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Lecture2
 

Lecture2

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    Lecture2 Lecture2 Presentation Transcript

    • Surveying I.
      Lecture 2.
    • Outline
      Levelling
      Structure of levels
      Adjustment of levels
      Error sources
      Procedure of levelling
    • 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
    • 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.
    • Levelling
    • Levelling
    • Levelling - Bookkeeping
      Rise and fall method:
    • Levelling - Bookkeeping
      Height of Collimation method:
    • 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
    • The bubble tube
      The radius determines the sensitivity of the bubble tube:
    • The bubble tube
      The determination of sensitivity:
    • The Surveyor’s telescope
      Object
      Eyepiece
      Object lens
      Virtual image
      Note that the virtual image is magnified and inverted!
    • 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.
    • 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
    • The Surveyor’s telescope
      Focusing the telescope
      External focusing
      Variable length
      Focusing lens
      Internal focusing
      Fixed length
    • 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
    • The Surveyor’s level
      Tilting level
      How can we view the bubble tube?
      • Using a mirror (older instrument)
      • Prismatic coincidence reader (modern instruments)
      Prism
      Bubble tube
      Bubble tube is horizontal (leveled)
      Bubble tube is tilted
    • 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.
    • 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.
    • 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
    • The levelling staff
    • 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:
    • Adjusting the level
      The two-peg test
      From the previous configuration:
    • Systematic errors in levelling
      The effect of curvature
      Solution: the instrument should be set up exactly in the middle between two points.
    • 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:
    • 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.
    • 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
    • Systematic errors in levelling
      Tilting of the staff
      Depends on the:
      • tilting angle
      • reading (the higher the reading is, the bigger the error is)
      Solution: staffs should be equipped with circular bubbles
    • 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
      • foresight - backsight
    • Systematic errors in levelling
      Settlement of the staff
      Solution: all lines should be run twice in the opposite directions.
    • 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.
    • 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.
    • Thanks for the Attention!