INTRODUCTION INTRODUCTION to to LEVELING LEVELING By By Robert . Robert J.J. Mergel Mergel,, P.E., P.E., P.S P.S. July, July,2004 2004
Vertical Vertical Distances Distances
Leveling Leveling isis the the operation in operation in surveying surveying performed performed in in surveying surveying to to determine determine and establish and establish the the elevations of points, elevations of points, the the difference difference in in elevation elevation between between points, points, and and to to control control grades in construction grades in construction surveys. surveys.
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Vertical Vertical Distances Distances Results Results from from Leveling Leveling
Design Design highways, highways, railroads, railroads, canals, canals, sewers, sewers, water water supply systems, having grade lines that best supply systems, having grade lines that best conform conform to to existing existing topography topography Lay Lay out out construction construction projects projects according according to to planned elevations planned elevations Calculate Calculate volumes volumes of of earthwork earthwork Investigate drainage characteristics Investigate drainage characteristics Develop Develop maps maps showing showing general general ground ground configuration configuration Study Study earth earth subsidence subsidence & & crustal crustal motion motion
Vertical Vertical Distances Distances Uses Uses of of Leveling Leveling Longitudinal Longitudinal profiles profiles Cross -sections Cross-sections Contouring Contouring -- Topography Topography •• Topography Topography by by Grid Grid Method Method •• Topography Topography by by Radiating Radiating Lines Lines
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Vertical Vertical Distances Distances
The TheELEVATION ELEVATIONof ofaapoint pointisisits its distance distanceabove aboveor orbelow belowaalevel level reference referencesurface surfaceor orplane. plane. The common reference The common referencesurface surfacewas was established as part of the established as part of theNorth North American AmericanVertical VerticalDatum Datumof of1929 1929 (NAVD (NAVD29). 29). This Thisdatum datumplane planewas was superseded by the North American superseded by the North American Vertical VerticalDatum Datumof of1988 1988(NAVD (NAVD88). 88). Throughout the U.S. there are over Throughout the U.S. there are over 500,000 500,000benchmarks benchmarksincluded includedin inthe the NAVD 88. NAVD 88.
Vertical Vertical Distances Distances Elevation Elevation of of aa point point == distance distance above above or or below below aa level level reference reference surface surface Elevation Elevation==906.75 906.75MSL MSL 906.75’
Datum DatumPlane PlaneMean MeanSea SeaLevel Level Elevation = 0.00 Elevation = 0.00
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Vertical Vertical Distances Distances
True TrueLevel LevelLine Lineof ofSight Sight––isisaacurved curvedline line which whichisisparallel parallelto tothe thecurvature curvatureof ofthe theearth. earth. Source: , 1998 Bossler Source: Moffitt Moffitt& &Bossler, Bossler, 1998
Vertical Vertical Distances Distances Curvature Curvature and and Refraction Refraction 2 2 eq. 4-1) Curvature: Curvature: ccff == 0.667; 0.667; M M2== 0.0239 0.0239 FF2 ((eq. 4-1) 2 ccmm == 0.0785 0.0785 K K2 where: where: ccff in in ft, ft, M M in in miles, miles, FF in in 1000s 1000s of of ftft ccmm in in m, m, K K in in km km 2 2 eq. 4-2) Refraction: 0.093M2;;== 0.0033 0.0033 FF2 ((eq. 4-2) Refraction: R Rff == 0.093M 2 R 0.011 K K2 Rmm == 0.011 where: where: R Rff in in ft, ft, M M in in miles, miles, FF in in 1000s 1000s of of ftft R in m, m, K K in in km km Rmm in
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Vertical Vertical Distances Distances Combined hff,,hhmm)) Combined Curvature Curvature & & Refraction Refraction ((h ((eq. eq. 44-3) -3) hhff == 0.574 0.574 M M22 hhff == 0.0206 0.0206 FF22 hhmm == 0.0675 0.0675 K K22 where: where: hhff in in ft; ft; hhmm in in m m M M in in miles; miles; K K in in km; km; FF in in 1000s 1000s of of ftft
Vertical Vertical Distances Distances Differential Differential Leveling Leveling The The most most common common method method used by surveyors and used by surveyors and contractors contractors to to establish establish elevations is through elevations is through differential differential leveling. leveling. The The level level instrument instrument involves involves the the same same principle principle as a carpenter’s level as a carpenter’s level –– aa spirit spirit vial vial isis used used to to establish establish the line of sight parallel the line of sight parallel to to aa level level plane. plane.
