1. Sz. Rózsa: Surveying I. – Lecture 2

2. Procedure of levelling Line levelling, detail point levelling
Outline
Sz. Rózsa: Surveying I. – Lecture 2
Structure of levels
Adjustment of levels
Error sources
Procedure of levelling
Line levelling, detail point levelling
Processing levelling data

3. The principle of levelling
Sz. Rózsa: Surveying I. – Lecture 2
Line of sight dB lB
(lA) dA
(lB) lA
equipotential
surface
topography A B
DHAB
DHAB=lA-lB=(lA)-dA-(lB)+dB
When dA=dB (spherical approximation, equal distance to A and B)
DHAB=(lA)-(lB)

4. The Surveyor’s level Tilting level Bubble tube Diaphragm Tilting screw
Sz. Rózsa: Surveying I. – Lecture 2
Tilting level
Bubble tube
Diaphragm
Tilting screw
Circular bubble
Tilting axis
Levelling head
Clamping screw - to fix the telescope in one vertical plane
Tangent screw (slow motion screw) - to finely rotate the telescope along a vertical axis

5. The Surveyor’s telescope
Sz. Rózsa: Surveying I. – Lecture 2
Object
Eyepiece
Object lens
Virtual image
Note that the virtual image is magnified and inverted!

6. The Surveyor’s telescope
Sz. Rózsa: Surveying I. – Lecture 2
The diaphragm (cross-hairs)
To provide visible horizontal and vertical reference lines in the telescope.
Line of collimation
With adjustment screws the diaphragm can be moved in the telescope to adjust the line of collimation.

7. The Surveyor’s telescope
Sz. Rózsa: Surveying I. – Lecture 2
Parallax
When focusing the telescope, the real image formed by the objective lens is made to coincide with the diaphragm.
What is the parallax?
When viewing two distant objects approximately along a straight line, and the eye is moved to one side, then the more distant object moves relative to the other in the same direction.
This can lead to observation errors (wrong reading, wrong sighting).
If the real image formed by the objective lens does not coincide with the diaphragm a parallax is observed -> the reading depend on the position of the eye!
diaphragm
image

8. The Surveyor’s telescope
Sz. Rózsa: Surveying I. – Lecture 2
Focusing the telescope
External focusing
Variable length
Focusing lens
Internal focusing
Fixed length

9. The Surveyor’s level Tilting level Bubble tube Diaphragm Tilting screw
Sz. Rózsa: Surveying I. – Lecture 2
Tilting level
Bubble tube
Diaphragm
Tilting screw
Circular bubble
Tilting axis
Tribrach
(Levelling head)
Clamping screw - to fix the telescope in one vertical plane
Tangent screw (slow motion screw) - to finely rotate the telescope along a vertical axis

10. The Surveyor’s level Tilting level Sz. Rózsa: Surveying I. – Lecture 2
How can we view the bubble tube?
Using a mirror (older instrument)
Prismatic coincidence reader (modern instruments)
Prism
Bubble tube
Bubble tube
Bubble tube is tilted
Bubble tube is horizontal (leveled)

11. The Surveyor’s level Setting up the level 1. Fix the level on a tripod
Sz. Rózsa: Surveying I. – Lecture 2
Setting up the level
1. Fix the level on a tripod
2. Center the circular bubble by adjusting the foot screws.
(to approximately level the instrument)
Primary axis
Secondary axis
3. Sight the levelling staff, and eliminate the parallax.
4. Adjust the sensitive bubble tube by the tilting screw.

12. The Surveyor’s level Automatic level
Sz. Rózsa: Surveying I. – Lecture 2
Automatic level
We must adjust the bubble tube before every reading when using the tilting level -> takes a lot of time, may cause blunders (large mistakes in the observations)
An automatic level contains an optical device, which compensates the tilting of the telescope - called compensator.

13. The Surveyor’s level Operation of the compensator
Sz. Rózsa: Surveying I. – Lecture 2
Operation of the compensator
Advantage: faster observations, elimination of a possible reason of blunders
Disadvantage: vibrations (wind, traffic, etc.) have a bad impact on the operation of the compensator

14. The levelling staff
Sz. Rózsa: Surveying I. – Lecture 2

15. Procedure of levelling Line levelling, detail point levelling
Outline
Sz. Rózsa: Surveying I. – Lecture 2
Structure of levels
Adjustment of levels
Error sources
Procedure of levelling
Line levelling, detail point levelling
Processing levelling data

16. Adjusting the level The two-peg test
Sz. Rózsa: Surveying I. – Lecture 2
The two-peg test
How much is the collimation error (a)?
Collimation error - the line of collimation is not horizontal, when the level is levelled
Establish a test line on an approximately flat surface.
Compute the elevation difference between the test points (A and B)!
The effect of collimation error cancels, when d1=d2.
Thus the height difference is:

