel is in deep waters. 10. Rudder is less effective when a ship is in shallow waters. What are the factors governing ship squat? The main factor is ship speed V. Detailed analysis has shown that squat varies as speed to the power of 2.08. However, squat can be said to vary approximately with the speed squared. In other words, we can take as an example that if we have the speed we quarter the squat. Put another way, if we double the speed we quadruple the squat!! In this context, speed V is the ship’s speed relative to the water. Effect of current/tide speed with or against the ship must therefore be taken into account. Another important factor is the block coefficient CB. Squat varies directly with CB. Oil Tankers will therefore have comparatively more squat than Passenger Liners. Procedures for reducing ship squat 1. Reduce the mean draft of the vessel if possible by the discharge of water ballast. This causes two reductions in one: (a) At the lower draft, the block coefficient CB will be slightly lower in value, although with Passenger Liners it will not make for a signifi-cant reduction. (b) At the lower draft, for a similar water depth, the H/T will be higher in value. It has been shown that higher H/T values lead to smaller squat values. 2. Move the vessel into deeper water depths. For a similar mean ship draft, H/T will increase, leading again to a decrease in ship squat. 3. When in a river if possible, avoid interaction effects from nearby moving ships or with adjacent riverbanks. A greater width of water will lead to less ship squat unless the vessel is outside her width of influence. 4. The quickest and most effective way to reduce squat is to reduce the speed of the ship. 16 False drafts If a moored ship’s drafts are read at a quayside when there is an ebb tide of say 4 kt then the draft readings will be false. They will be incorrect because the ebb tide will have caused a mean bodily sinkage and trimming effects. In many respects this is similar to the ship moving forward at a speed of 4 kt. It is actually a case of the squatting of a static ship. It will appear that the ship has more tonnes displacement than she actually has. If a Marine Draft Survey is carried out at the next Port of Call (with zero tide speed), there will be a deficiency in the displacement ‘constant.’ Obviously, larger ships such as Supertankers and Passenger Liners will have greater errors in displacement predictions. Summary In conclusion, it can be stated that if we can predict the maximum ship squat for a given situation then the following advantages can be gained: 1. The ship operator will know which speed to reduce to in order to ensure the safety of his/her vessel. This could save the cost of a very large repair bill. It has been reported in technical press that the repair bill for the QEII was $13 million … plus an estimate for lost Passenger bookings of $50 million!! 