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Vertical Vertical Distances Distances
Differential Differential leveling leveling uses uses an an instrument instrument called called aa “level” “level” and and aa level level rod rod (graduated (graduated pole) to determine pole) to determine the the elevation of new points elevation of new points (points (points whose whose elevation elevation are are unknown) unknown) in in relation relation to a bench mark to a bench mark (point (point of of known known elevation). elevation).
Vertical Vertical Distances Distances Differential Differential Leveling Leveling EQUIPMENT: EQUIPMENT: Optical OpticalLevels Levels Including Includingthe theDumpy Dumpy Level Leveland andthe theSelf Self Adjusting AdjustingLevel Level (Auto (AutoLevel), Level),and andthe the Level LevelRod. Rod. Digital Digital Levels Levelsare arenow now available. available. The TheLevel LevelRod Rodisis graduated in graduated inthe the same sameunits unitsas asthe the surveyors surveyorstapes. tapes.
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Vertical Vertical Distances Distances Differential Differential Leveling Leveling Precision Precision in in Leveling Leveling Increased Increased by by repeating repeating measurements measurements Making Making frequent frequent ties ties to to established established benchmarks benchmarks Using -quality instruments Using high high-quality instruments Keeping Keeping instruments instruments in in good good adjustment adjustment Performing Performing measurements measurements carefully carefully
Vertical Vertical Distances Distances A BENCH MARK is a permanent or semisemi-permanent point of known elevation. The physical characteristics of a bench mark varies significantly based on its intended purpose. Those set by National Geodetic Survey (NGS) and its forerunner U.S. Coast and Geodetic Survey (USC&GS) are 3” diameter metal discs set in concrete monuments (usually 36” deep) or in concrete bridge abutments or canal locks.
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Vertical Vertical Distances Distances BENCH MARK Cont. Other government agencies and even private companies set bench marks which can include railroad spikes driven into trees or utility poles, bolts on the tops of fire hydrants, or rims of manhole covers. These may or may not on a common reference datum and can in certain instances have an assumed elevation (e.g. elevation = 100.00’)
Vertical Vertical Distances Distances A LEVEL CIRCUIT is a systematic system of level observations for the purpose of establishing elevations of new bench marks.
B.M. 1 Existing
T.P.1
T.P. 2
B.M. 2 To Be Set
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Vertical Vertical Distances Distances
Known Elevation (B.M.)
Height of Instrument (H.I.) Level LevelInstrument Instrument
Back-sight Rod Reading (B.S.)
Level LevelRod Rod
BACKSIGHT (B.S.) is a sight observation (rod reading) taken on a point of known elevation to determine the height of instrument (H.I.) and usually entered in the second column of a set of level notes.
Vertical Vertical Distances Distances EXAMPLE EXAMPLE
Elevation 906.75’
Back-sight = 6.12
Height of Instrument = 912.87
HEIGHT OF INSTRUMENT (H.I.) is the elevation of the horizontal cross hair of the level, and is usually entered in the third column of a set of level notes and is determined by adding the backback-sight to the known elevation.
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Vertical Vertical Distances Distances
FORESIGHT FORESIGHT(F.S.) (F.S.)isisaasight sightobservation observationtaken takenon onan an unknown unknownpoint point for forthe thepurpose purposeof ofdetermining determiningits itselevation. elevation.
Fore-sight Rod Reading
Height of Instrument
Unknown Elevation
Vertical Vertical Distances Distances EXAMPLE EXAMPLE
Fore-sight = 7.11
Height of Instrument = 912.87
New Elevation = 905.76
The FORESIGHT subtracted from the HEIGHT OF INSTRUMENT to determine the elevation of a point and is usually entered in the fourth column of a set of level notes.
