# BM2 = 761.97 m

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15 Νοε 2013 (πριν από 4 χρόνια και 10 μήνες)

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Leveling

Faculty of Applied Engineering and
Urban Planning

Civil Engineering Department

2
nd

Semester 2008/2009

Surveying

1.
General Notes

2.
Common Mistakes

3.
Suggestions for Good Leveling

4.
Errors in Differential Leveling

Content

1.
Accuracy at field work comes first.

2.
If only difference between two points is needed, no
intermediate sights are required.

3.
BS and FS distances shall be equal

4.
Pay more attention to TP

5.
If the point to be measured for elevation is the
bottom of a bridge or a ceiling or the top of a barrier
such a wall or a column, staff is inverted so that
zero is at the point and negative sign is assigned to
the measured value.

General Notes

General Notes

-

Moving the turning point
-

use a well

defined TP

Field note mistakes
-

work within your group to check
you records

Mistakes with extended rod

make sure the leveling
rod is fully extended

Common Mistakes

Level rod not vertical

Settling of leveling rod

Leveling rod not fully extended or incorrect length

Level instrument not level

Environment
-

wind and heat

Common Mistakes

Level rod not vertical

Settling of leveling rod

Leveling rod not fully extended or incorrect length

Level instrument not level

Environment
-

wind and heat

Common Mistakes

Anchor tripod legs firmly

Check the bubble level before and after each reading

Take as little time as possible between BS and FS

Try to keep the distance to the BS and the FS equal

Share the rod person with the level of the rod

Suggestions for Good
Leveling

Systematic Errors

Random Errors

Blunders

Errors in Differential
Leveling

Due to Earth’s Curvature and Atmospheric Refraction

Systematic Errors

BC = refraction of line of
sight from horizontal

BD = Error due to earth's
curvature

CD = Actual net error in the
-

BG

Substituting R = 6365 km

BD = 0.0786 L
2
, Where BD is in m

L is in km

Refraction = BC≈BD/7 =0.0786 L
2
/7

Actual error in staff reading = CD = BD

BC , CD = 0.0786 L
2
/7

Therefore, to keep the effect of the earth's curvature
and atmospheric

refraction to a minimum
, it is advisable that the
distance between the level and the staff should not
exceed 100 m.

meters
in

CD
km
in

L
0.0673L
CD
2

m

100

L

mm,

1
CD
km

1

L

cm,

7
CD

Maladjustment of the level (collimation error)

Systematic Errors

)
(
tan
)
(
2
1
L
L
b
a
h

tan
tan
L

2
1
L

Correct elevation difference =m
-
n

)
(
)
(
)
(
)
(
2
1
2
1

b
a
b
a
h
EXAMPLE 4.2:

To check a level for the existence of collimation error, the level
was set up mid
-
way between points A and B and the following
1.92 m at A and 1.40 at B.
The level was then moved to
another position
and the
readings in Figure 4.14 were taken. Is there a
collimation
error? If the answer is yes, then calculate the angle of
inclination of the line of sight from the horizontal, as well as the
correct readings that should have been taken at A and B in the
second setup if there
was no collimation error.

SOLUTION:

There is a collimation error

From Equation (4.10),

0.52 = (1.75
-

1.20)
-

tan
α

(58
-

23) ,
α
=0
°
2'57"

Correct reading at A (m) =
1.75
-

58 tan
α

= 1.70 m

Correct reading at B (m) = 1.20
-

23 tan
α

= 1.18m

Check: difference in h =

1.70
-

1.18 = 0.52 m

2
1
55
.
0
2
.
1
75
.
1
h2
0.52m
1.40
-
.92
1
h
h
m
h

Questions?!

Reciprocal leveling

The elevation of point A in Figure is 917.34 m. From a setup on
the left bark, the BS reading at A was 1.44 m and the FS
reading at B was 1.90 m. At the second setup (on the right
bank) of the level, the BS reading at A was 1.80 m and the FS
reading at I3 was 2.34 m. Find the

elevation of point B.

SOLUTION:

Calculated RL for BM
2

= Known RL for BM
2

Where:

n

Level setups between two points

Δ
h

Elevation difference

Closure Error

ε

= h'

h

Where:

h'

Calculated Elevation

h

Known Elevation

Closure Error

Closure Error

i
i
i
j
i
Δh
for

correction

Closure
Δh

Measured

Δh

Corrected
ε
n
ni
Δh

correction

Closure

Closure Error

n
1

= 2,

Δ
h
1

= 1.74 m

n
2

= 1,

Δ
h
2

= 2.13 m

n
3

= 2,

Δ
h
3

=
-
3.10 m

n
4

= 4,

Δ
h
4

=
-
0.45 m

BM1 = 761.65 m

BM2 = 762.38 m

Closure Error

Δ
h
1

=

1.74 m

Δ
h
2

=

2.13 m

Δ
h
3

=

-
3.10 m

Δ
h
4

=

-
0.45 m

Σ
Δ
h =

0.32 m

BM2 = 762.38 m (known)

BM2 (Calculated)

= BM1 +
ΣΔ
h

= 761.65 m + 0.32 m

= 761.97 m

Closure Error

Closure Error
ε

= h'

h

= 761.97

762.38 =
-

0.41 m

BM2 = 762.38 m (known)

BM2 = 761.97 m (Calculated)

Closure Error

n
1

= 2,

Δ
h
1

= 1.74 m

n
2

= 1,

Δ
h
2

= 2.13 m

n
3

= 2,

Δ
h
3

=
-
3.10 m

n
4

= 4,

Δ
h
4

=
-
0.45 m

m

047
.
0
0.02
0.45
-

Δh

Corrected

02
.
0

(-0.41)
9
4
Δh
m

24
.
3
0.14
3.10
-

Δh

Corrected

14
.
0

(-0.41)
9
2
Δh
m

23
.
2
10
.
0
2.13

Δh

Corrected

10
.
0

(-0.41)
9
1
Δh
m

82
.
1
08
.
0
1.74

Δh

Corrected

08
.
0

(-0.41)
9
2
Δh
s
correction

Closure
2
4
1
3
1
2
1
1

ε

=
-

0.41 m

Group Work

Δ
h1 = 8.107 m

n1 = 4 setups

Δ
h2 =
-
17.212 m

n2 = 3 setups

Δ
h3 =
-
0.525 m

n3 = 4 setups

Δ
h4 =
-
2.387 m

n4 = 2 setups

Δ
h5 = 2.790 m

n5 = 4 setups

Δ
h6 = 9.206 m

n6 = 3 setups

Profile

Questions?!

Countouring

Faculty of Applied Engineering and
Urban Planning

Civil Engineering Department

2
nd

Semester 2008/2009

Surveying

Contouring

A contour
is an imaginary line connecting
points on the ground that have the same
elevation.

Contouring

A contour interval
the vertical distance or
elevation difference between two successive
contours

Depends on:

Scale

Purpose

Accuracy, time and cost

The topography

Area covered

Group Work

5

10

15

20

Group Work

20

15

10

5

Group Work

20

15

10

5

Group Work

5

10

15

20

Methods of Contouring

Griding

1

2

3

4

5

A

B

C

D

Methods of Contouring

Griding

12

14

13

10

11

12

11

cm

0.33
cm)

(1
10
13
10
11
x

x

1 cm

Methods of Contouring

Griding

h
2

h
1

h
o

(L)
h
h
h
h
x
1
2
1
o

x

L

Methods of Contouring

Griding

1

2

3

4

5

A

B

C

D

Discussion