带有缓和曲线的圆曲线逐桩坐标计算例题.doc

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1、带有缓和曲线的圆曲线逐桩坐标计算例题：某山岭区二级公路，已知交点的坐标分别为JD1（40961.914,91066.103）、JD2（40433.528,91250.097）、JD3（40547.416,91810.392），JD2里程为K2+200.000，R=150m缓,和曲线长度为40m,计算带有缓和曲线的圆曲线的逐桩坐标。（《工程测量》第202页36题）1坐标方位角1223转角缓和曲线角23（左转曲线）1604803783037821726LS2R180oh738224曲线内移值pLS224R0.444m5切线增长值qLSL3S切线长Th2(R240R2p)ta

2、n219.988mq151.438m6曲线要素曲线长LhR(外距切曲差Eh(R20)180p)sec2Lh2LSLh255.436mLy175.436mR49.781mDh2Th47.440m7ZHXZHX2YZHY2XHZX2YHZY2Eh23ThcosThsinThcosThsin-1(1802121238主点坐标HZ2340576.543m91200.296m40463.693m91398.500m2)293920QZXQZYQZX2EhcosEhY2EhsinEh40476.788m91274.728m解：（1）转角、缓和曲线角、曲线常数、曲线要素、主点里程、主

3、点坐标计算ZH桩号ZHJD（桩号）ThK2+048.562HY桩号HYZH（桩号）LSK2+088.562主点YH桩号YHHY（桩号）LyK2+263.998里程HZ桩号HZYH（桩号）LSK2+303.998QZ桩号QZHZ（桩号）Lh/2K2+176.280JD桩号JDQZ（桩号）Dh/2K2+200.000方法一：偏角法（坐标正算）（2））第一缓和段坐标计算073822121604803桩号弧长偏角方位角弦长XiYil桩点-ZY1li3L20ci12i(左转)c5lliSXXZHccosYYcsinciZH:K2+048.5620160480340576.54

4、391200.296i里程里程iSiii90R2L2iciiZHi+06011.43801230160353311.43840565.75491204.097+080HY31.43813423159134031.43840547.14992211.446K2+088.5624023247158151639.96840539.41991215.104（3））圆曲线段坐标计算切线ZYJD-01530941桩号弧长偏角方位角(左转)弦长XYiYYcsinli桩点里程-HY里程li90iRciZYJD-0-ici2RsiniXiXHYcicosci

5、HYiciHY:切线ZYJD0K2+088.562153094140539.41991215.104+10011.43821104150583711.43540529.42091220.652+12031.43860015147092631.38040513.05591232.122+14051.438949261432015+16071.4381338371393104QZ:K2+176.280+18091.438+200111.438+220131.438+240151.438+260171.43887.718164510136243186.47340476.7

6、8991274.728YH:K2+263.998175.4363330211193920165.60640457.48091359.018桩号弧长偏角方位角弦长XiYilHZ-桩点2i里程里程1lci32icll5iXXiHZccosiciYYcsiniHZiciiii22i3LS0(左转)90RLSYH:4023247261032439.96840457.48091359.018（2））第二缓和段坐标计算073822K2+263.998+28023.99805500259253723.99640459.29091374.911+3003.99800132258303

7、73.99840462.89791394.582HZK2+303.99832258303740463.69391398.500方法二：切线支距法（坐标系转换）（2））第一缓和段坐标计算121604803XiXZHxcos12ysin12YiYZHxsin12ycos12（本题为左转曲线）桩号li桩点里程-ZY里程l5xls40R2L2l3y6RLSl7S336R3L3XiYiZH:K2+048.562+060+080HYK2+088.562040576.54391200.29611.43811.4380.04240