Lecture2
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  • 1. Surveying I.
    Lecture 2.
  • 2. Outline
    Levelling
    Structure of levels
    Adjustment of levels
    Error sources
    Procedure of levelling
  • 3. Levelling
    MSL - Mean Sea Level
    Level line - a line with constant height (a curved line)
    Horizontal line - a tangential to the level line at the instrument
  • 4. Levelling
    Over short distances the horizontal line and level line coincide.
    For a distance of 100m the effect of the curvature is less than 1 mm.
    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.
  • 5. Levelling
  • 6. Levelling
  • 7. Levelling - Bookkeeping
    Rise and fall method:
  • 8. Levelling - Bookkeeping
    Height of Collimation method:
  • 9. Elements of Surveyor’s level
    How to set the line of sight to be exactly horizontal?
    More general: how to set anything to be exactly horizontal?
    The bubble tube
  • 10. The bubble tube
    The radius determines the sensitivity of the bubble tube:
  • 11. The bubble tube
    The determination of sensitivity:
  • 12. The Surveyor’s telescope
    Object
    Eyepiece
    Object lens
    Virtual image
    Note that the virtual image is magnified and inverted!
  • 13. The Surveyor’s telescope
    The diaphragm (cross-hairs)
    To provide visible horizontal and vertical reference lines in the telescope.
    Line of collimation
    With adjustment screws the diaphragm can be moved in the telescope to adjust the line of collimation.
  • 14. The Surveyor’s telescope
    Parallax
    When focusing the telescope, the real image formed by the objective lens is made to coincide with the diaphragm.
    What is the parallax?
    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.
    This can lead to observation errors (wrong reading, wrong targeting).
    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!
    diaphragm
    image
  • 15. The Surveyor’s telescope
    Focusing the telescope
    External focusing
    Variable length
    Focusing lens
    Internal focusing
    Fixed length
  • 16. The Surveyor’s level
    Tilting level
    Bubble tube
    Diaphragm
    Tilting screw
    Tilting axis
    Circular bubble
    Levelling head
    Clamping screw - to fix the telescope in one vertical plane
    Tangent screw (slow motion screw) - to finely rotate the telescope along a vertical axis
  • 17. The Surveyor’s level
    Tilting level
    How can we view the bubble tube?
    • Using a mirror (older instrument)
    • 18. Prismatic coincidence reader (modern instruments)
    Prism
    Bubble tube
    Bubble tube is horizontal (leveled)
    Bubble tube is tilted
  • 19. Secondary axis
    Primary axis
    The Surveyor’s level
    Setting up the level
    1. Fix the level on a tripod
    2. Center the circular bubble by adjusting the foot screws.
    (to approximately level the instrument)
    3. Sight the levelling staff, and eliminate the parallax.
    4. Adjust the sensitive bubble tube by the tilting screw.
  • 20. The Surveyor’s level
    Automatic level
    We must adjust the bubble tube before every reading when using the tilting level -> takes a lot of time, may cause blunders
    An automatic level contains an optical device, which compensates the tilting of the telescope - called compensator.
  • 21. The Surveyor’s level
    Operation of the compensator
    Advantage: faster observations, elimination of a possible reason of blunders
    Disadvantage: vibrations (wind, traffic, etc.) have a bad impact on the operation of the compensator
  • 22. The levelling staff
  • 23. Adjusting the level
    The two-peg test
    Collimation error - the line of collimation is not horizontal, when the level is levelled
    The effect of collimation error cancels, if d1=d2.
    Thus the height difference is:
  • 24. Adjusting the level
    The two-peg test
    From the previous configuration:
  • 25. Systematic errors in levelling
    The effect of curvature
    Solution: the instrument should be set up exactly in the middle between two points.
  • 26. Systematic errors in levelling
    The refraction
    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:
  • 27. Systematic errors in levelling
    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.
  • 28. Systematic errors in levelling
    The effect of collimation error
    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
  • 29. Systematic errors in levelling
    Tilting of the staff
    Depends on the:
    • tilting angle
    • 30. reading (the higher the reading is, the bigger the error is)
    Solution: staffs should be equipped with circular bubbles
  • 31. Systematic errors in levelling
    Settlement of the tripod
    Solution: the reading should be taken in both order, and the mean value of the height differences should be computed
    Orders:
    • backsight - foresight
    • 32. foresight - backsight
  • Systematic errors in levelling
    Settlement of the staff
    Solution: all lines should be run twice in the opposite directions.
  • 33. Procedure of levelling
    1. The instrument must be set up in the middle between two staffs.
    2. The bubble tube must be levelled before each reading.
    3. You must not use the parallax screw between the backsight and foresight readings
    4. The bubble tube must not be affected by strong heat.
    5. Readings must be taken 30-50 cm above the ground.
    6. Staff should be set up vertically.
    7. A change plate should be used to place the staff on the ground.
    8. Levelling must be done in two opposite directions.
  • 34. Procedure of levelling
    9. All the observations should be made with a constant speed.
    10. Observations should be made only in suitable weather: cloudy sky, constant temperature, early morning, or late afternoon.
    11. Staff should be calibrated.
    12. If there are three hairs in the diaphragm, one should use all of them to take a reading.
  • 35. Thanks for the Attention!