浮体静力学教学规划

~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................................163.3.1静水力曲线插值................................163.3.2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......................................23~1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AwA2L2ydxwL2（2）漂心纵向坐标xFM2L2xydxoyL2xMoyFAw（3）每厘米吃水吨数TPCAw(TPC1.025t/m3)100（4）型排水体积dAdz0 w（5）总排水体积k 1.006k（6）总排水量k（7）浮心纵向坐标xBM dix Adzyoz0FwMx yozB （8）浮心垂向坐标zBM dizA dzxoy 0 wMz xoyB （9）横稳心纵向坐标BMBMIT~IL21(2y)3dxTL122（10）纵稳心纵向坐标BMLBMILFLI2L2x2ydxLL2IIAx2LFLwF（11）每厘米纵倾力矩MTCMTCGML100L近似写成：MTCBM100LL（12）水线面系数CwpCwpAw（13）方形系数CBCBLBd（14）棱形系数CPCPALM10站处A2diydzM0（15）中横剖面系数CMCAMMBd~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。谢谢阅读以1m吃水处为例，说明第一步计算过程。如表1.1所示。精品文档放心下载1.11米吃水处计算用表1米水线计算表站号水线半宽yi/m乘数面积乘积Ⅱ×Ⅲ矩臂面积乘积Ⅳ×Ⅴ/mⅠⅡⅢⅣⅤⅥ-0.500.250-10.50000.50-1000.500.50-9.5010.1150.50.0575-9-0.51751.50.2480.50.124-8.5-1.05420.4420.750.3315-8-2.65231.0111.01-7-7.0741.59611.596-6-9.57652.0712.07-5-10.3562.41912.419-4-9.67672.69812.698-3-8.09482.90712.907-2-5.81493.06813.068-1-3.068103.02713.02700112.83112.83112.831122.50912.50925.018132.07412.07436.222141.67311.67346.692151.31811.31856.59160.98310.98365.898170.68210.68274.774180.47510.47583.8190.3780.750.283592.551519.50.3470.50.17359.51.64825200.2870.40.1148101.14820.30.220.30.06610.30.679820.60.1080.150.016210.60.17172总和32.507-9.84723~续表1.1 1米吃水处计算用表米水线计算表站号yi^3/m^3惯性矩乘积距中站面距离x^2/m^2IT/m^4IL/m^4Ⅲ×Ⅶx/mⅠⅦⅧⅨⅩⅪⅫ-0.500-2144100000-20400000.500-193610010.0015210.00076-183240.00101474.521.50.0152530.007626-172890.010169143.34420.0863510.064763-162560.086351339.45631.0303011.030301-141961.373735791.8444.0653574.065357-121445.420476919.29658.8697438.869743-1010011.82632828614.1549314.15493-86418.87323619.264719.6392919.63929-63626.18572388.512824.5660424.56604-41632.75472186.048928.8779328.87793-2438.5039149.0881027.7355827.735580036.9807701122.6892222.689222430.252345.2961215.7943615.7943641621.05914160.576138.9212618.92126163611.89501298.656144.6826084.6826088646.243478428.288152.2895292.289529101003.052706527.2160.9498620.949862121441.266483566.208170.3172150.317215141960.422953534.688180.1071720.107172162560.142896486.4190.054010.040508183240.05401367.41619.50.0417820.020891193610.027855250.534200.023640.009456204000.012608183.6820.30.0106480.00319420.6424.360.004259112.03120.60.001260.00018921.2449.440.00025229.12371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条静水力曲线谢谢阅读~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。谢谢阅读表1.2静水力曲线数据汇总表每厘米吃吃水水线面面漂心纵向水吨数TPC型排水体总排水体总排水量浮心纵向浮心垂向（m）积（m^2)坐标（m）（t/cm）积（m^3）积（m^3）（t）坐标（m）坐标（m）0.2545.46-3.310.475.685.725.86-3.310.250.581.69-1.040.8421.5821.7122.25-2.230.371130.03-0.611.3374.5174.9576.83-1.190.681.5159.58-1.201.64146.91147.79151.49-1.070.972191.70-2.291.96234.73236.14242.04-1.341.272.5225.47-3.272.31339.02341.06349.58-1.801.583243.96-3.102.50456.38459.12470.60-2.151.883.5256.33-2.672.63581.45584.94599.57-2.312.18续表1.2静水力曲线数据汇总表横稳心垂纵稳心垂每厘米纵倾力吃水向坐标向坐标矩水线面方形系数棱形系数中横剖面（m）BM(m)BML(m)MTC(t*m/cm)系数CCC系数CWPBPM0.253.62264.080.380.15790.07890.39770.19850.53.67201.031.110.28370.14980.42570.351913.31111.152.120.45150.25870.47940.53971.52.6775.202.830.55410.34010.52040.653522.3268.154.100.66560.40750.56130.72602.52.2066.605.790.78290.47090.60690.775931.9457.936.770.84710.52820.65050.81203.51.6750.967.590.89000.57680.68770.8388~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为浮心沿水平横向移动的距离，其数值完全由排水感谢阅读精品文档放心下载假设重心位置取在基线上，即KS=0。此时，复原力臂l=ycos∅+zsin∅，l=zsin∅。∅∅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，通过纵向精品文档放心下载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l=ycosφ+φzsinφ，算出复原力臂ls。最后画出各个倾斜角度下的ls-曲线图。φ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。精品文档放心下载再绘制一条水平直线，逆时针偏转60度，复制、移动使之与圆分别相切。该直线感谢阅读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。