Lecture 13--Techniques for Vertical Distance Measurements
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Transcript of Lecture 13--Techniques for Vertical Distance Measurements
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8/15/2019 Lecture 13--Techniques for Vertical Distance Measurements
1/23
Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
LEVELING:Errors and Adjustments
GE 10 Lecture 13
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8/15/2019 Lecture 13--Techniques for Vertical Distance Measurements
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
Objectives:
At the end of the lecture, the student should be able to:
Enumerate errors in leveling and determine ways on how
to eliminate or reduce them.
Define what an error of closure is in a level circuit.
Apply appropriate corrections to observed elevations of
points in a level route.
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8/15/2019 Lecture 13--Techniques for Vertical Distance Measurements
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
Outline:
I. Errors in Leveling
II. Adjustment of Intermediate Bench Marks
A. Error of Closure
B. Corrections to the Observed Elevations
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8/15/2019 Lecture 13--Techniques for Vertical Distance Measurements
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
Errors in Leveling
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8/15/2019 Lecture 13--Techniques for Vertical Distance Measurements
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
1. Imperfect adjustment of theInstrument
LOS should be parallel to the axis of the level tube.
Any inclination produces systematic error.
Error in rod reading is proportional to the distance from
the instrument to the rod.
Error in elevations will be eliminated when SDB.S. = SDF.S.
To minimize:
adjust the instrument
balance BS and FS distances
Errors in Leveling
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8/15/2019 Lecture 13--Techniques for Vertical Distance Measurements
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
2. Parallax
Effect: relative movement between the image
of the cross hairs and image of the objectwhen the eye is moved up and down.
Causes a random error
To eliminate: careful focusing
Errors in Leveling
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8/15/2019 Lecture 13--Techniques for Vertical Distance Measurements
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
3. Earth’s Curvature
Produces an error only when BS and FS
distances are not balanced. Error varies as the square of the distance from
instrument to rod.
correction: cm = 0.0785 K
2
To eliminate: balance each DB.S. by a
corresponding DF.S.
Errors in Leveling
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8/15/2019 Lecture 13--Techniques for Vertical Distance Measurements
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
4. Atmospheric RefractionVaries as the square of the distance
1/7 and opposite in sign of that error due to the Earth’s
curvature
Usually considered together with Earth’s curvature:
(c & r) = 0.0675 K2 meters
Often changes rapidly and greatly in a short distance
In ordinary leveling: effect is negligible In leveling of greater precision: can be minimized by
keeping the LOS well above the ground (at least ~0.7m)
Taking BS and FS readings in quick succession
Errors in Leveling
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8/15/2019 Lecture 13--Techniques for Vertical Distance Measurements
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
5. Variations in Temperature Cause: sun’s ray falling on top of the telescope, or on
one end and not on the other.
Effect: will produce a warping or twisting of its parts andhence may influence rod readings through temporarily
disturbing the instruments.
Error: usually random but under certain conditions it
may become systematic
To eliminate: shield the instrument from the rays of sun.
Errors in Leveling
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8/15/2019 Lecture 13--Techniques for Vertical Distance Measurements
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
6. Rod not of Standard Length If distributed over the length of the rod:
Systematic error is produced
Varies directly as the difference in elevation
Bears no relation to the length of the line over which levels
are run
To eliminate:
Compare the rod with a standard rod Apply correction analogous to a tape that is too short or too
long
Errors in Leveling
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8/15/2019 Lecture 13--Techniques for Vertical Distance Measurements
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
7. Expansion or contraction of the rod Cause: change in moisture content
Resultant error: systematic
Coefficient of thermal expansion (
e) is small
Error is of no particular consequence in ordinary
leveling
For precise leveling: gage points may be established
using metal plugs in the rod Correction for e may be based upon observed
temperatures of the rod.
