Lecture 1A - Horizontal and Vertical Positioning
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Transcript of Lecture 1A - Horizontal and Vertical Positioning
7/23/2019 Lecture 1A - Horizontal and Vertical Positioning
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Review of Horizontal and Vertical
PositioningLecture 1
GE 12 – General Surveying II
Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12
–General Surveying II
7/23/2019 Lecture 1A - Horizontal and Vertical Positioning
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Objectives
By the end of the class, the students must be
able to:
– Recall survey operations for determining
horizontal positions.
– Recall the various levelling techniques for
determining vertical positions
Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12
–General Surveying II
7/23/2019 Lecture 1A - Horizontal and Vertical Positioning
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HORIZONTAL POSITIONING
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Survey Operations for Horizontal
Positioning
• Intersection
• Resection
• Traverse• Triangulation
• Trilateration
Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12
–General Surveying II
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Survey Operations –
LOCATION BY INTERSECTION
• Operation employed if the
coordinates are given for
two ends of a line and
directions are observedfrom each end of this line
to a third point not on the
line in order to calculate
the coordinates of thethird point.
5Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12
–General Surveying II
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Survey Operations – RESECTION
• Operation employed when angles between lines to threepoints of known position are observed from a point of
unknown position in order to calculate the coordinates of
the unknown point.
6Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12
–General Surveying II
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Survey Operations – TRIANGULATION
• Triangulation System - consists of a series of joined oroverlapping triangles in which an occasional line is measured
and the balance of the sides are calculated from angles
measured at the vertices of the triangles.
7Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12
–General Surveying II
7/23/2019 Lecture 1A - Horizontal and Vertical Positioning
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Survey Operations – TRILATERATION
• Trilateration System - also
consists also of a series of
joined or overlapping triangles
but the lengths of the triangle’s
sides are measured and few
directions or angles are
observed (only those required
to establish azimuth); same
idea as in triangulation.
Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12
–General Surveying II
7/23/2019 Lecture 1A - Horizontal and Vertical Positioning
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Survey Operations - TRAVERSE
• Consists of a series of straight lines connecting successive
points whose lengths and directions have been determined
from field observations.
• Currently the most common of several possible methods for
establishing a series or network of monuments with knownpositions on the ground.
• Procedures will vary depending on the type of field angles
measured and whether bearings or azimuths are used to
describe directions.
9Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12
–General Surveying II
7/23/2019 Lecture 1A - Horizontal and Vertical Positioning
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Closed Traverse
Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12
–General Surveying II
Closed Loop Traverse
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Survey Operations - TRAVERSE
Types of Traverse According to Method of Turning the Angles1. Interior-angle Traverse
2. Deflection-angle Traverse
3. Traverse by Angle to the Right
4. Azimuth Traverse
11Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12
–General Surveying II
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In dealing with a closed traverse, we have computations in:
1) Determining latitudes and departures
2) Calculating total error of closure
3) Balancing the survey
4) Determining adjusted positions of traverse stations
5) Area computation
6) Area subdivision
Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12
–General Surveying II
7/23/2019 Lecture 1A - Horizontal and Vertical Positioning
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Projection of a line onto a reference
meridian or North-South line
Lines with Northerly bearings (+) LAT
Lines with Southerly bearings (-) LAT
Equal to distance*cosine of bearing angle
Latitude = d*Cos b
Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12
–General Surveying II
7/23/2019 Lecture 1A - Horizontal and Vertical Positioning
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Projection of a line onto a reference parallel
or East-West line Lines with Easterly bearings (+) DEP
Lines with Westerly bearings (-) DEP
Equal to distance*sine of bearing angle
Departure = d*Sine b
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–General Surveying II
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Is usually a short line of unknown length and direction connecting the initial
and final traverse stations
22
)()( Lat Dep LEC
Lat
DepTan
Note:
In computing for , use the absolute values for Dep and Lat. Determinethe quadrant where the line lies using corresponding signs of the 2 sums.
Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12
–General Surveying II
7/23/2019 Lecture 1A - Horizontal and Vertical Positioning
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Ratio of the linear error of closure to the perimeteror total length of the traverse
D LEC REC
REC = Relative Error of Closure
LEC = Linear Error of Closure
D = Total Length or perimeter of the traverse
Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12–
General Surveying II
7/23/2019 Lecture 1A - Horizontal and Vertical Positioning
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D
d
C c Llat
Dd C c Ddep
clat = correction to latitude
cdep= correction to departure
CL= total closure in lat = Lat
CD= total closure in dep= Dep
d = length of any course
D = total length of the traverse
Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12–
General Surveying II
7/23/2019 Lecture 1A - Horizontal and Vertical Positioning
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Lat
C Lat c L
lat
)(
Dep
C Depc Ddep
)(
Where:
clat = correction to latitude
cdep= correction to departure
CL= total closure in lat = Lat
CD= total closure in dep= Dep
Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12–
General Surveying II
7/23/2019 Lecture 1A - Horizontal and Vertical Positioning
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Line Length(m)Azimuth
(from South)Line
Length
(m)
Azimuth from
(South)
AB 495.85 185o30’ DE 1020.87 347o35’
BC 850.62 226o02’ EF 1117.26 83o44’
CD 855.45 292o22’ FA 660.08 124o51’
Compute for:
1. Latitude and Departure of each line2. Bearing of the side error, LEC, REC
3. Adjust the traverse using Compass Rule
Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12–
General Surveying II
7/23/2019 Lecture 1A - Horizontal and Vertical Positioning
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1. Latitude and Departure of each line
Line Distance (m) BearingLat
(N+, S-)
Dep
(E+, W-)
AB 495.85 N 05
o
30' E +493.57 +47.53BC 850.62 N 46o02' E +590.53 +612.23
CD 855.45 S 67o38' E -325.53 +791.09
DE 1020.87 S 12o25' E -996.99 +219.51
EF 1117.26 S 83o
44' W -121.96 -1110.58FA 660.08 N 55o09' W +377.19 -541.70
=5000.13
Lat=+16.81
Dep=+18.08
Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12–
General Surveying II
7/23/2019 Lecture 1A - Horizontal and Vertical Positioning
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Bearing of the side error:
'0547
075550268.1
81.1608.18tan
0
b
b
Bearing of the side error is S 47o05’ W
2. Bearing of the side error, LEC, REC
Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12–
General Surveying II
7/23/2019 Lecture 1A - Horizontal and Vertical Positioning
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Linear Error of Closure (LEC):
687.24
)08.18()81.16( 22
LEC = 24.69 m
Relative Error of Closure (REC):
200
1
52.202
1
13.5000
69.24
say
REC = 1/200
2. Bearing of the side error, LEC, REC
Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12–
General Surveying II
7/23/2019 Lecture 1A - Horizontal and Vertical Positioning
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LineDistance
(m)Latitude Departure
Correction
(by Compass Rule) Lat_adj Dep_lat
Lat
Dep
AB 495.85 493.57 47.53 -1.667 -1.793 491.903 45.737
BC 850.62 590.53 612.23 -2.860 -3.076 587.670 609.154
CD 855.45 -325.53 791.09 -2.876 -3.093 -328.406 787.997
DE 1020.87 -996.99 219.51 -3.432 -3.691 -1000.422 215.819
EF 1117.26 -121.96 -1110.58 -3.756 -4.040 -125.716 -1114.620
FA 660.08 377.19 -541.7 -2.219 -2.387 374.971 -544.087
Sum: 5000.13 16.81 18.08 -16.810 -18.080 0.000 0.000
3. Traverse Adjustment by Compass Rule
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3. Traverse Adjustment by Compass Rule
Line
Adjusted Values (By Compass Rule)
Latitude DepartureDistance
(m)Bearing
Azimuth (from
South)
AB 491.903 45.737 494.025 N 5
o
19' E 185
o
19'
BC 587.670 609.154 846.419 N 46o02' E 226o02'
CD -328.406 787.997 853.692 S 67o23' E 292o37'
DE -1000.422 215.819 1023.436 S 12o
10' E 347o
50'
EF -125.716 -1114.620 1121.687 S 83o34' W 83o34'
FA 374.971 -544.087 660.783 N 55o26' W 124o34'
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Line Lat Dep |Lat| |Dep|
Correction by
Transit RuleAdjusted Lat/Dep
Lat
Dep Lat_adj Dep_adj
AB 493.57 47.53 493.57 47.53 -2.855 -0.259 490.715 47.271
