浮体静力学课程设计

1、浮体静力学（一）课程设计姓 名：学 号：班 级：指导教师：完成日期：同组学生：目录1 静水力曲线计算11.1 计算原理11.2 计算过程31.3 计算结果42 稳性横截曲线计算72.1 计算原理72.2 计算过程82.3 计算结果143 稳性校核153.1 设计要求153.2 计算原理163.3 计算过程及结果173.3.1静水力曲线插值173.3.2根据静水力曲线及已知数据得到计算表格173.3.3静稳性曲线及动稳性曲线183.3.4稳性校核194 课程设计的收获23课程设计1 静水力曲线计算1.1 计算原理采用垂向沿吃水方向积分系统，利用梯形法列表计算。 （1）水线面面积 （2）漂心纵向坐

2、标 （3）每厘米吃水吨数() （4）型排水体积 （5）总排水体积 （6）总排水量 （7）浮心纵向坐标 （8）浮心垂向坐标 （9）横稳心纵向坐标24 （10）纵稳心纵向坐标（11）每厘米纵倾力矩近似写成：（12）水线面系数（13）方形系数（14）棱形系数10站处（15）中横剖面系数1.2 计算过程在excel中分别计算了0.25m,0.5m,1.0m,1.5m,2.0m,2.5m,3.0m，3.5m吃水处水线面各项几何要素，主要包括面积、面积矩、横向惯性矩、纵向惯性矩，这些数据经过计算处理后得到15条静水力曲线的具体数据。以1m吃水处为例，说明第一步计算过程。如表1.1所示。表1.1 1米吃水处

3、计算用表1米水线计算表站号水线半宽yi/m乘数面积乘积×矩臂/m面积乘积×-0.500.250-10.50000.50-1000.500.50-9.5010.1150.50.0575-9-0.51751.50.2480.50.124-8.5-1.05420.4420.750.3315-8-2.65231.0111.01-7-7.0741.59611.596-6-9.57652.0712.07-5-10.3562.41912.419-4-9.67672.69812.698-3-8.09482.90712.907-2-5.81493.06813.068-1-3.068103.0

4、2713.02700112.83112.83112.831122.50912.50925.018132.07412.07436.222141.67311.67346.692151.31811.31856.59160.98310.98365.898170.68210.68274.774180.47510.47583.8190.3780.750.283592.551519.50.3470.50.17359.51.64825200.2870.40.1148101.14820.30.220.30.06610.30.679820.60.1080.150.016210.60.17172总和32.507-9

5、.84723续表1.1 1米吃水处计算用表1米水线计算表站号yi3/m3惯性矩乘积×距中站面距离 x/mx2/m2IT/m4IL/m4-0.500-2144100000-20400000.500-193610010.0015210.00076-183240.00101474.521.50.0152530.007626-172890.010169143.34420.0863510.064763-162560.086351339.45631.0303011.030301-141961.373735791.8444.0653574.065357-121445.420476919.29658

6、.8697438.869743-1010011.82632828614.1549314.15493-86418.87323619.264719.6392919.63929-63626.18572388.512824.5660424.56604-41632.75472186.048928.8779328.87793-2438.5039149.0881027.7355827.735580036.9807701122.6892222.689222430.252345.2961215.7943615.7943641621.05914160.576138.9212618.92126163611.8950

7、1298.656144.6826084.6826088646.243478428.288152.2895292.289529101003.052706527.2160.9498620.949862121441.266483566.208170.3172150.317215141960.422953534.688180.1071720.107172162560.142896486.4190.054010.040508183240.05401367.41619.50.0417820.020891193610.027855250.534200.023640.009456204000.01260818

8、3.6820.30.0106480.00319420.6424.360.004259112.03120.60.001260.00018921.2449.440.00025229.12371总和184.8378246.45048329.4651.3 计算结果经过进一步处理（参见前面计算原理和excel中计算过程），得到15条静水力曲线的汇总表，如表1.2所示。利用CAD制图，得到静水力曲线图如图1.1所示。表1.2 静水力曲线数据汇总表吃水（m）水线面面积（m2)漂心纵向坐标（m）每厘米吃水吨数TPC（t/cm）型排水体积（m3）总排水体积（m3）总排水量（t）浮心纵向坐标（m）浮心垂向坐标（m

9、）0.2545.46-3.310.475.685.725.86-3.310.250.581.69-1.040.8421.5821.7122.25-2.230.371130.03-0.611.3374.5174.9576.83-1.190.681.5159.58-1.201.64146.91147.79151.49-1.070.972191.70-2.291.96234.73236.14242.04-1.341.272.5225.47-3.272.31339.02341.06349.58-1.801.583243.96-3.102.50456.38459.12470.60-2.151.883.5

