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189March 2011
CE 316
Horizontal Control Surveys
CHAPTER 6
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Angle, Bearings and Azimuths
Electronic Distance Measurement
Adjustments for use in plane surveying
Compass Surveys
Traverse Surveys
Triangulation and Trilateration
Accuracy
6.1 Introduction
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Units of Angle Measurement
Direction of turning (+)
Angular distance
R e f e r e n c e o r S
t a r t i n g L i n e
6.2 Angles, Bearings, and Azimuths
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221
1
2
2
2
1
2
1
4
8
12
441
48
1
2,
Area
Area
r
Area
r
Area A
Area
r
r
or
Spherical Excess ( ) [i.e. in excess of 180o
]
A
B Example
Calculate the spherical excess in surveying a right-triangle
with adjacent sides 20 miles long.
6.3 Adjustments for Use in Plane
Surveying
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The North American Datum of 1927 (NAD 27)
The horizontal control datum for North America that wasdefined by an azimuth on the Clarke 1866 ellipsoid with its
origin at Meades Ranch, Kansas.
f = 39o13’26.686” N
l
= 98o 32’ 30.506” W
NAD 1983
The result of the most recent adjustment
Based on GRS80 Ellipsoid
Compatible with GRS84
6.4 Horizontal Datums
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Magnetic Declination: The in which the compass
needle points is referred to as , and the angle
between magnetic north and the true north direction is called
magnetic declination, magnetic variation, or compass variation.
6.5 Compass Surveys
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Secular Variation: The magnetic declination
changes , and unpredictably with
time. This change is known to as secular variation.
Because of this, declination values shown on old
maps need to be updated if they are to be used
without large errors.
Annual VariationLocal Variation
Movement of
the MagneticNorth Pole
6.5 Compass Surveys
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If accurate declination values are needed, and if recent editions of the
charts are not available, up-to-date values for Canada may be obtained
from the most recent geomagnetic reference field models produced by
the Geological Survey of Canada. It is produced with numerous
observations of the magnetic field made on the ground, at sea, in the air,
and at satellite altitudes between 1960 and 1994. The latest CGRF is for
1995, but contains time terms that enable it to be used over the time
interval 1960 to 2000.
6.5.1 Canadian Geomagnetic Reference Field (CGRF)
6.5 Compass Surveys
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6.5.1 Canadian Geomagnetic Reference Field (CGRF)
6.5 Compass Surveys
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6.5.2 Compass Survey Application
Excerpt form field notes of the final survey of the bank of the Sacramento River
through Rancho Capay Josepa Sota by A.W. Von Schmidt, 18567 S.84
E. 0.87 Leave thick undergrowth,timber
scattering
8 S.79-3/4 E. 4.90
9 N.79-1/2 E. 4.24 To a cottonwood with 4 trunks.
Marked the south one, 54
inches diameter,
C.R.S.10.
10 S.81-1/2 E. 14.54 Enter thick undergrowth, bearsoff northeast.
11 S.71-1/4
E. 6.45 To a cottonwood 24 inches
diameter, marked “C.R.S.12”.
12 N.84-1/2 E. 3.12
13 South 2.10 Cross a slough 1 chain 50 links
wide, course southwest.
3.50
14 N.83-1/4 E. 25.00
Topographic Survey
Stadia Survey
6 7
8 9
10
N N
N
N N
N
N
11 12
13 14
6.5 Compass Surveys
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Surveyors Compass
Brunton
Compass
6.5.2 Compass Survey Application
6.5 Compass Surveys
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Traverse- a series of lines connecting successive established
points along the route of a survey
.
With stand alone EDM devices or theodolites, the traverse is donein two dimensions. With total station equipment, the traverse can
be done in three dimensions
Two general classes of traverses1) Open traverse
There is no way to check the values in this type of traverseand therefore should not be readily used.
2) Closed Traverse
A traverse that originates and terminates on a known point is
called a closed-loop traverse
6.6 Transverse Surveys
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6.6.1 Kinds of Horizontal Angles
interior angles [sum = (n-2)180
o
]angles to the right
deflection angles
BF
E
D
A
C
N
B
E
A
C
L(-)
R(+)
R(+)
6.6 Transverse Surveys
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6.6.2 Direction of Lines
Horizontal angle from reference line
astronomic
magnetic
assumed
6.6 Transverse Surveys
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6.6.3 Bearings
One system for designating direction
acute angle between reference meridian and line. ( N 46o E)
True - local astronomic (true) meridian
Magnetic -
Assumed - any adopted meridian Back bearings
B
A
C
S
Reference
Meridian
W E
N
o
o
o
6.6 Transverse Surveys
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Consists of the measurement of the angles of a series of overlappingtriangles, polygons, or quadrilaterals. The lines of this system that ties
together all triangulation stations at the vertices of the triangles. Thesesides vary in length from 5 to 160 km with an average of 25 km.
