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  1. 1. Surveying I.<br />Lecture 2.<br />
  2. 2. Outline<br />Levelling<br />Structure of levels<br />Adjustment of levels<br />Error sources<br />Procedure of levelling<br />
  3. 3. Levelling<br />MSL - Mean Sea Level<br />Level line - a line with constant height (a curved line)<br />Horizontal line - a tangential to the level line at the instrument<br />
  4. 4. Levelling<br />Over short distances the horizontal line and level line coincide.<br />For a distance of 100m the effect of the curvature is less than 1 mm.<br />The levelling device (called level) must be set up so, that the line of sight is perpendicular to the gravity vector (plumb line). -> the line of sight is horizontal.<br />
  5. 5. Levelling<br />
  6. 6. Levelling<br />
  7. 7. Levelling - Bookkeeping<br />Rise and fall method:<br />
  8. 8. Levelling - Bookkeeping<br />Height of Collimation method:<br />
  9. 9. Elements of Surveyor’s level<br />How to set the line of sight to be exactly horizontal?<br />More general: how to set anything to be exactly horizontal?<br />The bubble tube<br />
  10. 10. The bubble tube<br />The radius determines the sensitivity of the bubble tube:<br />
  11. 11. The bubble tube<br />The determination of sensitivity:<br />
  12. 12. The Surveyor’s telescope<br />Object<br />Eyepiece<br />Object lens<br />Virtual image<br />Note that the virtual image is magnified and inverted!<br />
  13. 13. The Surveyor’s telescope<br />The diaphragm (cross-hairs)<br />To provide visible horizontal and vertical reference lines in the telescope.<br />Line of collimation<br />With adjustment screws the diaphragm can be moved in the telescope to adjust the line of collimation.<br />
  14. 14. The Surveyor’s telescope<br />Parallax<br />When focusing the telescope, the real image formed by the objective lens is made to coincide with the diaphragm.<br />What is the parallax?<br />When viewing two distant objects approximately along a straight line, and the eye is moved to one side, then the more distant object moves relative to the other in the same direction.<br />This can lead to observation errors (wrong reading, wrong targeting).<br />If the real image formed by the objective lens does not coincide with the diaphragm a parallax is observed -> the reading depend on the position of the eye!<br />diaphragm<br />image<br />
  15. 15. The Surveyor’s telescope<br />Focusing the telescope<br />External focusing<br />Variable length<br />Focusing lens<br />Internal focusing<br />Fixed length<br />
  16. 16. The Surveyor’s level<br />Tilting level<br />Bubble tube<br />Diaphragm<br />Tilting screw<br />Tilting axis<br />Circular bubble<br />Levelling head<br />Clamping screw - to fix the telescope in one vertical plane<br />Tangent screw (slow motion screw) - to finely rotate the telescope along a vertical axis<br />
  17. 17. The Surveyor’s level<br />Tilting level<br />How can we view the bubble tube?<br /><ul><li> Using a mirror (older instrument)
  18. 18. Prismatic coincidence reader (modern instruments)</li></ul>Prism<br />Bubble tube<br />Bubble tube is horizontal (leveled)<br />Bubble tube is tilted<br />
  19. 19. Secondary axis<br />Primary axis<br />The Surveyor’s level<br />Setting up the level<br />1. Fix the level on a tripod<br />2. Center the circular bubble by adjusting the foot screws.<br />(to approximately level the instrument)<br />3. Sight the levelling staff, and eliminate the parallax.<br />4. Adjust the sensitive bubble tube by the tilting screw.<br />
  20. 20. The Surveyor’s level<br />Automatic level<br />We must adjust the bubble tube before every reading when using the tilting level -> takes a lot of time, may cause blunders<br />An automatic level contains an optical device, which compensates the tilting of the telescope - called compensator.<br />
  21. 21. The Surveyor’s level<br />Operation of the compensator<br />Advantage: faster observations, elimination of a possible reason of blunders<br />Disadvantage: vibrations (wind, traffic, etc.) have a bad impact on the operation of the compensator <br />
  22. 22. The levelling staff<br />
  23. 23. Adjusting the level<br />The two-peg test<br />Collimation error - the line of collimation is not horizontal, when the level is levelled<br />The effect of collimation error cancels, if d1=d2.<br />Thus the height difference is:<br />
  24. 24. Adjusting the level<br />The two-peg test<br />From the previous configuration:<br />
  25. 25. Systematic errors in levelling<br />The effect of curvature<br />Solution: the instrument should be set up exactly in the middle between two points.<br />
  26. 26. Systematic errors in levelling<br />The refraction<br />The air has different optical properties everywhere. Air pressure, humidity etc. Have an impact on the refractivity. Thus the light does not propagate along a straight line, but along a curve:<br />
  27. 27. Systematic errors in levelling<br />Solution: the instrument should be set up exactly in the middle between two points, thus the effect of curvature is the same for the backsight and foresight.<br />
  28. 28. Systematic errors in levelling<br />The effect of collimation error<br />Solution: the instrument should be set up exactly in the middle between two points and the collimation error must be constant, thus the effect is eliminated<br />
  29. 29. Systematic errors in levelling<br />Tilting of the staff<br />Depends on the:<br /><ul><li> tilting angle
  30. 30. reading (the higher the reading is, the bigger the error is)</li></ul>Solution: staffs should be equipped with circular bubbles<br />
  31. 31. Systematic errors in levelling<br />Settlement of the tripod<br />Solution: the reading should be taken in both order, and the mean value of the height differences should be computed<br />Orders:<br /><ul><li> backsight - foresight
  32. 32. foresight - backsight</li></li></ul><li>Systematic errors in levelling<br />Settlement of the staff<br />Solution: all lines should be run twice in the opposite directions.<br />
  33. 33. Procedure of levelling<br />1. The instrument must be set up in the middle between two staffs.<br />2. The bubble tube must be levelled before each reading.<br />3. You must not use the parallax screw between the backsight and foresight readings<br />4. The bubble tube must not be affected by strong heat.<br />5. Readings must be taken 30-50 cm above the ground.<br />6. Staff should be set up vertically.<br />7. A change plate should be used to place the staff on the ground.<br />8. Levelling must be done in two opposite directions.<br />
  34. 34. Procedure of levelling<br />9. All the observations should be made with a constant speed.<br />10. Observations should be made only in suitable weather: cloudy sky, constant temperature, early morning, or late afternoon.<br />11. Staff should be calibrated.<br />12. If there are three hairs in the diaphragm, one should use all of them to take a reading.<br />
  35. 35. Thanks for the Attention!<br />