2. The ship officers could load the ship up an extra few centimetres (except of course where load-line limits would be exceeded). If a 100 000 tonnes dwt Tanker is loaded by an extra 30 cm or an SD14 General Cargo ship is loaded by an extra 20 cm, the effect is an extra 3% onto their dwt. This gives these ships extra earning capacity. 3. If the ship grounds due to excessive squatting in shallow water, then apart from the large repair bill, there is the time the ship is ‘out of service’. Being ‘out of service’ is indeed very costly because loss of earnings can be as high as ?100 000 per day. 4. When a vessel goes aground there is always a possibility of leakage of oil resulting in compensation claims for oil pollution and fees for clean-up operations following the incident. These costs eventually may have to be paid for by the shipowner. 备注:Dr C.B.Barrass,Ship Design and Performance for Masters and Mates[M],Butterworth-Heinemann, 2004,148~179 <文献翻译一:译文> 船舶在开敞水域和受限航道的坐底现象 什么是船舶的坐底现象? 当船舶在水中向前航行时，她会推开在船首的水。为了不使得在船首处水中形成一个”空洞”，这个 排开的水必须返回船舷两侧和船底。返回的水流流线在船底加速。这导致了船底压力下降，使得船 舶在水中垂直下沉。 除了船底垂直下沉外，船舶一般表现为首倾或者尾倾。船舶坐底由两部分组成，即船体下沉加 上一个纵倾影响。如果船舶静态时是平吃水，船舶的纵倾效应取决于船型和船舶的方形系数。 在静态时船底富余水深整体上减少，不论船首和船尾，被称为船舶坐底。这在船舶静态时吃水 和前进中吃水没有差异。 如果船舶在浅水域中以很大的速度航行的话，比如过船舶静态时船底富余水深为1.0至1.5米， 那么由于过度的坐底可能使得船首或者船尾发生触底。 17 对于肥大型船舶，比如超级油轮或矿砂船，船舶触底一般发生在船首。对诸如定线客船或集装箱船，触底一般发生在船尾。这只是假设在静止时船舶表现为平吃水。 如果大于0.700，那么最大下沉将出现在船首 Cb 如果小于0.700，那么最大下沉将出现在船尾 Cb 如果非常接近0.700，那么最大下沉将出现在船尾、船中和船首。这里的船舶坐底只考虑了Cb 船体下沉而没有考虑船舶纵倾的影响。 这必须是普遍的，因为在过去的二十年，几个船型往往趋向于垂线间长变短和船宽变大。这导致了当船舶存在横摇时因坐底使得船中处搁浅。 为什么船舶坐底现象近40年来变得这么严重, 船舶坐底总是存在于较小和较慢的在航船舶。这些下沉仅数厘米，因此也就无关紧要了。 然而，从60年代中期到这个新千年，船舶的规模稳步增长，直到我们拥有了350000吨及以上载重吨的超级油轮。这些超级油轮在其访问的港口即使是在小静态时平吃水也只有1.0到1.5的富余水深。 除了船型的不断发展，船舶的速度也在不断增长。例如集装箱船，其速度已经逐渐从注册时的16节增至现在的25节。 船舶设计在20世纪80年达和90年代发生了巨大的变化。油轮的设计，我们拥有了564739载重吨的Jahre Viking号，其垂线间长达到440米。这相当于五个足球场的长度。 在2002年，迄今为止最大的集装箱船，即”香港快运”投入使用。载重吨82800，航速25.3节，垂线间长304米，船宽42.8米，吃水13米。 由于静态时船底龙骨下富余水深的减少和船速的增加，船舶坐底现象逐渐增多。他们现在可以在1.50到1.75米之间，这当然绝不是无关紧要的。 运输部”M”的通知 在英国，过去20年，英国运输部已发出的”M”通知有关船舶坐底和船舶浅水航行时所有的影响问题。这些警告所有和船员相关的危险。 船舶进入浅水域将有一个或者多个以下现象: 1. 波浪的作用增加，特别是船首波。 2. 船舶操纵变得更加迟缓。一个引航员的说法...就像在粥里。 3. 在桥上的吃水指示或回声测深仪的回波将最终确定吃水的变化。 4. 螺旋桨转速指示器将明显减少。如果该船在开敞水域，例如没有宽度的限制，这种减少将高达 额定转速的15%，而如果在受限航道，这中转速减少量将高达额定转速的20%。 5. 同时也将有船速的下降。如果在开敞水域，船速下降高达30%。如果在受限航道，船速下降则高 达60%。 6. 船体开始突然震动。这是因为夹带的水造成的自然频率，和船舶相关的另一种频率的共振效应。 7. 任何的横摇，纵摇和首摇运动将会减轻，从深水驶入浅水时。这是因为船底的狭小空间起到了 缓冲作用。 8. 回旋半径增加，在浅水中将增加一倍。 9. 与深水中相比，船舶制动距离和停车次数增加。 10. 在浅水域中舵效变差。 船舶坐底与那些因素有关? 主要因素是船速。详细的分析表明船舶下沉变化随着速度的变化而变化。然而，下沉量的变化 18 可以说与船速的平方相近。换言之，我们可以以此为例子，如果我们的速度下降一半，下沉量为四分之一;如果速度提高一倍，则下沉两将翻一翻。在这种情况下，船速为对水速度。因此，对于当前船舶的影响，还要考虑潮流的速度。另一个重要的因素是船舶的方形系数，船体下沉量与船舶方形系数成正比。油轮因此比客轮下沉更多。 减少船舶坐底的过程 1.如果可能的话，通过排放压载水来减少船舶的平均吃水。这将导致两个中的一个减少: (一)在吃水较小时，方形系数的值将会略微下降，但与客轮相比不会有一个明显的减少。 (二)在吃水较小时，对于相对水深来讲，H/T值将增加。它已表明，H/T值增加将使得船舶坐底降低。 