surveying i. lecture 2

Surveying I.

Lecture 2.

Sz. Rózsa: Surveying I. – Lecture 2

Outline

Structure of levelsAdjustment of levelsError sourcesProcedure of levellingLine levelling, detail point levellingProcessing levelling data



The principle of levelling

A

B

(lA)

(lB)

dA

DHAB

lA

dB

lB

DHAB=lA-lB=(lA)-dA-(lB)+dB

When dA=dB (spherical approximation, equal distance to A and B)

DHAB=(lA)-(lB)

topography

equipotentialsurface

Line of sight

The Surveyor’s level

Tilting level

Levelling head

Tilting screw

DiaphragmBubble 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


The Surveyor’s telescope

Object lens

Eyepiece

Object

Virtual image

Note that the virtual image is magnified and inverted!



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.


The Surveyor’s telescopeParallaxWhen 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



Focusing the telescope

External focusing

Internal focusing

Focusing lens

Variable length

Fixed length



Tilting level

Tribrach (Levelling head)

Tilting screw

DiaphragmBubble 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



Tilting levelHow 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



Setting up the level

Primary axis

Seco

ndar

y ax

is

1. Fix the level on a tripod

2. Center the circular bubble by adjusting the foot screws.(to approximately level the instrument)

3. Sight the levelling staff, and eliminate the parallax.

4. Adjust the sensitive bubble tube by the tilting screw.



Automatic levelWe 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.



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


The levelling staff


Outline



Adjusting the levelThe two-peg test

d1 d2

a1 b1

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 D


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

d +d1 2

a2 b2

A B d3 Q

2122 ddbaH AB D

11 baH AB D5. The true elevation difference is already computed from the previous configuration:

21

1122

ddbaba


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



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.


(lA)

(lB)

dA

DHAB

lA

dB

lB

topography


Line of sight


The refractionThe 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?



13,0:

22

2

22

2

rRkgintroducin

rR

Rd

RR

rd

EarththeofRadiusRrd

r

r

d

d

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.


d

r’radius of refractive curve

dr


The effect of collimation error

d1 d2

a1 b1

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


Systematic error in levellingTilting 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


di

di=li-licos

Systematic error in levellingSettlement of the tripod

hbaH AB dD 11 habHBA dD 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)


A B

dha1 b1

Measuring the height difference between A and B!

Measuring the height difference between B and A!

A B

dh

a2 b2

Let’s compute the mean value of the DHAB and DHBA:

2222

22112211 BAABBAABAB

HHabbahabhbaHHH DDDDD dd


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).


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 levellingIndex error of the staff

Problem: The bottom of the staff is not aligned with the 0 unit of the scale.

01

d

The effect of the index error on the reading:

l = (l) + d

Where l is the reading taken, while d is the index error



The effect of index error on a single height difference:

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)


Direction oflevelling

lBS

lFS

Staff

No.

1.

Staff

No.

2.

DH


What happens when two staffs are used?

Single height difference:

The sum of two height differences:

12



Staff

No.

1.

Staff

No.

2.

Staff

No.

1.




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.


DH1 = [(lBS)+d1]-[(lFS)+d2)]=(lBS)-(lFS)+d1-d2

DH2 = [(lBS)+d2]-[(lFS)+d1)]=(lBS)-(lFS)+d2-d1

Outline



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 readings4. 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.


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.


Outline



Line levellingPrinciple of levelling

What happens, when we want to measure the height difference of two distant points?


(lA)

(lB)

dA

DHAB

lA

dB

lB

topography


Line of sight

Line levellingThe previous procedure is repeated as many times as need to cover the distance between the points.

DH=Dh1+Dh2+Dh3+Dh4

The direction of levelling

DHDh1

Dh2

Dh3

Dh4


DH=SlBSSlFS

Outline



Processing Levelling Data


Line levelling (one-way)

A

B

MSLReference level

HA HB=?

A

BHA HB=?


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

DHAB=SRise-SFall=-0.505 m

102.950

Line Levelling – one way (the Rise&Fall Method)

PID d BS FS Rise Fall H

A 12 14 103.4551 20 08 33 14 58 0.2442 19 14 74 13 99 0.5663 15 08 69 09 13 0.561B 13 11 25 0.256

B 12 031 11 10 01 09 11 0.2922 13 13 53 15 19 -0.5183 18 15 22 09 41 0.412A 22 11 97 0.325


Line Levelling – two-way (the Rise&Fall Method)

DHAB=SRise-SFall=-0.505 m

DHBA=SRise-SFall=+0.511m

Let’s compute the mean height difference:

mHHH BAABAB 508.0

2511.0505.0

2DDD HB=103.455-0.508=102.947m


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!


Detail Point Levelling – The Height of Collimation MethodHeight 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.

A

MSLReference level

HAHoC=HA+AlBS

AlBS

Steps of Computation:

1. Compute the corrected elevation of the intermediate points!

2. Compute the Height of Collimation at each station!

3. Compute the elevation of the detail points (HoC-lIS)!

Detail Point Levelling – The Height of Collimation Method


AB

MSLReference level

HA HB

I1I2 I3

101

102 103

104

PID d Backsight (BS)

Intersight (IS)

Foresight (FS)

Rise/Fall Height of Collimation

Elevation

A 1214 103.455I1 0833 1458

101 1104102 1421103 1428104 1067

I2 1474 1399I3 0869 0913B 1124 102.947

-0.244

-0.566

+0.561-0.255S= -0.504 S= -0.508

D=-4mmTrue - Observed

(-1)

(-1)

(-1)

(-1)

103.210

102.643

103.203

104.043102.939102.622102.615

102.976

Thanks for the Attention!


surveying i. lecture 2

Documents

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surveyors telescopefocusing

surveyors leveloperation

nincs diacm surveying

sensitive bubble tube

tiltedbubble tube

levelling staff

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