基本型曲線中邊樁坐標(biāo)計(jì)算及測(cè)設(shè)課件講解

柳州鐵道職業(yè)技術(shù)學(xué)院建筑技術(shù)學(xué)院《鐵路工程測(cè)量》課程團(tuán)隊(duì)鐵路工程測(cè)量---基本型曲線中邊樁坐標(biāo)計(jì)算及測(cè)設(shè)基本型曲線中邊樁坐標(biāo)計(jì)算及測(cè)設(shè)一、線路中樁坐標(biāo)計(jì)算二、線路邊樁坐標(biāo)計(jì)算三、基本型曲線緩和曲線中邊樁坐標(biāo)計(jì)算一.簡(jiǎn)單型線路中樁坐標(biāo)計(jì)算設(shè)計(jì)給定的要素有：α——轉(zhuǎn)向角；R——圓曲線半徑；α1、α2——直線的的方位角主點(diǎn)里程KZY（或JD里程）；JD坐標(biāo)（XJD，YJD）；（一）簡(jiǎn)單型曲線中樁坐標(biāo)計(jì)算線路K2+400~K2+700設(shè)計(jì)資料：

轉(zhuǎn)向角α=-18°25′36″；R=400m；曲線長(zhǎng)L=128.642m;切線長(zhǎng)T=64.881m;α1=75°30′48″；α2=57°05′12″;JD=K2+560(1256.342，892.143）ZY=K2+495.119(1240.112，829.325)YZ=K2+623.761(1291.597，946.611)1.第一直線段中線樁坐標(biāo)計(jì)算示例(1)K2+400中樁:N=1240.112-(2495.119-2400)COS75°30′48″=1216.318E=829.325-(2495.119-2400)Sin75°30′48″=737.230

已知條件：轉(zhuǎn)向角α=-18°25′36″；R=400m；α1=75°30′48″；α2=57°05′12″；ZY=K2+495.119(1240.112，829.325)；YZ=K2+623.761(1291.597，946.611)(2)K2+420中樁:N=1240.112-(2495.119-2420)COS75°30′48″=1221.320E=829.325-(2495.119-2420)Sin75°30′48″=756.594

已知條件：轉(zhuǎn)向角α=-18°25′36″；R=400m；α1=75°30′48″；α2=57°05′12″；ZY=K2+495.119(1240.112，829.325)；YZ=K2+623.761(1291.597，946.611)練習(xí)：計(jì)算K2+440，K2+460，K2+480中樁坐標(biāo)K2+440(1226.323,775.958)K2+460(1231.326,795.322)K2+480(1236.330,814.687)

已知條件：轉(zhuǎn)向角α=-18°25′36″；R=400m；α1=75°30′48″；α2=57°05′12″；ZY=K2+495.119(1240.112，829.325)；YZ=K2+623.761(1291.597，946.611)2.圓曲線段中樁坐標(biāo)計(jì)算如圖所示，m為圓曲線上

任一點(diǎn)，里程為Km，則，ZY至m點(diǎn)的曲線長(zhǎng)度：Lm=Km-KzY那么，m點(diǎn)的坐標(biāo)計(jì)算過(guò)程如下：ZYYZ圓曲線上任一點(diǎn)（1）角度計(jì)算ZYYZCα1（2）弦長(zhǎng)計(jì)算（3）m點(diǎn)坐標(biāo)計(jì)算ZYYZCα1Nm=NZY+C.cos(α1-αm)Ym=YZY+C.sin(α1-αm)如果線路轉(zhuǎn)向角為正,計(jì)算過(guò)程有什么不一樣?圓線段中樁坐標(biāo)計(jì)算示例(1)K2+500中樁:Lm=Km-KzY=2500-2495.119=4.881mαm=90Lm/πR=(90×4.881)/(π×400)=0°20′58.4″C=2Rsinαm=2×400sin(0°20′58.4″)=4.881mNm=NZY+Ccos(α1-αm)=1240.112+4.881cos(75°30′48″-0°20′58.4″)=1241.362Em=EZY+Csin(α1-αm)=829.325+4.881sin(75°30′48″-0°20′58.4″)=834.043

已知條件：轉(zhuǎn)向角α=-18°25′36″；R=400m；α1=75°30′48″；α2=57°05′12″；ZY=K2+495.119(1240.112，829.325)；YZ=K2+623.761(1291.597，946.611)(2)K2+520中樁:Lm=Km-KzY=2520-2495.119=24.881mαm=90Lm/πR=(90×24.881)/(π×400)=1°46′55″C=2Rsinαm=2×400sin(1°46′55″)=24.877mNm=NZY+Ccos(α1-αm)=1240.112+24.877cos(75°30′48″-1°46′55″)=1247.081Em=EZY+Csin(α1-αm)=829.325+24.877sin(75°30′48″-1°46′55″)=853.206

