第一章_船体形状及近似计算

1、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 dBACMMdLBdBLCBddLAMAMLACMP（纵向）BdLAWdACWVP1-2 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 1）横剖

2、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 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 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 单位: mm舷边折角线100200300400500600700800900100011001200130014001500内

3、外0-2138.62207.72245.62277.02306.22334.02360.12385.5-2399.01-2215.32251.02283.62314.22344.12374.02404.22434.6-2451.12-1102.42231.32259.92287.02315.42344.82374.52404.32434.12464.0-2480.23-454.61098.01912.02261.12283.82308.42335.72364.02392.62421.42450.12479.0-2494.54-399.7965.71516.72256.32280.92303.1

4、2327.32353.92381.22408.72436.32463.92491.6-2506.65-511.01076.61641.82272.42295.42319.02343.02369.22396.32423.42450.62477.72504.8-2519.6644.8622.11183.11735.32288.12310.72333.92358.22384.22410.72437.32464.02490.62517.3-2102.82277.42532.07166.0730.51276.61817.02302.42325.62349.32373.72398.72424.22449.

5、82475.52501.32527.1-2112.22287.72541.38271.1827.41375.51907.22315.52338.32362.02385.82410.52435.52460.62485.62510.72535.8-2121.72298.12549.99361.9905.11448.41966.42328.62351.72374.82398.02421.12444.22467.32490.52513.62536.7-2128.82308.22550.010507.9967.81491.02005.62339.32362.52384.62406.62428.42450

6、.22472.02493.72515.52537.2-2136.12317.72550.011526.31015.41523.02030.52345.22366.52387.82409.12430.52451.82473.12494.42515.72537.0-2146.02324.22550.012501.3978.21455.01931.82350.82371.32387.82408.92430.02451.02472.12493.22514.32535.3-2155.42329.72550.013469.0913.51358.11802.62330.82353.22374.22396.8

7、32419.42442.12464.72487.32509.92532.5-2152.32320.82550.014431.7837.71242.81647.62051.62334.32351.12376.42401.72427.12452.42477.72503.12528.4-2141.82302.22549.915397.6770.71143.81516.91890.02287.32314.62343.72372.82401.82430.92460.02489.02518.1-2113.12270.42544.816336.2651.4972.31303.01656.82230.9224

8、6.62278.52310.32342.12374.02405.82437.72469.52501.42058.12212.02501.417255.9514.1789.71067.41362.91702.92106.62145.92185.22224.52263.42303.12342.42381.72421.01929.52080.72423.818154.5343.4543.0748.0964.61209.61745.11794.21843.31892.51941.61990.72039.92089.02138.11618.81742.12146.01927.7111.6219.8345

9、.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1200240036004800600072008400960010800水线水线水线水线水线水线水线水线水线0-49623053980498365926939127557380195410971583332048656386723

10、884328707247114342045255332104238580469743098870894959690368026913724463856326745784485689261962710040101604-444958046860774385179150955999051007010200102005-64127691847790639496982510011101521020010200102006-8188910195559830100161013310183102001020010200102007-93789892100881017510200102001020010200

11、1020010200102008-9809101711020010200102001020010200102001020010200102009-99581020010200102001020010200102001020010200102001020010-99581020010200102001020010200102001020010200102001020011-98771019010200102001020010200102001020010200102001020012-96101006610200102001020010200102001020010200102001020013

12、-914897229958100751013510182102001020010200102001020014-838490499418966998479967100401010610146102001020015-72397976842987759005926794169600973199591006116-5634643869307295758278238015828185339169-17-3764452049845333559858596083644188218027899918-2000265030403320354037303960435049208560814019-950152

13、019202140222019501850229028104850657020-13072012301489140884039042057025704220半宽值基线站号上甲板舷墙与首楼单位: mm (续表)1200360060008400纵剖线纵剖线纵剖线纵剖线07555922612525-138801498015291737091861349013586146862865534373501014213325144253208224252187940131031420341368026065804129191401952136942346312766138666229226139812640

