第一章 船体形状及近似计算

1、绪论船舶稳性船舶稳性船舶抗沉性船舶抗沉性wlwlrt船舶快速性船舶快速性wlwl船舶耐波性（适航性）船舶耐波性（适航性）船舶操纵性船舶操纵性第一章第一章 船体形状及近似计算船体形状及近似计算基平面基平面中站面中站面中线面中线面船体型表面船体型表面型线图所表示的船体外形称为船体型表面型线图所表示的船体外形称为船体型表面甲板线龙骨基线中横剖面设计水线面中纵剖面尾首船舯 )(21afdddloalpplwldm设计水线龙骨线ddfdabdfdm舷墙顶线龙骨板甲板甲板边线首垂线尾垂线基线设计水线基线lbaw blacwwpbdam dbacmmdlbdblcb ddlamamlacmp（纵向）bdla

2、wdacwvp 1-2 船体型线图与型值表船体型线图与型值表 船体型线图所表示的船体表船体型线图所表示的船体表面称为面称为（1）横剖线图）横剖线图平行于中站面的一组平行于中站面的一组横剖面；横剖面；（2）半宽水线图）半宽水线图平行于基线面的一平行于基线面的一组水平剖面；组水平剖面；（3）纵剖线图）纵剖线图平行于中线面的一组平行于中线面的一组纵剖面。纵剖面。361028410244001312300200100142223151610191821172080060070050011001000900a1300140012001550-1-23610284-1-28850纵剖850纵剖cbll 单

3、位: mm舷边折角线100200300400500600700800900100011001200130014001500内外0-2138.62207.72245.62277.02306.22334.02360.12385.5-2399.01-2215.32251.02283.62314.22344.12374.02404.22434.6-2451.12-1102.42231.32259.92287.02315.42344.82374.52404.32434.12464.0-2480.23-454.61098.01912.02261.12283.82308.42335.72364.02392.

4、62421.42450.12479.0-2494.54-399.7965.71516.72256.32280.92303.12327.32353.92381.22408.72436.32463.92491.6-2506.65-511.01076.61641.82272.42295.42319.02343.02369.22396.32423.42450.62477.72504.8-2519.6644.8622.11183.11735.32288.12310.72333.92358.22384.22410.72437.32464.02490.62517.3-2102.82277.42532.071

5、66.0730.51276.61817.02302.42325.62349.32373.72398.72424.22449.82475.52501.32527.1-2112.22287.72541.38271.1827.41375.51907.22315.52338.32362.02385.82410.52435.52460.62485.62510.72535.8-2121.72298.12549.99361.9905.11448.41966.42328.62351.72374.82398.02421.12444.22467.32490.52513.62536.7-2128.82308.225

6、50.010507.9967.81491.02005.62339.32362.52384.62406.62428.42450.22472.02493.72515.52537.2-2136.12317.72550.011526.31015.41523.02030.52345.22366.52387.82409.12430.52451.82473.12494.42515.72537.0-2146.02324.22550.012501.3978.21455.01931.82350.82371.32387.82408.92430.02451.02472.12493.22514.32535.3-2155

7、.42329.72550.013469.0913.51358.11802.62330.82353.22374.22396.832419.42442.12464.72487.32509.92532.5-2152.32320.82550.014431.7837.71242.81647.62051.62334.32351.12376.42401.72427.12452.42477.72503.12528.4-2141.82302.22549.915397.6770.71143.81516.91890.02287.32314.62343.72372.82401.82430.92460.02489.02

8、518.1-2113.12270.42544.816336.2651.4972.31303.01656.82230.92246.62278.52310.32342.12374.02405.82437.72469.52501.42058.12212.02501.417255.9514.1789.71067.41362.91702.92106.62145.92185.22224.52263.42303.12342.42381.72421.01929.52080.72423.818154.5343.4543.0748.0964.61209.61745.11794.21843.31892.51941.