已知條件：轉(zhuǎn)向角α=-18°25′36″；R=400m；α1=75°30′48″；α2=57°05′12″；ZY=K2+495.119(1240.112，829.325)；YZ=K2+623.761(1291.597，946.611)練習(xí)：計(jì)算：K2+540，K2+560，K2+580，K2+600，K2+620中樁坐標(biāo)K2+540(1253.751,872.059)K2+560(1261.354,890.554)K2+580(1269.873,908.647)K2+600(1279.285,926.292)K2+620(1289.568,943.443)

已知條件：轉(zhuǎn)向角α=-18°25′36″；R=400m；α1=75°30′48″；α2=57°05′12″；ZY=K2+495.119(1240.112，829.325)；YZ=K2+623.761(1291.597，946.611)3.第二直線段中線樁坐標(biāo)計(jì)算示例(1)K2+640中樁:N=1291.597+(2640-2623.761)COS57°05′12″=1300.421E=946.611+(2640-2623.761)Sin57°05′12″=960.244

已知條件：轉(zhuǎn)向角α=-18°25′36″；R=400m；α1=75°30′48″；α2=57°05′12″；ZY=K2+495.119(1240.112，829.325)；YZ=K2+623.761(1291.597，946.611)練習(xí)：計(jì)算K2+660;K2+680;K2+700中樁坐標(biāo)

K2+660(1311.288,977.033)K2+680(1322.155,993.823)K2+700(1333.023,1010.613)

已知條件：轉(zhuǎn)向角α=-18°25′36″；R=400m；α1=75°30′48″；α2=57°05′12″；ZY=K2+495.119(1240.112，829.325)；YZ=K2+623.761(1291.597，946.611)二、簡(jiǎn)單型線路邊樁坐標(biāo)計(jì)算線路K5+000~K5+400設(shè)計(jì)資料：

曲線1：轉(zhuǎn)向角α=-28°25′42″；R=300m；L=148.850m;

T=75.991m;α1=100°18′48″；α2=71°53′06″;JD=K5+120(863.234，945.113）ZY=K5+044.009(876.839,870.35)YZ=K5+192.860(886.861,1017.337)曲線2：轉(zhuǎn)向角α=+33°21′55″；R=200m；L=116.467m;

T=59.937m;α1=71°53′06″；α2=105°15′01″;JD=K5+310(923.283,1128.670）ZY=K5+250.063(904.647,1071.704)YZ=K5+366.530(907.517,1186.496)路基寬度為12m,左右等寬，分別計(jì)算左右邊樁坐標(biāo)。（一）第一直線（K5+000~+044.009)

邊樁計(jì)算示例(1)K5+000左6m寬度樁:N=876.839-44.009COS100°18′48″+6

COS(100°18′48″-90)=890.621E=870.350-44.009Sin100°18′48″+6Sin(100°18′48″-90)=828.125

已知：轉(zhuǎn)向角α=-28°25′42″；R=300m；L=148.850m;

T=75.991m;α1=100°18′48″；α2=71°53′06″;JD=K5+120(863.234，945.113）ZY=K5+044.009(876.839,870.35)YZ=K5+192.860(886.861,1017.337)

(2)K5+000右6m寬度樁:N=876.839-44.009COS100°18′48″+6COS(100°18′48″+90)=878.815E=870.350-44.009Sin100°18′48″+6Sin(100°18′48″+90)=825.977

已知：轉(zhuǎn)向角α=-28°25′42″；R=300m；L=148.850m;

T=75.991m;α1=100°18′48″；α2=71°53′06″;JD=K5+120(863.234，945.113）ZY=K5+044.009(876.839,870.35)YZ=K5+192.860(886.861,1017.337)

練習(xí):(1)計(jì)算K5+020左右各6m寬度樁左(887.040,847.802)右(875.234,845.654)(2)計(jì)算K5+040左右各6m寬度樁左(883.460,867.480)右(871.653,865.3310

已知：轉(zhuǎn)向角α=-28°25′42″；R=300m；L=148.850m;

T=75.991m;α1=100°18′48″；α2=71°53′06″;JD=K5+120(863.234，945.113）ZY=K5+044.009(876.839,870.35)YZ=K5+192.860(886.861,1017.337)（二）第一圓曲線（K5+044.009~+192.860段)