2.船舶开至更深的水域。对于类似的平均吃水和H/T值的增加将导致船舶坐底进一步降低。 3.当在一条河流中，如果可能的话，避免邻近船只和岸壁的影响。航道宽度越大船舶坐底将越小，除非该船只在航道的影响宽度内。 4.最快捷和有效地方法是减小船速来降低坐底。 负吃水 如果一系泊船的吃水从岸边看时，当存在落潮流为4节时，读出来的吃水是错误的。他们将不正确是因为落潮会造成船舶下沉和纵倾。在很多方面相当于船舶正以4节的速度前进。实际上它是一个船舶静态的下沉。 船舶将会表现为比实际排水量要大的吨数。如果在下一个港口开展吃水调查(零潮速)，将会有一个不足之处是位移不变。显然，这样超级油轮和定期客船将有较大的预测误差。 综述 总之，可以说，如果我们可以预测船舶在特定情况下的最大下沉量，那么我们得到的以下好处便会增加: 1( 船舶驾驶员便会知道船速降到多少能够确保船舶的安全。这可以节省一大笔的修理费。据报道， QEII的维修费为1300万美元...外加5000万美元的旅客预订损失。 2( 船员可以额外的增加几厘米吃水(当然除了在载重线的限制将被超出外)。 3( 如果由于过浅水时船舶过度下沉使得船舶搁浅，然后除了大修的费用外，船舶将一定时间暂停 运营，而被停运的船舶确实很费钱，因为收入损失达每天100000英镑。 4( 当船舶搁浅时总是伴随着一种索赔石油污染和清理费用的可能性。这些费用最终可能要船舶所 有人来支付。 19 <文献翻译二:原文> The Maximum Sinkage of a Ship T. P. Gourlay and E. O. Tuck Department of Applied Mathematics, The University of Adelaide, Australia A ship moving steadily forward in shallow water of constant depth h is usually subject to downward forces and hence squat, which is a potentially dangerous sinkage or increase in draft. Sinkage increases ghwith ship speed, until it reaches a maximum at just below the critical speed . Here we use both a linear transcritical shallow-water equation and a fully dispersive finite-depth theory to discuss the flow near that critical speed and to compute the maximum sinkage, trim angle, and stern displacement for some example hulls. Introduction For a thin vertical-sided obstruction extending from bottom to top of a shallow stream of depth h and ,infinite width, Michell (1898) showed that the small disturbance velocity potential (x,y) satisfies the linearized equation of shallow-water theory(SWT) ,, ， ,,0xxyy (1) 2F=U/gh,,,,FhhWhere, with the Froude number based on x-wise stream velocity U and water depth h. This is the same equation that describes linearized aerodynamic flow past a thin airfoil (see e.g., FhNewman 1977 p. 375), with replacing the Mach number. For a slender ship of a general cross-sectional shape, Tuck (1966) showed that equation (1) is to be solved subject to a body boundary condition of the form 'US()x,,(x,0)=y,2h (2) where S(x) is the ship’s submerged cross-section area at station x. The boundary condition (2) indicates that the ship behaves in the (x ,y) horizontal plane as if it were a symmetric thin airfoil whose thickness S(x)/h is obtained by averaging the ship’s cross-section thickness over the water depth. There are also boundary ,,conditions at infinity, essentially that the disturbance velocity vanishes in subcritical flow ,,0(). As in aerodynamics, the solution of (1) is straightforward for either fully subcritical flow (where it is elliptic) or fully supercritical flow (where it is hyperbolic). In either case, the solution has a singularity as F1,,,0h, or .In particular the subcritical (positive upward) force is given by Tuck (1966) as 2,UF=B'(x)S'()logdxdx,,,,,,221Fh,,h (3) with B(x) the local beam at station x. Here and subsequently the