帶有緩和曲線的圓曲線逐樁坐標計算例題

1、+160精心整理+160精心整理精心整理精心整理帶有緩和曲線的圓曲線逐樁坐標計算例題：某山嶺區(qū)二級公路，已知交點的坐標分別為JD1（40961.914,91066.103）、JD2（40433.528,91250.097）、JD3（40547.416,91810.392）,JD2里程為K2+200.000,R=150m,緩和曲線長度為40m,計算帶有緩和曲線的圓曲線的逐樁坐標。（工程測量第202頁36題）解：（1）轉(zhuǎn)角、緩和曲線角、曲線常數(shù)、曲線要素、主點里程、主點坐標計算1坐標方位角a12160。4803a2378。30372轉(zhuǎn)角a（左轉(zhuǎn)曲線）82。17263緩和曲線角卩二卩二LX空Oh2R

2、兀7。3822”4曲線內(nèi)移值L2p=S24R0.444m5切線增長值LLq=ss2240R219.988m6曲線要素切線長aT=(R+p)tanbqh2151.438m曲線長兀L=R(a2P)+2Lh0180SL=255.436mhL=175.436my外距/、aE=(R+p)secR49.781m切曲差D=2TLhhh47.440m7主點里程ZH樁號ZH=JD（樁號）-ThK2+048.562HY樁號HY=ZH(樁號)+LSK2+088.562YH樁號YH=HY(樁號)+LyK2+263.998HZ丿樁號HZ=YH（樁號）+LSK2+303.998QZ樁號QZ=HZ(樁號)-L/2K2+17

3、6.280JD樁號JD=QZ(樁號)+D/2K2+200.0008主點坐標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（左轉(zhuǎn)）弦長Xg*a=a-B=153。0941切線ZYJD0樁號里程K221104150583710+12060015長31.438l-=樁點里程-H11.438

4、a=aB1530941a=方位角（左轉(zhuǎn)）弦長Xg*a=a-B=153。0941切線ZYJD0樁號里程K221104150583710+12060015長31.438l-=樁點里程-H11.438a=aB1530941a=a-B-AciZYJD0i90Q兀（3）圓曲線段坐標計+14051.43871.43894926133837c=2RsinAii11.43514709261432015139310431.380X=X+cco致ihyic-40539.41940529.42040513.055Y=Y+csina.tHYcT91215.10491220.65291232.122（2）第一緩和段坐標

5、計算b二7。38,225二160。4803012樁號弧長l-=樁點里程-ZY里程偏角1riA=一rBi3(L丿0Sy方位角a=aA（左轉(zhuǎn)廠弦長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)第二緩和段坐標計算0二738220樁號弧長=HZ里程-樁點里程偏角1(iA=_0i3(L丿0方位角a=a+A(左轉(zhuǎn))弦長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：切線支距法（坐標系轉(zhuǎn)換）（2）第一緩和段坐標計算二160。480312X=X+xcosa+ysinaY=Y+xsina一ycosa（本題為左轉(zhuǎn)曲線）iZH1212iZH1212樁號-=樁點里程-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)圓曲線段坐標計算00=7O3822p=.444mq=19.988mJ160。A803ZH(40576543,91200.296)X=X+xcosa+ysinaY=Y+xsina一ycosaiZH12l-12iZH1242樁號l-=樁點里程-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)第二緩和段坐標計算a二78。303712X=X-xcosa+ysinaY=Y一xsina一ycosa(本題為左轉(zhuǎn)曲線)iHZ2323iHZ2323樁號l=樁點-ZYi里程里程,i5x一l一40R2L1317y一6RL336R3L?ccXiYiYH