BC 590.53 612.23 590.53 612.23 -3.416 -3.331 587.114 608.899
CD -325.53 791.09 325.53 791.09 -1.883 -4.305 -327.413 786.785
DE -996.99 219.51 996.99 219.51 -5.768 -1.194 -1002.758 218.316
EF -121.96 -1110.58 121.96 1110.58 -0.706 -6.043 -122.666 -1116.623
FA 377.19 -541.7 377.19 541.70 -2.182 -2.948 375.008 -544.648
Sum: 16.81 18.08 2905.77 3322.64 -16.810 -18.080 0.000 0.000
4. Traverse Adjustment by Transit Rule
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Line
Adjusted Values (By Transit Rule)
Latitude Departure Distance
(m)
Bearing Azimuth (from
South)
AB 490.715 47.271 492.987 N 5o30' E 185o30'
BC 587.114 608.899 845.849 N 46o03' E 226o03'
CD -327.413 786.785 852.191 S 67o24' E 292o36'
DE -1002.758 218.316 1026.248 S 12o17' E 347o43'
EF -122.666 -1116.623 1123.340 S 83o44' W 83o44'
FA 375.008 -544.648 661.266 N 55o27' W 124o33'
4. Traverse Adjustment by Transit Rule
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VERTICAL POSITIONING
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Leveling
Operation of measuring vertical distances,either directly or indirectly, to determine theelevation of points or their differences in
elevation.
Used for topographic mapping, suitabilityanalysis, and design, layout and construction of
structures to best conform to the configurationof the ground.
Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12–
General Surveying II
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Level Surface
Vertical Line
Horizontal Line
Elevation
Mean Sea Level (MSL)
(Vertical Datum)
Diff in Elev.
(Level Line)
Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12–
General Surveying II
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Orthometric
Height (H)
Ellipsoidal
Height (h)
Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12–
General Surveying II 30
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Terms
Mean Sea Level - arithmetic mean of water elevations over a
specific 19-year cycle; close approximation of the Geoid;
conforms to the earth’s gravitational field
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General Surveying II 31
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Bench Mark (B.M.) - a definite point on an object, the elevation
and location of which are known; serves as point of
reference for levels; may be permanent (P.B.M.) or
temporary (T.B.M.)
Terms
Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12
–General Surveying II
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Terms
Set-up - consists of a point supporting a backsight rod, a point supporting the
foresight rod, and a leveling instrument positioned between them
Section - an unbroken series of set-ups, made between two (2) permanent
control points.
Level Loop / Circuit - a line of levels that ends at the same point of its beginning
Level Network - consists of a number of intersecting lines of levels that are tied
into known benchmarks
Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12
–General Surveying II 33
e c t i o n
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B.M.
T.P. 1
T.P. 2 B .
S . B
. S .
F.S.
F.S.
Terms
Turning point - a fixed point or object, often temporary in character,
between two bench marks upon which foresight and backsight rod
readings are taken; a B.M. may be used as a T.P.
Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12
–General Surveying II
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Backsight (B.S.) - a rod reading taken on a point of known elevation (BM or TP)usually taken with the level sighting back along the line
Backsight distance - horizontal distance from level to rod on a B.S.
Terms
B.M.
T.P. 1
T.P. 2 B .
S .
B . S .
F.S.
F.S.
Backsight
Distance
Backsight
Distance
Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12
–General Surveying II
7/23/2019 Lecture 1A - Horizontal and Vertical Positioning
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Foresight (F.S.) - a rod reading taken on a point of unknown elevationForesight distance - horizontal distance from level to rod on a F.S.
Intermediate Foresight (I.F.S.) - other staff reading between the backsight and
foresight in the same set-up of the instrument.
Terms
B.M.
T.P. 1
T.P. 2 B .
S .
B . S .
F.S.
F.S.
