cve202 lecture notes-4 leveling 1

Elementary Surveying, 11e © 2006 Prentice-Hall, Inc.. 1/19

Leveling: Theory and Methods

IntroductionLeveling: The general term applied to any of the various processes by which elevations of points or differences in elevation are determined.Leveling results are used

To design highways, railroads, canals, sewers, water supply systems etc, having grade lines that best conform the existing topography,To lay out construction projects according to planned elevations,To calculate volume of earthworks and other materials,To investigate drainage characteristics of an area, etc.



Definitions of Basic Terms in Leveling



Curvature and RefractionHorizontal line departs from a level line because of curvature of the earth.The deviation DB is expressed approximately by

where K is the distance AB in kilometers. Curvature and refraction

20785.0 KCm =



Curvature and RefractionLight rays passing through the earth’s atmosphere are bent or refracted toward the earth’s surface.Thus theoretical horizontal line of sight AH is bent to the curved form AR.For a horizontal sight, refraction in meters is expressed approximately by

Curvature and refraction

Refraction

2011.0 KRm =



Curvature and RefractionThe combined effect of curvature and refraction is expressed approximately by

where K is the distance AB in kilometers.For sight of 100 m length:hm= 0.00068 m.Proper field procedures can practically eliminate the error due to curvature and refraction.

Curvature and refraction

20675.0 Khm =



Determining Differences in ElevationMeasuring vertical distances by taping or EDMsDifferential leveling

Differential leveling theory and applications can be expressed by two equations, which are repeated over and over.

HI = elev + BSand

elev = HI - FS


Leveling: Theory and MethodsDetermining Differences in Elevation

Differential leveling



Determining Differences in ElevationBarometric Leveling

For example:A change of approximately

1000 ft in elevation corresponds to a change of 1 in. of mercury in atmospheric pressure.



Determining Differences in ElevationTrigonometric leveling (short lines)

V = S cos zor

V = S sin α

Alternatively,V = H cot z

orV= H tan α

∆elev = hi + V - r



Determining Differences in ElevationTrigonometric leveling (long lines)

Earth curvature and refraction must be considered.

∆elev = hi + V + (C - R) - r


Leveling: Equipment for Differential Leveling

Categories of LevelsDumpy Levels,Tilting Levels,Automatic Levels, andDigital Levels.

All have two common components:A telescope to create a line of site and enable a reading to be taken on a graduated rod, andA system to orient the line of site in a horizontal plane

Level vials (dumpy and tilting levels)Automatic compensators (automatic and digital levels)

Automatic levels are the typemost commonly employed today.


Telescopes




Level VialsTube-type level vialsBull’s-eye level vials

Tube-type level vials Bull’s-eye level vials



Automatic LevelsAfter the bull’s-eye bubble is manually centered, an automatic compensator levels the line of sight, and keeps it level.

Compensator of self-leveling level.


TripodsLeveling instruments are all mounted on tripods.




Hand LevelUsed on

low- precision work, ormore precise work to obtain quick checks.differential leveling in quickly checking proposed location

It is held in one hand and leveled by rising and lowering the objective end until the cross line bisects the bubble.



Level Rods (Staff)a) Philadelphia Rod (front)b) Philadelphia Rod (rear)c) Double faced leveling rodd) Lenker direct reading rod



Testing and Adjusting the Line of Sight

( ) ( ) ( ) ( )

2

:yields error)n (colimatio for Solvig22

ABAB

ABAB

RrrR

RrrR

+−−=

−−−=−−−

ε

εεεεε



ExampleA horizontal collimation test is performed on an automatic levelas in the following figure. With the instrument setup at point 1, the rod reading at A was 1.667 m, and to B it was 1.722 m. After moving and levelling the instrument at point 2, the rod reading to A was 1.543 and to B was 1.586 m. What is the collimation error of the instrument, and the corrected reading to B from point 2?



Examples:

Please solve Example 4.1, 4.2, and 4.3 in your text book.

cve202 lecture notes-4 leveling 1

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