模板-平曲线、竖曲线计算

1、平曲线、竖曲线计算一平曲线计算1.1导线点计算设计线大致如下所示：根据地形图可以得出起点（A）、交点（B）、终点（C）的坐标，如下所示：A：（2851409.8403，499372.7174）B：（2850975.9989，499081.6896）C：（2850174.8905，499707.7816）路线长度、方位角计算（1）AB 段DB = J(28514.8043 2850975.9989)2 +(499372.7174 499081.6896)2 = 522.4132 _499372.7174 499081.6896 _ab - arCtg 2851409.8403 - 2850975

2、.9989 -(2)BC 段DC = J(2850174.8905 2850975.9989)2 + (499707.7816 499081.6896)2 = 1016.7428 =499707.7816 - 499081.6896 =bc - arCtg 2850174.8905 - 2850975.9989 =(3)转角计算a = 107。5302 92。5956” = 14。53061.2平曲线参数计算已知a =14。5306，R=1000m，% = 120m。平曲线各参数计算如下：=59.993Ls Ls 3 _ 120120=59.993=2240R 22240 x 10002Ls2

3、Ls412021204八小八p = 0.600m24 R 2384R 324 x 1000 2384 x 10003p = 28.6479 L = 28.6479 x -120 = 3。26，15 TOC o 1-5 h z 0R1000a14o5306T = (R + p )tg + q = (1000 + 0.600) x tg+ 59.993 = 190.704m22L = (a 2P ) R + 2Ls = (14。5306 + 2x3。2615)x3142x 1000 + 2x 120 = 379.795m 0 180180a14o5306E = (R + p )sec R = (1

4、000 + 0.600) x sec1000 = 9.101m22J = 2T L = 2 x 190.704 379.795 = 1.613m各参数代表含义为：:路线转角；R :圆曲线半径；Ls :缓和曲线长度；q :切线增长值；p :圆曲线半径移值；P:缓和曲线角；T :切线长；L :平曲线长；E：外距；J：校正值1.3平曲线特征点桩号计算根据1.1计算可知交点桩号为K0+821.441,则平曲线特征点桩号计算如下所示：ZH = JD T = 821.441 190.704 = 630.736 = K0 + 630.736HY = ZH + Ls = 630.736 +120 = 750.

5、736 = K0 + 750.736QZ = HY + L 2 Ls = 750.736 + 379.795 2 x 120 = 820.634 = K0 + 820.634 22YH = QZ + L 2 Ls = 820.634 + 379.795 2 x 120 = 890.531 = K0 + 890.531 22HZ = YH + Ls = 890.531 +120 = 71010.531 = K1 + 010.5311.4特征点坐标计算根据坐标计算公式有：ZH点坐标X zH = X JD + T cos(9 AB +180) = 3850231.315 +190.704 cos(1

6、07。5302 +180) = 3850289.879丫布=YD + Tsin (9 +180) = 497311.415 + 190.704sin(107。5302 +180) = 497129.926HZ点坐标X 成=X D + T cos 9 bc = 3850231.315 + 190.704cos870004” = 3850221.339Y = YD + Tsin。BC = 3850231.315 + 190.704sin87。0004” = 497501.859113计算YH点时必须先计算该点到ZH点的切线横距x,113x= 1 -一 +-+40 R 2 Ls 23456R 4 L

7、s 4 599040R 6 Ls 61 :缓和曲线上任意一点到ZH （或HZ）点的曲线长；Ls :缓和曲线长度；R :圆曲线半径。Xhy = X/h +兀 RLs ；3012 )cos先令 1 = Xhy = X/h +兀 RLs ；3012 )cos9AB k=3850289.879 +119.957 / cos30 =3850289.879 +119.957 / cos30 x1202k 3.142 x 1000 x 120 )x cos107。5302 k30 x 1202、3.142 x 1000 x 120)=3850255.325Yhy = Yzh +=3850255.325Yhy

8、 = Yzh +兀 RLs ；3012 )sin9 ABu 3012 、+ 6兀 RLs )=497?+119.957/cos30 x120=497?+119.957/cos30 x1202、k 3.142 x 1000 x 120)x sin107。5302k30 x 1202、3.142 x 1000 x 120)=497244.823QZ点坐标计算曲中点（QZ）至缓圆点（HY）的曲线长1 = 69.898m。XQZ=X XQZ=X HY + 2 R sin.cosk9 AB +6 誓/、=3850255.325 + 2=3850255.325 + 2x 1000sinf 90 x 69.

9、898 k 3.142 x 1000 )一x cos 107。5302k90 x (89.898 +120)、3.142 x 1000)=3850240.266(901、(901、.sinAB匕 90(1 + Ls、 + 6兀R)=3850255.325 + 2x 1000sinf 90 x 69,898 13.142 x 1000 )rx sin =3850255.325 + 2x 1000sinf 90 x 69,898 13.142 x 1000 )rx sin 107。5302-90 x (89.898 +120)3.142 x 1000=497313.065YH点坐标计算（同HY点坐

10、标计算X =119.957m)XYH = Xhz +cosBCu 30l2 、+ 6nRLs )=3850221.339 +119.957/r cos30 x12023.142 x 1000 x 120)x cos。命30 x 1202、87。0004“ 一3.142 x 1000 x 120)=3850230.010r 3012、k 兀 RLs )sinr 3012、k 兀 RLs )sinBC=497501.859 + 119.957/cos30 x1202k 3.142 x 1000 x 120)x sin30 x1202、r87o0004- k3.142 x 1000 x 120 )=

11、497382.192二竖曲线计算1、变坡点1根据设计知：I； = 1.230%,i2 = -0.700%, w = i2 一=-1.930%（凸型），拟 R=14000m,则:竖曲线长度 L = Rw = 14000 x1.930%=270.20m切线长 T=L/2=135.10mT 2竖曲线变坡点纵距E = - = 0.65m2 R竖曲线起终点高程计算（变坡点桩号K0+440，高程H=83.41m）竖曲线起点桩号=（K0+440）-135.10=K0+304.900竖曲线起点高程=83.41-135.10 x1.230%=81.75m竖曲线终点桩号=（K0+440）+135.10=K0+575.10竖曲线终点高程=83.41-135.1x0.700%=82.46m竖曲线桩号高程计算：本计算所采用的计算公式为左半部分：H = Hqd +叫-2R右半部分：H = hszd + 2 - 2R其中：一曲线上任意点到曲线起点（左半曲线）或终点（右半曲线）的水平距离;H SQD-竖曲线起点设计高程；日迪一竖曲线终点设计高程；表2.1竖曲线高程计算结果桩号X (m)h =赤(m)设计高程（m）K0+32015.1000.00881.93K0+34035.1000.04482.14K0+36055.1000.10882.32K0+38075.1000.20182.47K0+40095.100