曲线坐标计算及曲线偏角计算.ppt

知识回顾知识回顾曲线曲线平面曲线平面曲线竖曲线竖曲线立交曲线立交曲线单圆曲线单圆曲线复曲线复曲线反向曲线反向曲线回头曲线回头曲线螺旋曲线螺旋曲线凸型竖曲线凸型竖曲线凹型竖曲线凹型竖曲线圆圆 曲曲 线线缓和曲线缓和曲线本次课主要内容本次课主要内容一、圆曲线元素的计算一、圆曲线元素的计算二、圆曲线主点里程的计算二、圆曲线主点里程的计算三、圆曲线坐标计算三、圆曲线坐标计算四、长弦偏角法细部点测设四、长弦偏角法细部点测设 重点重点重点，难点重点，难点圆曲线的测设流程圆曲线的测设流程一、圆曲线元素的计算一、圆曲线元素的计算圆曲线元素：圆曲线元素：圆曲线主点圆曲线主点：直圆点直圆点ZYZY、曲中点曲中点QZQZ、圆直点圆直点YZYZ切线长切线长T T、曲线长曲线长L L、外矢距外矢距E E、切曲差切曲差D D直圆点直圆点ZYZY曲中点曲中点QZQZ圆直点圆直点YZYZ交点交点JDJD切线长切线长T T切线长切线长T T曲线长曲线长L L外矢距外矢距E EOR已已 知知 数数 据据：圆曲线半径圆曲线半径R R和偏角和偏角本次课主要内容本次课主要内容一、圆曲线元素的计算一、圆曲线元素的计算二、圆曲线主点里程的计算二、圆曲线主点里程的计算三、圆曲线主点的测设三、圆曲线主点的测设四、长弦偏角法细部点测设四、长弦偏角法细部点测设 二、圆曲线主点里程的计算二、圆曲线主点里程的计算直圆点直圆点ZYZY交点交点JDJD圆直点圆直点YZYZ曲中点曲中点QZQZ切线长切线长T T曲线长曲线长L LO O已知：已知：R交点交点JDJD里程里程、圆曲线半径、圆曲线半径R R、偏角、偏角本次课主要内容本次课主要内容一、圆曲线元素的计算一、圆曲线元素的计算二、圆曲线主点里程的计算二、圆曲线主点里程的计算三、圆曲线主点的测设三、圆曲线主点的测设四、长弦偏角法细部点测设四、长弦偏角法细部点测设 三、圆曲线主点的测设三、圆曲线主点的测设直圆点直圆点ZYZY曲中点曲中点QZQZ圆直点圆直点YZYZ交点交点JDJD2 2切线长切线长T T测设直圆点测设直圆点ZY交点交点JDJD1 1交点交点JDJD3 3180-180-切线长切线长T T外矢距外矢距E E测设圆直点测设圆直点YZ测设曲中点测设曲中点QZO本次课主要内容本次课主要内容一、圆曲线元素的计算一、圆曲线元素的计算二、圆曲线主点里程的计算二、圆曲线主点里程的计算三、圆曲线主点的测设三、圆曲线主点的测设四、长弦偏角法细部点测设四、长弦偏角法细部点测设 几个概念几个概念1.右偏右偏2.偏角偏角3.正拨正拨左偏左偏反拨反拨顺时针拨动顺时针拨动逆时针拨动逆时针拨动YZRO四、长弦偏角法细部点测设四、长弦偏角法细部点测设1.测设前提测设前提：曲线较长，地形变化较大：曲线较长，地形变化较大2.测设原理测设原理3.测设数据的计算测设数据的计算ZYJD第一个点第一个点第二个及第二个及以后的点以后的点检核（检核（YZYZ）A已知：偏角已知：偏角、半径、半径R R、JDJD里程、桩距里程、桩距j112d=YZROJDZY4.4.测设数据计算举例测设数据计算举例【解解】采用长弦偏角法计算：JDJD里程里程ZYZY点里程点里程细部点里程细部点里程偏角和弦长偏角和弦长P1P25.5.细部点测设细部点测设YZOJDZY横向闭合差（半径方向）：横向闭合差（半径方向）：纵向闭合差（切线方向）：纵向闭合差（切线方向）：点的平面位置测设方法点的平面位置测设方法:1.直角坐标系法（大地坐标）。直角坐标系法（大地坐标）。2.极坐标法（切线支距）。极坐标法（切线支距）。3.角度交会法（偏角法）。角度交会法（偏角法）。4.距离交会法（适用于障碍测量）。距离交会法（适用于障碍测量）。(1)坐标计算原理：XOYA(x1,y1)B(x2,y2)LXYx=x2-x1y=y2-y1x=LCosaay=LSinaX2=X1+LCosaY2=y1+LSina（2）偏角法计算YZROMZYJDCaT任意点偏角计算：a=（l1180）/(R)/2=（l190）/(R)l1任意点弦长计算：C=2R Sina实例分析：已知圆曲线ZY点里程K0+040.1，坐标为（2757352.935，533279.718），直线上点K0+000坐标为（2757387.004，533258.568），曲线要素已知，试求各加桩点偏角以及逐桩坐标。a=730616R=500T=370.69L=637.96序号序号里程里程半径半径曲线曲线L L加桩长度加桩长度偏角（角度）偏角（角度）角度角度弦长弦长ZYZYK0+040.1K0+040.1637.96637.963.14159273.14159271 1K0+060K0+060500500637.96637.963.14159273.141592719.919.91.1401860121.1401860121 18 825.7525.7519.898719.89872 2K0+080K0+080500500637.96637.963.14159273.141592739.939.92.2861016022.2861016022 217179.979.9739.889439.88943 3K0+100K0+100500500637.96637.963.14159273.141592759.959.93.4320171923.4320171923 3252555.2655.2659.864259.86424 4K0+120K0+120500500637.96637.963.14159273.141592779.979.94.5779327824.5779327824 4343440.5640.5679.81579.8155 5K0+140K0+140500500637.96637.963.14159273.141592799.999.95.7238483735.7238483735 5434325.8925.8999.733999.73396 6K0+160K0+160500500637.96637.963.14159273.1415927119.9119.96.8697639636.8697639636 6525211.1511.15119.613119.6137 7K0+180K0+180500500637.96637.963.14159273.1415927139.9139.98.0156795538.0156795538 80 056.4556.45139.444139.4448 8K0+200K0+200500500637.96637.963.14159273.1415927159.9159.99.1615951439.1615951439 99 