All angles are measured precisely. Instrumental errors are eitherremoved or predetermined and more rigorous procedures are employed to
reduce observational errors
6.7 Triangulation
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The scale of the network is controlled by measuring the lengths ofcertain lines called base l ines . the latitude, longitude and azimuth of one
point on the base line are found and from this, the latitude and longitude
of all points in the network can be computed.
Thus, figures must be geometrically strong and permit eachside to be calculated two ways (great care needed in selecting
stations).
6.7 Triangulation
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Strength of figure R is computed from the formula:
1222 10xC-D R
B
A B A
D
where:
D is the number of new direction observed in the figure (obtained by
inspection)
C is the number of independent mathematical conditions to besatisfied in the figure.
d are the common differences per second in log sin of the angles
opposite the side to be calculated.
6.7 Triangulation
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6.7 Triangulation
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6.7 Triangulation
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6.7.1 Simple Chain Triangulation
Used for lower order surveys
Simplest and quickest method.
6.7 Triangulation
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6.7.2 Polygon Triangulation
6.7 Triangulation
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6.7.3 Quadrilateral Triangulation
highest accuracy
6.7 Triangulation
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6.8 Trilateration
PELLY
FLAGSTAFF
GYPSY
CESSNA
50 KM
DUKE PARKER
INUK
HAMMER
SCOTT
B
C
A
Known Data
Length and azimuth of base line AB
Latitude and longitude of points A and B
Measured Data
Length of all triangle sides
Computed Data
Latitude and longitude of pointC and other new points
Length and azimuth of line AC
Length and azimuth betweenany two points
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6.8 Trilateration
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6.8 Trilateration
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6.8.1 Shoran Trilateration (1949-1957)
Continuous readings of the microwaves as the plane flies across aline connecting the two points. From which the distance between the
two points can be calculated.
2.5 million mi2 measured in Canada’s North were surveyed in thismanner to give 119 2nd order stations at average of 400 km spacing
Lines of 150 km to 500 km are used
Has an standard dev. of 7.3m ±16ppm for a single reading
6.8 Trilateration
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6.8.1 Shoran Trilateration (1949-1957)
6.8 Trilateration
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6.8.2 Aerodist Trilateration (1965-1973)
Similar to Shoran trilateration but the microwaves have a higherfrequency and a smaller wavelength (1/4 m)
Has an standard dev. of 1.0m ±8ppm for a single reading
This was used to create 185 1st order stations in Canada’s North
6.8 Trilateration
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A survey station of a network is classified according to whether the
semi-major axis of the 95 percent confidence region, with respect toother stations of the network, is less than or equal to: r = C (d+0.2).
Where:
r is in centimeters
d is distance in kilometers to any station
C is a factor assigned according to the order of survey.Order C
1st 2
2nd 5
3rd 12
4th 30
For a required order classification of the
connection between stations the semi-major
axis must be less than r = C (d + 0.2)
Computed position of
station relative to another
station d km away
Ellipse of 95%
confidence
6.9 Accuracy and Precision in
Horizontal Surveys
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6.10.1 Transit
Cross hair reticule
with capstan screws
Telescope bubble
Vertical Circle
Vertical tangent screws
Vernier “A” scale Upper clamp
Upper tangent screw
Threaded tripod plate
Focus knob
Vertical clamp
Standard Plate level
Vernier “B” Scale
Horizontal circle housing
Optical Plummet (n/a)
Levelling screws (4)
Sliding base
ENGINEERS
6.10 Horizontal Survey Equipment
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6.10.1 Transit
6.10 Horizontal Survey Equipment
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Cross hair reticule
with capstan screws
Eye piece focus
Vertical Circle
Vertical tangent screw
Optical vertical scale
Vertical Clamp
Upper tangent screw Telescope
Focus knob
Horizontal clamp
Rough horizontal adjustment
Optical Plummet
Levelling screws (3)
Automatic Vertical circle indexing
Wild T-3 0.2” Theodolite
6.10.2 Theodolite
6.10 Horizontal Survey Equipment
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Automatic vertical circle indexing Compensator and prism refer readings to direction of gravity
X-type(K&E)
Two plane-parallel plates that combine the two read-outs.
V-type (K&E)
Four hinged system of reduced pendulum length
Relatively insensitive to vibrations during observations.
Efficient air-damped system, composed of a piston and cylinder provides
excellent stabilizing characteristics.
Compensator is arrested when
the instrument is set for
horizontal readings.
6.10.2 Theodolite
6.10 Horizontal Survey Equipment
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Transit Adjustments
Vertical circle perpendicular to horizontal
B A C K
S I G H T
CLCR
“True” line
production
6.10.3 Transit Readings
6.10 Horizontal Survey Equipment
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6.10.4 Digital Theodolites
6.10 Horizontal Survey Equipment
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6.10.4 Digital Theodolites
6.10 Horizontal Survey Equipment
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AZIMUTH BY GYRO ATTACHMENT
Gyro motor suspended by a thin metal tape from one end of a sealed tube thatcan be mounted vertically on the standards of a theodolite
Tube, enclosure, gyro motor and suspension are so designed that, when theunit is attached to the horizontal axis of a leveled theodolite, the metal tape
holding the rotating gyro coincides with the vertical axis of the instrument and
also with the direction of gravity.