邊樁坐標(biāo)計(jì)算示例如圖所示，m為圓曲線上

任一點(diǎn)，里程為Km，則，ZY至m點(diǎn)的曲線長(zhǎng)度：Lm=Km-KzY那么，m點(diǎn)的切線方位角計(jì)算過(guò)程如下：ZYYZ圓曲線上任一點(diǎn)ZYYZCα1βm=2αm則m點(diǎn)切線方位角=α1-2αm(1)K5+060左6m寬度樁計(jì)算:Lm=Km-KzY=5060-5044.009=15.991mαm=90Lm/πR=(90×15.991)/(π×300)=1°31′37″C=2Rsinαm=2×300sin(1°31′37″)=15.988mN=NZY+Ccos(α1-αm)+6cos(α1-2αm-90)=876.839+15.988cos(100°18′48″-1°31′37″)+6cos(100°18′48″-2×1°31′37″-90)=880.349E

=EZY+Csin(α1-αm)+6Sin(α1-2αm-90)=870.350+15.9881sin(100°18′48″-1°31′37″)+6Sin(100°18′48″-2×1°31′37″-90)=886.909

第一圓曲線（K5+044.009～+192.860段)計(jì)算示例已知：轉(zhuǎn)向角α=-28°25′42″；R=300m；L=148.850m;

T=75.991m;α1=100°18′48″；α2=71°53′06″;JD=K5+120(863.234，945.113）ZY=K5+044.009(876.839,870.35)YZ=K5+192.860(886.861,1017.337)(2)K5+060右6m寬度樁計(jì)算:Lm=Km-KzY=5060-5044.009=15.991mαm=90Lm/πR=(90×15.991)/(π×300)=1°31′37″C=2Rsinαm=2×300sin(1°31′37″)=15.988mNm=NZY+Ccos(α1-αm)+6cos(α1-2αm+90)=876.839+15.988cos(100°18′48″-1°31′37″)+6cos(100°18′48″-2×1°31′37″+90)=868.444Em=EZY+Csin(α1-αm)+6Sin(α1-2αm+90)=870.350+15.9881sin(100°18′48″-1°31′37″)+6Sin(100°18′48″-2×1°31′37″+90)=885.393

已知：轉(zhuǎn)向角α=-28°25′42″；R=300m；L=148.850m;

T=75.991m;α1=100°18′48″；α2=71°53′06″;JD=K5+120(863.234，945.113）ZY=K5+044.009(876.839,870.35)YZ=K5+192.860(886.861,1017.337)練習(xí):(1)計(jì)算K5+080左右各6m寬度樁左(878.521,906.420)右(866.543,905.700)(2)計(jì)算K5+100左右各6m寬度樁左(877.998,926.010)右(865.998,926.089)

已知：轉(zhuǎn)向角α=-28°25′42″；R=300m；L=148.850m;

T=75.991m;α1=100°18′48″；α2=71°53′06″;JD=K5+120(863.234，945.113）ZY=K5+044.009(876.839,870.35)YZ=K5+192.860(886.861,1017.337)（三）第二直線（K5+192.86~+250.063)計(jì)算示例(1)K5+200左6m寬度樁:N=886.861+(200-192.86)COS71°53′06″+6

COS(71°53′06″-90)=894.784E=1017.337+(200-192.86)Sin71°53′06″+6Sin(71°53′06″-90)=1022.258

已知：轉(zhuǎn)向角α=-28°25′42″；R=300m；L=148.850m;

T=75.991m;α1=100°18′48″；α2=71°53′06″;JD=K5+120(863.234，945.113）ZY=K5+044.009(876.839,870.35)YZ=K5+192.860(886.861,1017.337)(1)K5+260左6m寬度樁計(jì)算:Lm=Km-KzY=5260-5250.063=9.937mαm=90Lm/πR=(90×9.937)/(π×200)=1°25′24″C=2Rsinαm=2×200sin(1°25′24″)=9.935mNm=NZY+Ccos(α1+αm)+6cos(α1+2αm-90)=904.647+9.935cos(71°53′06″+1°25′24″)+6cos(71°53′06″+2×1°25′24″-90)=913.289Em=EZY+Csin(α1+αm)+6Sin(α1+2αm-90)=1071.704+9.935sin(71°53′06″+1°25′24″)+6Sin(71°53′06″+2×1°25′24″-90)=1079.640

（四）第二圓曲線（K5+250.063～+366.530)計(jì)算示例已知：轉(zhuǎn)向角α=+33°21′55″；R=200m；L=116.467m;

