缓和曲线五大要素计算表格

注：1、表中蓝色部分为需要对照设计院给的参数表填写。2、表中绿色部分为计算器程序所需的线元参数。设有缓和曲线的要素计算公式平曲线要素计算结果计算公式备注缓和曲线长l0180已知（m）曲线半径R800已知（m）交点前直线切线角A度分秒曲线长Lc341.36087564631893346.83交点前直线切线角A3.3084986354转向角α372023转向角α0.6517010946α=β1-β2β1交点前方位角、β2交点后方位角；α右转为正，左转为负(弧度制)曲线方向判别Q1左=-1,右=1内移距p1.6875p=l02/24Rl0缓和曲线长（指的是一段的长不是两段的和）切垂距m89.96203125m=l0/2-l03/240R2缓和曲线缓和曲线角β00.1125β0=l0/2R缓和曲线(弧度制)切线长T360.8483421014T=(R+p)*TAN(α/2）+m曲线长L701.3608756463L=(R*α*π)/180+l0外视距E46.2164268454E=(R+p)sec(α/2）-R切曲差q20.3358085566q=2T-L交点里程JD149748.27JD=ZH+T已知ZH点切线方位角3.3084986354189.5630HY点切线方位角3.4209986354196.0088YH点切线方位角3.84769973220.4570HZ点切线方位角3.96019973226.9027直缓点ZH里程149387.42ZH=JD-T线元切线方位角度分秒缓圆点HY里程149567.42HY=ZH+l0角度1893347曲中QZ里程149738.10QZ=HY+L/2-l0196032圆缓点YH里程149908.78YH=QZ+L/2-l02202725缓直点HZ里程150088.78HZ=YH+l02265410缓直点HZ里程150088.78HZ=JD+T-q校核无误注:曲线终点里程必须沿曲线计算，不能沿切线计算。只有把终点里程算出来后，才能接着算下一直线里程；excel表格中角度是弧度制设有缓和曲线的主要素坐标计算平曲线要素计算结果计算公式备注交点前直线切线角A度分秒方位角θ13.3084994596交点前导线沿线路前进方向的方位角方位角θ11893347方位角θ23.9602005541交点后导线沿线路前进方向的方位角方位角θ22265410交点X04348804.953交点大地坐标交点Y0498489.564曲线半径R800改手动输入为自动代入转向角α0.6517010946α=θ1-θ2曲线方向判别Q1左=-1,右=1内移距p1.6875p=l02/24R前缓和曲线长l1180后缓和曲线长l2180切线长T1360.8483421014T=(R+p)*TAN(α/2）+m切线长T2360.8483421014T=(R+p)*TAN(α/2）+m切垂距m89.96203125m=l0/2-l03/(240R2)外视距E46.2164268454E=(R+p)sec(α/2）-R切曲差q20.3358085566q=2T-L曲线长L701.3608756463L=(R*α*π)/180+l0交点里程JD149748.27JD=ZH+T直缓点ZH149387.421657899ZH=JD-T缓圆点HY149567.421657899HY=ZH+l0曲中QZ149738.102095722QZ=HY+L/2-l0圆缓点YH149908.782533545YH=QZ+L/2-l0缓直点HZ150088.782533545HZ=YH+l0ZH(x)4349160.78676438X=X0+T1*COS(θ1+π）ZH(y)498549.512795853Y=Y0+T1*SIN(θ1+π）HZ(X)4348558.40756562X=X0+T1*COS(θ2)HZ(Y)498226.074199847Y=Y0+T1*SIN(θ2)HY(X)4348984.63420271X=XZH+x*COS(θ1)-Q*sin(θ1）HY(Y)498512.990516157Y=YZH+x*SIN(θ1)+Qy*cos(θ1）θθ=θ1+i*l^2/(2*ls*R)待求点切线方位角YH(X)4348686.16364159X=XHZ-x*COS(θ2)-Qy*sin(θ2）YH(Y)498352.731165511Y=YHZ-x*SIN(θ2)+Qy*cos(θ2）θθ=θ1-i*l^2/(2*ls*R)待求点切线方位角待求点支距坐标