Transcript The theodolite and angles

Types of angles
Z
A
L
M
MLN – Horizontal angle
ALM – Vertical angle
NLB – Vertical angle
ZLA – Zenith angle
ZLB – Zenith angle
R
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
In a well condition theodolite
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•
•
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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
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
Major Components of a theodolite
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•
•
•
•
Telescope
Vertical circle+ horizontal circle
Horizontal/vertical clamp
Horizontal/vertical slow motion screws
Plate bubble (Level tube)
Optical reading theodolite
Setting up a theodolite
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•
•
•
•
Centering
Levelling
Elimination of parallax
Sighting the target
Reading the angle
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)
In the figure, the horizontal angle was measured at B to C and A.
Compute the angle CBA.
Station at Station observed
B
C
A
Face left
deg
00
83
min
03
50
Face Right
sec
20
10
deg
180
263
min
03
50
sec
50
40
A
B
C
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.
Total station
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)
HEIGHT OF REMOTE POINT
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)
(zenith angle ) .
Vertical angles
V%.
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)
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
85 36´
274 28´
4
24´
4  28´
4
B
98º 48´
261 08´
-8
48´
-8 52´
-8 50´
26´