带有缓和曲线的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1坐标方位角2160二48，0302378,3037”2转角口（左转曲线）821726“3缓和曲线角P=用上也LoLh2R冗7二3822

2、4曲线内移值_Ls2P-24R0.444m5切线增长值LsLSq22240R219.988m6曲线要素切线长Th=(R+p)tan+q2151.438m曲线长Lh=R(-2Po)+2Ls180Lh=255.436mLy=175.436m外距Eh=(R+p)sec-R249.781m切曲差Dh=2Th-Lh47.440m7主点里程ZH桩号ZH=JD（桩号）-ThK2+048.562HY桩号HY=ZH（桩号）+LsK2+088.562YH桩号YH=HY（桩号）+LyK2+263.998HZ桩号HZ=YH（桩号）+LsK2+303.998QZ桩号QZ=HZ（桩号）-Lh/2K2+176.280JD桩

3、号JD=QZ（桩号）十Dh/2K2+200.0008主点坐标ZHXzh=X?+Thcos2140576.543mYzh=丫2+ThSinG2191200.296mHZXhz-X2+Thcosa2340463.693mYhz=Y2+ThSin“2391398.500mQZ14%=%3-彳(180j)2939r20FXqz=X2+EhcosEh40476.788mYqz=Y2+EhsinaEh91274.728m方法一：偏角法（坐标正算）第一缓和段坐标计算f=73822-F=1604803桩号弧长ii点里程-zYt程2。偏13方位角0c=12&（左转）弦长Ci90R2LSXiXi=XZH+ci8s

4、sYiY=Yzh+JsinotciZH:K2+048.5620160480340576.54391200.296+06011.43801230160353311.43840565.75491204.097+08031.43813423159134031.43840547.14992211.446HYK2+088.5624023247158151639.96840539.41991215.104I网工弧长li士，为程-HY里程偏用A=,J_9JR冗（左转）Otci=OtZYJD-国-也Ci=2RsinAXX斗丫4Cico现YYBy甘SinC（cHY:K2+088.5625:线=CgYJD0153

5、094140539.41991215.104+10011.43821104150583711.43540529.42091220.652+12031.43860015147092631.38040513.05591232.122+14051.438949261432015+16071.4381338371393104QZ:K2+176.28087.718164510136243186.47340476.78991274.728+18091.438+200111.438+220131.438+240151.438+260171.438YH:K2+263.998175.43333011939161

6、5.640457.91359(3)圆曲线段坐标计算U切线=azYD-Po=15309,41”6212006480.018(4)第二缓和段坐标计算一：=73822桩号弧长li=HZ里不|-桩点1程偏角=llh3ILS方位角O(c=32+G)弦长c-90RLSXiXi=XHZ+CcoSjCiYiYXhz+csinacYH:K2+263.9984023247261032439.96840457.48091359.018+28023.99805500259253723.99640459.29091374.911+3003.9980013225830373.99840462.89791394.582HZ

7、K2+303.998口32258303740463.69391398.500f1/iNl府,也出HhiiI一方法二：切线支距法(坐标系转换)(2)第一缓和段坐标计算112=1604803Xi=XZH+xcos%2+ysin%2Y=YZH+xsin%2一ycos12(本题为左转曲线)桩号li小点里不S-ZY里程i5x-|40R2l2i3i7y_336RLs336RLsXiYiZH:K2+048.562040576.54391200.2+06011.43811.4380.04240565.75591204.(+08031.43831.4170.86340547.15692211.4HYK2+088

8、.5624039.9291.77840539.41991215.1(3)圆曲线段坐标计算0=73822p=0.444mq=19.988m口12=1604803ZH(40576.543,91200.296)Xi=XZHxcos122yysin-：12Y=YZHxsin_：12_ycos：12桩号li点里-HY里程邛可+自JRXp=Rsin中+qyp=Rf_cosCp严XiHY:K2+088.56240539.419!912+10011.43812003051.1963.72640529.419!912+12031.43819385270.4249.17740513.052!912+14051.4

9、38271714+16071.438345536QZ:K2+176.28087.718410843118.68437.48740476.788912+18091.438423358+200111.438+220131.438+240151.438+260171.438YH:K2+263.998175.436743904164.638110.74040457.479913(4)第二缓和段坐标计算口12=783037”Xi=XHZ-xcosa23+ysina23Yi=YHZ-xsin23-ycos23(本题为左转曲线)桩号li型点里不i-ZY里程xl40R2l2l3l7y=-3-6RLS336R3L3sSSXiYiYH:K2+2