xx=l-l^5/(40*R^2*ls^2)（缓和曲线上）待求点支距坐标yy=l^3/(6*R*ls)-l^7/(336R^3*ls^3)（缓和曲线上）待求点支距坐标xx=q-R*SIN(Ψ)（圆曲线上）待求点支距坐标yy=p+R*（1-cos(Ψ))（圆曲线上）ΨΨ=(ls/2R)-(l-ls)/R（圆曲线上）本曲线段线元要素汇总表计算结果里程线元切线方位角坐标度分秒XY直缓点ZH149387.4218933474349160.78676438498549.512795853缓圆点HY149567.421960324348984.63420271498512.990516157圆缓点YH149908.7822027254348686.16364159498352.731165511缓直点HZ150088.7822654104348558.40756562498226.074199847注：1、表中蓝色部分为需要对照设计院给的参数表填写。2、表中绿色部分为计算器程序所需的线元参数。设有缓和曲线的要素计算公式平曲线要素计算结果计算公式备注缓和曲线长l0190已知（m）曲线半径R1600已知（m）交点前直线切线角A度分秒曲线长Lc678.1267699421451145交点前直线切线角A2.5341453518转向角α31515转向角α0.5425792312α=β1-β2β1交点前方位角、β2交点后方位角；α右转为正，左转为负(弧度制)曲线方向判别1左=-1,右=1内移距p0.9401041667p=l02/24Rl0缓和曲线长（指的是一段的长不是两段的和）切垂距m94.988836263m=l0/2-l03/240R2缓和曲线缓和曲线角β00.059375β0=l0/2R缓和曲线(弧度制)切线长T540.2855652895T=(R+p)*TAN(α/2）+m曲线长L1058.126769942L=(R*α*π)/180+l0外视距E61.7154973132E=(R+p)sec(α/2）-R切曲差q22.444360637q=2T-L交点里程JD68267.87JD=ZH+T已知ZH点切线方位角2.5341453518145.1958HY点切线方位角2.5935203518148.5978YH点切线方位角3.0173495831172.8814HZ点切线方位角3.0767245831176.2833直缓点ZH里程67727.58ZH=JD-T线元切线方位角度分秒缓圆点HY里程67917.58HY=ZH+l0角度1451145曲中QZ里程68256.65QZ=HY+L/2-l01483552圆缓点YH里程68595.71YH=QZ+L/2-l01725253缓直点HZ里程68785.71HZ=YH+l01761660缓直点HZ里程68785.71HZ=JD+T-q校核无误注:曲线终点里程必须沿曲线计算，不能沿切线计算。只有把终点里程算出来后，才能接着算下一直线里程；excel表格中角度是弧度制设有缓和曲线的主要素坐标计算平曲线要素计算结果计算公式备注交点前直线切线角A度分秒方位角θ12.5341453518交点前导线沿线路前进方向的方位角方位角θ11451145方位角θ23.0767245831交点后导线沿线路前进方向的方位角方位角θ2176170交点X03477399.9966交点大地坐标交点Y0510030.3442曲线半径R1600转向角α0.5425792312α=θ1-θ2曲线方向判别1左=-1,右=1内移距p0.9401041667p=l02/24R前缓和曲线长l1190后缓和曲线长l2190切线长T1540.2855652895T=(R+p)*TAN(α/2）+m切线长T2540.2855652895T=(R+p)*TAN(α/2）+m切垂距m94.988836263m=l0/2-l03/240R2外视距E61.7154973132E=(R+p)sec(α/2）-R切曲差q22.444360637q=2T-L曲线长L1058.126769942L=(R*α*π)/180+l0交点里程JD68267.87JD=ZH+T直缓点ZH67727.5844347105ZH=JD-T缓圆点HY67917.5844347105HY=ZH+l0曲中QZ68256.6478196815QZ=HY+L/2-l0圆缓点YH68595.7112046525YH=QZ+L/2-l0缓直点HZ68785.7112046525HZ=YH+l0ZH(x)3477843.62923975