1. Surveying I.
Lecture 4.

2. Setting up a theodolite
Setting up the tripod (the head of the tripod should be approximately horizontal) above the control point
Fix the instrument on the tripod.
Sight the control point in the optical plummet using the footscrews of the instrument.
Level the instrument by adjusting the length of the legs of the tripod using the circular bubble.
Find the normal point of the bubble tube.

3. Setting up a theodolite
Level the instrument accurately using the bubble tube and the three levelling screws.
Finally loosen the instrument on the tripod, and slide it above the control point on the head of the tripod.
Fix the instrument on the tripod.

4. Systematic errors of angle measurements
Systematic errors can be caused by:
structural failures or misalignments of the instrument
the observer
external conditions during the observation (weather, etc)
Systematic errors can be eliminated by:
eliminating the reason of the systematic error (adjustment of the instrument, following the rules - weather)
using suitable measuring procedures
computing the effect of the error, and correcting the observations

5. Systematic errors of angle measurements
Let’s suppose that the systematic errors are independent -> can be treated separately.
Diaphragm is tilted
We have to use the same point to sight a target.
Intersection of the crosshairs.

6. Systematic errors of angle measurements
Collimation error
The line of sight is not perpendicular to the transit axis.

7. Systematic errors of angle measurements
The effect of collimation error on the horizontal readings:

8. Systematic errors of angle measurements
since:
and:
When the angles are small:
and:
Thus:

9. Systematic errors of angle measurements
Readings in two faces!

10. Systematic errors of angle measurements
The transit axis is not adjusted
The transit axis is not perpendicular to the standing axis.
From the OP’P1’ triangle:
From the P’P1P1’ triangle:
since
Readings in two faces!
then

11. Systematic errors of angle measurements
Excentricity of the telescope
The line of sight do not intersect the standing axis.
Readings in two faces!

12. Systematic errors of angle measurements
Excentricity of the horizontal circle
The center of the horizontal circle do not coincide with the standing axis.
Sine theorem:
Readings in two faces or
using two indices!
Dangerous error source: r=14cm, (d)=10-6m, w=90 -> (d)=14,4”

13. Systematic errors of angle measurements
Tilting of the horizontal circle
The plane of the horizontal circle is not perpendicular to the standing axis.
Graduation error of the horizontal circle
Could be neglected for modern instruments. However repeated measurements should be taken by rotating the horizontal circle with 180°/# of repetitions.

14. before each repetition!
Systematic errors of AM - Setting up errors
Centering error
The extension of the standing axis does not go through the station.
Centering should be
checked
before each repetition!

15. Systematic errors of AM - Ext. conditions
Deformation of the tripod
FL and FR readings
in the opposite order!
The tripod may revolve due to direct and uneven sunlight.
Experience show that the speed of revolution is constant.
Effect of refraction
The light does not propagate along a straight line.
Majority of the impact is on the vertical angle measurements.
Will be discussed later.

16. The Horizontal Reading
Readings are taken in two faces: Face left (FL) <-> Face right (FR)
How can the horizontal reading computed from the FL and FR readings?
In theory the difference between FL and FR reading should be exactly 180°.

17. The Horizontal Reading
BUT: Systematic errors exist - like the collimation error
The effect has opposite sign in the FL and FR reading.

18. The Horizontal Reading
Example
FL:
FR:
The difference should be 180°, but it is 180°00’29’’.
2d = 29’’ -> d = 14,5’’
Horizontal Reading = FL + d = 88° 05’ 40’’

19. The Zenith Angle
In theory the sum of the FL and FR readings should be 360°.

20. The Zenith Angle
What happens, when the index is not in the vertical direction?

21. The Zenith Angle How can we compute the zenith angle? FL: 68-15-22
FR:
2d=360°-FL-FR=18’’
d=9’’
Z = FL+d =

22. Thank You for Your Attention!