带有缓和曲线的圆曲线逐桩坐标计算例题

1、+160精心整理+160精心整理精心整理精心整理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a12160。4803a2378。30372转角a（左转曲线）82。17263缓和曲线角卩二卩二LX空Oh2R

2、兀7。3822”4曲线内移值L2p=S24R0.444m5切线增长值LLq=ss2240R219.988m6曲线要素切线长aT=(R+p)tanbqh2151.438m曲线长兀L=R(a2P)+2Lh0180SL=255.436mhL=175.436my外距/、aE=(R+p)secR49.781m切曲差D=2TLhhh47.440m7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丿桩号HZ=YH（桩号）+LSK2+303.998QZ桩号QZ=HZ(桩号)-L/2K2+17

3、6.280JD桩号JD=QZ(桩号)+D/2K2+200.0008主点坐标ZHX=X+Tcosa7H2h2140576.543mY=Y+TsinaZH2h2191200.296mHZX=X+TcosaHZ2h2340463.693mY=Y+TsinaHZ2h2391398.500mQZa=a-(180oa)Eh23229。3920X=X+EcosaQZ2hEh40476.788mY=Y+EsinaQZ2hEn91274.728m方位角（左转）弦长Xg*a=a-B=153。0941切线ZYJD0桩号里程K221104150583710+12060015长31.438l-=桩点里程-H11.438

4、a=aB1530941a=方位角（左转）弦长Xg*a=a-B=153。0941切线ZYJD0桩号里程K221104150583710+12060015长31.438l-=桩点里程-H11.438a=aB1530941a=a-B-AciZYJD0i90Q兀（3）圆曲线段坐标计+14051.43871.43894926133837c=2RsinAii11.43514709261432015139310431.380X=X+cco致ihyic-40539.41940529.42040513.055Y=Y+csina.tHYcT91215.10491220.65291232.122（2）第一缓和段坐标

5、计算b二7。38,225二160。4803012桩号弧长l-=桩点里程-ZY里程偏角1riA=一rBi3(L丿0Sy方位角a=aA（左转厂弦长c=l亠ii-90R2L2SXiX=X+ccosaiZHic-YiY=Y+csinaiZHic-ZH：K2+048.5620160480340576.54391200.296+06011.43801230160353311.43840565.75491204.097+08031.43813423159134031.43840547.14992211.446HYK2+088.5624023247158151639.96840539.41991215.104

6、QZ：K2+176.28087.718164510136243186.47340476.78991274.728+18091.438+200111.438+220131.438+240151.438+260171.438YH：K2+263.998175.4363330211193920165.60640457.48091359.018(4)第二缓和段坐标计算0二738220桩号弧长=HZ里程-桩点里程偏角1(iA=_0i3(L丿0方位角a=a+A(左转)弦长c=1亠ii-90R2LSXiX=X+ccosaiHZicjYiY=Y+csinaiHZicjYH：K2+263.998402324726

7、1032439.96840457.48091359.018+28023.99805500259253723.99640459.29091374.911+3003.9980013225830373.99840462.89791394.582HZK2+303.998a32258303740463.69391398.500精心整理精心整理精心整理精心整理方法二：切线支距法（坐标系转换）（2）第一缓和段坐标计算二160。480312X=X+xcosa+ysinaY=Y+xsina一ycosa（本题为左转曲线）iZH1212iZH1212桩号-=桩点里程-ZY里程,15x一l-40R2L1317y一6R

8、L336R3L3XiYiZH：K2+048.5620sSS40576.54391200.296+06011.43811.4380.04240565.75591204.096+08031.43831.4170.86340547.15692211.446HYK2+088.5624039.9291.77840539.41991215.104(3)圆曲线段坐标计算00=7O3822p=.444mq=19.988mJ160。A803ZH(40576543,91200.296)X=X+xcosa+ysinaY=Y+xsina一ycosaiZH12l-12iZH1242桩号l-=桩点里程-HY里程180vl

9、肘叫xp=Rsin申+qyp=R(1-cos+pXiYiHY：K2+088.56240539.41991215.104+10011.43812003051.1963.72640529.41991220.651+12031.43819385270.4249.17740513.05291232.122+14051.438271714+16071.438345536QZ：K2+176.28087.718410843118.68437.48740476.78891274.728+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a二78。303712X=X-xcosa+ysinaY=Y一xsina一ycosa(本题为左转曲线)iHZ2323iHZ2323桩号l=桩点-ZYi里程里程,i5x一l一40R2L1317y一6RL336R3L?ccXiYiYH