X=X0+T1*COS(θ1+π）ZH(y)509721.963634774Y=Y0+T1*SIN(θ1+π）HZ(X)3476860.84736095X=X0+T1*COS(θ2)HZ(Y)510065.36690828Y=Y0+T1*SIN(θ2)HY(X)3477685.52743051X=XZH+x*COS(θ1)+y*sin(θ1）HY(Y)509827.284619452Y=YZH+x*SIN(θ1)-y*cos(θ1）θθ=θ1+i*l^2/(2*ls*R)待求点切线方位角YH(X)3477050.1371523X=XHZ+x*COS(θ2+π)+y*sin(θ2+l*π/2）YH(Y)510049.302450872Y=YHZ+x*SIN(θ2+π)-y*cos(θ2+l*π/2）θθ=θ1-i*l^2/(2*ls*R)待求点切线方位角待求点支距坐标xx=l-l^5/(40*R^2*ls^2)（缓和曲线上）待求点支距坐标yy=l^3/(6*R*ls)-l^7/(336R^3*ls^3)（缓和曲线上）待求点支距坐标xx=q-R*SIN(Ψ)（圆曲线上）待求点支距坐标yy=p+R*（1-cos(Ψ))（圆曲线上）ΨΨ=(ls/2R)-(l-ls)/R（圆曲线上）本曲线段线元要素汇总表计算结果里程线元切线方位角坐标度分秒XY直缓点ZH67727.5814511453477843.62923975509721.963634774缓圆点HY67917.5814835523477685.52743051509827.284619452圆缓点YH68595.7117252533477050.1371523510049.302450872缓直点HZ68785.711761703476860.84736095510065.36690828注：1、表中蓝色部分为需要对照设计院给的参数表填写。2、表中绿色部分为计算器程序所需的线元参数。设有缓和曲线的要素计算公式平曲线要素计算结果计算公式备注缓和曲线长l0190已知（m）曲线半径R1600已知（m）交点前直线切线角A度分秒曲线长Lc299.3515371647176170交点前直线切线角A3.0767245831转向角α173125转向角α0.3058447107α=β1-β2β1交点前方位角、β2交点后方位角；α右转为正，左转为负(弧度制)曲线方向判别-1左=-1,右=1内移距p0.9401041667p=l02/24Rl0缓和曲线长（指的是一段的长不是两段的和）切垂距m94.988836263m=l0/2-l03/240R2缓和曲线缓和曲线角β00.059375β0=l0/2R缓和曲线(弧度制)切线长T341.7347780153T=(R+p)*TAN(α/2）+m曲线长L679.3515371647L=(R*α*π)/180+l0外视距E19.8434420957E=(R+p)sec(α/2）-R切曲差q4.1180188658q=2T-L交点里程JD69945.11JD=ZH+T已知ZH点切线方位角3.0767245831176.2833HY点切线方位角3.0173495831172.8814YH点切线方位角2.8302548723162.1617HZ点切线方位角2.7708798723158.7597直缓点ZH里程69603.38ZH=JD-T线元切线方位角度分秒缓圆点HY里程69793.38HY=ZH+l0角度1761660曲中QZ里程69943.05QZ=HY+L/2-l01725253圆缓点YH里程70092.73YH=QZ+L/2-l0162942缓直点HZ里程70282.73HZ=YH+l01584535缓直点HZ里程70282.73HZ=JD+T-q计算有误注:曲线终点里程必须沿曲线计算，不能沿切线计算。只有把终点里程算出来后，才能接着算下一直线里程；excel表格中角度是弧度制设有缓和曲线的主要素坐标计算平曲线要素计算结果计算公式备注交点前直线切线角A度分秒方位角θ13.0767245831交点前导线沿线路前进方向的方位角方位角θ1176170方位角θ22.7708798723交点后导线沿线路前进方向的方位角方位角θ21584535交点X03475703.8818交点大地坐标交点Y0510140.5217曲线半径R1600转向角α0.3058447107α=θ1-θ2曲线方向判别-1左=-1,右=1内移距p0.9401041667p=l02/24R前缓和曲线长l1190后缓和曲线长l2190切