integrations are over the wetted length of 20 LL,,,X22the ship, i.e., where L is the ship’s waterline length. This force F is usually negative, i.e., downward, and for a fore-aft symmetric ship, the resulting midship sinkage is given hydrostatically by 2FV,,hsC,S,,22L,,1,Fh (4) VSxdx,(),where is the ship’s displaced volume, and 2L,,,,,'()'()logCdxdBxSxs,,2AV,W (5) ABxdx,()C,1.4w,swhere is the ship’s waterplane area. The nondimensional coefficient has been shown by Tuck & Taylor(1970) to be almost a universal constant, depending only weakly on the ship’s hull shape. Hence the sinkage appears according to this linear dispersionless theory to tend to infinity as F,1F,1hh.However, in practice, there are dispersive effects near which limit the sinkage, and which cause it to reach a maximum value at just below the critical speed. Accurate full-scale experimental data for maximum sinkage are scarce. However,, according to linear inviscid theory, the maximum sinkage is directly proportional to the ship length for a given shape of ship and depth-to-draft ratio (see later). This means that model experiments for maximum sinkage (e.g., Graff et al 1964) can be scaled proportionally to length to yield full-scale results, provided the depth-to-draft ratio remains the same. The magnitude of this maximum sinkage is considerable. For example, the Taylor Series A3 model studied by Graff et al (1964) had a maximum sinkage of 0.89% of the ship length for the depth-to-draft ratio h/T = 4.0. This corresponds to a midship sinkage of 1.88 meters for a 200 meter ship. Experiments on maximum squat were also performed by Du & Millward (1991) using NPL round bilge series hulls. They obtained a maximum midship sinkage of 1.4% of the ship length for model 150B with h/T =2.3. This corresponds to 2.8 meters midship sinkage for a 200 meter ship. Taking into account the fact that there is usually a significant bow-up trim angle at the speed where the maximum sinkage occurs, the downward displacement of the stern can be even greater, of the order of 4 meters or more for a 200-meter long ship. It is important to note that only ships that are capable of traveling at transcritical Froude numbers will ever reach this maximum sinkage. Therefore, maximum sinkage predictions will be less relevant for slower ships such as tankers or bulk carriers. Since the ships or catamarans that frequently travel at transcritical Froude numbers are usually comparatively slender, we expect that slender-body theory will provide good results for the maximum sinkage of these ships. For ships traveling in channels, the width of the channel becomes increasingly important around F,1hwhen the flow is unsteady and solitons are emitted forward of the ship (see e.g.,Wu & Wu 1982). Hence experiments performed in channels cannot be used to accurately predict maximum sinkage for ships in open water. The experiments of Graff et al were done in a wide tank, approximately 36 times the model beam, and are the best results available with which to compare an open-water theory. However, even with F,1hthis large tank width, sidewalls still affect the flow near , as we shall discuss. 