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Vertical Vertical Distances Distances
TURNING POINT (T.P.) is a temporary point whose elevation is determined during the process of leveling. It is determined by subtracting the FORESIGHT (F.S.) from the height of instrument.
Vertical Vertical Distances Distances Maximum MaximumHorizontal HorizontalDistance: Distance: The Themaximum maximumhorizontal horizontal distance between the instrument and the rod is usually distance between the instrument and the rod is usuallyless less than than300 300feet feet. . Level Instrument
Rod
D < 300’
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Vertical Vertical Distances Distances EXAMPLE: EXAMPLE: PUTTING PUTTINGIT ITALL ALLTOGETHER TOGETHER T.P.1
1 FS = 7.1
BS =
2 6.1 = BS
6 8.7
T.P. 2
=9 .04
6.89
B FS = 5.95
.45 S=8
FS
FS =
B.M. 1 Elev. 906.75
= Instrument Setup
.67 BS = 5
B.M. 2 To Be Set
Vertical Vertical Distances Distances Set Set up up the the standard standard field field table table for for entering entering leveling leveling field field notes. notes. Enter -sights and Enter the the back back-sights and the the foresights foresights in in the the appropriate appropriate column column and and row. row. Note Note that that the the back backsights sights and and the the foresights foresights go go on on the the row rowof of the the point point where the measurement (rod reading) is taken. where the measurement (rod reading) is taken. Sum -sights and Sum the the back back-sights and the the foresights. foresights. IF IF and and ONLY ONLY IF IF the the circuit circuit returns returns to to the the same same Bench Bench Mark, Mark, there there sums sums should should be be equal. equal.
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Vertical Vertical Distances Distances From From Previous Previous Example Example
BACKSIGHT (B.S.) is a sight observation (rod reading) taken on a point of known elevation to determine the height of instrument (H.I.) and usually entered in the second column of a set of level notes. HEIGHT OF INSTRUMENT (H.I.) is the elevation of the horizontal cross hair of the level, and is usually entered in the third column of a set of level notes and is determined by adding the back-sight to the known elevation.
Vertical Vertical Distances Distances Point
BS (+)
HI
FS (-)
BM 1
6.12
TP 1
8.76
7.11
BM 2 (TP)
5.67
6.89
TP 2
8.45
9.04
BM 1 SUMS
Elev 906.75
5.95 29.00
28.99
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Vertical Vertical Distances Distances Point
BS (+)
HI
BM 1
+6.12
= 912.87
TP 1
8.76
7.11
BM 2 (TP)
5.67
6.89
TP 2
8.45
9.04
BM 1 SUMS
FS (-)
Elev 906.75
5.95 29.00
28.99
Vertical Vertical Distances Distances The The FORESIGHT FORESIGHT subtracted subtracted from from the the HEIGHT HEIGHT OF OF INSTRUMENT INSTRUMENT to to determine determine the the ELEVATION ELEVATION of of aa point point and and isis usually usually entered entered in in the the fourth fourth column column of of aa set set of of level level notes. notes. The The ELEVATION ELEVATION of of the the point point isis entered entered in in the the fifth fifth column column on on the the same same row row as as the the point point name. name.
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Vertical Distances Distances Vertical Point
BS (+)
HI
BM 1
6.12
912.87
TP 1
8.76
- 7.11
BM 2 (TP)
5.67
6.89
TP 2
8.45
9.04
BM 1 SUMS
FS (-)
Elev 906.75 = 905.76
5.95 29.00
28.99
Vertical Vertical Distances Distances
The process is repeated until the ELEVATIONS of all of the points are determined. This includes the elevation of the original BENCH MARK. The difference in the beginning and ending BENCH MARK ELEVATION should be the same and the difference in the sums of the BACK-SIGHTS AND FORESIGHTS.
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Vertical Vertical Distances Distances Point
BS (+)
HI
BM 1
6.12
912.87
TP 1
8.76
914.72
7.11
905.76
BM 2 (TP)
5.67
913.30
6.89
907.63
TP 2
8.45
912.71
9.04
904.26
5.95
906.76
BM 1 SUMS
29.00
FS (-)
Elev 906.75
28.99
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