Fieldwork Surveying -Surveying- Angular Measurement
- 1. Fieldwork Surveying FS01 4. Lecture Angular measurement Presentation was supported by 105 1052201A003 FCE CTU in Prague Internal Project 1
- 3. Line of sight – the join of the points S and P Horizontal direction – the intersection between the vertical plane i where is line of sight and the horizontal plane Horizontal angle ω – the angle between the vertical planes 1 and 2 (in the horizontal plane ) 3
- 4. Zenith angle zi – the angle in the vertical plane i measured between the vertical and the line of sight Elevation angle ε1 – the angle between the horizontal plane and the line of sight (the angle is above the horizontal plane ) Depression angle ε2 – the angle between the horizontal plane and the line of sight (the angle is under the horizontal plane ) 4
- 5. Units 1° (degree) = (π/180) rad 1g (gon) = (π /200) rad Full angle Right angle 2 π π /2 360° 90° 400 gon = 400g 100 gon = 100g Sexagesimal x centesimal measure 5
- 6. Theodolites = instruments for angular measurements Classification with respect to a construction: • optical-mechanical theodolites • electronic theodolites – a distance meter is usually built-in (so-called total stations) 6
- 7. Classification with respect to accuracy: • one-minute theodolites – the least division of the scale is 1 or 2 minutes (sexagesimal or centesimal) • one-second theodolites – the least division of the scale is 1 or 2 seconds (sexagesimal or centesimal) 7
- 10. Scales for reading of angles (one-minute theodolite) 10
- 11. Preparation of a theodolite for a measurement • levelling the alidade axis V of the instrument is vertical • centering the axis V goes through the survey station procedure of the instrument centering and levelling – see practical classes 11
- 12. Axes of the theodolite Z – collimation axis (axis of the sight) V – alidade axis H – horizontal axis (telescope rotary axis ) L – level axis (axis of the alidade level) 12
- 13. Requirements for the axes 1. L V 2. Z H 3. H V Fulfilment of these requirements has to be tested and an adjustment of the instrument has to be performed if it is necessary . 13
- 14. ad 1. if this requirement is not fulfilled, the alidade level has to be adjusted ad 2. if it is not realized collimation error measurement of horizontal angles in both positions of the telescope is used to avoid this error ad 3. if it is not realized error in incline measurement of horizontal angles in both positions of the telescope is used to avoid this error 14
- 15. Detection of theodolite axis errors 15
- 16. Errors in the construction of a theodolite • an excentricity of the alidade The axis V does not go through the centre of the horizontal circle. • an irregular dividing of the horizontal circle This error is not important at modern instruments. 16
- 17. Errors caused by standing of the instrument or the target • wrong levelling of the instrument • wrong centering of the instrument • wrong centering of the target • unstable tripod of the instrument It is not possible to avoid these errors by procedure of the measurement. 17
- 18. Errors caused by the observer • pointing error It depends on features of the telescope and the target, on the atmospheric conditions and on abilities of the observer. • reading error It depends on the least division of the reading scale and on the visual acuity of the observer. 18
- 19. Pointing 19
- 20. Measurement of a horizontal angle in one set 20
- 21. Procedure face left position 1. P1 2. P2 change the position of the telescope face right position 3. P2 4. P1 21
- 22. Station Horizontal directions No. Direction to point No. 1st set Aver. Red. 2nd set Aver. Red. {(6) + (8)} / 2 (1) (2) (3) (4) (5) (6) (7) (8) (9) I α1 P1 II α4 Ø 1-4 I α2 S P2 II α3 Ø 2-3 ω I 72 18 1 II 272 19 18 50 I 186 91 2 3 II 386 91 50 91 25 114 72 75 I 0 00 5 II 199 98 99 00 I 164 27 6 7 II 364 26 26 50 164 27 50 I 341 00 25 9 II 160 59 12 59 48 I 107 42 06 8 11 II 287 41 10 41 38 126 41 50 22
- 23. Measurement of directions set in one set with repeated pointing at the first point Station Horizontal directions No. Direction to point No. 1st set Aver. Red. 2nd set Aver. Red. {(6) + (8)} / 2 (1) (2) (3) (4) (5) (6) (7) (8) (9) I 0 03 11 II 200 04 03 00 50 00 0 00 00 I 18 28 12 II 218 29 28 25 50 00 18 25 00 I 113 76 13 II 313 78 77 73 00 50 113 73 50 I 0 03 50 5 11 II 200 04 03 00 75 25 0 00 25 23
- 24. Measurement of zenith angles A horizontal angle is the difference between two directions which are read on the horizontal circle (the difference between the left and the right target). A zenith angle is read on the vertical circle after pointing at a target (the direction to the zenith is given vertical). 24
- 25. The vertical circle rotates with tilting of the telescope and indexes of the reading scale are (or should be) in horizontal position during a measurement of the zenith angle. The correct position of the indexes is ensured by • collimation (index) level – older types of theodolites, • compensator – it works automatically (modern instruments). 25
- 26. The mentioned requirements for axes of the theodolite have to be fulfilled during a measurement of zenith angles too. In addition to these requirements, a reading on the vertical circle should be 100 gon if the line of sight is horizontal. There is so-called index error if this requirement is not fulfilled. It is possible to avoid this error by measurement in both positions of the telescope and by calculation of a correction. 26
- 27. Measurement of a zenith angle in both positions of the telescope 27
- 28. If there is no index error, then z1 + z2 = 400g If there is an index error, then z1 + z2 = 400g + 2i and the corrected zenith angle z = z1 – i 1 2 400 2 g z z i 28
- 29. 29 Zenith angles z Distances Reading z Measurement Aver. (10) (11) (12) (13) (14) (15) (16) (17) (18) I z1 z horiz. II z2 slope. 8 Σ i = vertic. I 92 40 92 39 horiz. II 307 62 slope. 9 Σ 400 02 i = 0,01 vertic. I 91 15 91 15 50 horiz. II 308 84 slope. 1 0 Σ 399 99 i = -0,005 vertic.
- 30. Electronic theodolites • another name – total stations • battery-powered (internal or external) • measured values are on the display (digital form) • some instruments have a built-in compensator of the alidade axis position • the correction of the index error can be introduced to measured values automatically • therefore it is often possible to measure only in the face left position of the telescope 30
- 31. • measured values can be recorded to the memory of the instrument • there are function buttons for setting of an arbitrary value of the horizontal circle reading, buttons for units option etc. • descriptive or numeral information can be inserted in memory of some instruments • some of the most modern instruments are motorized and then automatic pointing of the instrument is possible 31