带有缓和曲线圆曲线逐桩坐标计算例题

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）解：（ 1）转角、缓和曲线角、曲线常数、曲线要素、主点里程、主点坐标计算12345678坐标方位角转角缓和曲线角曲线内移值切线增长值切线长曲线 曲线长要素外距切曲差ZHHY主点YH里程HZQZJDZH主点HZ坐标QZ1

2、223（左转曲线 ）LS180oh2R2pLS24 RqLSL3S2240 R2Th( R p) tanq2L hR(2 0 )1802LSEh(Rp) secR2Dh2ThLh桩号 ZHJD （桩号）Th桩号 HYZH （桩号）LS桩号 YHHY （桩号）Ly桩号 HZYH （桩号）LS桩号 QZHZ （桩号）Lh / 2桩号 JDQZ （桩号）D h / 2X ZHX 2Th cos21YZHY2Th sin21X HZX2Th cos23YHZY2Th sin23E h23- 1 (180)2X QZX 2Eh cosEh160 48 0378 30 3782 17 267 38 220

3、.444m19 .988 m151.438mLh255.436mLy175.436m49 .781m47 .440 mK2+048.562K2+088.562K2+263.998K2+303.998K2+176.280K2+200.00040576 .543m91200.296m40463.693m91398.500m29 39 2040476.788mYQZY2 Eh sin Eh91274.728m方法一：偏角法（坐标正算）（2）第一缓和段坐标计算07382212160 48 03桩号弧长偏角方位角弦长5XiYi桩点- ZY2X iX ZH ci cos ciYiYZH ci sin cl

4、i1 lici12icil i里程里程0li2 2ii(左转)90R LS3 LSZH:0160480340576.54391200.296K2+048.562+06011.43801230160353311.43840565.75491204.097+08031.43813423159134031.43840547.14992211.446HY4023247158151639.96840539.41991215.104K2+088.562（3）圆曲线段坐标计算切线ZYJD-0153 09 41桩号弧长偏角方位角 (左转)弦长XYl i桩点- HYl i90-ci 2R sinXiXHY ci

5、 cos ciYiYHY ci sin ci里程里程iRciZY JD0iiHY:切线ZY JD040539.41991215.104K2+088.562153 09 41+10011.438211 04150583711.43540529.42091220.652+12031.43860015147092631.38040513.05591232.122+14051.438949261432015+16071.4381338371393104QZ:87.71816 45 10136243186.47340476.78991274.728K2+176.280+18091.438+200111.

6、438+220131.438+240151.438+260171.438YH:K2+263.99175.43633 302111939208（4）第二缓和段坐标计算07 38 22165.60640457.48091359.018桩号弧长偏角liHZ里程 -桩点里程1li2i03LSYH:402 3247K2+263.998+28023.99805500+3003.99800132HZK2+303.998方位角ci32i(左转)261 03 24259 25 37258 30 3732258 3037弦长5cil il i 2 290R LS39.96823.9963.998XiYiXiXHZ

7、ci cos ciYiYHZci sinci40457.48091359.01840459.29091374.91140462.89791394.58240463.69391398.500方法二：切线支距法（坐标系转换）（2）第一缓和段坐标计算12 160 48 03X iX ZHx cos 12 y sin12 YiYZHx sin12ycos12 （本题为左转曲线）桩号li 桩点里程 -ZY里程l 5yl 3l7XiYix l2 26RL336R3 340RLsLSSZH:040576.54391200.296K2+048.562+06011.43811.4380.04240565.755

8、91204.096+08031.43831.4170.86340547.1 5692211.446HY4039.9291.77840539.41991215.104K2+088.562（3）圆曲线段坐标计算0 7 38 22 p=0.444m q=19.988m12 160 48 03 ZH （40576.543,91200.296）X iX ZHx cos12y sin12 YiYZHx sin12ycos12桩号li桩点-HY180 li0xPRsinqyP R 1 cospXiY里程里程RiHY:40539.41991215.104K2+088.562+10011.43812003051

9、.1963.72640529.41991220.651+12031.43819385270.4249.17740513.05291232.122+14051.438271714+16071.438345536QZ:87.718410843118.68437.48740476.78891274.728K2+176.280+18091.438423358+200111.438+220131.438+240151.438+260171.438YH:K2+263.998175.436743904164.638110.74040457.47991359.018（4）第二缓和段坐标计算12 78 30 37XiX HZ桩号YH:K2+263.998+280+300HZK2+303.998x cos 23 y sin23 YiYHZx sin23y cos23 （本题为左转曲线）li 桩点里程 -ZY里程x ll 5yl