9、61990.72039.92089.02138.11618.81742.12146.01927.7111.6219.8345.0488.5663.6857.21150.21232.01313.81395.51477.31559.11640.91722.71023.81123.51742.120-86.9171.7316.6432.2547.8663.4779.1894.91010.3195.1233.01047.821-134.5284.3-345.621-站号舭部折角线半 宽 值水 线某万吨级货轮型值表1200240036004800600072008400960010800水线水线水线水线

10、水线水线水线水线水线0-49623053980498365926939127557380195410971583332048656386723884328707247114342045255332104238580469743098870894959690368026913724463856326745784485689261962710040101604-444958046860774385179150955999051007010200102005-64127691847790639496982510011101521020010200102006-81889101955598301001

11、61013310183102001020010200102007-937898921008810175102001020010200102001020010200102008-9809101711020010200102001020010200102001020010200102009-99581020010200102001020010200102001020010200102001020010-99581020010200102001020010200102001020010200102001020011-987710190102001020010200102001020010200102

12、00102001020012-96101006610200102001020010200102001020010200102001020013-914897229958100751013510182102001020010200102001020014-838490499418966998479967100401010610146102001020015-72397976842987759005926794169600973199591006116-5634643869307295758278238015828185339169-17-37644520498453335598585960836

13、44188218027899918-2000265030403320354037303960435049208560814019-950152019202140222019501850229028104850657020-13072012301489140884039042057025704220半宽值基线站号上甲板舷墙与首楼单位: mm某万吨级货轮型值表 (续表)1200360060008400纵剖线纵剖线纵剖线纵剖线07555922612525-1388014980152917370918613490135861468628655343735010142133251442532082242

14、521879401310314203413680260658041291914019521369423463127661386662292261398126401374072285446112540138408228541691246213562922854991240713507102285499124001350011228541141245213552122285426312451136451322854552126711377214228792222128371393515228430351013054141541621791640101811334214454172010207840

15、14445136871600518530625012800-13900162401916501220015850-1425016600站号舷墙与首楼高度值上甲板单位: mmcx0dgfedllcx1x2x3xx-1xny1y0ynyn-1y3y2-a0a1an-1a2- 10021yya1210 nccddaaaaa niinnnnnnnndcccddynlyyyyyynlyyyynlyyyyaaaaxya001101101101210221212121dnyy 021cy2y1edyy3lxdxlxel)(xfy y2210)(xaxaaxfy3202210322d)(dlalaxxaxaa

16、xyslllla0、a1、a2为常数（1-5）cy2y1edyy3lxdxlxel)(xfy y321yyys（1-6）当x= l时，y1=a0-a1l+a2l2当x= 0时，y2=a0当x= +l时，y3=a0+a1l+a2l2)()()()(210221002210allaalalaaalalaas）320322lala)()()(210allaa1-73/202llll34,31解联立方程得1-8)4(31321yyys)4(s.m.)4(6321321yyylyyyls令令l为底边长度，为底边长度，l=2l，上式成为，上式成为1-9cx0dgfedllcx1x2x3x x-2x ny1

17、y0y ny n-1y3y2-s1s n-1s3-x x-1y4x4efyxnnnyyyyyyyls 1232104242431(1-10)注意注意: 等分数等分数 n 必必须是偶数须是偶数! nnnyyyyyyyls12321042424s.m.(1-11) nnnyyyyyyyls212222132123210实际计算总面积可写成：实际计算总面积可写成： nnnyyyyyyyls2122221s.m.2123210332210)(xaxaxaaxfy4321yyyys320332210322d)(dlalaxxaxaxaaxysllll（1-12）（1-13）cy2y1edy3y4hlxo

18、lflhyl当 x=+h 时，3322101hahahaay当 x=h 时，3322101hahahaay当 x=h/3 时，33221022719131hahahaay当 x=h/3 时，33221022719131hahahaay将上述个将上述个y 值代入到值代入到（1-13）式，整理后）式，整理后得到：得到：)271271()9191()3131()(332210hahahaas（1-14）0271271329191031312hh解联立方程lhlh89438341lhlh83418943)33(834321yyyyls)33(s.m.)33(843214321yyyylyyyyls（1

19、-15）（1-16）)33233(837654321yyyyyyyls)33233(s.m.7654321yyyyyyyls16s.m.（1-15）（1-17） )332233(833233210nnnnyyyyyyyyls)332233(s.m.3233210nnnnyyyyyyyylscedy0y1y2llxys0-1s1-2（1-19）曲线曲线cd下的总面积：下的总面积：)85(12121010yyyls)58(12121021yyyls)4(312102110yyylss 【 5，8，1 】 法法（只适用于求面积）（只适用于求面积）cedy0y1y2llxys0-1s1-2（1-20）

