基礎測量學課程綱要

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农屋衣常
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2 6-2 Textbook INTRODUCTION 測量為什麼要觀測角度? 為什麼只觀測水平角及縱角, 而不觀測斜角?

Direction of turning Angular distance Types of angles

3 6-3 Definition of Angles Three basic requirements to determine an angle are: Reference or starting line Direction of turning Angular distance Types of angles acquired in surveying: Horizontal angles 水平角 Vertical angles 縱角

4 6-4 Purposes of Observing Angles Angle measurements can be used for positioning 定位 of unknown points N P(EP, NP) θa θb A(EA, NA) B(EB, NB) E Before Global Positioning System (GPS) 全球定位系統 is invented, angle and distance observations were the key data for control survey 控制測量 Observations of vertical angles can be used for trigonometric leveling 三角高程測量 and many engineering surveys 工程測量

5 6-5 Textbook 7.4~ DIRECTION OF A LINE 方向與角度有何不同? 什麼叫北方? 北方是固定的嗎?

6 6-6 Directions Direction 方向 is an angle referring to the north There are two kinds of expression for directions Azimuths 方位角 Bearings 方向角 In surveying, we use azimuth

6-7 The Reference North Direction is referred to the reference north 參考北 True (geodetic) north (T.N.) 真北 is determined by the earth rotation pole Grid north (G.

7 6-7 The Reference North Direction is referred to the reference north 參考北 True (geodetic) north (T.N.) 真北 is determined by the earth rotation pole Grid north (G.N.) 方格北 is determined by the adopted plane coordinate system Magnetic north (M.N.) 磁北 M.N. G.N. T.N. 方位角 Magnetic Declination 磁偏角 A

8 6-8 Azimuths Azimuths 方位角 are horizontal angles observed clockwise from the north For surveying, azimuths are referred to the grid north Quadrants 象限 of the azimuth system IV III φp I II 這些定義與數學上的有何不同

9 6-9 Bearings Bearings 方向角 are Acute horizontal angles observed from either the north or south toward the east or west Examples: N70 E S35 E S55 W N30 W 航海人如何描述方向

10 6-10 Comparison of Azimuths and Bearings Quadrant Formulas for computing bearing angles from azimuths I (NE) Bearing = Azimuth II (SE) Bearing = Azimuth III (SW) Bearing = Azimuth IV (NW) Bearing = Azimuth Azimuth Bearing 54 N54 E 112 S68 E 231 S51 W 345 N15 W IV III φp I II

right) between the bearings (1) N46 24 13 E and

11 6-11 A Practical Problem Convert the following bearings to azimuths and compute the angle (to the right) between the bearings (1) N E and S E 如何計算兩個方向角的夾角 (2) S W and N W

12 6-12 Notations of Azimuths The azimuth of a line AB is expressed as φab The azimuth of a line BA is expressed as φba N And φ B(E, N ) L And φ BA AB B B AB A(EA, NA) B E C θbac θcab A 給直線兩端點坐標如何計算其方位角

13 6-13 Computing Azimuths Given φab and θabc is observed, compute φbc θabc must be an angle to the right

14 6-14 A Practical Problem Given azimuth AB= , angles to the right ABC= , BCD= , please compute the azimuth of line CD 依據此描述你可以畫出示意圖嗎

6-15 An Application Computation of Azimuths for a Traverse 導線 Station Measured Angles to the Right A 115 10' B 129 11' C

15 6-15 An Application Computation of Azimuths for a Traverse 導線 Station Measured Angles to the Right A ' B ' C 88 35' D ' E ' F ' A Total Azimuth 41 35' ' ' ' ' ' 41 35'

16 6-16 Textbook 8.1~ INSTRUMENTS FOR ANGLE MEASUREMENT

17 6-17 Theodolites or Transits Theodolites or transits 經緯儀 have been applied for angle measurement for centuries. Nowadays, they are combined with an EDM and are transformed to be total stations.

18 6-18 Types of Theodolite Based on instrument structure: Based on reading installation: Repeating Theodolite 複測經緯儀具雙軸分別帶動儀器上下盤旋轉轉上盤度盤讀數改變轉下盤則讀數不變又稱雙軸經緯儀 Direction Theodolite 方向經緯儀為單軸經緯儀只能轉動上盤 Vernier Theodolite 游標經緯儀具金屬或玻璃度盤及游標尺讀數裝置 Optical Theodolite 光學經緯儀具玻璃度盤藉光學組合稜鏡讀數 Electronic Theodolite 電子經緯儀具光柵度盤或絕對編碼度盤透過紅外線辨識直接顯示讀數 Based on precision: Normal or Engineering Theodolite 普通或工程經緯儀觀測精度低於5 Precise or Geodetic Theodolite 精密或大地經緯儀觀測精度高於5