Foresight
Distance
Foresight
Distance
Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12
–General Surveying II
7/23/2019 Lecture 1A - Horizontal and Vertical Positioning
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B.M.
T.P. 1T.P. 2 B
. S .
B .
S .
F.S.
F.S.
Datum
H.I.1
H.I.2
Terms
Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12
–General Surveying II
Height of the instrument (H.I.) - elevation of the line of sight of the telescope
above the datum when the instrument is leveled
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Basic Equation in Leveling
Elev B = Elev A + BS - FS
STA. B.S. H.I. F.S ELEV.
BM1 8.46 755.11
763.57
TP1 1.23 762.34
Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12
–General Surveying II 38
Known Elev + BS = HI
HI – FS = New Elev
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Sample Computation – Differential Leveling
PROCEDURES:
1. A line of levels is run from BM A to BMB
2. Leveling instrument is set-up at any convenient
location along the level route and backsight is taken on
a rod held vertically on BM A.
3. The rodman moves forward along the general direction
of BMB and hold the rod at a convenient turning point
(TP1). (Making sure that the backsight distance is
approximately equal to the foresight distance.)
4. Then, the level is transferred again and a backsight is
taken at (TP1) and foresight at (TP2). Repeat
procedures until foresight is taken on BMB.Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12
–General Surveying II
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Sample Computation – Differential Leveling
MSL
Line of Sight
H.I.
BS
FS
ELEV BM1
BM1
TP1
H.I. = ELEVBM1 + BS
Elevi = H.I. - F.S.
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–General Surveying II
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Sta. B.S. H.I F.S. Elev
B.M. 1 3.251 ________ 72.105
T.P.1 2.539 ________ 0.012 ______
T.P.2 3.572 ________ 0.338 ______
B.M.2 0.933 ________ 3.112 ______
T.P.3 0.317 ________ 3.306 ______
T.P.4 0.835 ________ 2.716 ______
T.P.5 0.247 ________ 3.542 ______
B.M.3 3.786 ______
75.356
H.I. = B.S. + ElevBM
Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12
–General Surveying II
Sample Computation – Differential Leveling
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Sta. B.S. H.I F.S. Elev
B.M. 1 3.251 ________ 72.105
T.P.1 2.539 ________ 0.012 ______
T.P.2 3.572 ________ 0.338 ______
B.M.2 0.933 ________ 3.112 ______
T.P.3 0.317 ________ 3.306 ______
T.P.4 0.835 ________ 2.716 ______
T.P.5 0.247 ________ 3.542 ______
B.M.3 3.786 ______
75.356
Elevi= H.I. - F.S.
75.344
Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12
–General Surveying II
Sample Computation – Differential Leveling
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Sta. B.S. H.I F.S. Elev
B.M. 1 3.251 ________ 72.105
T.P.1 2.539 ________ 0.012 ______
T.P.2 3.572 ________ 0.338 ______
B.M.2 0.933 ________ 3.112 ______
T.P.3 0.317 ________ 3.306 ______
T.P.4 0.835 ________ 2.716 ______
T.P.5 0.247 ________ 3.542 ______
B.M.3 3.786 ______
75.356
77.883
81.117
78.938
75.949
74.068
70.773
75.344
77.545
78.005
75.632
73.233
70.526
66.987
Arithmetic Check:
BM1elev 72.105
+ +
∑ B.S. 11.694- -
∑ F.S. 16.812
= _______
BM3elev 66.987
H.I. = B.S. + ElevBM Elev
i= H.I. - F.S.
OK!∑ B.S. = 11.694 ∑ F.S. = 16.812
Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12
–General Surveying II
Sample Computation – Differential Leveling
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Personal Errors – Unequal Backsight & Foresight Distances
Sources of Errors in Leveling
Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12
–General Surveying II
Ghilani, et. al.
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Errors due to the Curvature of the Earth
Sources of Errors in Leveling
Department of Geodetic EngineeringTraining Center for Applied Geodesy and Photogrammetry GE 12
–General Surveying II
http://www.oregon.gov/ODOT/HWY/GEOMETRONICS/docs/Leveling_Errors.pdf
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• When a line of level makes a complete circuit, almost invariably the
BMelevinitial ≠ Bmelevfinal
• This difference is the error of running the circuit and is called the Error
of Closure.
