Surveying I. Lecture 2.

daughterduckUrban and Civil

Nov 15, 2013 (3 years and 8 months ago)

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Surveying I.



Lecture 2.

Outline

Levelling

Structure of levels

Adjustment of levels

Error sources

Procedure of levelling



Levelling

MSL
-

Mean Sea Level

Level line
-

a line with constant height (a curved line)

Horizontal line
-

a tangential to the level line at the instrument

MSL
line
Level
h

line
horizontal
curvature
of
effect
n
collimatio
of
Line
Levelling

Over short distances the horizontal line and level line coincide.

For a distance of 100m the effect of the curvature is less than 1
mm.


The levelling device (called level) must be set up so, that the line of
sight is perpendicular to the gravity vector (plumb line).
-
> the line
of sight is horizontal.

sight
of
line
Horizontal
height
in
Difference
staff
Graduated
staff
Graduated
Level
Levelling

Levelling

Levelling
-

Bookkeeping

Rise and fall method:

Levelling
-

Bookkeeping

Height of Collimation method:

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

The bubble tube

The radius determines the sensitivity of the bubble tube:

R
2
R
1


R greater thanR
1 2
The bubble tube

The determination of sensitivity:

R
1

L
l
1
R
1

L
l
2



radians
L
l
l



1
2




8
.
206264
"


radians


The Surveyor’s telescope

Object lens

Eyepiece

Object

Virtual image

Note that the virtual image is magnified and inverted!

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.

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
targeting).


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

The Surveyor’s telescope

Focusing the telescope

External focusing

Internal focusing

Focusing lens

Variable length

Fixed length

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

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)

The Surveyor’s level

Setting up the level

Primary axis

Secondary axis

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.

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


An automatic level contains an optical device, which
compensates the tilting of the telescope
-

called compensator.

The Surveyor’s level

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

The levelling staff

Adjusting the level

The two
-
peg test



d
1
d
2
a
1
b
1
A
B
P
1
d


2
d



Collimation error
-

the line of collimation is not horizontal,
when the level is levelled

The effect of collimation error cancels, if d
1
=d
2
.

Thus the height difference is:

1
1
b
a
H
AB



Adjusting the level

The two
-
peg test



3
2
1
d
d
d



3
d






3
2
3
2
1
2
d
b
d
d
d
a
H
AB











d +d
1 2
a
2
b
2
A
B
d
3
Q


2
1
2
2
d
d
b
a
H
AB






1
1
b
a
H
AB



From the previous configuration:







2
1
1
1
2
2
d
d
b
a
b
a






Systematic errors in levelling

MSL
line
Level
h

line
horizontal
curvature
of
effect
n
collimatio
of
Line
The effect of curvature

Solution:

the instrument should be set up exactly
in the middle between two points.

Systematic errors 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:

Systematic errors in levelling

r

d
13
,
0
:
2
2
2
2
2
2










r
R
k
g
introducin
r
R
R
d
R
R
r
d
Earth
the
of
Radius
R
r
d
r
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.

Systematic errors in levelling

The effect of collimation error



d
1
d
2
a
1
b
1
A
B
P
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 errors in levelling

Tilting of the staff


l
l

Depends on the:



tilting angle



reading (the higher the reading is, the bigger the error is)

Solution:

staffs should be equipped with circular
bubbles

Systematic errors in levelling

Settlement of the tripod

a
1
b
1
A
B
h

h
b
a
H
AB





1
1
a
2
b
2
A
B
h
b
a
H
AB





2
2
Solution:

the reading should be taken in both
order, and the mean value of the height differences
should be computed

Orders:



backsight
-

foresight



foresight
-

backsight

Systematic errors in levelling

Settlement of the staff

Solution:

all lines should be run twice in the
opposite directions.

Procedure of levelling

1.
The instrument must be set up in the
middle

between two staffs.

2.
The bubble tube must be levelled before
each

reading.

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.

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.

Thanks for the Attention!