T=59.937m;α1=71°53′06″；α2=105°15′01″;JD=K5+310(923.283,1128.670）；ZY=K5+250.063(904.647,1071.704)YZ=K5+366.530(907.517,1186.496)(2)K5+260右6m寬度樁計(jì)算:Lm=Km-KzY=5260-5250.063=9.937mαm=90Lm/πR=(90×15.991)/(π×200)=1°25′24″C=2Rsinαm=2×200sin(1°25′24″)=9.935mNm=NZY+Ccos(α1+αm)+6cos(α1+2αm+90)=904.647+9.935cos(71°53′06″+1°25′24″)+6cos(71°53′06″+2×1°25′24″+90)=901.713Em=EZY+Csin(α1+αm)+6Sin(α1+2αm+90)=1071.704+9.935sin(71°53′06″+1°25′24″)+6Sin(71°53′06″+2×1°25′24″+90)=1082.801

已知：轉(zhuǎn)向角α=+33°21′55″；R=200m；L=116.467m;

T=59.937m;α1=71°53′06″；α2=105°15′01″;JD=K5+310(923.283,1128.670）；ZY=K5+250.063(904.647,1071.704)YZ=K5+366.530(907.517,1186.496)練習(xí):(1)計(jì)算K5+280左右各6m寬度樁左(917.712,1099.751)右(905.878,1101.740)(2)計(jì)算K5+300左右各6m寬度樁左(920.105,1120.204)右(908.132,1121.001)

已知：轉(zhuǎn)向角α=+33°21′55″；R=200m；L=116.467m;

T=59.937m;α1=71°53′06″；α2=105°15′01″;JD=K5+310(923.283,1128.670）；ZY=K5+250.063(904.647,1071.704)YZ=K5+366.530(907.517,1186.496)1、基本型曲線的組成

由直線——緩和曲線——圓曲線——緩和曲線——直線的順序組成直線JDZHHYYHYH

三、基本型曲線緩和曲線中邊樁坐標(biāo)計(jì)算2、基本型曲線計(jì)算的已條件

一般地，基本型曲線的已知條件包括：曲線半徑R，緩和曲線長(zhǎng)度l0，曲線轉(zhuǎn)向角α，第一直線方位角，JD里程及坐標(biāo)。

基本型曲線直線段上坐標(biāo)計(jì)算同前。計(jì)算之前先計(jì)算曲線常數(shù)及要素，然后計(jì)算ZH和HZ的坐標(biāo)，然后依次計(jì)算便可。

3.第一緩和曲線（K5+031.488~+056.488段)

中邊樁計(jì)算公式

假設(shè)線路左轉(zhuǎn),ZH坐標(biāo)坐標(biāo)已知（XZH，YZH）第一直線方位角為α1。α1

⑴角度計(jì)算公式（ZH至n點(diǎn)的弧長(zhǎng)為ln）

⑵偏距計(jì)算公式（ZH至n點(diǎn)的弧長(zhǎng)為ln）

XYα1

⑶n點(diǎn)中樁坐標(biāo)及n點(diǎn)切線方位角計(jì)算

Xn=XZH+Xcosα1+Ycos(α1-90)

Yn=YZH+Xsinα1+Ysin(α1-90)

(4)n里程右側(cè)V米及左側(cè)V米邊樁坐標(biāo)計(jì)算

X右=Xn+Vcos（αn+90）Y右=Yn+VSin（αn+90）X左=Xn+Vcos（αn-90）Y左=Yn+VSin（αn-90）

4.基本型曲線緩和曲線中邊樁坐標(biāo)計(jì)算示例線路K5+000~K5+300設(shè)計(jì)資料：

曲線1：轉(zhuǎn)向角α=-28°25′42″；緩和曲線長(zhǎng)度l0=25m，R=300m；L=173.850m;

T=88.512m;α1=100°18′48″；α2=71°53′06″;JD=K5+120(863.234，945.113）；ZH=K5+031.488(879.080,858.031)；HY=K5+056.488(874.947,882.685)YH=K5+180.339(883.313,1005.374)；HZ=K5+205.339(890.755,1029.239)路基頂寬度為12m,左右等寬，計(jì)算中邊樁坐標(biāo)。

K5+050中樁及左6m邊樁坐標(biāo)計(jì)算示例

（1）方位角計(jì)算

=90×18.5122/(π×300×25)=1°18′32″

已知轉(zhuǎn)向角α=-28°25′42″；緩和曲線長(zhǎng)度l0=25m，R=300m；α1=100°18′48″；α2=71°53′06″;JD=K5+120(863.234，945.113）；ZH=K5+031.488(879.080,858.031)；HY=K5+056.488(874.947,882.685)；H=K5+180.339(883.313,1005.374)；HZ=K5+205.339(890.755,1029.239)

（2）偏距計(jì)算:由公式

計(jì)算得:X=18.511Y=0.139