chapter Control Survey for Small Regions 导线平差计算基础知识

第六章小区域控制测量

6.3导线平差计算基础知识

主讲教师：罗显圣chapter6

ControlSurveyforSmallRegions

6.3BasicknowledgeoftraverseadjustmentcalculationThelecturer:ShengxianLuo,lecturer,Engineer方位角的定义从直线起点的标准方向北端起，顺时针方向量至直线的水平夹角，称为该直线的方位角；其角值范围为0°--360°。12标准方向北端方位角22222DefinitionofazimuthAzimuthisusuallydefinedasahorizontalanglemeasuredclockwisefromthenorthendofthereferencemeridiantotheline.

Themagnitudeofanazimuthcanfallanywhere0°to360°.正、反坐标方位角直线1-2：点1是起点，点2是终点。

α12—正坐标方位角；α21—反坐标方位角。直线2-1：

所以一条直线的正、反坐标方位角互差180ºα21α12xyoxx12ForwardandbackazimuthsLinefrompoint1topoint2：point1isthestartpoint，point2istheendpoint

α12—Forwardazimuth，

α21—BackazimuthLinefrompoint2topoint1：Theforwardandbackazimuthsofalinealwaysdifferbyexactly180°

象限角某直线的象限角是由直线起点的标准方向北端或南端起，沿顺时针或逆时针方向量至该直线的锐角，用R表示。直线R与α的关系O1O2O3O4（北）（西）y（东）（南）xoⅠⅣⅢⅡRO1RO3RO2RO4αO1αO2αO3αO41234αO1=RO1αO2=180°－RO2αO3=180°＋RO3αO4=360°－RO4BearingBearingofalineisananglemeasuredclockwiseoranticlockwisefromnorthorsouthofthereferencemeridianandisdenotedbytheletterR.relationshiplinenortheastsouthwest坐标方位角的推算α12已知，通过连测求得12边与23边的连接角为β2（右角）、23边与34边的连接角为β3（左角），现推算α23、α34。1234xxxα23α34α12β2β3前进方向GridazimuthcalculationsForwarddirectionLettheknowngridazimuthofline12beα12andtheobservedhorizontalanglebetweenadjacentline12andline23isβ2（right-handangle）

，anglebetweenadjacentline23andline34isβ3（left-handangle），thegridazimuthα23、α34arecalculatedasfollows.由图中分析可知1234xxα23α12β2α21前进方向xα34β3α32Forwarddirection

Itcanbeconcludedfromtheanalysisinthefigure坐标方位角推导公式当β角为左角时，取“＋”；若为右角时，取“－”。注意：计算中，若α前>360°，减360°；若α前<0°，加360°。或AgeneralformulafortheCalculationofthegridazimuthIfhorizontalanglesaretheleft-handangles,thesign+ischosen，Ifhorizontalanglesaretheright-handangles,thesign-ischosen，Besides，noterangeofgridazimuthfrom0°to360°,iftheresultforagridazimuthisgreaterthan

360°,then360°mustbesubtractedfromit,orifitislessthan0°then360°mustbeaddeintoit.例题：已知α12=46°，β2、β3及β４的角值均注于图上，试求其余各边坐标方位角。解：4x23146°125°10´5136°30´247°20´前进方向α23=α12＋180°－β2α34=α23＋180°＋β3=417°20´>360°（417°20´－360°）=

57°20´α45=α34＋180°－β4<0°（－10°＋360°）=

350°=

100°50´=46°＋180°－125°10´=100°50´＋180°＋136°30´=－10°=57°20´＋180°－247°20´Example:Theknowngridazimuthofline12is46°，angleβ2、angleβ3andangleβ４areallmarkedinthefigure，trytocalculateallgridazimuthsofotherlines。Forwarddirection坐标正算公式由A、B两点边长DAB和坐标方位角αAB，计算坐标增量。见图有：DAB

ABABXy0

XAB

YAB

XAB=DAB

cos

AB

YAB=DAB

sin

AB其中，ΔXAB=XB-XAΔYAB=YB-YACoordinatecalculationCalculatecoordinatesdifferenceaccordingtothehorizontaldistancebetweenpointAandpointB（DAB）andthegridazimuthofthelineAB.Asshowninthefigurebelow.坐标反算公式由A、B两点坐标来计算αAB、DAB

DAB

ABABXy0

XAB

YABαAB的具体计算方法如下（1）计算：Coordinateanti-calculationCalculateαAB、DABaccordingtothecoordinatesofpointAandpointB.ThemethodofcalculatingαABasshownthecalculationbelowcalculation坐标反算公式αAB的具体计算方法如下（1）计算：根据ΔXAB、ΔYAB的正负号判断αAB所在的象限。CoordinatecalculationThespecificmethodofcalculatingαAB

Accordingtothesignsofcoordinatedifferences，itcanbedeterminedwhichquadranttheαABbelongsto.各位同学，今天我们学习