线长T1341.7347780153T=(R+p)*TAN(α/2）+m切线长T2341.7347780153T=(R+p)*TAN(α/2）+m切垂距m94.988836263m=l0/2-l03/240R2外视距E19.8434420957E=(R+p)sec(α/2）-R切曲差q4.1180188658q=2T-L曲线长L679.3515371647L=(R*α*π)/180+l0交点里程JD69945.11JD=ZH+T直缓点ZH69603.3752219847ZH=JD-T缓圆点HY69793.3752219847HY=ZH+l0曲中QZ69943.0509905671QZ=HY+L/2-l0圆缓点YH70092.7267591494YH=QZ+L/2-l0缓直点HZ70282.7267591494HZ=YH+l0ZH(x)3476044.89784292X=X0+T1*COS(θ1+π）ZH(y)510118.369567483Y=Y0+T1*SIN(θ1+π）HZ(X)3475385.3612855X=X0+T1*COS(θ2)HZ(Y)510264.325336254Y=Y0+T1*SIN(θ2)HY(X)3475855.60805158X=XZH+x*COS(θ1)+y*sin(θ1）HY(Y)510134.434024891Y=YZH+x*SIN(θ1)-y*cos(θ1）θθ=θ1+i*l^2/(2*ls*R)待求点切线方位角YH(X)3475563.75435422X=XHZ+x*COS(θ2+π)+y*sin(θ2+l*π/2）YH(Y)510199.021393532Y=YHZ+x*SIN(θ2+π)-y*cos(θ2+l*π/2）θθ=θ1-i*l^2/(2*ls*R)待求点切线方位角待求点支距坐标xx=l-l^5/(40*R^2*ls^2)（缓和曲线上）待求点支距坐标yy=l^3/(6*R*ls)-l^7/(336R^3*ls^3)（缓和曲线上）待求点支距坐标xx=q-R*SIN(Ψ)（圆曲线上）待求点支距坐标yy=p+R*（1-cos(Ψ))（圆曲线上）ΨΨ=(ls/2R)-(l-ls)/R（圆曲线上）本曲线段线元要素汇总表计算结果里程线元切线方位角坐标度分秒XY直缓点ZH69603.3817616603476044.89784292510118.369567483缓圆点HY69793.3817252533475855.60805158510134.434024891圆缓点YH70092.731629423475563.75435422510199.021393532缓直点HZ70282.7315845353475385.3612855510264.325336254注：1、表中蓝色部分为需要对照设计院给的参数表填写。2、表中绿色部分为计算器程序所需的线元参数。设有缓和曲线的要素计算公式平曲线要素计算结果计算公式备注缓和曲线长l0120已知（m）曲线半径R2500已知（m）交点前直线切线角A度分秒曲线长Lc850.23337932041584535交点前直线切线角A2.7708798723转向角α221410转向角α0.3880933517α=β1-β2β1交点前方位角、β2交点后方位角；α右转为正，左转为负(弧度制)曲线方向判别1左=-1,右=1内移距p0.24p=l02/24Rl0缓和曲线长（指的是一段的长不是两段的和）切垂距m59.998848m=l0/2-l03/240R2缓和曲线缓和曲线角β00.024β0=l0/2R缓和曲线(弧度制)切线长T551.3447097142T=(R+p)*TAN(α/2）+m曲线长L1090.2333793205L=(R*α*π)/180+l0外视距E48.0621682808E=(R+p)sec(α/2）-R切曲差q12.456040108q=2T-L交点里程JD73005.2JD=ZH+T已知ZH点切线方位角2.7708798723158.7597HY点切线方位角2.7948798723160.1348YH点切线方位角3.1349732241179.6207HZ点切线方位角3.1589732241180.9958直缓点ZH里程72453.86ZH=JD-T线元切线方位角度分秒缓圆点HY里程72573.86HY=ZH+l0角度1584535曲中QZ里程72998.97QZ=HY+L/2-l016085圆缓点YH里程73424.09YH=QZ+L/2-l01793715缓直点HZ里程73544.09HZ=YH+l01805945缓直点HZ里程73544.09HZ=JD+T-q校核无误注:曲线终点里程必须沿曲线计算，不能沿切线计算。