Errors in Leveling
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8/15/2019 Lecture 13--Techniques for Vertical Distance Measurements
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
8. Rod not held plumb Result: rod readings that are too large
Appreciable inclinations of the rod must be avoided
particularly for high rod readings Can be eliminated by:
Swinging the rod
Use a rod level
Errors in Leveling
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8/15/2019 Lecture 13--Techniques for Vertical Distance Measurements
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
9. Faulty turning points
Error: random
Cause: when TPs are not well definedTo eliminate: choose definite and stable points
Errors in Leveling
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
10. Settlement of tripod or turning pointsSettlement of tripod:
FS will be too small Elev will be too high
Settlement of a TP:
BS will be too great HI will be too high
Overall effect: observed elevations are too high!
To eliminate:
choose stable locations
Take BS and FS readings in quick succession preferably
alternating order of sights
Errors in Leveling
l
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8/15/2019 Lecture 13--Techniques for Vertical Distance Measurements
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
11. Bubble not exactly centered atinstant of sighting
Result: produces random error which tends to vary as thedistance from instrument to rod.
The longer the sight, the greater is the care that should
be observed in leveling the instrument.
Errors in Leveling
E i L li
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
12. Inability of the observer to read the rodexactly or to set the target exactly on the LOS
Causes a random error of a magnitude depending upon
the:
Instrument
Weather conditions
Length of sight
Observer
To reduce: by proper choice of the length of sight
Errors in Leveling
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8/15/2019 Lecture 13--Techniques for Vertical Distance Measurements
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
Adjustment of Intermediate
Bench Marks
Error of Closure
Corrections to the Observed Elevations
Sample Problem
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8/15/2019 Lecture 13--Techniques for Vertical Distance Measurements
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
Error of Closure When a line of level makes a complete circuit, almost
invariably the BMelevinitial ≠ BMelevfinal
This difference is the error of running the circuit and iscalled the Error of Closure
Result intermediate BMs are also in error
Problems:
Determining the error for intermediate points Adjusting their corresponding elevations
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
Corrections to the Observed ElevationsThe appropriate correction to the observed elevation of a
given bench mark in the circuit is directly proportional to
the distance of the BM from the point of beginning
C E
L
d C
C = correction to be applied to a BMd = distance of a BM from the point of beginningL = length of the circuitEC = error of closure of the level circuit = Elevobserved - Elevtheoretical
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8/15/2019 Lecture 13--Techniques for Vertical Distance Measurements
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
Example
Point
Distance
from B.M.1
(km)
Observed
elevation
(m)
B.M.1 0 150.92
B.M.2 0.35 238.45
B.M.3 0.89 203.3
B.M.4 1.24 165.81
B.M.1 1.78 151.04
The accepted elevation of theinitial bench mark B.M.1 of a levelcircuit is 150.92 m. The length of the circuit is 1.78 km. The final
elevation of B.M.1 as calculatedfrom the level notes is 151.04 m.The observed elevations of benchmarks and the distances to thebench marks from BM1 are shown
in the third and second columns,respectively, of the accompanyingtabulation. The adjusted elevationsof these intermediate points arerequired.
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10 – General Surveying I
Solution to the Sample Problem
Point
Distance
from B.M.1
(km)
Observed
elevation
(m)
Corrections
(m)
Adjusted
Elevation
(m)
B.M.1 0 150.92 0.00
B.M.2 0.35 238.45 -0.02 238.43
B.M.3 0.89 203.3 -0.06 203.24
B.M.4 1.24 165.81 -0.08 165.73
B.M.1 1.78 151.04 -0.12 150.92
C E
L
d C
EC = Elevobs - Elevtheo = 151.04 – 150.92 = 0.12 m
L = 1.78 km
C = - d (in km) * 0.12 m1.78 km
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10–
General Surveying I
References
• Anderson, James & E. Mikhail (1998), Surveying:
Theory and Practice 7th Edition, McGraw-Hill
Companies, Inc.• Davis, Raymond E., et.al. (1981), Surveying: Theory and
Practice 6th Edition, McGraw-Hill Companies, Inc.
• La Putt, Juny P. (1987), Elementary Surveying 3rd
Edition, Cacho Hermanos Inc.
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8/15/2019 Lecture 13--Techniques for Vertical Distance Measurements
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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10–
General Surveying I
Thank you for your attention!