21 Transcritical shallow-water theory (TSWT) ,,0It is not possible simply to set ‚ in (1) in order to gain useful information about the flow near F,1h. As with transonic aerodynamics, it is necessary to include other terms that have been neglected in the linearized derivation of SWT (1). An approach suggested by Mei (1976) (see also Mei & Choi,1987) is to derive an evolution equation F,1hof Korteweg-de Varies (KdV) type for the flow near. The usual one-dimensional forms of such equations contain both nonlinear and dispersive terms. It is not difficult to incorporate the second space dimension y into the derivation, resulting in a two-dimensional KdV equation, which generalizes (1) by adding two terms to give 312,,，,,,,，,,h0xxyyXXXxxxxU3 (6) ,,,XXXxxxxThe nonlinear term in but not the dispersive term in was included by Lea & Feldman (1972). Further solutions of this nonlinear but nondispersive equation were obtained by Ang (1993) for a ship in a channel. Chen & Sharma (1995) considered the unsteady problem of soliton generation by a ship in a channel, using the Kadomtsev-Petviashvili equation, which is essentially an unsteady version of equation (6). Although they concentrated on finite-width domains, their method is also applicable to open water, albeit computationally intensive. Further nonlinear and dispersive terms were included by Chen (1999), allowing finite-width results to be computed over a larger range of Froude numbers. Mei (1976) considered the full equation (6) in open water and provided an analytic solution for the ,,XXXlinear case where the term is omitted. He showed that for sufficiently slender ships the nonlinear term in equation (6) is of less importance than the dispersive term and can be neglected; also that the reverse is true for full-form ships where the nonlinear term is dominant. This is also discussed in Gourlay (2000). As stated earlier, most ships that are capable of traveling at transcritical speeds are comparatively slender. For these ships it is dispersion, not nonlinearity, that limits the sinkage in open water. Nonlinearity is usually included in one-dimensional KdV equations by necessity, as a steepening agent to provide a ,xxxxbalance to the broadening effect of the dispersive term in .In open water, however, there is already ,yyan adequate balance with the two-dimensional term in . This is in contrast to finite-width domains, which tend to amplify transcritical effects and cause the flow to be more nearly unidirectional. Hence nonlinearity becomes important in finite-width