lecture 13--techniques for vertical distance measurements

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

LEVELING:Errors and Adjustments

GE 10 Lecture 13


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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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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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Errors in Leveling


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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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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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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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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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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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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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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. 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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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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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

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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

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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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Adjustment of Intermediate

Bench Marks

Error of Closure

Corrections to the Observed Elevations

Sample Problem


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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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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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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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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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Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 10–

General Surveying I

Thank you for your attention!

lecture 13--techniques for vertical distance measurements

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