• Result intermediate BMs are also in error
• Problems:
Determining the error for intermediate points
Adjusting their corresponding elevations
Error of Closure
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• The 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 BM
d = distance of a BM from the point of beginning
L = length of the circuit
EC = error of closure of the level circuit = Elevobserved - Elevtheoretical
Corrections to the Observed Elevations
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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
Solve for the adjusted
elevations of the intermediate
points based on the given
leveling data on the table.
Sample Problem:
Corrections to the Observed Elevations
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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 m
1.78 km
Corrections to the Observed Elevations
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Methods in Leveling
1. Direct or Spirit Leveling (Differential, Double Rod, Three Wire)
2. Indirect or Trigonometric Leveling
3. Reciprocal Leveling
4. Stadia Leveling
5. Barometric Leveling6. Profile Leveling
7. Borrow-Pit Leveling
8. Gravimetric Leveling
9. Inertial Positioning System
10. GPS Survey
Department of Geodetic Engineering
Training Center for Applied Geodesy and Photogrammetry GE 12–
General Surveying II 50
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• The operation of determining the elevation ofpoints some distance apart by a series of set-ups of a leveling instrument along a designatedroute.
• Measure vertical distances directly
• Most precise method of determining elevations
• Forms of direct leveling include:
• Differential, Double Rod and Three Wire Leveling
Methods in Leveling – Direct/Spirit
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Training Center for Applied Geodesy and Photogrammetry GE 12–
General Surveying II
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Methods in Leveling – Differential
• Requires a series of set ups of the instrument along the general
route and, for each set up, a rod reading back to a point of known
elevation and forward to a point of unknown elevation.
• Determining the elevation of points some distance apart.
• CHECKS:
1. Rerunning levels on the same route
2. “Tying on” to a previously established BM near the end of the
level line3. Returning to the initial BM level loop
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General Surveying II 52
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Methods in Leveling – Differential
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General Surveying II 53
Note: effect of earth’s curvature and refraction is reduced to negligible amount
BM1
BM2
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Methods in Leveling – Differential
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General Surveying II 54
BM1
(known)
TP1
TP2 BM2
(known)
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Methods in Leveling – Differential
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General Surveying II 55
Sta. B.S. H.I F.S. Elev
B.M. 1 3.251 ________ 72.105
T.P.1 2.539 ________ 0.012 ______
T.P.2 3.572 ________ 0.338 ______ B.M.2 0.933 ________ 3.112 ______
T.P.3 0.317 ________ 3.306 ______
T.P.4 0.835 ________ 2.716 ______
T.P.5 0.247 ________ 3.542 ______
B.M.3 3.786 ______
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LEVELS FOR BENCHMARKS ALONG RIDGE ROAD
Sta. B.S. H.I F.S. Elev
B.M. 1 3.251 75.356 72.105
T.P.1 2.539 77.883 0.012 75.344
T.P.2 3.572 81.117 0.338 77.545
B.M.2 0.933 78.938 3.112 78.005
T.P.3 0.317 75.949 3.306 75.632
T.P.4 0.835 74.068 2.716 73.233
T.P.5 0.247 70.773 3.542 70.526
B.M.3 3.786 66.987 [ 66.980]
∑ B.S.= 11.694 ∑ F.S.= - 16.812
11.694
B.M. 1 72.105 - 5.118 66.987
Error of Closure = 66.987-66.980 = +0.007 m
Methods in Leveling – Differential
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Department of Geodetic Engineering
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General Surveying II 57
Methods in Leveling – Double Rod
BM1
(known)
TP1 H
TP1 L
TP2 H
TP2 L
BM2
(unknown)
Methods in Leveling–
Double
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TRAINING CENTER FOR APPLIED GEODESY AND PHOTOGRAMMETRY
COLLEGE OF ENGINEERING, UNIVERSITY OF THE PHILIPPINES, DILIMAN
Arithmetic Check:
Mean Elev BM = 149.246
(149.149 + 149.343)/2
∑BS = +19.838
∑FS = - 15.126
Sum = (+ 4.714)/2 = + 2.356
Elev BMA = + 146.890
Sum/2 = + 2.356
BMB elev = + 149.246
Methods in Leveling –
DoubleRod
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General Surveying II 59
Methods in Leveling – Three Wire
Ghilani, et. al.
