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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(+)


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6.6.2 Direction of Lines

Horizontal angle from reference line

astronomic

magnetic

assumed


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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


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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


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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


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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


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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


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6.10.4 Digital Theodolites


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6.10.4 Digital Theodolites


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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


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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


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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


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6.10.7 Targets


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6.10.8 GDF3 Tribrach


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


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


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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


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


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


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6.14.2 Prism


ce 316 ch 6 6-03-3 student

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