Week 05
Assist. Prof. Dr. Himmet KARAMAN
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Topics
Reciprocal Leveling
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ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Reciprocal Leveling
Topographic features, such as rivers and lakes,
make it difficult or impossible to keep plus and minus
sights short and equal.
Reciprocal leveling is utilized at such locations.
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ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Reciprocal Leveling (2)
As in the figure, a level is set up on one side of a
river at X, near A, and rod readings are taken on
points A and B. Since XB is very long, several
readings are taken for averaging.
This is done by reading, turning the leveling screws
to throw the instrument out of level, re-leveling, and
reading again.
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ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Reciprocal Leveling (3)
The process is repeated several times.
The instrument is moved close to Y and the
same procedure followed.
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ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Reciprocal Leveling (4)
Two differences in elevation between A and B,
determined with an instrument at X and Y, normally
will not agree because of curvature, refraction, and
personal and instrumental errors.
Refraction changes can occur if there is a long delay
between two observations.
If the precision appears satisfactory an average of
the two elevation differences is accepted as the
correct value.
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ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Effect of Curvature and Refraction
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ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Refraction and Curvature Effect
∆elevation + r + R = hi + C + V and V = H tan α
∆elevation = hi + V + (C – R) - r
Recorded Staff Reading
Refraction (R)
Observed Ray
Refracted Ray
r
B
α
H
Curvature (C)
hi
A (known elevation)
8 Note: The effects of earth curvature and refraction can be eliminated by reciprocal observations.
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Reciprocal Leveling (5)
This technique can also be performed
simultaneously with two different instrument to
reduce the effect of refraction changes.
In this case;
H
Z Z
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H B  H A  s1  m  tan
r 
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where
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Z AB  Z BA  200 g r
k  1
200 g / 
s
s : horizontal distance
k : refraction index.
Z : zenith angle
Hm= (HA+HB)/2
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BA
AB
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ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
An Example
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ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Example
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HA = 600,000m
ZBA' = 110,0250g
iB = 1,20m
rA = 1,15m
SBA' = 700,050m
ZAB' = 90,0000g
iA = 1,50m
rB = 1,20m
SAB' = 700,000m
R = 6370 km
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HA = HA'
HB = HB'
ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Solution for the Vertical Angles
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ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Solution for the Average Horizontal Distance
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ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Solution of the Height Difference
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ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
Solution for the Height of the Opposite Side
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ISTANBUL TECHNICAL UNIVERSITY - DEPARTMENT OF GEOMATICS ENGINEERING
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