channels to such an extent that steady flow becomes impossible in a narrow range of speeds close to critical (see e.g., Constantine 1961, Wu & Wu 1982). Therefore, for slender ships in shallow water of large or in finite width, we can solve for maximum squat using the simple transcritical shallow-water (TSWT) equation ,,,，,，,,0xxyyxxxx (7) 2,h3,(Writing ), subject to the same boundary condition (2). The term in ƒ provides dispersion that 22 was absent in the SWT,and limits the maximum sinkage. Conclusions We have used two slender-body methods to solve for the sinkage and trim of a ship traveling at arbitrary Froude number, including the transcritical region. The transcritical shallow water theory (TSWT) developed by Mei (1976) has been extended and exploited numerically, using numerical Fourier transform methods to give sinkage and trim via a double numerical integration. This theory has also been extended to the case of a ship moving in a channel of finite width; however, the numerical difficulty in computing the resulting force integral, and its limited validity, mean that the open-water theory is more practically useful. The finite-depth theory (FDT) developed by Tuck & Taylor (1970) has also been improved and used for general hull shapes. This theory gives a sinkage force and trim moment that are slightly oscillatory in Fh. Since the theory involves summing infinite-depth and finite-depth contributions, both of which vary 2Uwith at high Froude numbers, any error will grow approximately quadratically with U. Therefore we cannot use this theory at large supercritical Froude numbers. Also, the difficulty in finding the infinite-depth contributions numerically, as well as the extra numerical integration needed to compute the force and moment, make the FDT slightly more dif. cult to implement than TSWT. In practice, scenarios in which ships are at risk of grounding will normally have h/L < 0.125. Since the TSWT is a shallow water theory and it works well at h/L = 0.125, we expect that it will give even better results at smaller, practically useful values of h=L. Also, since the TSWT and FDT give almost identical results for h/L <0.125, and the TSWT is a much simpler theory, we recommend it as a simple and accurate method for predicting transcritical squat in open water. 备注:T.P.Gourlay and E.O.Tuck,The Maximum Sinkage of a ship[J],Jourmal of Ship Research, 2001,50~58 <文献翻译二:译文> 船舶最大下沉量 T. P. Gourlay and E. O. Tuck 澳大利亚阿德莱德大学 一艘在等深为h的浅水中平稳前行的船舶通常趋向于受到向下的合力并产生船体下沉, 这种下 gh沉是一种潜在的下沉或吃水增加。下沉量随船速增加而增加，直至临界速率。此处我们同时利 用”线性跨临界浅水方程”和”完全分散限深理论”研究典型船体在接近临界速度时的水流和计算 这些船体的最大下沉量、纵倾角和船尾位移。 引言 对于在水深为h且无宽度限制的浅水流中的一艘瘦长型的从船底至顶均为垂直舷侧的物体, ,Michell (1898) 证明了小扰动速率的电位 (x,y)满足浅水理论(SWT)线性方程 ,, ， ,,0xxyy 2F=U/gh,,,,Fhh其中, 且 ，傅汝德数建立在 x-wise 流速 U 和水深h的基础上。此方程与 23 描述通过瘦长型翼型的线性空气动力学的流体的方程 (见Newman 1977 p. 375)是大致相同的, 不同 Fh的是用r代替了马赫数。