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Surveying I.
Lecture 2.
Sz. Rózsa: Surveying I. – Lecture 1
Outline
Structure of levels
Adjustment of levels
Error sources
Procedure of levelling
Line levelling, detail point levelling
Processing levelling data
Sz. Rózsa: Surveying I. – Lecture 1
Sz. Rózsa: Surveying I. – Lecture 1
The principle of levelling
A
B
(lA)
(lB)
A
HAB
lA
B
lB
HAB=lA-lB=(lA)-A-(lB)+B
When A=B (spherical approximation, equal distance to A and B)
HAB=(lA)-(lB)
topography
equipotentialsurface
Line of sight
The Surveyor’s level
Tilting level
Levelling head
Tilting screw
Diaphragm
Bubble tube
Tilting axis
Clamping screw - to fix the telescope in one vertical plane
Tangent screw (slow motion screw) - to finely rotate the telescope along a vertical axis
Circular bubble
Sz. Rózsa: Surveying I. – Lecture 1
Elements of Surveyor’s level
How to set the line of sight to be exactly horizontal?
More general: how to set anything to be exactly horizontal?
The bubble tube
Sz. Rózsa: Surveying I. – Lecture 1
The bubble tube
The radius determines the sensitivity of the bubble tube:
R2R1
R greater thanR1 2
Sensitivity: how much the bubble moves due to a given amount of inclination. The more the bubble moves, the more sensitive the bubble tube is.
Sz. Rózsa: Surveying I. – Lecture 1
The bubble tube
The determination of sensitivity:
R1
L
l1
R1
L
l2
radians
L
ll 12
8.206264" radians
Sz. Rózsa: Surveying I. – Lecture 1
Kepler-type telescope
Object lens
Eyepiece
Object
Virtual image
Note that the virtual image is magnified and inverted!
Sz. Rózsa: Surveying I. – Lecture 1
The Surveyor’s telescope
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.
Sz. Rózsa: Surveying I. – Lecture 1
The Surveyor’s telescope
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
Sz. Rózsa: Surveying I. – Lecture 1
The Surveyor’s telescope
Focusing the telescope
External focusing
Internal focusing
Focusing lens
Variable length
Fixed length
Sz. Rózsa: Surveying I. – Lecture 1
The Surveyor’s level
Tilting level
Tribrach (Levelling head)
Tilting screw
Diaphragm
Bubble tube
Tilting axis
Clamping screw - to fix the telescope in one vertical plane
Tangent screw (slow motion screw) - to finely rotate the telescope along a vertical axis
Circular bubble
Sz. Rózsa: Surveying I. – Lecture 1
The Surveyor’s level
Sz. Rózsa: Surveying I. – Lecture 1
The Surveyor’s level
Sz. Rózsa: Surveying I. – Lecture 1
The Surveyor’s level
Tilting level
How can we view the bubble tube?
• Using a mirror (older instrument)• Prismatic coincidence reader (modern instruments)
Bubble tube
Prism
Bubble tube is tilted Bubble tube is horizontal (leveled)
Bubble tube
Sz. Rózsa: Surveying I. – Lecture 1
The Surveyor’s level
Setting up the level1. Fix the level on a tripod
2. Center the circular bubble by adjusting the foot screws.(to approximately level the instrument)
Sz. Rózsa: Surveying I. – Lecture 1
The Surveyor’s level
Setting up the level
3. Sight the levelling staff:
first: rotate the telescope in the direction of the staff
second: use the fine motion screws to ensure precise sighting
(note: on some instruments the fine motion screw works only, when
the alidade is fixed using the fixing clamp)
4. Adjust the levelling bubble using the levelling screw.
Sz. Rózsa: Surveying I. – Lecture 1
The Surveyor’s level
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.