14、137407228544611254013840822854169124621356292285499124071350710228549912400135001122854114124521355212228542631245113645132285455212671137721422879222212837139351522843035101305414154162179164010181133421445417201020784014445136871600518530625012800-13900162401916501220015850-1425016600站号舷墙与首楼高度值上甲板

15、单位: mmCx0DGFEdllcx1x2x3xx-1xny1y0ynyn-1y3y2-a0a1an-1a2- 10021yya1210 ncCDdaaaaA niinnnnnnnndccCDdynLyyyyyynLyyyynLyyyyaaaaxyA001101101101210221212121dnyy 021Cy2y1EDyy3Lxdxlxel)(xfy y2210)(xaxaaxfy3202210322d)(dlalaxxaxaaxyslllla0、a1、a2为常数（1-5）Cy2y1EDyy3Lxdxlxel)(xfy y321yyys（1-6）当x= l时，y1=a0-a1l+a2l

16、2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(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1-932143yyylsCx0DGFEdllcx1x2x3x x-2x ny1y0y ny n-1y3y2-s1s n-1s3-x x-1y4x4efyxnnnyyyyyyylS 1232104242431(1-10)注意注意: : 等分数等分数

17、 n n 必须是偶数必须是偶数! ! 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）Cy2y1EDy3y4hlxolFlhyL当 x=+h 时，3322101hahahaay当 x=h 时，3322101hahahaay当 x=h/3 时，33221022719131h

18、ahahaay当 x=h/3 时，33221022719131hahahaay将上述四个将上述四个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（1-15）（1-16）)33233(837654321yyyyyyylS)33233(S.M.7654321yyyyyyyLS16S.M.（1-15）（1-1

19、7） )332233(833233210nnnnyyyyyyyylS)332233(S.M.3233210nnnnyyyyyyyyLSCEDy0y1y2llxyS0-1S1-2（1-19）曲线曲线CDCD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）)103(241210210yyylM 【 3，10，1 】法（只适用于求静矩法（只适用于求静矩） )310(241210221yyylM x0 x2x

20、3x5x 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)33(83)85(1216543216545432321yyyyyylyyylyyyylyyylSCBx0 x2x3x5x 1/2y1y0y 5y 6y3

21、y2x6y4x4x 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 1/22483.82496801589.711/2159079512319.642/519279928232022602.6211 1/252052603390432733.64141093527341093542818.421256372818563752867.94141

22、147228681147262898.912/51289911602899470151311047009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)IIIIIIIVVVIVIIVIIIIX001/20-5000016.3212.6-4-50.4201.6250.0500.128.618.6-3-25.877.4636.1636.139.2218.4-2-36.873.6

23、778.71557.449.419.4-1-9.49.4830.6830.659218000729.01458.068.118.118.18.1531.4531.476.7213.4226.853.6300.8601.584.614.6313.841.497.397.392.424.8419.276.813.827.6100.21/20.150.52.50.00.098-54544.46240.1站号y3【例2 】计算表格niinynLyyynLS121)(（1-24）（1-25）y2y1y3eglLl-x1x2x1 假定用三次抛物线代替曲线CD，即y=a0+a1x+a2x2+a3x3式中：a

24、0，a1，a2，a3为常数，曲线CD下面积由积分公式给出：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

25、-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。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

26、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/31.732051/20.866032.71133（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000.0000

27、010.000001pi/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）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/(3

28、7454. 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 0.049180.118460.0058320.246470.239310.0589830.577350.284450.1642341.041140.239310.2491651.550900.118460.18372 0.661916/)6/(53847. 06/)6/(53847. 06/6/90618. 06/6/90618. 06/22064. 066192. 03d tg513/ 0iiiypLxxSy0y1y2y3y4y5

29、543211/2T)42423221(3)424(3)4(6543212/105432112/1050yyyyyyyTyyyyyTyyyTydzST1. 1.增加中间坐标增加中间坐标LLLy0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）船体曲线在端点上船体曲线在端点上目测，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