Geoscience Reference
In-Depth Information
2.2 Height Measurement
2.2.1 Leveling
Principle of Leveling
Leveling is a method used for accurate determination of height difference between
two points. The basic principle of leveling is that a precisely graduated staff is held
vertically over the two points whose height difference is to be determined and then
the scale readings are made with the horizontal line of sight. The difference
between the two readings will be the height difference between the two points.
As shown in Fig.
2.7
, A and B are two surface points with unknown height
difference. Leveling rods (leveling staffs) R
1
and R
2
are held vertically on each
point while a level is placed at point S
1
in between these two points. From the
horizontal line of sight, a reading of the rod R
1
is made as “a” (known as the
backsight reading) and that of the rod R
2
is “b” (known as the foresight reading).
Then the height difference h
AB
between A and B is:
h
AB
¼
a
b
:
ð
2
:
6
Þ
b.
Knowing the height H
A
of point A, we can obtain the height of point B following
H
B
¼
The height difference is positive when a
>
b and negative when a
<
H
A
+ h
AB
. To determine the height H
P
of an arbitrary point P, one needs to
move the level to S
2
and the rod R
1
to point C after the height difference between
A and B is determined. Then, the height difference h
BC
between points B and C can
be obtained. Likewise,
the difference
in height between A and P is
h
AP
¼
.
The height of point P is:
h
AB
+ h
BC
+
H
P
¼
H
A
þ
h
AP
:
ð
2
:
7
Þ
Such a method of transferring heights is referred to as geometric leveling.
Level and Leveling Rod
It can be seen from the principle of leveling that the leveling instrument should be
developed to set up a horizontal line of sight. Therefore, the level should have a
telescope capable of creating a line of sight (collimation axis) and a component that
can direct the line of sight to the horizontal direction (a bubble is one of the simplest
kinds). To make the line of sight horizontal and rotate horizontally, foot screws and
a vertical axis are also necessary. Integrating these components as shown in Fig.
2.8
will constitute the simplest level. These principal components should satisfy the
following conditions:
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