20、)103(241210210yyylm 【 3，10，1 】法（只适用于求静矩）】法（只适用于求静矩） )310(241210221yyylm x0 x2x3x5x 1/2y1y0y 5y 6y3y2x6y4x4x 3/2x1y0=1589.7y1/2=2040.5y1= 2319.6y3/2=2483.8y2= 2602.6 y3= 2733.6y4= 2818.4y5= 2867.9y6= 2898.9 l= 3000mmx0 x2x3x5x 1/2y1y0y 5y 6y3y2x6y4x4x 3/2x165432104242431yyyyyyylsob)4.04.0(2425)58(121

21、)33(83)85(1216543216545432321yyyyyylyyylyyyylyyylscbx0 x2x3x5x 1/2y1y0y 5y 6y3y2x6y4x4x 3/2x1)424232221(31654322/312/10yyyyyyyyylsob)424(31)424(61654322112/1021yyyyylyyyyylsoby 值(1)(2)(3)(1)(2)(3)(mm)坐标系数坐标系数坐标系数曲线ob曲线cb曲线ob1/22040.5240811 1/22483.82496801589.711/2159079512319.642/519279928232022602

22、.6211 1/252052603390432733.64141093527341093542818.421256372818563752867.94141147228681147262898.912/51289911602899470151311047009面积(mm2)470153864096852647008821l(mm):3000序号excel 电子计算表格电子计算表格yx水线半宽辛氏系数面积函数力臂函数静矩函数惯性矩函数惯性矩函数y(m)s.m.(ii)(iii)x(iv)(v)(v)(vi)(iii)(viii)iiiiiiivvviviiviiiix001/20-5000016

23、.3212.6-4-50.4201.6250.0500.128.618.6-3-25.877.4636.1636.139.2218.4-2-36.873.6778.71557.449.419.4-1-9.49.4830.6830.659218000729.01458.068.118.118.18.1531.4531.476.7213.4226.853.6300.8601.584.614.6313.841.497.397.392.424.8419.276.813.827.6100.21/20.150.52.50.00.098-54544.46240.1站号y3表1-5 【例3 】计算表格niin

24、ynlyyynls121)(（1-24）（1-25）三、三、乞贝雪夫法乞贝雪夫法y2y1y3eglll-x1x2x1 假定用三次抛物线代替曲线cd，即y=a0+a1x+a2x2+a3x3式中：a0，a1，a2， a3为常数，曲线cd下面积将由积分公式给出：230332210322d)(dallaxxaxaxaaxysllll（1-26）所设的三次抛物线在e、f和g三点有 x=x1 时， y1=a0a1x1a2x12a3x13 x= x0 时， y2=a0 x= x1 时， y3=a0a1x1a2x12a3x13将上式代入（1-25）式，得 s=p(3a02a2x12)=3pa02px12a2由

25、于式（1-26）与式（1-27）代表同一面积，故两式中的a0、a2各项系数应分别相等，即32132223lpxlpllxlp7071. 021321解联立方程由此得曲线cd下的面积（1-27）y3y-2y1y2y4y-3y-1y0y-4x-2x2x4x-3x-1x0 x-4lllx3x1)(32321yyyls或)(3321yyyls（1-29）（1-28）对于n =212时的纵坐标位置（书表1-10）niinnynlyyyynls1121)(（1-30）对于n个纵坐标的乞贝雪夫公式为采用不等间距的纵坐标和不同的乘数niiinnyplypypyplydxs12211)(（1-30） 高斯法具有

26、比辛浦生法或乞贝雪夫法更为精确的优点，如五个纵坐标的高斯法可达到九个纵坐标的辛浦生法或九个纵坐标的乞贝雪夫法的同样精度。四、四、高斯法高斯法式中：l曲线底边总长；n 纵坐标数；y i 不等间距的纵坐标值；pi 纵坐标前的乘数；l底边半长。y0y1y2y3y4/12/6/4/3y= t g x（1）精确解22064. 0coslndtg3/03/ 0 xxxs坐标号横坐标(x)纵坐标(y)梯形乘数( t . m .)面积函数000.000001/20.000001pi/120.2679510.267952pi/60.5773510.577353pi/41.0000011.000004pi/31.

