1、Unit 4 Angle and DirectionMeasurementContentsI Basic termsII Horizontal angle and vertical angleIII Angle measurementBasic TermsVertical line A vertical line at any point on the earths surface is the line that follows the direction of gravity at that point.地球表面任一點的垂線是指這點上沿著重力的方向的線【可譯為：地球表面任一點的垂線方向是過

2、該點的重力方向】）The direction of gravityIt is the direction that a string will assume if a weight is attached at that point and the string is suspended freely at the point.（如果在這點上用線懸掛一個重物，當線自由【即無干擾】靜止【suspended暫停的、懸浮的】時，這條線所呈現【assume呈現】的方向即重力方向。）Note: At a given point there is only one vertical line. （在給定的

3、一個點上只有一條垂線。）Horizontal lineA horizontal line at a point is any line that is perpendicular to the vertical line at the point. （一點上的水平線是垂直【perpendicular垂直的】于過該點的垂線的直線。） Note: At any point there are an unlimited number of horizontal lines. （過任一點的水平線有無數【unlimited】條。）Horizontal planeA horizontal plane at

4、 a point is the plane that is perpendicular to the vertical line at the point. （過一點的水平面是垂直于過該點的垂線的平面）Note: There is only one horizontal plane through a given point. （過給定的一個點只有一個水平面）Vertical planeA vertical plane at a point is any plane that contains the vertical line at the point. （過一點的豎直面是包含【contai

5、n】過該點的垂線的任一平面）Note: There are an unlimited number of vertical planes at a given point. （過給定的一點有無數個豎直面） Horizontal Angle and Vertical Angle（水平角和豎直角）（水平角和豎直角）Horizontal angleVertical angleThe Zenith天頂距Horizontal anglelDefinitionlA horizontal angle is the angle formed in a horizontal plane by two inter

6、secting vertical planes, or a horizontal angle between two lines is the angle between the projections of the lines onto a horizontal plane. （水平角是指在一個水平面內由兩相交【intersect相交v.】的豎直面形成的角，或者說，兩條線之間的水平角是這兩條線在水平面上的投影線的夾角）Example of page 16 For example, observations to different elevation points B and C from

7、A will give the horizontal angle bac which is the angle between the projections of two lines (AB and AC) onto the horizontal plane.（例如，在A點觀測不同高度的B和C點，其水平角bac是由AB和AC兩條線在水平面上的投影構成的）FunctionThe horizontal angle is used primarily to obtain relative direction to a survey control point, or topographic det

8、ail points, or to points to be set out. （水平角主要【primarily】用來由聯測控制點獲得相對方向，或者地形測量碎部點、或者放樣點【or to points to be set out應該是or points to be set out才對吧？direction to a survey control point、topographic detail points、points to be set out并列都是obtain的賓語。】）Vertical AngleA vertical angle is an angle in a vertical p

9、lane which referenced to a horizontal line by plus or minus angles, or to a vertical line from the zenith direction. （豎直角是在一個豎直面內參考于【reference參考】水平線的正（仰）角或負（俯）角，或者相對于一個天頂方向的垂線的角）Plus and minus vertical anglesPlus and minus vertical angles are sometimes referred to as elevation or depression angles.正

10、負豎直角有時分別【respectively分別地】被稱為仰角【elevation angle】或俯角【depression angle】）A vertical angle thus lies between 0and 90. （豎直角位于【lie位于】0 90度之間）The ZenithZenith is the term describing points on a celestial sphere that is a sphere of infinitely large radius with its center at the center of the earth. （天頂方向是一個術

11、語，用來描述在天球【celestial sphere天球】上的點，天球是一個半徑無限【infinitely無限地】大的球，其中心在地球中心。）The zenith is an angle measured in a vertical plane downward from an upward directed vertical line through the instrument. （天頂距是一個在豎直面內從一個過儀器的被定向為向上的豎直方向線 向下測量的角。）The range and function of the zenithIt is between 0 and 180. （它的范圍

12、是從0到180度）The zenith angle is equal to 90 minus the vertical angles. （顯然，天頂距等于90度減去豎直角）Vertical angles or zeniths are used in the correction of slope distance to the horizontal or in height determined.（豎直角或天頂距用于斜距化平距的改正或者高程的測量）一般情況下，經緯儀測量的角度在水平方向的叫水平角，在豎直方向的叫垂直角，垂直角是從測站到目標的方向（測線）與水平面之間的夾角。而天頂距是測線與豎直方