10、256.33-2.672.63581.45584.94599.57-2.312.18续表1.2 静水力曲线数据汇总表吃水（m）横稳心垂向坐标BM(m)纵稳心垂向坐标BML(m)每厘米纵倾力矩MTC(t*m/cm)水线面系数CWP方形系数CB棱形系数CP中横剖面系数CM0.253.62 264.08 0.38 0.1579 0.0789 0.3977 0.1985 0.53.67 201.03 1.11 0.2837 0.1498 0.4257 0.3519 13.31 111.15 2.12 0.4515 0.2587 0.4794 0.5397 1.52.67 75.20 2.83 0.55

11、41 0.3401 0.5204 0.6535 22.32 68.15 4.10 0.6656 0.4075 0.5613 0.7260 2.52.20 66.60 5.79 0.7829 0.4709 0.6069 0.7759 31.94 57.93 6.77 0.8471 0.5282 0.6505 0.8120 3.51.67 50.96 7.59 0.8900 0.5768 0.6877 0.8388 图1.1 静水力曲线图2 稳性横截曲线计算2.1 计算原理在大倾角稳性状态下，初稳性公式已经不符合实际情况，所以大倾角状态下的静稳性臂能够表示为l=ls-lg,其中，ls为浮心沿水平横

12、向移动的距离，其数值完全由排水体积决定，为形状稳性臂，lg=B0Gsin，数值主要由重心位置决定，为重量稳性臂。假设重心位置取在基线上，即KS=0。此时，复原力臂ls=ycos+zsin，lg=zGsin。由所给型值表可以得到各站各吃水不同倾斜角度时的横剖面面积、质心坐标，通过纵向积分法可求出在不同倾角下的排水量、浮心横向、纵向坐标。再由ls=ycos+zsin，算出复原力臂ls。最后画出各个倾斜角度下的ls-曲线图。旋转点取法：首先选取5条水线（1.0m,1.5m,2m, 2.5m, 3.0m），在最高水线和最低水线之间绘制一圆，保证圆与最高水线和最低水线相切。 再绘制一条水平直线，逆时针偏

13、转60度，复制、移动使之与圆分别相切。该直线与1000水线、3000水线分别交于两点，记为A、B，连接A、B，得一直线，该直线与各水线的交点记为偏转点。如图2.1所示。 图2.1 船体横剖线图和旋转点2.2 计算过程（1）根据型值表，取各站横剖面型值。（2）选择计算倾斜水线，假定中心位置和横倾角间隔大小。 计算水线选择3m，2.5m，2m，1.5m和1m。假设中心位置区在基线上，横倾角间隔为10°，分别计算10°、20°、30°、40°、50°、60°、70°倾斜角时的排水体积和浮心位置。（3）计算复原力臂。根据面

14、域法分别求出各站横剖面的面积以及质心位置，根据纵向积分法求出各倾斜水线下的排水体积V和浮心位置B（y，z）。V=-L2L2AsdxL×(Asi-As0+Asn/2)y=Mxoz/VMxoz=-L2L2yAsdxdyiAwi-y0As0+ynAsn/2z=Mxoy/VMxoz=-L2L2zAsdxdziAwi-z0As0+znAsn/2然后根据假定重心高度zs为零的复原力臂ls=ycos+zsin计算复原力臂。（4）根据V和ls绘制稳性横截曲线。下面以1.5m水线为例，计算1.5m处的横稳性，如表2.1。表2.1 1.5m水线稳性横截图计算表/°10站号S/mm²y

15、/mmz/mmMxoz/m³Mxoy/m³乘数S*乘数Mxoz*乘数Mxoy*乘数0000000.500021060225146.02081084.8090.1548151.15014111.0602250.1548151.15014143511652400.0191036.9621.4047273.6414513.5116521.4047273.6414565314607527.1023998.83142.8013415.30839615.3146072.8013415.30839686389587615.1478984.49613.9305416.29052416.38

16、95873.9305416.290524107013270591.8594934.44484.150876.55351317.013274.150876.553513125414774525.1026991.78972.8433125.37031715.4147742.8433125.370317143474968340.85761021.4381.1844693.54946413.4749681.1844693.549464161928145145.56381030.9820.2806681.98788311.9281450.2806681.98788318885830.416.684797

17、8.95930.014780.86719210.885830.014780.86719220499817.52.4119972.64580.0012060.4861450.50.2499090.0006030.243073总和35.2429716.7661334.96195计算结果/m³/radlsyz140.97190.1745330.6407660.475730.992026/°20站号S/mm²y/mmz/mmMxoz/m³Mxoy/m³乘数S*乘数Mxoz*乘数Mxoy*乘数0000000.500021325987601.7132129