17. Adjusting the level
Sz. Rózsa: Surveying I. – Lecture 2
3. Move the instrument to an external point on the extension of the AB line.
4. Compute the elevation difference from the observations (note that the elevation difference contains the effect of the collimation error)!
5. The true elevation difference is already computed from the previous configuration:
6. Thus the collimation error is:

18. Procedure of levelling Line levelling, detail point levelling
Outline
Sz. Rózsa: Surveying I. – Lecture 2
Structure of levels
Adjustment of levels
Error sources
Procedure of levelling
Line levelling, detail point levelling
Processing levelling data

19. Systematic error in levelling
Sz. Rózsa: Surveying I. – Lecture 2
The effect of curvature
Line of sight
(lA) dA dB lB
(lB) lA
equipotential
surface
DHAB
topography
Solution: Since the equipotential surface is approximately spherical, the effect of curvature is a function of the instrument-staff distance. When the backsight and foresight distances are equal, the effect of curvature cancels out.

20. Systematic error in levelling
Sz. Rózsa: Surveying I. – Lecture 2
The refraction
The air has different optical properties everywhere. Air pressure, humidity etc. Have an impact on the refractivity. Thus the light does not propagate along a straight line, but along a curve:
For points with the same elevation, the effect of refraction can be neglected.
What to do, when they are not?

21. radius of refractive curve
Systematic error in levelling
Sz. Rózsa: Surveying I. – Lecture 2 d dr r’
radius of refractive curve
Solution: the instrument should be set up exactly in the middle between two points, thus the effect of curvature is the same for the backsight and foresight.

22. Systematic error in levelling
Sz. Rózsa: Surveying I. – Lecture 2
The effect of collimation error
Solution: the instrument should be set up exactly in the middle between two points and the collimation error must be constant, thus the effect is eliminated

23. Systematic error in levelling
Sz. Rózsa: Surveying I. – Lecture 2
Tilting of the staff di a
The effect depends on the:
tilting angle
reading (the higher the reading is, the bigger the error is)
di=li-licosa
Solution: staffs should be equipped with circular bubbles and kept vertical

24. Systematic error in levelling
Sz. Rózsa: Surveying I. – Lecture 2
Settlement of the tripod
Measuring the height difference
between A and B!
Measuring the height difference
between B and A! dh dh a1 b1 a2 b2 A B A B
Let’s compute the mean value of the DHAB and DHBA:
Solution: the reading should be taken in both order, and the mean value of the height differences should be computed (assuming constant observation speed)

25. Systematic error in levelling
Sz. Rózsa: Surveying I. – Lecture 2
Settlement of the staff
Problem:
The staff has a subsidence during the observations. a change plate must be used to support the staff.
Solution:
all lines should be run twice in the opposite directions;
a change plate must be used to support the staff.
Graduation error of the staff
Problem: The cm graduation on the staff is not accurate. The units have different lengths.
Solution: staffs must be calibrated regularly (the graduation must be checked in laboratories).

26. Systematic error in levelling
Sz. Rózsa: Surveying I. – Lecture 2
Index error of the staff
Problem: The bottom of the staff is not aligned with the 0 unit of the scale.
The effect of the index error on the reading:
l = (l) + d
Where l is the reading taken, while d is the index error d

27. Systematic error in levelling
Sz. Rózsa: Surveying I. – Lecture 2
The effect of index error on a single height difference:
Direction of
levelling
Staff No. 1.
Staff No. 2.
lBS
lFS DH
DH = lBS-lFS
DH = [(lBS)+d1]-[(lFS)+d2)]=lBS-lFS+d1-d2
When only one staff is used, then the effect of index error cancels out (d1=d2)

28. Systematic error in levelling
Sz. Rózsa: Surveying I. – Lecture 2
What happens when two staffs are used?
Single height difference:
DH = [(lBS)+d1]-[(lFS)+d2)]=lBS-lFS+d1-d2
Staff No. 1. 1
Staff No. 2. 2
Staff No. 1.
The sum of two height differences:
DH = [(lBS)+d1]-[(lFS)+d2)]=lBS-lFS+d1-d2
DH = [(lBS)+d2]-[(lFS)+d1)]=lBS-lFS+d2-d1

29. Systematic error in levelling
Sz. Rózsa: Surveying I. – Lecture 2
DH1 = [(lBS)+d1]-[(lFS)+d2)]=(lBS)-(lFS)+d1-d2
DH2 = [(lBS)+d2]-[(lFS)+d1)]=(lBS)-(lFS)+d2-d1
DH1 +DH2 = S(lBS)-S(lFS)
When two staffs are used, an even number of stations have to be created in the levelling line. In this case the effect of the index error of the staff cancels out.

