1. Surveying I.
Lecture 3.

2. Outline
The theodolite and its structure
Telescope
Reading device
Bubble tubes
Vertical circle

3. Measuring angles What is Surveying?
The art of making measurements of the relative positions of natural and man-made features on the Earth’s surface, and the presentation of this information either graphically or numerically.
Relative positions (2D case):
One needs to find two points and measure the distance between them. Hence we can create a coordinate system.
Control points
Base line

4. Measuring angles
Let’s determine the position of a third, unknown point (C).
We have two unknowns:
We need two measurements:
two distances
one distance and an angle
two angles

5. Measuring angles

6. Measuring angles What kind of instrument do we need? It should
contain two fixed graduated circles
an upper part, which can be revolved around a vertical axis and eqiped with an index
a telescope, which can be rotated around a horizontal axis
bubble tubes to set up the instrument

7. The vernier theodolite

8. The theodolite The vernier
60 subdivision between the index and the 20-minute graduation of the vernier equals the distance of 59 unit of the main scale.

9. Modern theodolites
no verniers - glass circles, units are graduated by photographic methods, readings are taken using optical systems
optical plummet (in tribrach or in alidade)
advanced models - digital reading

10. Telescope Imaging of the objective
Geodetic telescopes can be used between 2f and infinity.
Internal focusing (see Lecture 2)

11. Methods of circle reading
Graduated microscope and the coincidence method
Graduated microscope

12. Methods of circle reading
Coincidence method
Two indices in diametral position
Both of them and both portion of the horizontal circle are imaged in the reading eyepiece.

13. Methods of circle reading

14. Levelling the instrument
The horizontal circle must be truly horizontal during the measurements.
How to achieve this?
Remember the structure of the levelling instrument:
Bubble tube
Diaphragm
Tilting screw
Circular bubble
Tilting axis
Levelling head
In this case the bubble tube must be adjusted.

15. The bubble tube Finding the normal point of the bubble tube
Let’s suppose that the bubble tube is not adjusted, but we do want to use it to level the alidade.
When the bubble is centered, the alidade is tilted.
Normal point: the setting of the bubble, when the alidade is horizontal or the standing axis is vertical.

16. The bubble tube Step 1. Step 2.
Center the bubble, then rotate the alidade around the standing axis with 180 degree.
Step 2.
Check the reading of the left end of the bubble.
Standing axis L R R L
Plate bubble
Alidade L R R L

17. The bubble tube
The normal point is exactly the average of the two values.
In our case: 3 units.
If we set the bubble to this unit, the alhidade is horizontal. R L R L

18. Leveling the instrument
Finding the normal point of the bubble tube
Leveling the alidade

19. The vertical circle
Is necessary for measuring the angle between the vertical and the line of collimation (z)
The index of the vertical circle must always be horizontal!

20. The vertical circle The vernier theodolite
The index must be levelled before each reading on the vertical circle.

21. The vertical circle Modern theodolites:
In modern theodolites an optical system compensates the tilting of the standing axis. The optical system consists of prisms and a pendulum.
Askania compensator
Standing axis
is vertical
Standing axis
is tilted

22. The vertical circle Liquid compensator
Supposing that the standing axis is tilted, and the line of collimation is horizontal.

23. Setting up a theodolite
The theodolite must be centered and levelled.

24. 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.

25. 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.

26. Thank You for Your Attention!