18、7.2320.7978641.72011311.3259870.7978641.72011343926681855.45861214.3813.3591134.76848913.9266813.3591134.768489656352871012.821161.8515.707536.54736515.6352875.707536.547365866139051143.5991146.1437.5636587.58048316.6139057.5636587.5804831071866121104.9921086.777.9411467.81019717.1866127.9411467.810

19、1971256579591001.8271144.4985.6682966.47552415.6579595.6682966.475524143650316692.98971140.7912.5296324.16424613.6503162.5296324.164246161919090309.00811073.260.5930142.05968311.919090.5930142.05968318833609.936.1829956.18360.0301620.79708410.833610.0301620.797084204742386.3445949.47590.0030090.4502

20、780.50.2371190.0015040.225139总和36.9865734.1919242.14832计算结果/m³/radlsyz147.94630.3490661.2584430.9244421.139558/°30站号S/mm²y/mmz/mmMxoz/m³Mxoy/m³乘数S*乘数Mxoz*乘数Mxoy*乘数0521086.62432.2692583.0021.2674231.3459670.50.2605430.6337110.672984222309931382.5361813.5583.0844274.04603412.2

21、309933.0844274.046034447566591300.1671521.1556.184457.23561314.7566596.184457.235613663375771413.4431425.2048.9578039.03234216.3375778.9578039.032342872313801538.4481395.24111.125110.0895217.2313811.125110.089521077867231485.5461325.93311.5675310.3246717.78672311.5675310.324671263272281395.8291402.8

22、218.8317288.87596916.3272288.8317288.8759691441737091064.7411386.4994.4439195.78684414.1737094.4439195.786844162042636519.3171199.8241.0607752.45080412.0426361.0607752.4508041877563961.3429936.24340.047580.72618710.7756390.047580.72618720442483.912.8777922.63420.0056980.4082510.50.2212420.0028490.20

23、4125总和42.1443355.9398859.44509计算结果/m³/radlsyz168.57730.5235991.8547671.3273411.410512/°40站号S/mm²y/mmz/mmMxoz/m³Mxoy/m³乘数S*乘数Mxoz*乘数Mxoy*乘数017282402468.9842918.684.2669965.0441790.50.864122.1334982.522089235352141826.8622299.3176.4583488.12857813.5352146.4583488.1285784595219

24、41649.4011907.9359.81755611.356415.9521949.81755611.3564674252551725.7241773.44612.8139413.1682917.42525512.8139413.16829882648831822.7441719.29715.0647614.2097918.26488315.0647614.209791088135431760.8191638.95615.5190614.4450118.81354315.5190614.445011274397841699.8891749.35812.6468113.0148417.4397

25、8412.6468113.014841451951031445.3611788.6147.5087989.29203315.1951037.5087989.292033162461920840.31691511.352.0687933.72082212.461922.0687933.72082218709665.195.6964923.00150.0679120.65502210.7096650.0679120.65502220400810.324.1903890.990.0096960.3571180.50.2004050.0048480.178559总和50.8620984.1043290

26、.69143计算结果/m³/radlsyz203.44830.6981322.4128581.6535761.783085/°50站号S/mm²y/mmz/mmMxoz/m³Mxoy/m³乘数S*乘数Mxoz*乘数Mxoy*乘数034612552461.1323303.9598.51860711.435850.51.7306284.2593045.717923251946062039.6582748.62210.5952214.2780115.19460610.5952214.27801474236501865.1162310.21413.84

27、59717.1502217.4236513.8459717.15022687899341911.5362136.58316.8022818.7804218.78993416.8022818.78042896222801978.1092057.00819.0339219.793119.6222819.0339219.793110101696511931.4281985.00519.6419520.18681110.1696519.6419520.186811289009531892.2882130.79116.8431618.9660718.90095316.8431618.9660714670

28、38931733.3582273.5711.6202515.2417716.70389311.6202515.241771636459141349.0312220.184.9184518.09458613.6459144.9184518.09458618638587.5144.8324930.05480.0924880.59392110.6385870.0924880.59392120343072.545.1087854.9190.0154760.2932990.50.1715360.0077380.14665总和62.99163117.6607138.9495计算结果/m³/rad

29、lsyz251.96650.8726652.8904211.8678792.20584/°60站号S/mm²y/mmz/mmMxoz/m³Mxoy/m³乘数S*乘数Mxoz*乘数Mxoy*乘数050422582307.6773483.46511.635917.564530.52.5211295.817958.782265265266072022.7912974.69213.2019619.4146516.52660713.2019619.41465485424161901.6832547.40216.2449721.7609618.54241616.24