精品文档放心下载~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。谢谢阅读计算水线选择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。感谢阅读（3）计算复原力臂。根据面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∅和浮心位置B（yφ，zφ）。谢谢阅读V∅=∫2Asdx≈δL×(∑Asi(As0+Asn)/2)∅MAdx≈δd[∑yA(yA+yA)/2]xoz=∫2wis02z∅=Mxoy/V∅~MAdx≈δd[∑A(zA+A)/2]xoz=∫2wis0=yφcosφ+zφsinφ计算复原然后根据假定重心高度为零的复原力臂l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。谢谢阅读表2.11.5m水线稳性横截图计算表φ/°10乘Mxoz*乘Mxoy*乘站号S/mm²y/mmz/mmMxoz/m³Mxoy/m³数S*乘数数数0000000.50001060225146.0201084.80.154811.1501411.06020.154811.1501428095125513511652400.0191036.91.404723.6414513.51161.404723.6414546275275314607527.102998.832.801345.3083915.31462.801345.3083963141607166389587615.147984.493.930546.2905216.38953.930546.2905288611487147013270591.859934.444.150876.5535117.01324.150876.55351104483735414774525.102991.782.843315.3703115.41472.843315.37031126972774273474968340.8571021.41.184463.5494613.47491.184463.54946146389468941928145145.5631030.90.280661.9878811.92810.280661.9878816882834583885830.16.6847978.950.014780.8671910.88580.014780.8671918493232499817.2.4119972.640.001200.486140.50.24990.000600.243072055865093335.24216.766134.9619总和9735计算结果▽/m³φ/radlsyφzφ140.9710.174530.640760.47570.9920293636φ/°20~乘Mxoz*乘Mxoy*乘站号S/mm²y/mmz/mmMxoz/m³Mxoy/m³数S*乘数数数0000000.50001325987601.7131297.20.797861.7201111.32590.797861.7201122324387433926681855.4581214.33.359114.7684813.92663.359114.76848468139813956352871012.821161.85.707536.5473615.63525.707536.54736651587566139051143.591146.17.563657.5804816.61397.563657.58048894383058371866121104.991086.77.941147.8101917.18667.941147.81019102767126756579591001.821144.45.668296.4755215.65795.668296.47552127986459643650316692.9891140.72.529634.1642413.65032.529634.16424147912616261919090309.0081073.20.593012.0596811.91900.593012.05968161643943833609.36.1829956.180.030160.7970810.83360.030160.7970818936241244742386.3445949.470.003000.450270.50.23710.001500.22513205998194936.98634.191942.1483总和5722计算结果▽/m³φ/radlsyφzφ147.9460.349061.258440.92441/°30乘Mxoz*乘Mxoy*乘站号S/mm²y/mmz/mmMxoz/m³Mxoy/m³数S*乘数数数521086.2432.262583.01.267421.345960.50.26050.633710.672980690237431422309931382.531813.53.084424.0460312.23093.084424.04603265874937447566591300.161521.16.184457.2356114.75666.184457.235614755359363375771413.441425.28.957809.0323416.33758.957809.03234630432773272313801538.441395.211.125110.089517.231311.125110.08958841282~77867231485.541325.911.567510.324617.786711.567510.32461063337233763272281395.821402.88.831728.8759616.32728.831728.875961292189288941737091064.741386.44.443915.7868414.17374.443915.78684141999409942042636519.3171199.81.060772.4508012.04261.060772.45080162454365477563961.3429936.240.047580.7261810.77560.047580.7261818347397442483.12.8777922.630.005690.408250.50.22120.002840.204122094281429542.14455.939859.4450总和3389计算结果▽/m³φ/radlsyφzφ168.5770.523591.854761.32731.41051397412φ/°40乘Mxoz*乘Mxoy*乘站号S/mm²y/mmz/mmMxoz/m³Mxoy/m³数S*乘数数982918.64.266995.044170.50.86412.133492.522080486928935352141826.862299.36.458348.1285713.53526.458348.12857221788148859521941649.401907.99.8175511.356415.95219.8175511.35644135694674252551725.721773.412.813913.168217.425212.813913.1682644649554982648831822.741719.215.064714.209718.264815.064714.2097849769836988135431760.811638.915.519014.445018.813515.519014.44501095661436174397841699.881749.312.646813.014817.439712.646813.01481295814841451951031445.361788.67.508799.2920315.19517.508799.29203141148303832461920840.3161511.32.068793.7208212.46192.068793.72082169532232709665.95.6964923.000.067910.6550210.70960.067910.655021811522652220400810.24.1903890.990.009690.357110.50.20040.004840.17855~368058950.86284.104390.6914总和0923计算结果▽/m³φ/radlsyφzφ203.4480.698132.412851.65351.78308328765φ/°50乘Mxoz*乘Mxoy*乘站号S/mm²y/mmz/mmMxoz/m³Mxoy/m³数S*乘数数数34612552461.133303.98.5186011.43580.51.73064.259305.71792025975284351946062039.652748.610.595214.278015.194610.595214.2780282221062174236501865.112310.213.845917.150217.423613.845917.150246147257287899341911.532136.516.802218.780418.789916.802218.7804668382348296222801978.102057.019.033919.793119.622219.033919.7931890828210169651931.421985.019.641920.1868110.16919.641920.186810180551655189009531892.282130.716.843118.966018.900916.843118.96601289167536767038931733.352273.511.620215.241716.703811.620215.2417148757935736459141349.032220.14.918458.0945813.64594.918458.094581618161416638587.144.832930.050.092480.5939210.63850.092480.59392185448818781343072.45.1087854.910.015470.293290.50.17150.007730.1466520596936862.991117.660138.949总和6375计算结果▽/m³φ/radlsyφzφ251.9660.872662.890421.86782.2058455179φ/°60乘Mxoz*乘Mxoy*乘站号S/mm²y/mmz/mmMxoz/m³Mxoy/m³数S*乘数数数050422582307.673483.411.635917.56450.52.52115.817958.78226~765329565266072022.792974.613.201919.414616.526613.201919.4146219265076585424161901.682547.416.244921.760918.542416.244921.7609430276167698496481937.532351.319.084023.159819.849619.084023.1598643634483410675491995.172261.421.299524.1425110.67521.299524.142584797949911214411965.912204.622.046524.7242111.21422.046524.724210748485428510044791926.712365.519.353423.7610110.04419.353423.761012370783798379478851796.482561.014.278220.354717.947814.278220.35471442845854551638701585.772783.08.1887414.371315.16388.1887414.3713167638778716892971508.843252.22.548885.4940611.68922.548885.4940618677819781262256.84.5483821.970.022170.215560.50.13110.011080.10778206438287474.306142.075186.073总和6846计算结果▽/m³φ/radlsyφzφ297.2261.047193.124641.91202.50412787149φ/°70Mxoz*Mxoy*乘站号S/mm²y/mmz/mmMxoz/m³Mxoy/m³乘数S*乘数乘数数63333202123.793562.913.450622.56500.53.16666.72511.2825008446322275665501946.083115.714.725123.575717.566514.7223.57572886755517594464781866.902701.217.635725.517419.446417.6325.517448641378571310713531904.492494.920.403826.7299110.71320.4026.7299641723753383711534081960.282400.522.610027.6883111.53422.6127.6883821664308004311214411944.732358.321.809126.4476111.21421.8026.4476107857142911~10958331898.992524.620.809727.6661110.95820.8027.66611251658333978389397701769.892742.315.822424.516118.939715.8224.516114671677246763755581581.923054.910.085619.477016.375510.0819.4770162613858563834367311610.853896.55.5360513.391413.43675.53613.39141876883105884700731286.063864.70.604541.816720.50.23500.3020.908362046243627283.587156.4227.200总和156548计算结果▽/m³φ/radlsyφzφ334.3481.221733.194421.87182.7181369831稳性横截曲线φ/°▽/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一系列数据点，如表2.2所示。谢谢阅读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性横截曲线1m1.5m2m2.5m3mφ▽/m³ls▽/m³ls▽/m³ls▽/m³ls▽/m³ls/°1064.150.70140.970.64236.980.64350.540.65482.850.662065.911.34147.951.26253.741.27375.841.29511.691.283077.031.90168.581.85281.861.89411.631.91523.621.74~40102.132.44203.452.41323.072.48445.432.39531.242.1450146.412.95251.972.89362.052.93468.512.72533.532.4460203.643.26297.233.12393.293.24485.622.92532.102.6570258.203.32334.353.19419.623.48498.023.01527.882.77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Z=2.295mf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。谢谢阅读载况~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排水量360.1323.9299.7303.1360.1323.9299.7303.1360.1323.9Disp.(t)重心垂向坐标2.3882.412.5312.5522.8882.912.5313.0523.3883.41Zg(m)重心纵向坐标-2.14-1.69-1.69-1.61-2.24-1.79-1.79-1.71-2.34-1.89Xg(m)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；精品文档放心下载c、求浮心纵向坐标xG，漂心纵向坐标xF，横稳心距基线高zM，纵稳心距基线感谢阅读高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-ZG感谢阅读e、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)；感谢阅读h、求首尾吃水，dF=d+ddF,dA=d+ddA；感谢阅读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~d2.38687