Gyro motor spinning at 22,000 rpm about this horizontal axis tries to maintain inspace its initial random spinning plane created by is moment of inertia.
The gyro, fixed to the instrument, which is earth-bound, is pulled out of its originalspinning plane by the .
This interference causes the gyro to oscillate around the plumb line until the spin
axis is oriented in the north-south plane and the rotation of the gyro correspond tothe rotation of the earth.
The gyro attachment is orientated on the instrument so that the gyro spin axisand the telescopic line of sight fall in the same vertical plane when the light mark
is centered on the index.
When this is achieved, the telescope is pointed orientated toward true or
north.
6.10.5 Gyro-Theodolites6.10 Horizontal Survey Equipment
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6.10.5 Gyro-Theodolites
6.10 Horizontal Survey Equipment
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Wild ZNL Zenith Nadar
Plummet (up/down)
GDF3 Tribrach
Std. Dev. For plumbing
4-direction
1:30,000
6.10.6 Optical Plummets
6.10 Horizontal Survey Equipment
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Wild ZL Automatic
Plummet (down version
for precise plumbing)
Two Pendulumcompensators working
at right angles to each
other.
Requires special
tribrach and tripod
Std. Dev. For plumbing
4-direction
±1:200,000
6.10.6 Optical Plummets
6.10 Horizontal Survey Equipment
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6.10.7 Targets
6.10 Horizontal Survey Equipment
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6.10.8 GDF3 Tribrach
6.10 Horizontal Survey Equipment
6 11 B h M k f H i t l
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6.11 Bench Marks for Horizontal
Control
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Measurements of accelerations over time
Done while instrument is carried from point to point
Acceleration and time measurements are taken independently inthree mutually orthogonal planes which are oriented:
3) direction of
gravity
1) north - south
2) east - west
6.12.1 Operating Principles of ISS
[Inertial Measurement Unit (IMU)]
6.12 Inertial Surveying Systems (ISS)
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Vertical accuracy approx.
0.15 to 0.5 m in 60 to 100 kmrespectively.
High cost - only suitablefor large projects
Fixed incremental
force increases
Diminishing
displacementincrements
Null
NullConstant
displacement
6.12.2 Mobile Leveling
6.12 Inertial Surveying Systems (ISS)
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LASER DEVICE FOR SEWER ALIGNMENT
6.13 Alignment Surveys
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Lieca Pipe Laser
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6.14.1 Introduction
Includes electro-optical (light) and electromagnetic (microwave) instruments.
Distance is computed based on the time taken for these waves to travel fromstation to station.
1st Generation (1950’s) Tellurometer used microwavesGeodimeter used light waves
6.14 Electronic Distance Measurement
MRA 1 MRA 2
Geodometer
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3rd Generationdevelopment of highlycoherent laser light.
4th GenerationTotal Stations
6.14 Electronic Distance Measurement
2nd Generation (1960’s) Miniturization of electronicsDevelopment of small light emittingdiodes (LED) that can operate on low
power.
TOPCON
GTS-2
Mekometer CA 1000
HP 3800
MA 100 1mm+/- 2ppm
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the prism is used to reflect the light source
emitted from the total station back to the instrument.
the accuracy of the measurement depends on precise alignment of:
1) the center of total station,
2) the prism center,
3) the plumbing and pivot point of the prism.
Ideally, the plumbing and pivot point and the prism center shouldcoincide to reduce error from not perfectly pointing the prism at the
total station.
6.14.2 Prism
6.14 Electronic Distance Measurement
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The plumbing and pivot point is thereference point that should belocated directly above the ground
mark and may be moved foreward or
back according to the prism centre.
The prism centre is the visualreference point as sighted from any
angle.
6.14.2 Prism
6.14 Electronic Distance Measurement
Plumbing and Pivotpoint
PrismCentre
Lines of
Sight
GPS Antena
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Ideal reflecting point provided by locating the plumbing and pivot
point at the prism centre (-40mm prism constant)
Prism centre and plumbing and
pivot point (-40 mm prism constant)
Error in pointing the prism
at the instrument 5o
Plumbing and pivot point
(-30mm prism constant
Line of site and ideal line
Instrument
6.14.2 Prism
6.14 Electronic Distance Measurement
Fog & clouds
Measurements not possible
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Magnitude of error at 100 m with zero prism constant
Prism Center
Plumbing and pivot point
Line of sight
error = 3.7 mm
Error in pointing the prism
at the instrument 5o
Ideal line
Line of site
Instrument
6.14.2 Prism
6.14 Electronic Distance Measurement
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6.14.2 Prism
6.14 Electronic Distance Measurement