30. Procedure of levelling Line levelling, detail point levelling
Outline
Sz. Rózsa: Surveying I. – Lecture 2
Structure of levels
Adjustment of levels
Error sources
Procedure of levelling
Line levelling, detail point levelling
Processing levelling data

31. Procedure of levelling
Sz. Rózsa: Surveying I. – Lecture 2
1. The instrument must be set up with the same distance to the staffs.
2. The bubble tube must be levelled before each reading (tilting level).
3. You must not use the parallax screw between the backsight and foresight readings
4. The bubble tube must not be affected by strong heat.
5. Readings must be taken cm above the ground.
6. Staff should be set up vertically.
7. A change plate should be used to place the staff on the ground.
8. Levelling must be done in two opposite directions.

32. Procedure of levelling
Sz. Rózsa: Surveying I. – Lecture 2
9. All the observations should be made with a constant speed.
10. Observations should be made only in suitable weather: cloudy sky, constant temperature, early morning, or late afternoon.
11. Staff should be calibrated.
12. If there are three hairs in the diaphragm, one should use all of them to take a reading.
13. When two staffs are used, an even number of stations must be used to create the levelling line.

33. Procedure of levelling Line levelling, detail point levelling
Outline
Sz. Rózsa: Surveying I. – Lecture 2
Structure of levels
Adjustment of levels
Error sources
Procedure of levelling
Line levelling, detail point levelling
Processing levelling data

34. Line levelling Principle of levelling dA dB (lA) lA (lB) lB DHAB
Sz. Rózsa: Surveying I. – Lecture 2
Principle of levelling
Line of sight
(lA) dA dB lB
(lB) lA
equipotential
surface
DHAB
topography
What happens, when we want to measure the height difference of two distant points?

35. The direction of levelling
Line levelling
Sz. Rózsa: Surveying I. – Lecture 2
The previous procedure is repeated as many times as need to cover the distance between the points.
The direction of levelling
Dh1 DH
Dh2
Dh3
Dh4
DH=Dh1+Dh2+Dh3+Dh4
DH=SlBS-SlFS

36. Procedure of levelling Line levelling, detail point levelling
Outline
Sz. Rózsa: Surveying I. – Lecture 2
Structure of levels
Adjustment of levels
Error sources
Procedure of levelling
Line levelling, detail point levelling
Processing levelling data

37. Processing Levelling Data
Sz. Rózsa: Surveying I. – Lecture 2
Line levelling (one-way) A B
MSL
Reference level HA
HB=?

38. Line Levelling – one way (the Rise&Fall Method)
Sz. Rózsa: Surveying I. – Lecture 2
d=19
d=20m
d=15
d=13 A 1 HA
HB=? 2 3 B
PID d BS FS
Rise
Fall H A 12 14 1 20 08 33 14 58
0.244 2 19 14 74 13 99
0.566 3 15 08 69 09 13
0.561 B 13 11 25
0.256
0.561
1.066
DHAB=SRise-SFall= m

39. Line Levelling – two-way (the Rise&Fall Method)
Sz. Rózsa: Surveying I. – Lecture 2
PID d BS FS
Rise
Fall H A 12 14 1 20 08 33 58
0.244 2 19 74 13 99
0.566 3 15 69 09
0.561 B 11 25
0.256 03 10 01
0.292 53
-0.518 18 22 41
0.412 97
0.325
DHAB=SRise-SFall= m
DHBA=SRise-SFall=+0.511m
Let’s compute the mean height difference:
HB= = m

40. Detail Point Levelling – The Height of Collimation Method
Sz. Rózsa: Surveying I. – Lecture 2
Detail Point Levelling: The elevation of some detail points (characteristic points of objects) should be determined. A B HA HB
The elevation of the characteristic points of the ditch should be determined!
MSL
Reference level

41. Detail Point Levelling – The Height of Collimation Method
Sz. Rózsa: Surveying I. – Lecture 2
Height of collimation: The elevation of the horizontal line of sight. It can be computed by adding the elevation of the backsight point and the backsight reading.
Steps of Computation:
Compute the corrected elevation of the intermediate points!
Compute the Height of Collimation at each station!
Compute the elevation of the detail points (HoC-lIS)!
AlBS A
HoC=HA+AlBS HA
MSL
Reference level

42. Detail Point Levelling – The Height of Collimation Method
Sz. Rózsa: Surveying I. – Lecture 2 A
101
104 I1 I2 I3 B HA
102 HB
103
MSL
Reference level
PID d
Backsight (BS)
Intersight (IS)
Foresight (FS)
Rise/Fall
Height of Collimation
Elevation A
1214 I1
0833
1458
101
1104
102
1421
103
1428
104
1067 I2
1474
1399 I3
0869
0913 B
1124
-0.244
(-1)
-0.566
(-1)
+0.561
(-1)
-0.255
(-1) S= S=
True - Observed
D=-4mm

43. Thanks for the Attention!
Sz. Rózsa: Surveying I. – Lecture 2
Thanks for the Attention!