Z
L
R
A
MLN – Horizontal angle
ALM – Vertical angle
NLB – Vertical angle
ZLA – Zenith angle
ZLB – Zenith angle
M
N
B

The theodolite
Measure: 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

• 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

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

• Telescope
• Vertical circle+ horizontal circle
• Horizontal/vertical clamp
• Horizontal/vertical slow motion screws
• Plate bubble (Level tube)

Optical reading theodolite

• Centering
• Levelling
• Elimination of parallax
• Sighting the target
• Reading the angle

• 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 )

In the figure, the horizontal angle was measured at B to C and A.
Compute the angle CBA.
Station at Station observed Face left
B C
A deg min sec
00 03 20
83 50 10 deg
180
263
Face Right min sec
03
50
50
40
A
B
C

• 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.

ZA (Line of Sight / Collimation
Axis)
SA (vertical axis :Standing Axis)
KA (Trunian Axis)
V (Zenith Angle)
VK (Vertical Circle)
Hz (Horizontal Angle)
HK (Horizontal Circle )

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)

Vertical angles
( zenith angle ) .
V% .

• 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)

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
Point observed
F.L
F.R
Reduced
F.L
Reduced
F.R
Mean vertical angle
A
B
85

36´ 274

28´ 4

24´ 4

28´ 4

26´
98º 48´
261

08´ -8

48´ -8

52´ -8

50´