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Department of Geodetic Engineering
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Methods in Leveling – Three Wire
(Homework)
BACKSIGHT FORESIGHT
STA. HAIR RDGS MEAN RDG s H.I. F.S. MEAN RDG s ELEV.
BM1
1.152 ________ ________ ________
________ ________ 444.2420.935
0.718
TP1
2.784
________ ________ ________
1.117
________ ________ ________ 2.420 0.899
2.057 0.682
TP2
1.713
________ ________ ________
1.900
________ ________ ________ 1.440 1.537
1.166 1.172
BM2
1.450
________ ________ ________ 1.177
0.904
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Methods in Leveling – Trigonometric
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Methods in Leveling – Reciprocal
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• Trigonometric + Direct leveling
• Vertical distances are determined by tacheometry by using transit
and level rod.
• Process of taking stadia measurements consists of observing,
through the telescope, the apparent locations of the two stadiahairs, which is held in a vertical position.
Methods in Leveling – Stadia
Department of Geodetic Engineering
Training Center for Applied Geodesy and Photogrammetry GE 12–
General Surveying II
BACKSIGHT FORESIGHT
STA. INTERVAL
VERT.
ANGLE ROD RDG VD INTERVAL
VERT.
ANGLE
ROD
RDG VD ΔELEV ELEV
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Methods in Leveling – Stadia
Department of Geodetic Engineering
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General Surveying II
a
V
H = Ks cos2α + C cos α
V = ½ Ks sin2α + C sin α
K = (f/i) = stadia interval factor
C = f + c = stadia constant
s = stadia intervalα = vertical angle
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• Operation of determining elevations of points at short measured
intervals along a definitely located line, such as the center line for a
highway, railroad, canal or a sewer. (usually by direct leveling)
• Stakes or other marks are placed at regular intervals along the line;
the intervals between stakes usually is 100m, 50m, 20m and 10m.
Methods in Leveling – Profile
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Training Center for Applied Geodesy and Photogrammetry GE 12–
General Surveying II
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Methods in Leveling – Profile
Department of Geodetic Engineering
Training Center for Applied Geodesy and Photogrammetry GE 12–
General Surveying II
Ghilani, et.al.
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Methods in Leveling – Profile
Department of Geodetic Engineering
Training Center for Applied Geodesy and Photogrammetry GE 12–
General Surveying II
Ghilani, et.al.
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Methods in Leveling – Profile
Department of Geodetic Engineering
Training Center for Applied Geodesy and Photogrammetry GE 12–
General Surveying II
STA. B.S. H.I F.S. I.F.S ELEV.
BM 30 3.478 33.478 30.000
0 + 00 3.617
0 + 05 5.141
+ 10 1.720
TP 1 3.314 0.913
+ 20 2.860
+ 29.5 1.852
+ 30 1.805
TP 3 0.081 2.289
TP 4 0.333 3.661
BM 30 1.974
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References
Davis, R.E., et. al (1981). Surveying: Theory and Practice. USA: McGraw-Hill, Inc.
Ghilani, C.D., et.al. (2008). Elementary Surveying: an Introduction to Geomatics. USA:Pearson Education, Inc.
La Putt, J.P. (2007). Elementary Surveying. Philippines: National Book Store.
Schofield, W.. Et. Al (2007). Engineering Surveying. UK: Elsevier Ltd.
Anderson, James & E. Mikhail (1998), Surveying: Theory and Practice 7th Edition,McGraw-Hill Companies, Inc.
• GE 10 Leveling Principles and Operations/ Leveling Errors and Adjustments LectureNotes prepared by Engr. Jeark A. Principe.
* GE 10 Triangulation and Trilateration Lecture Notes prepared by Engr. Jeark A.Principe.