Introduction to Theodolite
THEODOLITE
An instrument used for the measurement of angles is called a theodolite,
horizontal and vertical angles are fundamental measurements in surveying.
The horizontal angle is used primarily to obtain direction to a survey control point,, or to points
to be set out.
The vertical angle, is used in obtaining the elevation of points (trigonometric leveling) and
in the reduction of slope distance to the horizontal.
many types of theodolites are used to measure angles are available to meet
varying requirements of accuracy ranging from 1 minutes to precision
instruments which read direct to 0.1 second .
Measuring a horizontal angle :
• The horizontal angle between two lines is the angle between the
projections of the lines on to a horizontal plane .
• Line of sight of the instrument is directed toward the FROM or back sight
station and the circle reading is observed as 00⁰ 00´ and it is recorded as
the initial circle reading .
• The final reading is obtained by loosing the upper clamp , rotating the
alidade about the vertical axis , and directing the line of sight toward the
TO or foresight station .
• If the alidade has been turned in a clockwise direction , the reading will
increase by the angle of rotation .
• The difference between the initial reading and the final reading is the
angle through which the line of sight was turned in going from the back
sight station to the foresight station .
M
o
Line of sight
P
90
270
122⁰ 43´
180
Horizontal
circle
Back sight
M
M
0
270
P
Line of sight
90
180
Foresight
Initial reading=122 43
Final reading =176 13
The angle from M to P =53 30
176⁰ 13´
Angle Observation tools
• Transit and Theodolite used in making angle observations in near past.
• Today, the total station instrument has replaced transits and theodolites.
• Theodolite is more accurate than compass, accuracy of compass is not better than
30’.
• Theodolites are in three types:
– Vernier Transit (vernier reading system for the horizontal and vertical circle)
– Optical
(Micrometer system)
– Digital or Electronic
• Accuracy ranging from 1‘ to very precise instruments which read to up 0.1 second.
Angle Observation tools
Venire Transit
Optical
Electronic
Vernier Circle readings
Viewing through reading microscope (optical system)
Measurement of a vertical angle
• A vertical angle is the difference of direction between two intersecting
lines measured in a vertical plane .
• And it is the angle above or below a horizontal plane through the point of
observation .
• Angles above the horizontal plane of observation are called plus angles or
angles of elevation or positive angles .
• Those below the horizontal plane are minus angles or angles of depression
.
• Vertical angles are measured in trigonometric leveling and in stadia work
as an important part of the field procedure .
Electronic readings
Optical Theodolite Parts
1-Telescope , 2- horizontal and
vertical circles , 3- focusing
ring or screw , 4- eyepiece
ring or screw , 5- micrometer
drum or screw , 6- horizontal
clamp screw , 7- horizontal
slow motion , 8- vertical
clamp screw , 9- vertical slow
motion , 10- reflecting mirror
(illumination) , 11- optical
plummet or centering rod , 12three leveling head screws ,
13- circular and tubular
bubbles , 14- fixing screw and
more.
Sources of Errors (Theodolite)


Errors in theodolite results from :
 Instrument
 Natural
 Personal
Usually it is impossible to determine the exact value
of an angle , so, measured value contain an error.
Sources of errors in Theodolite work :
•
•
•
•
•
•
•
•
•
Errors in theod. Surveys results from :
- instrumental
- natural
- personal
Normally it is impossible to determine the exact value of an angle , and
therefore the error in this measured value .
Precise results can be obtained by :
A- following specified field procedure .
B-manipulating the instrument carefully .
C-checking measurements .
Instruments Errors
1.
2.
3.
4.
5.
Plate bubble out of adjustment .
Axis of sight not perpendicular to the horizontal axis .
Horizontal axis not perpendicular to the vertical axis .
Axis of the telescope bubble not parallel to the axis of sight .
5- Eccentricity of centers .
Vertical
Horizontal
Natural errors :
•
•
•
•
Wind
Temperature changes
Refraction
Setting of the tripod
Personal errors :
•
•
•
•
•
•
•
Instrument not set up exactly over the point .
Level bubble not centered perfectly .
Improper use of clamps and tangent screws .
Poor focusing .
Parallax .
Unsteady tripod .
Careless plumbing and placement of the rod .
Mistakes :
•
•
•
•
•
Sighting on , or setting up over the wrong point .
Recording an incorrect value .
Reading the wrong circle .
Turning the wrong tangent screw .
Using haphazard field procedure .
Sights and Marks
Double centering :
• In a well adjusted theodolite , the line of sight is normal to the horizontal
axis , horizontal axis must be perpendicular to the vertical axis , line of
sight must be parallel to the axis of the telescope bubble tube , horizontal
circle and verniers must be concentric , ---• A maladjustment of the theodolite in one or more of these respects is to
be expected . In fact , a theodolite is never in perfect adjustment .
• Errors due to maladjustment can be eliminated by DOUBLE CENTERING
or double sighting .(making a measurements of a horizontal or a vertical
angle once with the telescope in the direct position , face left , and once
with the telescope in the reversed or face right ).
• Double centering eliminates blunders and instrumental errors , and
increase accuracy of the measured angle .
Measuring FL and FR
Double Face Observations
Sta.
face
Circle reading
mean
B
L
122⁰ 20´ 26"
122⁰ 20’ 29”
R
302⁰ 20’ 32”
L
165⁰ 46’ 11”
R
345⁰ 46’ 15”
L
182⁰ 06’ 14”
R
02⁰ 06’ 16”
DL
222⁰ 15’ 42”
R
42⁰ 15’ 48”
C
D
B
E
D
C
E
165⁰ 46’ 13”
182⁰ 06’ 15”
222⁰ 15’ 45”
Trigonometric Levelling
• Used where difficult terrain, such as mountainous areas.
• May used where the height difference is large but the horizontal
distance is short such as heighten up a cliff or a tall building.
• Δh can be determined by measuring
– The inclined or Horizontal distance
– The zenith or altitude angle.
• Slope distance is measured using electromagnetic distance measurers
(EDM) and the vertical (or zenith) angle using a theodolite.
• When these two instruments are integrated into a single
instrument it is called a ‘total station’.
• Total stations contain algorithms that calculate and display the
horizontal distance and vertical height.
Calculations
• If S distance measured
• If (H) horizontal distance measured
Calculations
• The difference in elevation can be calculated
– hi= height of the instrument above an occupied point.
– r = the reading on the rod .
• The above figure applied where lengths are shorter than about 300 m.
• For lengths longer than 300 m, the earth curvature and refraction that
must be considered.
E
B
α
D
C
F
A
G
DATUM
CE  DE sin   DC tan 
CF  total effect of curvature and refraction
EF  CE  CF
hAB  AD  CF  CE  EB
CF=effect of
curvature
And refraction
• To eliminate the uncertainty in the curvature and refraction correction ,
reciprocal vertical angle observation procedure must be applied .
• The correct difference in elevation between the two ends of the line is
then the mean of the two values computed both ways with out taking into
account curvature and refraction .
Reciprocal measurement
• The combined effect of curvature and refraction over 100 m =0.7 mm,
over 200 m = 3 mm, over 300 m = 6 mm, over 400 m = 11 mm and over
500 m = 17 mm.
• For uphill sights curvature and refraction is added to a positive V
to increase the elevation difference.
• For downhill sights, it is again added, but to a negative V, which
decreases the elevation difference.
• If reciprocal applied, the combined effect is canceled.