13、向（也就是天頂）的夾角。1996年中華人民共和國工程測量基本術語標準水平角 horizontal angle測站點至兩個觀測目標方向線垂直投影在水平面上的夾角垂直角 vertical angle觀測目標的方向線與水平面間在同一豎直面內的夾角天頂距 zenith distance測站點鉛垂線的天頂方向到觀測方向線間的夾角測站 observation station觀測時設置儀器或接收天線的位置照準點 sighting point觀測時儀器照準的目標點Angle MeasurementInstrument for Measuring anglesHow to MeasureAzimuth and

14、BearingInstrument for MeasurementFor the most part, the instrument used in the measurement of angles is called a transit or theodolite, although angles can be measured with clinometers, sextants (hydrographic surveys), or compasses. （在極大程度上【for the most part】，用來測角的工具被稱為經緯儀，雖然角度可以用傾斜儀【一種測量物體隨時間的傾斜變化和

15、鉛垂線隨時間變化的儀器】、六分儀（用于海道測量）、或羅盤儀來測）TheodoliteThe theodolite contains a horizontal and vertical circles of either glass or silver. （經緯儀有一個玻璃的或鍍銀的水平度盤和豎直度盤）The horizontal and vertical circles of theodolite can be linked to circular protractors graduated from 0 to 360 in a clockwise manner set in horizont

16、al and vertical plane. （經緯儀的水平度盤和豎直度盤與順時針刻【graduate】了0到360度刻劃的圓分度器【circular protractor】相連）The units of angular measurement employed in practice are degrees, minutes, and seconds, the sexagesimal system. （通常角度測量法【angular measurement角度測量法】使用的單位是六十進制【sexagesimal六十進制的】的度、分、秒）Circle度盤The horizontal circl

17、e is used when measuring or laying off horizontal angles and the vertical circle is used to measure or lay off vertical angles or zenith angles. （測或撥水平角時用水平度盤，測或撥豎直角或天頂距時用豎直度盤【lay off翻譯為撥、放樣的意思】） 度盤 circle (1996年國家標準）裝在測角儀器上用以量測角度的圓盤How to Measure angleModern electronic digital theodolites contain c

18、ircular encoders that sense the rotations of the spindles and the telescope, convert these rotations into horizontal and vertical (or zenith) angles electronically, and display the value of the angles on LCDs or LEDs. （現代的電子數字經緯儀包含編碼【encoder編碼】度盤，能夠感知軸【spindle軸、紡錘】和望遠鏡的旋轉，并使之電子地轉換為水平角度和豎直角度，并在液晶顯示器【

19、LCDs】或發光二極管顯示器【LEDs】上顯示出來）These readouts can be recorded in a conventional field book or can be stored in a data collector for future printout or computation. （這些顯示可以被一個傳統的【conventional】野外電子手簿或數據收集器【存儲卡】記錄，以便日后打印或計算）The instrument contains a pendulum compensator or some other provision for indexing

20、the vertical circle readings to an absolute vertical direction. （這種儀器具有一個懸掛【pendulum鐘擺】補償器【compensator】或其它裝置，使豎盤指標【indexing指標】讀數指向一個絕對豎直方向）The circle can be set to zero readings by simple press of a button or initialized to any value on the instrument. （這個度盤可以通過簡單的按一個鍵就將其置零，或初始化成任一值）Azimuth and Bear

21、ingAzimuth is the horizontal angle measured in a clockwise direction from the plane of the meridian. Note: Meridian is a line on the mean surface of the earth joining the north and south poles. （方位角是從子午面【plane of the meridian 】起算按順時針旋轉的角，子午線是在地球平均表面連接北極與南極的線）uAzimuth ranges in magnitude from 0 to 36

22、0.方位角的取值范圍從0度到360度方位角 Azimuth (1996國家標準）通過測站的子午線與測線間順時針方向的水平夾角Bearing is the traditional way of stating the orientation of the line. It is actually the angle measured from the north or south. （方向角是一種傳統的描述【state說明】直線方向【orientation方向、方位】的方法）（實際上，它是從南或北方向開始量測的角）The bearing, which can be measured clockwise or counterclockwise from the north or