19 6-19 Total Stations A total Station 全測站儀 is a combination of theodolite and EDM Modern specification Electronic theodolite Automatic compensator for leveling (dual-axis compensator) Microprocessor for operation Keyboard and display

20 6-20 The Fundamental Reference Axes Vertical axis 直立軸 VV Horizontal axis 橫軸或水平軸 HH H The axis of sight 視準軸 SS Axis of the plate level vial 水準管軸 LL Conditions of proper adjustment LL VV L HH VV SS HH HH SS and VV having a point intersection VV passing through the center of the horizontal plate S V H S L V

21 6-21 Tribrach A tribrach 三角基座 is an attachment plate used to attach a surveying instrument, for example a theodolite, total station, GPS Antenna or target to a tripod.

22 6-22 Textbook 8.7~ ANGLE MEASUREMENTS

23 6-23 Kinds of Horizontal Angles Interior (or exterior) angles Angles to the right Deflection angles

24 6-24 Observation Modes The angle measurement with a total station or theodolite has two observation modes 觀測模式 Direct or face-left 正鏡: when the vertical circle 垂直度盤 is on the left Reversed or face-right 倒鏡: when the vertical circle is on the right 哪個是正鏡哪個是倒鏡用正鏡或用倒鏡有區別嗎

25 6-25 Observing Horizontal Angles Always measure the angle to the right Instrument is set up at S, backsight 後視 reading is HA, and foresight 前視 reading is HB Take the average of the direct or face-left 正鏡 and reversed or face-right 倒鏡 modes 正鏡 = θ1 HB H A ' ' H H 倒鏡 θ= 2 B A 後視 A 正 HA 倒 H A 正倒鏡平均 = θ 1 (θ 2 + θ1 ) (HB + HB ) (H A + H A ) = 2 2 S θ 前視 B 正 HB 倒 H B

26 6-26 Sights of Observation For distance and angle measurements For distance measurement For angle measurement

27 6-27 Field Notes and Calculation An example of field notes and calculation for horizontal angle observations 測站觀測點鏡位水平角讀數 A O B A O B 正倒正倒正倒正倒正倒鏡平均角度備註 A O B A O B

28 6-28 Vertical Angles Vertical angles can be measured as: Zenith angles z 天頂距 Altitude angles α 高度角 Altitude angles may be: Above the horizontal plus angles or angles of elevation α 仰角 Below the horizontal minus angles or angles of depression β 俯角 Zenith Altitude Angle α β

29 6-29 Observing Vertical Angles Most modern instrument has a full vertical circle of zenith reading 全圓周式天頂距 A zenith angle can be measured by: Direct mode ZD Reversed mode ZR The sum of ZD and ZR should be 360 If there is no indexing error 指標差, then: Direct mode Z=ZD Reversed mode Z=360 -ZR Therefore 正鏡倒鏡正倒鏡讀數相加 = 360o

30 6-30 Indexing Error If an indexing error 指標差 exists, the observed value will be: Direct mode Reserved mode Therefore 正鏡指標差 i And still 指標差 i 倒鏡

31 6-31 Field Notes and Calculation An example of field notes and calculation for vertical angle observations 測站觀測點鏡位垂直角讀數 A O B 正倒正倒指標差垂直角高度角正倒鏡分別對水平角及縱角觀測的作用為何

32 6-32 Textbook 8.19~ ADJUSTMENT AND ERRORS OF INSTRUMENTS

33 6-33 Adjustment of Total Station Instruments S V Optical Collimator System H H S L LL VV HH VV SS HH V HH SS and VV having a point intersection VV passing through the center of the horizontal plate L

34 6-34 Reduction of Observation Errors The following observation errors can be largely reduced by using direct and reversed readings 正倒鏡讀數 Horizontal axis not perpendicular to vertical axis HH VV Axis of sight not perpendicular to horizontal axis SS HH Eccentricity of centers Vertical-circle indexing error

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VLBI2010 [2] 1 mm EOP VLBI VLBI [3 5] VLBI h [6 11] VLBI VLBI VLBI VLBI VLBI GPS GPS ( ) [12] VLBI 10 m VLBI 65 m [13,14] (referen 31 2 Vol. 31, No. 2 2013 5 PROGRESS IN ASTRONOMY May., 2013 doi: 10.3969/j.issn.1000-8349.2013.02.08 VLBI 1,2 1 ( 1. 200030 2. 100049 ) VLBI VLBI VLBI VLBI VLBI VLBI P228.6 A 1 (VLBI) 20 60 (ITRF) (EOP)