CVE202 Lecture Notes-4 Leveling 1
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Transcript of 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.
Elementary Surveying, 11e © 2006 Prentice-Hall, Inc.. 2/19
Leveling: Theory and Methods
Definitions of Basic Terms in Leveling
Elementary Surveying, 11e © 2006 Prentice-Hall, Inc.. 3/19
Leveling: Theory and Methods
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 =
Elementary Surveying, 11e © 2006 Prentice-Hall, Inc.. 4/19
Leveling: Theory and Methods
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 =
Elementary Surveying, 11e © 2006 Prentice-Hall, Inc.. 5/19
Leveling: Theory and Methods
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 =
Elementary Surveying, 11e © 2006 Prentice-Hall, Inc.. 6/19
Leveling: Theory and Methods
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
Elementary Surveying, 11e © 2006 Prentice-Hall, Inc.. 7/19
Leveling: Theory and MethodsDetermining Differences in Elevation
Differential leveling
Elementary Surveying, 11e © 2006 Prentice-Hall, Inc.. 8/19
Leveling: Theory and Methods
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.
Elementary Surveying, 11e © 2006 Prentice-Hall, Inc.. 9/19
Leveling: Theory and Methods
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
Elementary Surveying, 11e © 2006 Prentice-Hall, Inc.. 10/19
Leveling: Theory and Methods
Determining Differences in ElevationTrigonometric leveling (long lines)
Earth curvature and refraction must be considered.
∆elev = hi + V + (C - R) - r
Elementary Surveying, 11e © 2006 Prentice-Hall, Inc.. 11/19
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.
Elementary Surveying, 11e © 2006 Prentice-Hall, Inc.. 12/19
Telescopes
Leveling: Equipment for Differential Leveling
Elementary Surveying, 11e © 2006 Prentice-Hall, Inc.. 13/19
Leveling: Equipment for Differential Leveling
Level VialsTube-type level vialsBull’s-eye level vials
Tube-type level vials Bull’s-eye level vials
Elementary Surveying, 11e © 2006 Prentice-Hall, Inc.. 14/19
Leveling: Equipment for Differential Leveling
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.
Elementary Surveying, 11e © 2006 Prentice-Hall, Inc.. 15/19
TripodsLeveling instruments are all mounted on tripods.
Leveling: Equipment for Differential Leveling
Elementary Surveying, 11e © 2006 Prentice-Hall, Inc.. 16/19
Leveling: Equipment for Differential Leveling
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.
Elementary Surveying, 11e © 2006 Prentice-Hall, Inc.. 17/19
Leveling: Equipment for Differential Leveling
Level Rods (Staff)a) Philadelphia Rod (front)b) Philadelphia Rod (rear)c) Double faced leveling rodd) Lenker direct reading rod
Elementary Surveying, 11e © 2006 Prentice-Hall, Inc.. 18/19
Leveling: Equipment for Differential Leveling
Testing and Adjusting the Line of Sight
( ) ( ) ( ) ( )
2
:yields error)n (colimatio for Solvig22
ABAB
ABAB
RrrR
RrrR
+−−=
−−−=−−−
ε
εεεεε
Elementary Surveying, 11e © 2006 Prentice-Hall, Inc.. 19/19
Leveling: Equipment for Differential Leveling
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?
Elementary Surveying, 11e © 2006 Prentice-Hall, Inc.. 20/19
Leveling: Equipment for Differential Leveling
Examples:
Please solve Example 4.1, 4.2, and 4.3 in your text book.