Unit7MethodsofElevationDetermination（2）HeNanGeologyMinaralCollegeYangLikun01TrigonometricLevelingCONTENTS目錄PARTONETrigonometricLeveling01TrigonometricLevelingTrigonometric

levelingisusedwheredifficultterrain,suchasmountainousareas,precludestheuseofconventionaldifferentialleveling.三角高程測量適用于困難地形，例如在山區，不能使用常規的微差水準測量的地方。trigonometric[?tr?ɡ?n??metr?k]adj.

三角法的；三角學的preclude[pr??klu?d]v.排除TrigonometricLevelingThemodernapproachistomeasuretheslopedistanceandverticalangletothepointinquestion.現代的三角高程測量方法是測量到未知點的斜距和垂直角。TrigonometricLevelingSlopedistanceismeasuredusingelectromagneticdistancemeasurersandthevertical(orzenith)angleusingatheodolite,orthetotalstationthatintegratethesetwoinstrumentsintoasingleinstrument.斜距由電磁波測距儀測得，垂直角（或天頂距）由經緯儀測得，或者利用整合了這兩種儀器為一體的全站儀來測。TrigonometricLevelingTotalstationscontainbuilt-inmicroprocessorsthatcalculateanddisplaythehorizontaldistancefromthemeasuredslopedistanceandverticalheight.全站儀包含了內置的微處理器，用來根據測得的斜距和垂直角計算和顯示水平距離。TrigonometricLevelingThislatterfacilityhasresultedintrigonometricallevelingbeingusedforawidevarietyofheightingprocedures,includingcontouring.[k?n'tu?ri?]這種后來的設備使三角高程測量被廣泛用于多種高度測量工作，包括測繪等高線。the

latter

，后者；theformer

，前者contouringn.等高線；proceduren.程序、手續TrigonometricLevelingABSihabvαFigure1ThebasicconceptoftrigonometricallevelingcanbeseenfromFigure1.三角高程測量的基本原理可以看圖1。TrigonometricLevelingABSihabvαFigure1WhenmeasuringtheverticalangleαandthehorizontaldistanceSisused,thenthedifferenceinelevationhABbetweengroundpointsAandBistherefore:當我們用α和S分別表示垂直角和水平距離時，A點和B點之間的高差為：

hAB=S×tanα+i–vTrigonometricLevelingABSihabvαFigure1whereiistheverticalheightofthemeasuringcenteroftheinstrumentaboveAandvistheverticalheightofthecenterofthetargetaboveB.i是A點上儀器中心的高度，v是B點上目標中心的垂直高度。TrigonometricLevelingTheverticalanglesarepositiveforanglesofelevationandnegativeforanglesofdepression.垂直角為仰角時為正，俯角時為負。Thezenithanglesarealwayspositive,butnaturallywhengreaterthan90°theywillproduceanegativeresult.天頂距總是正的，但是自然的當超過了90°時，它們將產生一個相反的結果。

TrigonometricLevelingTrigonometricallevelingmethodofdeterminingdifferenceinelevationislimitedtohorizontaldistancelessthan300mwhenmoderateprecisionissufficient,andtoproportionatelyshorterdistancesashighprecisionisdesired.普通精度要求下，三角高程測量方法測高差水平距離不能超過300m，如果要求高的精度，則要相應縮短距離。TrigonometricLevelingForthedistancebeyond300mtheeffectsofcurvatureandrefractionmustbeconsideredandapplied.因為超過300m時，地球曲率和折光影響必需考慮。TrigonometricLevelingToeliminatetheuncertaintyinthecurvatureandrefractioncorrection,vertical-angleobservationsaremadeatbothendsofthelineascloseinpointoftimeaspossible.為了消除地球曲率和折光改正的不確定因素，垂直角觀測時應采用在觀測方向兩端盡量同時對向觀測的方法。TrigonometricLevelingThispairofobservationsistermedreciprocalvertical-angleobservation.這種觀測稱為垂直角對向觀測。reciprocal[r??s?pr?kl]adj.反向的TrigonometricLevelingThecorrectdifferenceinelevationbetweenthetwoendsofthelineisthemeanofthetwovaluescomputedbothwayseitherwithorwithouttakingintoaccountcurvature[?k??v?t??(r)]andrefraction線兩端正確的高程之差是計算得到的兩高程值的平均值，不管計算有無考慮球氣差.TrigonometricLevelingTheimportantnotesshouldbementionedhereisthatsurveyorsusedtoworkingwithspiritlevelshavereferencedorthometricheights(H)tothe“average”surfaceoftheearth,asdepictedbyMSL.這里需要注意的是，測量者在水準測量工作中使用的是參考地球“平均”表面的正高，這個平均表面描述為MSL。orthometric['?th?metr?k]adj.正交的TrigonometricLevelingHowever,theelevationcoordinate(h)