30、49721.76096698496481937.5342351.33619.0840323.1598419.84964819.0840323.159848106754941995.1772261.49721.299524.14259110.6754921.299524.1425910112144171965.9142204.68422.0465824.72425111.2144222.0465824.7242512100447931926.7172365.50719.3534823.76103110.0447919.3534823.761031479478851796.4842561.0281

31、4.2782420.3547517.94788514.2782420.354751651638701585.7772783.0638.18874814.3713715.163878.18874814.371371816892971508.8463252.2772.5488885.49406111.6892972.5488885.49406120262256.684.5483821.9740.0221730.2155680.50.1311280.0110870.107784总和74.30668142.0754186.0736计算结果/m³/radlsyz297.22671.047198

32、3.1246471.9120142.504129/°70站号S/mm²y/mmz/mmMxoz/m³Mxoy/m³乘数S*乘数Mxoz*乘数Mxoy*乘数063333202123.793562.90813.4506422.565040.53.166666.72532211.28252275665501946.0883115.78614.7251723.5757517.5665514.7251723.57575494464781866.9082701.26417.6357125.5174319.44647817.6357125.51743610713534

33、1904.4912494.97220.4038326.72997110.7135320.4038326.729978115340821960.2812400.56622.6100427.68833111.5340822.6100427.6883310112144171944.7382358.35721.8091126.4476111.2144221.8091126.447612109583351898.9912524.66520.8097827.66613110.9583320.8097827.666131489397701769.8962742.37115.8224624.5161718.9

34、397715.8224624.516171663755581581.9223054.96110.0856319.4770816.37555810.0856319.477081834367311610.853896.5765.53605813.3914813.4367315.53605813.39148204700731286.0643864.7620.6045441.816720.50.2350360.3022720.90836总和83.58715156.4654227.2008计算结果/m³/radlsyz334.34861.221733.1944291.8718832.71813

35、1稳性横截曲线/°/m³ls变化比例10140.97190.64076664.0765920147.94631.258443125.844330168.57731.854767185.476740203.44832.412858241.285850251.96652.890421289.042160297.22673.124647312.464770334.34863.194429319.44292.3 计算结果将大家分工合作读取的5个吃水处数据汇总，得到排水体积和对应的ls一系列数据点，如表2.2所示。最终得到的稳性横截曲线如图2.2所示。表2.2 稳性横截曲线数据汇总稳

36、性横截曲线1m1.5m2m2.5m3m/°/m³ls/m³ls/m³ls/m³ls/m³ls1064.150.70140.970.64236.980.64350.540.65482.850.662065.911.34147.951.26253.741.27375.841.29511.691.283077.031.90168.581.85281.861.89411.631.91523.621.7440102.132.44203.452.41323.072.48445.432.39531.242.1450146.412.95251.972

37、.89362.052.93468.512.72533.532.4460203.643.26297.233.12393.293.24485.622.92532.102.6570258.203.32334.353.19419.623.48498.023.01527.882.77得到稳性横截图：图2.2 稳性横截曲线图3 稳性校核3.1 设计要求给出资料：受风面积A=166.9m2受风面积形心距水线高Zf=2.295m航区：近海计算载况：校核以下某一种载况下的稳性，与规范要求值比较，并对结果的合理性进行分析，并提出改善的措施。载况载况载况1载况2载况3载况4载况5载况6载况7载况8载况9载况10排水

38、量Disp.(t)360.1323.9299.7303.1360.1323.9299.7303.1360.1323.9重心垂向坐标Zg(m)2.3882.412.5312.5522.8882.912.5313.0523.3883.41重心纵向坐标Xg(m)-2.14-1.69-1.69-1.61-2.24-1.79-1.79-1.71-2.34-1.89载况选择：载况23.2 计算原理给定某一装载状态的浮态及初稳性的计算方法为：a、重量和重心位置的计算，xG,yG,zG,已给出；b、求平均吃水d ，根据静水力曲线图插值得；c、求浮心纵向坐标xG，漂心纵向坐标xF，横稳心距基线高zM，纵稳心距基

39、线高zML，同样可据静水力曲线图插值得；d、求每厘米纵倾力矩，MTC=*GML/(100*L) ，GML=ZML-ZGe、求纵倾力矩，MT=(XG-XB) ；f、求纵倾值，dd=MT/(100*MTC)；g、求首尾吃水增量，ddF=(L/2-xF)(dd/L)，ddA=-(L/2+xF)(dd/L)；h、求首尾吃水，dF=d+ddF, dA=d+ddA ；i、未修正初稳性高，GMo=zM-zG；j、自由液面修正值，dGM；k、修正后初稳性高，GM=GMo-dGM。3.3 计算过程及结果3.3.1静水力曲线插值由静水力曲线插值得出dxBzBxFBMLMTCBM/m³2.38687-1.