xB-1.692223

zB1.51

xF-3.16777

BML67.32244

MTC5.4683

BM2.22932

▽/m³314.114343.3.2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t△323.9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*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)初稳心高(m)纵稳心高(m)2.386872.3876326452.3863159111.3293266.42244~3.3.3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-zGsinϕ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（ϕ）；将所得静稳性曲线积分则可得动稳性曲线。谢谢阅读表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Z=2.41mg横倾角lsinθllld0.104712042θSZ×(3)d0ld(m)g(m)(m·°)(°)(m·rad)查曲线(2)-(4)(5)的积分和（1）（2）（3）（4）（5）（6）（7）10.000.650.170.410.241.200.0220.001.290.340.820.474.760.0830.001.910.501.210.7110.630.1940.002.490.641.540.9518.900.3350.002.920.771.861.0628.960.5160.003.160.872.101.0639.590.6970.003.180.942.270.9149.480.86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。精品文档放心下载~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：精品文档放心下载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）。谢谢阅读最小倾覆力矩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：15.28CCC2014C3式中，C1、C2、C3、C3为系数，因此要求横摇角，必须先求各个系数：精品文档放心下载a、 确定C1:船舶自摇周期满足：T0.58fB2KG2 GM0因B/d=7.2m/2.39m=3.01,可查得f取1.03，KG=2.41， 0精品文档放心下载又船舶在近海航区，对照课本上的表格可查得Tϕ=3.933s时：精品文档放心下载C1=0.37b、确定C2：C20.130.6KG=0.13+0.6*2.41/2.39=0.735；d精品文档放心下载c、确定C3:C3也根据B/d查得，B/d=7.2m/2.39m=3.01,查表可得：精品文档放心下载C3=0.013；d、确定C4：由于Ab/LB=9/40/7.2=0.03125=3.125%,则感谢阅读C4=0.57；则横摇角15.28CCC2=24.23014C3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感谢阅读~图3.3 风浪联合作用下稳性曲线图由图中插值可