圓曲線和緩和曲線坐標(biāo)推算(附帶例題)

1、v1.0可編輯可修改圓曲線和緩和曲線坐標(biāo)推算公式、直線上的坐標(biāo)推算9X i = X m Li cosaoYi=Ym Lisinao式中：Xm Ym-一直線段起點(diǎn) M坐標(biāo)Li直線段上任意點(diǎn)i到線路起點(diǎn)M的距離a o直線段起點(diǎn)M到JD1的方位角二、圓曲線上任一點(diǎn)的坐標(biāo)推算、圓曲線上任一點(diǎn)i相對(duì)應(yīng)的圓心角：i=180-LXi=Rsin式中：Li 圓曲線上任一點(diǎn)i離開ZY或YZ點(diǎn)的弧長(zhǎng)ii、圓曲線上任一點(diǎn)i的直角坐標(biāo)：Yi=R (1 cos .)(可不計(jì)算)、圓曲線ZY或YZ點(diǎn)到任一點(diǎn)i的偏角:Li、圓曲線ZY或YZ點(diǎn)到任一點(diǎn)i的弦長(zhǎng):Ci = 2Rsin() 2Rsin( i)2、圓曲線ZY或YZ點(diǎn)

2、到任一點(diǎn)i的弦長(zhǎng)的方位角:Hi - Hzy jd 或yz jd、所以圓曲線上任意點(diǎn)i的坐標(biāo)為:Xi = X ZY 或 YZYL YZY或YZCi cosaiCisinai例題: 已知一段圓曲線，R=3500m, Ls=,交點(diǎn)里程K50+, ZY點(diǎn)至U JD方向方位角為 A=129° 23' ，右偏 9° 3' ，ZY點(diǎn)里程 K49+, YZ點(diǎn)里程 K50+,起點(diǎn)坐標(biāo)為x= , y=,求K50+200處中點(diǎn)坐標(biāo)及左右各偏的坐標(biāo)。解：K50+200處的曲線長(zhǎng)度為 Li =K50+200 相對(duì)應(yīng)的方位角：a=180-Li = 80 322.393= 5 16 39

3、.52R35009090K50+200相對(duì)應(yīng)的偏角：i ='=-Li= 322.393= 2 38 19.762 R 3500K50+200到 zy 點(diǎn)的弦長(zhǎng)：Ci = 2Rsin i = 2 3500 sin2 38 19.76 = 322.279mzy點(diǎn)到K50+200中樁的方位角：ai= azy jdi=129 23 18.32 38 19.76 =132 1 38.06K50+200左、右偏的方位角：2左=A a 90 =134 39 57.82 90 =44 39 57.822右=Ai a 90 =134 39 57.82 90 =134 39 57.82所以K50+200處

4、的坐標(biāo)為：Xi=XZY Cicosa=389823.196 322.279 cos132 1 38.06 =389607.4354Yi = YZY Cisinai=507787.251 322.279 sin132 1 38.06 =508026.6484K50+200左偏的坐標(biāo)為：X左=Xi 12.5cos%=389607.4354 12.5 cos44 39 57.82 =3896163256Y左=丫1 12.5sina左=508026.6484 12.5 sin44 39 57.82 =508035.4656K50+200右偏的坐標(biāo)為：X = Xi 12.5cosa&=38960

5、7.4354 12.5 cos134 39 57.82 =389598.6482 丫右=Yi 12.5sina右=508026.6484 12.5 sin134 39 57.82 =508035.5386三、緩和曲線上任一點(diǎn)的坐標(biāo)推算.l2180切線角：i=7丁2RLs緩和曲線上任意點(diǎn)i的偏角:L21803 6RLSs緩和曲線ZH或HZ點(diǎn)到任意點(diǎn)i的方位角為：aj=azH jd或hz jd緩和曲線上任意點(diǎn)i的坐標(biāo)為:xi=LiL540R2L2syi=l36RLSs緩和曲線ZH或HZ點(diǎn)到任意點(diǎn)i的弦長(zhǎng):G=qx2 y2所以緩和曲線上任意點(diǎn)i的坐標(biāo)為:X i= X ZHsHZCic0sYi = Y

6、zH 或 HZCisinai例題:已知一段緩和曲線，ZH點(diǎn)到JD方向方位角為 A=183° 17' ，線路左偏43° 31' 02，ZH點(diǎn)里程為 K52+, ZH點(diǎn)坐標(biāo) x= , y = , R= 960rm Ls = 120rm求K52+100處的中點(diǎn)坐標(biāo)及左右各偏的坐標(biāo)。解：根據(jù)已知條件可知：K52+100到zh點(diǎn)的曲線長(zhǎng)度Li =2 24 25.64180-=0 48 8.55L218098.3852180i 2RLS2 960 120sK52+100相對(duì)應(yīng)的偏角：_ i _ L2180 _ 98.3852i=3 6RLS6 960 120sZH點(diǎn)至U

7、 K52+100的方位角：a = aZH 1di = 183 17 08.90 48 8.55 =182 29 0.35ijK52+100左、右偏的方位角：2左=ai 90 =180 52 43.26 90 =180 52 43.262左=ai 90 =180 52 43.26 90 =270 52 43.26K52+100的直角坐標(biāo)為：L5Xi=L -仁=98.38540R2L2s98.385540 9602 1202=98.3676mYi =L398.3853=1.3778m6RLS 6 960 120 s緩和曲線ZH點(diǎn)到K52+100的弦長(zhǎng)：Ci = Jx2 y2 = J98.36762 1.37782 =98.377m所以K52+100的中線坐標(biāo)為：Xi=XZH Cicosa=388071.927 98.377 cos182 29 0.35 =387973.6424Yi = YCisinai=508789.089 98.377 sin182 29 0.35 =508784.8263K52+100左偏的坐標(biāo)為：X左=Xi 12.5cosafe=3879736424 12.5 cos180 52 43.26 =387961.1439Y左=丫1 12.5sina左=508784.8263 12.5 sin180 52 43.26 =508784.6346K50+200右偏