40、6922231.51-3.1677767.322445.46832.22932314.114343.3.2根据静水力曲线及已知数据得到计算表格表3.1 浮态与初稳性计算浮态与初稳性计算项目单位符号及公式计算结果排水量t323.9平均吃水md2.38687重心纵向坐标mxG-1.69浮心纵向坐标mxB-1.692223重心垂向坐标mzG2.41纵稳心距基线高mzML=BML+zB68.83244纵向初稳心高mGML=ZML-ZG66.42244每厘米纵倾力矩t*mMTC=*GML/(100*L)5.378557079漂心纵向坐标mxF-3.16777纵倾力臂mXG-XB0.002223纵倾力矩t

41、*mMT=(XG-XB)0.7200297纵倾值mdd=MT/(100*MTC)0.001316734首吃水增量mddF=(L/2-xF)(dd/L)0.000762645尾吃水增量mddA=-(L/2+xF)(dd/L)-0.000554089首吃水mdF=d+ddF2.387632645尾吃水mdA=d+ddA2.386315911横稳心距基线高mzM=BM+zB3.73932未修正初稳心高mGMo=zM-zG1.32932自由液面修正值mdGM0实际初稳心高mGM=GMo-dGM1.32932浮态和初稳性计算结果：表3.2 浮态与初稳性计算结果平均吃水(m)首吃水(m)尾吃水(m)初稳心

42、高(m)纵稳心高(m)2.386872.3876326452.3863159111.3293266.422443.3.3静稳性曲线及动稳性曲线绘制静稳性曲线首先根据老师给的稳性插值数据，绘制出稳性横截曲线，然后在所绘制的稳性横截曲线上找到对应排水量的在不同倾角下的ls，再按式l=ls-zGsin 计算各倾角下的复原力臂在绘制该排水量时的静稳性曲线l=f（）；将所得静稳性曲线积分则可得动稳性曲线。表3.3 静稳性臂和动稳性臂计算装载情况： 载况序号：2排水量Disp.= 323.9t重心高度Zg= 2.41m横倾角(m)Zg×(3) (m)(m·°)0.104712

43、042(°)(m·rad)查曲线(2)-(4)(5)的积分和（1）（2）（3）（4）（5）（6）（7）10.00 0.65 0.17 0.41 0.24 1.20 0.02 20.00 1.29 0.34 0.82 0.47 4.76 0.08 30.00 1.91 0.50 1.21 0.71 10.63 0.19 40.00 2.49 0.64 1.54 0.95 18.90 0.33 50.00 2.92 0.77 1.86 1.06 28.96 0.51 60.00 3.16 0.87 2.10 1.06 39.59 0.69 70.00 3.18 0.94 2.2

44、7 0.91 49.48 0.86 由表中数据可作出静稳性曲线图和动稳性曲线图，分别如图3.1和图3.2所示。图3.1 静稳性曲线图图3.2 动稳性曲线图3.3.4稳性校核稳性横准数K是对船舶稳性重要基本要求之一。规则规定：船舶在所核算的各种装载情况下的稳性，应符合以下不等式：K>1或K=1 式中，K为稳性衡准数；Mq为最小倾覆力矩（lq为最小倾覆力臂），表示船舶在最危险情况下抵抗外力矩的极限能力；Mf为风压倾斜力矩（lf为风压倾斜力臂），表示在恶劣海况下风对船舶作用的动倾力矩（力臂）。最小倾覆力矩Mq（或力臂lq）的计算根据课本所给公式，横摇角满足以下公式： 式中，C1、C2、C3、C

45、3为系数，因此要求横摇角，必须先求各个系数：a、 确定C 1:船舶自摇周期满足：因B/d=7.2m/2.39m=3.01,可查得f取1.03，KG=2.41， GM0=1.33则算出T=3.933s.又船舶在近海航区，对照课本上的表格可查得T=3.933s时：C1=0.37b、 确定C 2：=0.13+0.6*2.41/2.39=0.735；c、 确定C 3:C3也根据B/d查得，B/d=7.2m/2.39m=3.01,查表可得：C3=0.013；d、 确定C 4：由于Ab/LB=9/40/7.2=0.03125=3.125%,则C4=0.57；则横摇角 =24.23然后根据数据可以绘出风浪联合作用下的动稳性曲线图，如图3.3图3.3 风浪联合作