Sz. Rózsa: Surveying I. – Lecture 1
The Surveyor’s level
Sz. Rózsa: Surveying I. – Lecture 1
The Surveyor’s level
Operation of the compensator
Advantage: faster observations, elimination of a possible reason of blundersDisadvantage: vibrations (wind, traffic, etc.) have a bad impact on the operation of the compensator
Sz. Rózsa: Surveying I. – Lecture 1
The levelling staff
Sz. Rózsa: Surveying I. – Lecture 1
Outline
Structure of levels
Adjustment of levels
Error sources
Procedure of levelling
Line levelling, detail point levelling
Processing levelling data
Sz. Rózsa: Surveying I. – Lecture 1
Adjusting the level
The two-peg test
d1 d2
a1b1
A BP
1d 2d
Collimation error - the line of collimation is not horizontal, when the level is levelled
The effect of collimation error cancels, when d1=d2.
Thus the height difference is: 11 baH AB
Sz. Rózsa: Surveying I. – Lecture 1
How much is the collimation error ()?
1. Establish a test line on an approximately flat surface.
2. Compute the elevation difference between the test points (A and B)!
Adjusting the level
321 ddd
3d
323212 dbdddaH AB
d +d1 2
a2b2
A B d3 Q
2122 ddbaH AB
11 baH AB 5. The true elevation difference is already computed from the previous configuration:
21
1122
dd
baba
Sz. Rózsa: Surveying I. – Lecture 1
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)!
6. Thus the collimation error is:
Outline
Structure of levels
Adjustment of levels
Error sources
Procedure of levelling
Line levelling, detail point levelling
Processing levelling data
Sz. Rózsa: Surveying I. – Lecture 1
Systematic error in levelling
The effect of curvature
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.
Sz. Rózsa: Surveying I. – Lecture 1
(lA)
(lB)
A
HAB
lA
B
lB
topography
equipotentialsurface
Line of sight
Systematic error in levelling
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?
Sz. Rózsa: Surveying I. – Lecture 1
Systematic error in levelling
13,0:
22
2
22
2
r
Rkgintroducin
r
R
R
d
R
R
r
d
EarththeofRadiusRr
d
r
r
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.
Sz. Rózsa: Surveying I. – Lecture 1
d
r’radius of refractive curve
r
Systematic error in levelling
The effect of collimation error
d1 d2
a1b1
A BP
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
Sz. Rózsa: Surveying I. – Lecture 1
Systematic error in levelling
Tilting of the staff
The effect depends on the:• tilting angle• reading (the higher the reading is, the bigger the error is)
Solution: staffs should be equipped with circular bubbles and kept vertical
Sz. Rózsa: Surveying I. – Lecture 1
i
i=li-licos
Systematic error in levelling
Settlement of the tripod
hbaH AB 11 habHBA 22
Solution: the reading should be taken in both order, and the mean value of the height differences should be computed (assuming constant observation speed)
Sz. Rózsa: Surveying I. – Lecture 1
A B
h
a1 b1
Measuring the height difference between A and B!
Measuring the height difference between B and A!
A B
h
a2 b2
Let’s compute the mean value of the HAB and HBA:
2222
22112211 BAABBAABAB
HHabbahabhbaHHH
Systematic error in levelling
Settlement of 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
Solution: staffs must be calibrated regularly (the graduation must be checked in laboratories).
Sz. Rózsa: Surveying I. – Lecture 1
Problem: The staff has a subsidence during the observations. a change plate must be used to support the staff.
Problem: The cm graduation on the staff is not accurate. The units have different lengths.
Systematic error in levelling
Index error of the staff
Problem: The bottom of the staff is not aligned with the 0 unit of the scale.
01
The effect of the index error on the reading:
l = (l) +
Where l is the reading taken, while is the index error
Sz. Rózsa: Surveying I. – Lecture 1
Systematic error in levelling
The effect of index error on a single height difference:
H = lBS-lFS
H = [(lBS)+1]-[(lFS)+2)]=lBS-lFS+1-2
When only one staff is used, then the effect of index error cancels out (1=2)
Sz. Rózsa: Surveying I. – Lecture 1
Direction oflevelling
lBS
lFS
Sta
ff N
o.
1.
Sta
ff N
o.
2.
H
Systematic error in levelling
What happens when two staffs are used?
Single height difference:
The sum of two height differences:
1
2
Sz. Rózsa: Surveying I. – Lecture 1
H = [(lBS)+1]-[(lFS)+2)]=lBS-lFS+1-2
Sta
ff N
o.