只有把终点里程算出来后，才能接着算下一直线里程；excel表格中角度是弧度制设有缓和曲线的主要素坐标计算平曲线要素计算结果计算公式备注交点前直线切线角A度分秒方位角θ12.7708798723交点前导线沿线路前进方向的方位角方位角θ11584535方位角θ23.1589732241交点后导线沿线路前进方向的方位角方位角θ21805945交点X03472713.99交点大地坐标交点Y0511302.643曲线半径R2500转向角α0.3880933517α=θ1-θ2曲线方向判别1左=-1,右=1内移距p0.24p=l02/24R前缓和曲线长l1120后缓和曲线长l2120切线长T1551.3447097142T=(R+p)*TAN(α/2）+m切线长T2551.3447097142T=(R+p)*TAN(α/2）+m切垂距m59.998848m=l0/2-l03/240R2外视距E48.0621682808E=(R+p)sec(α/2）-R切曲差q12.456040108q=2T-L曲线长L1090.2333793205L=(R*α*π)/180+l0交点里程JD73005.2JD=ZH+T直缓点ZH72453.8552902858ZH=JD-T缓圆点HY72573.8552902858HY=ZH+l0曲中QZ72998.971979946QZ=HY+L/2-l0圆缓点YH73424.0886696062YH=QZ+L/2-l0缓直点HZ73544.0886696062HZ=YH+l0ZH(x)3473227.88150857X=X0+T1*COS(θ1+π）ZH(y)511102.901901689Y=Y0+T1*SIN(θ1+π）HZ(X)3472162.72856446X=X0+T1*COS(θ2)HZ(Y)511293.060796876Y=Y0+T1*SIN(θ2)HY(X)3473115.69183961X=XZH+x*COS(θ1)+y*sin(θ1）HY(Y)511145.47819729Y=YZH+x*SIN(θ1)-y*cos(θ1）θθ=θ1+i*l^2/(2*ls*R)待求点切线方位角YH(X)3472282.72021341X=XHZ+x*COS(θ2+π)+y*sin(θ2+l*π/2）YH(Y)511294.186385195Y=YHZ+x*SIN(θ2+π)-y*cos(θ2+l*π/2）θθ=θ1-i*l^2/(2*ls*R)待求点切线方位角待求点支距坐标xx=l-l^5/(40*R^2*ls^2)（缓和曲线上）待求点支距坐标yy=l^3/(6*R*ls)-l^7/(336R^3*ls^3)（缓和曲线上）待求点支距坐标xx=q-R*SIN(Ψ)（圆曲线上）待求点支距坐标yy=p+R*（1-cos(Ψ))（圆曲线上）ΨΨ=(ls/2R)-(l-ls)/R（圆曲线上）本曲线段线元要素汇总表计算结果里程线元切线方位角坐标度分秒XY直缓点ZH72453.8615845353473227.88150857511102.901901689缓圆点HY72573.86160853473115.69183961511145.47819729圆缓点YH73424.0917937153472282.72021341511294.186385195缓直点HZ73544.0918059453472162.72856446511293.060796876注：1、表中蓝色部分为需要对照设计院给的参数表填写。2、表中绿色部分为计算器程序所需的线元参数。设有缓和曲线的要素计算公式平曲线要素计算结果计算公式备注缓和曲线长l0100已知（m）曲线半径R3000已知（m）交点前直线切线角A度分秒曲线长Lc228.44187640451805945交点前直线切线角A3.1589732241转向角α61622转向角α0.1094806255α=β1-β2β1交点前方位角、β2交点后方位角；α右转为正，左转为负(弧度制)曲线方向判别-1左=-1,右=1内移距p0.1388888889p=l02/24Rl0缓和曲线长（指的是一段的长不是两段的和）切垂距m49.999537037m=l0/2-l03/240R2缓和曲线缓和曲线角β00.0166666667β0=l0/2R缓和曲线(弧度制)切线长T214.3923119558T=(R+