941.7441.74159.219159.2199 9K0+220K0+220500500637.96637.963.14159273.1415927179.9179.910.3075107310.307510731010181827.0427.04178.931178.9311010K0+240K0+240500500637.96637.963.14159273.1415927199.9199.911.4534263211.453426321111272712.3312.33198.571198.5711111K0+260K0+260500500637.96637.963.14159273.1415927219.9219.912.5993419112.599341911212353557.6357.63218.132218.1321212K0+280K0+280500500637.96637.963.14159273.1415927239.9239.913.745257513.74525751313444442.9342.93237.605237.6051313K0+300K0+300500500637.96637.963.14159273.1415927259.9259.914.8911730914.891173091414535328.2228.22256.984256.9841414K0+320K0+320500500637.96637.963.14159273.1415927279.9279.916.0370886816.0370886816162 213.5213.52276.26276.261515K0+340K0+340500500637.96637.963.14159273.1415927299.9299.917.1830042717.183004271717101058.8258.82295.425295.425QZQZK0+359.08K0+359.08500500637.96637.963.14159273.1415927318.98318.9818.2762077518.276207751818161634.3534.35313.598313.598序号序号里程里程半径半径曲线曲线L L加桩长度加桩长度偏角（角度）偏角（角度）角度角度弦长弦长1717K0+380K0+380500500637.96637.963.14159273.1415927339.9339.919.4748354519.474835451919282829.4129.41333.393333.3931818K0+400K0+400500500637.96637.963.14159273.1415927359.9359.920.6207510420.620751042020363638.738.7352.181352.1811919K0+420K0+420500500637.96637.963.14159273.1415927379.9379.921.7666666321.76666663212146460 0370.828370.8282020K0+440K0+440500500637.96637.963.14159273.1415927399.9399.922.9125822222.912582222222545445.345.3389.326389.3262121K0+460K0+460500500637.96637.963.14159273.1415927419.9419.924.0584978124.0584978124243 330.5930.59407.669407.6692222K0+480K0+480500500637.96637.963.14159273.1415927439.9439.925.204413425.20441342525121215.8915.89425.849425.8492323K0+500K0+500500500637.96637.963.14159273.1415927459.9459.926.3503289926.35032899262621211.181.18443.858443.8582424K0+520K0+520500500637.96637.963.14159273.1415927479.9479.927.4962445827.496244582727292946.4846.48461.69461.692525K0+540K0+540500500637.96637.963.14159273.1415927499.9499.928.6421601728.642160172828383831.7831.78479.338479.3382626K0+560K0+560500500637.96637.963.14159273.1415927519.9519.929.7880757629.788075762929474717.0717.07496.793496.7932727K0+580K0+580500500637.96637.963.14159273.1415927539.9539.930.9339913630.93399136303056562.372.37514.05514.052828K0+600K0+600500500637.96637.963.14159273.1415927559.9559.932.0799069532.0799069532324 447.6747.67531.101531.1012929K0+620K0+620500500637.96637.963.14159273.1415927579.9579.933.2258225433.225822543333131332.9632.96547.94547.943030K0+640K0+640500500637.96637.963.14159273.1415927599.9599.934.3717381334.371738133434222218.2618.26564.56564.563131K0+660K0+660500500637.96637.963.14159273.1415927619.9619.935.5176537235.51765372353531313.553.55580.954580.9543232K0+678.K0+678.0606500500637.96637.963.14159273.1415927637.96637.9636.5524154936.55241549363633338.78.7595.558595.558缓和曲线要素计算：缓和曲线要素计算：缓和曲线要素计算：