对于一艘常见横截面形状的瘦长型船舶来说, Tuck (1966) 指出解决方 程(1)受到如下形式的船体边界条件的限制 'US()x,,(x,0)=y,2h 其中 S(x) 是在x处水下横截面区域.边界条件(2) 指示船舶在 (x ,y) 水平面处的表现如一个瘦长形的对称翼型，其厚度S(x)/h是通过对水深求全船横截面厚度的平均数获得。在无限宽水流中同样 ,,0,,也有边界条件，主要是扰动速率 在缓流 ()中消失了. 同空气动力学中一样, 方程(1)的解答仅仅针对充分缓流(椭圆形)或充分缓流(双曲线形). 对 F1,,,0h以上任何一种缓流, 方程的解答中都存在奇点如, 或 。特别地，亚临界力(正向上)由Tuck (1966)给出 2,UF=B'(x)S'()logdxdx,,,,,,221Fh,,h LL,,,X22B(x) 是x位置处的横梁. 此处和之后的积分下限是在船舶浸湿长度之内，即 这里L是船舶水线面的长度。 这个F力通常是负的，即方向向下，并且对于一艘首尾对称的船舶， 静力学中给出最终的船中下沉量 2FV,,hsC,S,,22L,,1,Fh VSxdx,(),其中 是船舶排水容量，且 2L,,,,,'()'()logCdxdBxSxs,,2AV,W ABxdx,()C,1.4w,s其中 是船舶水线面区域。 由Tuck & Taylor(1970)给出的非色散系数 已被证明接近恒定不变，只是很微弱的受船壳形状影响。 F,1h此处下沉量根据线性非色散理论将趋向于无穷大。然而，实际情况中，在 附近存在的色散效应限制了下沉量并导致其在临界速度处达到最大值。 精确的最大下沉量的全船实验数据也非常的有限。然而，根据线性无粘理论，最大下沉量对于给定的船型跟船长成正比(见下文)。这意味着最大下沉量的模拟实验，能够给出全面的结果，提供的深吃水船舶也保持不变。 这个最大下沉量的幅度相当大。例如，1964年Graff er al 研究的Taylor系列A3模型在水深吃水比为4时具有船长的0.89%的下沉量。这相当于一艘200米的船舶，船中部下沉1.88米。在1991年Du & Millward利用NPL系列船壳进行了船舶坐底量实验。他们获得了在水深吃水比为2.3时150B型的船舶中部最大下沉量为船长的1.4%。这相当于200米长的船舶船中下沉2.8米。考虑到这个因素，当最大下沉发生时通常会有一个显著地船首纵向上扬角度，船尾处的下沉更加大，对于一艘200米船舶来讲可能更多。 24 值得注意的是只有的傅汝得数相应的船舶才能达到这个最大下沉量。因此，对于油轮或者散货船起最大下沉量的预测将会减少。由于航行的傅汝德系数内的船舶大都比较瘦长，我们希望细长体理论能够提供一个关于最大下沉量的好结果。 F,1h对于航道中行驶的船舶，当在附近且流布稳定时航道的宽度变得更加重要(如见，Wu & Wu 1982)。Hence在航道中的实验不能很准确的用来预测船舶在开敞水域的最大下沉量。Graff et al 在大水箱中的实验，相当于实验宽度的36倍，跟开敞水域理论相比已经是个不错的结果。然而，尽管 F,1h有如此大的试验箱，当时岸壁效应依旧产生影响，因此仍需要讨论。 浅水理论 F,1,,0h这是不可能简单的在(1)中设置，为了增加在时的有用信息。根据空气动力学，还需要包括其他在SWT中忽略的方面。 F,1h在1976年Mei建议的方法是一个时KdV方程。通常的一维形式既包括此类方程非线性和色散条款。由于不难推到纳入第二空间的维数，通过添加两个方面给出二维KdV方程，从而给出了 312,,，,,,,，,,h0xxyyXXXxxxxU3 ,,,XXXxxxx中的非线性项被 Lea & Feldman (1972)加入其中，但没有包括中的色散项。这个非线性但非色散方程的对水道中的船舶的进一步求解被 Ang (1993) 获得。 Chen & Sharma (1995) 考虑到了水道中船舶产生的孤波的不稳定问题， 利用 Kadomtsev-Petviashvili 方程, 即方程(6)一种不规则形式。 尽管主要针对的是宽度有限的水域，他们的方法仍适用于开放水域，虽然这样的计算量较庞大。非线性和色散方面的内容进一步被陈(1999)列入，从而允许有限宽度的结果计算覆盖傅汝德数的较大范围。 ,,XXXMei (1976) 研究了方程(6)在开放水域中的完全形式并对忽略了项的线性情况提供了解析解法。他阐明了对于船体足够细长的船舶，方程(6)中的非线性项不如色散项重要并可以被忽略;同样，反过来说对于船体肥大的船舶非线性项则是主要的。这在 Gourlay (2000)中也有涉及。 如前所述，大多数可以跨临界速度航行的船舶相对而言都是较为细长的。 对于这些船舶，色散限制了其在开放水域中的下沉量，而不是非线性。非线性项因其必要性通常包含在一维KdV方程中， ,,yyxxxx作为steepening中介以平衡中的色散项的宽化效应。但是在开放水域，在中的二维项对该效应已有足够的平衡。 这是相对于宽度有限水域来说的，在限宽水域有扩大跨临界效应的趋势，并引起水流更加接近于单一方向。 此时非线性特性在限宽水道变得如此重要，以至于在接近临界速度的狭小速度范围内稳定的水流可能性极小(见 Constantine 1961, Wu & Wu 1982). 因此，对大宽度或无限宽度的浅水域中的瘦长型船舶来说， 我们可以利用简化跨临界浅水域(TSWT) 方程解决最大下沉 ,,,，,，,,0xxyyxxxx 2,,h3,(注:)，服从边界条件(2). 公式中的项提供了SWT中缺少的色散性并限制了最大下沉量。 结论 我们已经用两个细长体理论来解决客船在任意傅汝德系数的下沉和纵倾，包括跨区域的。有Mei在1976年提出的TSWT理论利用数值模拟进行了扩展和利用，通过数值傅里叶变换给出一种双重数值积 25 分方法来计算下沉和纵倾。这个理论同样被用于宽度受限的航道中运动的船舶。然而，其在数值计算上的困难意味着在开敞水域理论更加的实用。 由Tuck & Taylor (1970)开发的FDT技术同样被发展和用于一般的船型。这个理论给出的下沉力和纵倾有略微的研究价值。由于涉及到受限和无限宽度的条件限制，在傅汝的系数较大时都发生变化。任何错误都将增加二次。因此，在傅汝得数较大时不能用此理论。此外，在寻找无限宽度条件时也存在困难，以及需要额外的数值积分来计算力和力矩，使FDT的偏差变小，从而比TSWT更实用些。 在实践中，在h/l小于0.125时通常存在触底的危险。由于TSWT理论适合于浅水区和h/l为0.125时，我们希望它能够给出在h=l时较小的，实际有用过的值。此外，由于TSWT和FDT在h/l<0.125时给出的结果几乎相同，而TSWT是一个更加简单的理论。我们推荐它作为开敞水域中船体坐底的一个简单实用的预测方法。 26