p)*TAN(α/2）+m曲线长L428.4418764045L=(R*α*π)/180+l0外视距E4.6394687331E=(R+p)sec(α/2）-R切曲差q0.3427475072q=2T-L交点里程JD76068.31JD=ZH+T已知ZH点切线方位角3.1589732241180.9958HY点切线方位角3.1423065574180.0409YH点切线方位角3.0661592653175.6780HZ点切线方位角3.0494925986174.7231直缓点ZH里程75853.92ZH=JD-T线元切线方位角度分秒缓圆点HY里程75953.92HY=ZH+l0角度1805945曲中QZ里程76068.14QZ=HY+L/2-l0180227圆缓点YH里程76182.36YH=QZ+L/2-l01754041缓直点HZ里程76282.36HZ=YH+l01744323缓直点HZ里程76282.36HZ=JD+T-q校核无误注:曲线终点里程必须沿曲线计算，不能沿切线计算。只有把终点里程算出来后，才能接着算下一直线里程；excel表格中角度是弧度制设有缓和曲线的主要素坐标计算平曲线要素计算结果计算公式备注交点前直线切线角A度分秒方位角θ13.1589732241交点前导线沿线路前进方向的方位角方位角θ11805945方位角θ23.0494925986交点后导线沿线路前进方向的方位角方位角θ21744323交点X03469638.896交点大地坐标交点Y0511249.196曲线半径R3000转向角α0.1094806255α=θ1-θ2曲线方向判别-1左=-1,右=1内移距p0.1388888889p=l02/24R前缓和曲线长l1100后缓和曲线长l2100切线长T1214.3923119558T=(R+p)*TAN(α/2）+m切线长T2214.3923119558T=(R+p)*TAN(α/2）+m切垂距m49.999537037m=l0/2-l03/240R2外视距E4.6394687331E=(R+p)sec(α/2）-R切曲差q0.3427475072q=2T-L曲线长L428.4418764045L=(R*α*π)/180+l0交点里程JD76068.31JD=ZH+T直缓点ZH75853.9176880442ZH=JD-T缓圆点HY75953.9176880442HY=ZH+l0曲中QZ76068.1386262464QZ=HY+L/2-l0圆缓点YH76182.3595644486YH=QZ+L/2-l0缓直点HZ76282.3595644486HZ=YH+l0ZH(x)3469853.2559305X=X0+T1*COS(θ1+π）ZH(y)511252.922073081Y=Y0+T1*SIN(θ1+π）HZ(X)3469425.41232831X=X0+T1*COS(θ2)HZ(Y)511268.91364056Y=Y0+T1*SIN(θ2)HY(X)3469753.26415631X=XZH+x*COS(θ1)+y*sin(θ1）HY(Y)511251.739623462Y=YZH+x*SIN(θ1)-y*cos(θ1）θθ=θ1+i*l^2/(2*ls*R)待求点切线方位角YH(X)3469525.03683541X=XHZ+x*COS(θ2+π)+y*sin(θ2+l*π/2）YH(Y)511260.270106526Y=YHZ+x*SIN(θ2+π)-y*cos(θ2+l*π/2）θθ=θ1-i*l^2/(2*ls*R)待求点切线方位角待求点支距坐标xx=l-l^5/(40*R^2*ls^2)（缓和曲线上）待求点支距坐标yy=l^3/(6*R*ls)-l^7/(336R^3*ls^3)（缓和曲线上）待求点支距坐标xx=q-R*SIN(Ψ)（圆曲线上）待求点支距坐标yy=p+R*（1-cos(Ψ))（圆曲线上）ΨΨ=(ls/2R)-(l-ls)/R（圆曲线上）本曲线段线元要素汇总表计算结果里程线元切线方位角坐标度分秒XY直缓点ZH75853.9218059453469853.2559305511252.922073081缓圆点HY75953.921802273469753.26415631511251.739623462圆缓点YH76182.3617540413469525.03683541511260.270106526缓直点HZ76282.3617443233469425.41232831511268.91364056