27、732051/20.866032.71133（2）梯形法22594. 071133. 212)22(dtg432103/ 0yyyyylxxs（3）辛浦生第二法坐标号横坐标(x)纵坐标(y)辛氏乘数(s.m.)面积函数000.0000010.000001pi/120.2679541.071802pi/60.5773521.154703pi/41.0000044.000004pi/31.7320511.732057.9585522107. 095855. 71231)424(31d tg432103/ 0yyyyylxxsy= t g x0.37454(/6)0.83250(/6)/3/6（4）

28、乞贝雪夫法坐标号横坐标(x)纵坐标(y)100.0879320.3397230.5773540.8765551.426823.30837)6/(83250. 06/)6/(83250. 06/6/)6/(37454. 06/)6/(37454. 06/22056. 030837. 35/35d tg513/ 0iiylxxs（3）高斯法坐标号横坐标(x)纵坐标(y)乘数(g.m.)面积函数1 0.049180.118460.0058320.246470.239310.0589830.577350.284450.1642341.041140.239310.2491651.550900.11846

29、0.18372 0.661916/)6/(53847. 06/)6/(53847. 06/6/90618. 06/6/90618. 06/22064. 066192. 03d tg513/ 0iiiyplxxs五、五、增加中间坐标增加中间坐标 和端点坐标修正和端点坐标修正y0y1y2y3y4y5543211/2t)42423221(3)424(3)4(6543212/105432112/1050yyyyyyytyyyyytyyytydzst1. 1.增加中间坐标增加中间坐标llly0一般用目测，使梯形obcd面积=曲线下oacb的面积。2. 2. 端点坐标修正端点坐标修正 （1）船体曲线在端点

30、上）船体曲线在端点上 用目测，使三角形deg面积与曲线下dcg的面积相等，ef平行于da，df就是坐标修正值y0。 （2）船体曲线超过了端点）船体曲线超过了端点lly0y0y1y2ly0y1 用目测，使三角形abd面积与曲线下abc的面积相等，df平行于be，ef就是坐标修正值y0。 （3）船体曲线不到端点）船体曲线不到端点面积abe=ly1 /2面积bed=面积aef =ly0 /2根据三角形abe与三角形efd相似,可以证明:则面积abd=l(y1 - y0 )/2tyoy1yoyo(a)(b)(c)(d)ttt 用梯形法进行有关横剖面计算时，剖面底部的坐标值也应给予适当修正，其原理与上述

31、方法相同。用梯形法修正横剖面的计算用梯形法修正横剖面的计算六、六、积分曲线特性积分曲线特性y2y1y1dxdy1y2yxg(a)(b)(c)xyyd1xyyd12b1b2xgy2y1y1dxdy1y2yxg(a)(b)(c)xyyd1xyyd12b1b2caxy0d常数 xxyxy01d)(xfy 原曲线（导数曲线）一次积分曲线/面积曲线y2y1y1dxdy1y2yxg(a)(b)(c)xyyd1xyyd12b1b2 xxyxy01dxyyd/d1 原曲线在原曲线在x轴上的交点轴上的交点对应积分曲线的极大值或对应积分曲线的极大值或极小值极小值（即在o和c 两点导数变号dy1 /dx=0 ）。0

32、dd212xydxyd 原曲线的极大值或原曲线的极大值或极小值对应积分曲线的极小值对应积分曲线的拐点拐点m ，即在该点有：，即在该点有：0ddxyy2y1y1dxdy1y2yxg(a)(b)(c)xyyd1xyyd12b1b2p1q1q2p2 原曲线的二次积分原曲线的二次积分曲线曲线op2b2称为称为静矩曲线静矩曲线 xxxxxyxyy00012ddd)(dddd1222xyxyxyy2y1y1dxdy1y2yxg(a)(b)(c)xyyd1xyyd12b1b2p1q1q2p2 静矩曲线静矩曲线的二次的二次导数曲线是原曲线导数曲线是原曲线y2y1y1dxdy1y2yxg(a)(b)(c)xyyd1xyyd12b1b2p1q1q2p2 原曲线原曲线opc下的面下的面积对通过积对通过c点的纵坐标点的纵坐标cb的静矩的静矩m0等于其积分曲等于其积分曲线线op1b1下的面积。或者下的面积。或者等于其重积分曲线等于其重积分曲线op2b2