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Types of angles

Types of angles. A. Z. MLN – Horizontal angle ALM – Vertical angle NLB – Vertical angle ZLA – Zenith angle ZLB – Zenith angle. M. L. R. N. B. The theodolite Measure: vertical and horizontal angles.

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Types of angles

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  1. Types of angles A Z MLN – Horizontal angle ALM– Vertical angle NLB– Vertical angle ZLA– Zenith angle ZLB– Zenith angle M L R N B

  2. The theodoliteMeasure: vertical and horizontal angles • Main components - sighting telescope, horizontal and vertical circles and leveling system. Horizontal (Trunian) axis Line of sight Vertical axis Axis of plate level

  3. In a well condition theodolite • 1- Line of sight axis + H-H axis • 2-H-H axis + V-V axis • 3- V-V axis + L-L axis • If these axis are not perfectly perpendicular , errors in angles will occur • To reduce these errors the mean of the face left and face right reading is taken

  4. Types of theodolite • 1- Optical reading theodolite • 2- Digital reading theodolite • The total station : Digital reading theodolite • +EDM( electronic distance measurement device ) • + processor and memory

  5. Major Components of a theodolite • Telescope • Vertical circle+ horizontal circle • Horizontal/vertical clamp • Horizontal/vertical slow motion screws • Plate bubble (Level tube)

  6. Optical reading theodolite

  7. Setting up a theodolite • Centering • Levelling • Elimination of parallax • Sighting the target • Reading the angle

  8. Measuring horizontal angles • Sight point A on face left • Set reading on horizontal circle ( e.g. 00 00´ 00˝) • Direct the telescope to point B and record ‘face left’ directions (e.g. 35 26´ 20˝) • Reverse the telescope to ‘face right’ and read direction to point B ( 215 26 40˝) • Back to point A on face right and record the reading (180 00 20)

  9. In the figure, the horizontal angle was measured at B to C and A. Compute the angle CBA. • Station at Station observed Face left Face Right • deg min sec deg min sec • B C 00 03 20 180 0350 • A 83 50 102635040 A B C

  10. Errors in Angle Measurement • Mistakes –pointing, setting up over the wrong point, booking, reading • Random – settling of tripod, wind, temperature, refraction • Systematic/instrumental • Horizontal axis not perpendicular to the vertical axis • Axis of sight not perpendicular to the horizontal axis • Axis of the plate bubble not perpendicular to the vertical axis.

  11. Total station ZA (Line of Sight / CollimationAxis) SA (vertical axis :Standing Axis) KA(TrunianAxis) V(Zenith Angle) VK(VerticalCircle) Hz(HorizontalAngle) HK(HorizontalCircle)

  12. HEIGHT OF REMOTE POINT

  13. SD(Slope Distance) HD(Horizontal Distance) dH(Difference of Height) hr(Height of Reflector) hi(Height of Instrument) E0(Easting of Station) N0(Northing of Station) H0(Height of Station) E(Easting of Target Point) N(Northing of Target Point) H(Height of Target Point)

  14. Vertical angles (zenith angle ) . V%.

  15. The vertical angle • Is the angle above or below a horizontal plane through the point of observation • The angle above the horizontal plane is +ve vertical angle (angle of elevation) • The angle below the plane is –ve angle (angle of depression)

  16. Measuring vertical angles Theodolite is set over point P the following vertical angles circle readings were recorded on targets at points A and B. Calculate the vertical angles to points A and B

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