1.
Sta
ff N
o.
2.
Sta
ff N
o.
1.
H = [(lBS)+1]-[(lFS)+2)]=lBS-lFS+1-2
H = [(lBS)+2]-[(lFS)+1)]=lBS-lFS+2-1
Systematic error in levelling
H1 +H2 = (lBS)-(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.
Sz. Rózsa: Surveying I. – Lecture 1
H1 = [(lBS)+1]-[(lFS)+2)]=(lBS)-(lFS)+1-2
H2 = [(lBS)+2]-[(lFS)+1)]=(lBS)-(lFS)+2-1
Outline
Structure of levels
Adjustment of levels
Error sources
Procedure of levelling
Line levelling, detail point levelling
Processing levelling data
Sz. Rózsa: Surveying I. – Lecture 1
Procedure of levelling
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 30-50 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.
Sz. Rózsa: Surveying I. – Lecture 1
Procedure of levelling
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.
Sz. Rózsa: Surveying I. – Lecture 1
Outline
Structure of levels
Adjustment of levels
Error sources
Procedure of levelling
Line levelling, detail point levelling
Processing levelling data
Sz. Rózsa: Surveying I. – Lecture 1
Line levelling
Principle of levelling
What happens, when we want to measure the height difference of two distant points?
Sz. Rózsa: Surveying I. – Lecture 1
(lA)
(lB)
A
HAB
lA
B
lB
topography
equipotentialsurface
Line of sight
Line levelling
The previous procedure is repeated as many times as need to cover the distance between the points.
H=h1+h2+h3+h4
The direction of levelling
H
h1
h2
h3
h4
Sz. Rózsa: Surveying I. – Lecture 1
H=lBSlFS
Outline
Structure of levels
Adjustment of levels
Error sources
Procedure of levelling
Line levelling, detail point levelling
Processing levelling data
Sz. Rózsa: Surveying I. – Lecture 1
Processing Levelling Data
Sz. Rózsa: Surveying I. – Lecture 1
Line levelling (one-way)
A
B
MSLReference level
HA HB=?
A
BHA HB=?
Sz. Rózsa: Surveying I. – Lecture 1
PID d BS FS Rise Fall HA
1
1
d=20m
20
12 14
14 58 0.244
103.455
2
2
d=19
19
08 33
13 99 0.566
d=15
3
3 15
14 74
09 13 0.561
d=13
B 13
08 69
11 25 0.256
0.561 1.066
HAB=Rise-Fall=-0.505 m
102.950
Line Levelling – one way (the Rise&Fall Method)
PID d BS FS Rise Fall HA 12 14 103.4551 20 08 33 14 58 0.2442 19 14 74 13 99 0.5663 15 08 69 09 13 0.56
1B 13 11 25 0.256
B 12 031 11 10 01 09 11 0.29
22 13 13 53 15 19 -0.5183 18 15 22 09 41 0.41
2A 22 11 97 0.32
5
Sz. Rózsa: Surveying I. – Lecture 1
Line Levelling – two-way (the Rise&Fall Method)
HAB=Rise-Fall=-0.505 m
HBA=Rise-Fall=+0.511m
Let’s compute the mean height difference:
mHH
H BAABAB 508.0
2
511.0505.0
2 HB=103.455-0.508=102.947m
Sz. Rózsa: Surveying I. – Lecture 1
Detail Point Levelling – The Height of Collimation Method
Detail Point Levelling: The elevation of some detail points (characteristic points of objects) should be determined.
A
B
MSLReference level
HA HB
The elevation of the characteristic points of the ditch should be determined!
Sz. Rózsa: Surveying I. – Lecture 1
Detail Point Levelling – The Height of Collimation Method
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.
Levelling - Bookkeeping
Rise and fall method:
Sz. Rózsa: Surveying I. – Lecture 1
Levelling - Bookkeeping
Height of Collimation method:
Sz. Rózsa: Surveying I. – Lecture 1
Thanks for the Attention!
Sz. Rózsa: Surveying I. – Lecture 1
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