m e thod of li ne a r m easurement indirect measurement

Chapter-2

Direct Measurement

Indirect Measurement

Method of linear measurement

Taping corrections

Optical measurement

Tachometry

EDM Measurement

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Methods

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There are 3 methods of making linear measurements.

1- Direct Method.

2- Optical Method.

3- E.D.M Method.

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Taping Corrections

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Incorrect length

Slope

Temperature

Sag

Stretch

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Slope

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Trigonometry

Horizontal: h = s*cos()

Calculation

s

v

hs

vC

hshshsv

hsC

2

))((

22

222

s

h

v

Slope Example

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If s = 300.00’

= 5°

h = 300 cos(5) = 298.86’

v = 300 sin(5) = 26.15’

If you had measured v = 26.15’

CS = v2/2S = 26.152/600.00 = 1.14’

h = v – CS = 300.00 – 1.14 = 298.86’

s

h

v

Temperature

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))((0000065.

/0000116.

/0000065.

))((

LTTC

C

Fk

LTTkC

st

st

Temperature Example

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Tape calibrated to 100.00’ at 68°F

Determine Dist AB = 368.50’ at 22°F

Calculate true distance

CT = .0000065(22-68)(368.50) = -0.11’

True Dist AB = 368.50 - 0.11 = 368.39’

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Sag and Tension

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2

2

2

32

2424 P

LW

P

LwCs

psiE

AE

LPPC

Steel

sp

000,000,29

)(

sPP

AEWP

204.0

If P = 18-lb, PS = 12-lb, L = 100’, A = 0.015 in2,

CP = (18–12)100/(0.015*29,000,000) = 0.0014’

W = 2.8, A = 0.015, PS = 12

Trial and error -> P = 31 lb

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Taping Precision

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1/2500 - Poor

1/5000 - Average

1/10,000 - Good

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Stadia is a tacheometric form of distance measurement that relies

on a fixed-angle intercept while tacheometry is the procedure

by which horizontal distances and difference in elevations are

determined indirectly using subtended intervals and angles

observed with a transit or theodolite on a graduated rod or scale.

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From the previous figure,

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Example: HORIZONTAL SIGHTS

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Solution:

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Inclined Stadia Sights

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Example: INCLINED SIGHTS

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Measuring an angle

Horizontal angles: use level,

transit, or theodolite

Vertical angle: use transit or

theodolite

Either:

- graduated circles

or

- digital readout

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Both: Principles of Surveying.

2nd ed. C. A. Herubin, 1978

Angles: readability

Horizontal & vertical circles

typically graduated to 1o for

construction grade

instruments, 5’ or better for

survey instruments

Vernier improves resolution

by 10x or better

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Digital readouts to 5”

or better

Principles of Surveying. 2nd ed. C. A. Herubin, 1978

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Electronic Distance Measurement

Optical: uses parallax.

Inexpensive but error

≥ 1%

Ultrasonic: mid-priced.

Accuracy ~ 0.1%

Laser: moderate to very

expensive. Accuracy 1 ppt or

better

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Measuring elevations

Known as “leveling”

Uses a level (optical or laser)

& a rod

All measurements are

relative (to a starting

elevation)

Height of instrument

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Optical vs. laser leveling

Optical leveling requires 2 workers

Laser leveling can be done alone,

but easiest when rod is equipped

with autodetector (high/low/on

signals)

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Top: Principles of Surveying. 2nd ed. C. A. Herubin, 1978

Bottom: Topcon web site

Putting it together

Two ways of mapping a region:

Traversing – used to locate

specific features

Triangulation – used to

establish a control network

over a region

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Both: Elements of Surveying.

U. S. Army, TM 5-232, 1971

Types of traverses

Allowable “misclosure”

First order, Class I:

- 4 mm in 1 km

- 127 mm in 1000 km

Third order:

- 12 mm in 1 km

- 380 mm in 1000 km

Land surveys: ???

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Both: Elements of Surveying.

U. S. Army, TM 5-232, 1971

The total station

Combines theodolite, EDM, data

logger & surveying software

Log ~ 8000 points, download data

to computer

Why doesn’t ES have one???

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Electronic Distance Measurement (EDM): is an instrument that transmits a carrier signal of electromagnetic energy from its position to a receiver located at another position Quick and precise measurements.

Save time and money

Automatically display direct readout measurements.

Mistakes are reduced

EDM instruments are combined with digital theodolites and microprocessors to produce total station instruments.

Precise taping is one of the most difficult and painstaking of all surveying tasks.

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Basic Instruments

An electronic distance-measuring devise

A reflector consists of several prisms mounted on a tripod

Measuring unit or

transmitter Reflector

From EDM

To EDM

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Types of EDMs Based on the wavelengths of the electromagnetic energy which they

transmit, there are two types of EDMs.

1. Electro-optical instruments: • transmit light in short wavelengths of about 0.4 to 1.2 µm.

(laser and infrared) • This light is visible or just above the visible (laser and infrared). • Almost all short-range EDMs for measuring up to a few miles

are of the infrared type. • Laser type are visible

2. Microwave instruments: • Transmit long wavelengths of about 10 to 100 µm. • The waves penetrate through fog or rain • More affected by humidity than are the light-wave instruments.

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Wavelength

a) Longer wavelength

b) Shorter wavelength

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Principles of electronic distance measurement

Distance are observed electronically by determine the

number of full and partial waves.

Knowing the precise length of the wave, the distance can be

determined.

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procedure for measuring

1. The EDM device is set up, centred , and levelled at one end of the line.

2. The prism assembly is placed at the other end of the line

3. The telescope is sighted toward the prism and the power is turned on.

4. The instrument transmits a signal to the reflector.

5. The reflector returns the signal to the receiver, so it its travel path is double the distance.

6. The EDM device determines the number of waves in the double path, multiplied by the wavelength, and divided by 2 to obtain the distance.

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Some fractional part of the wavelength would in general be expected, therefore the distance between the EDM instrument and reflector is expressed as:

2

pnL

Where L distance between the EDM and the reflector.

λ is the wave length

n is the number of full wavelength

p the length of the fractional part.

180o

90o

360o

270o 0o 135o

0.375λ

λ / 2

λ

One cycle

A wave length of electromagnetic energy illustrating phase angle

•The fractional length is determine by the EDM instrument from measurement

of phase angle of the returned signal.

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Example:

Assume that a wavelength is precisely 20.000m. Assume also

that the number of full waves is 9 and phase angle of the

returned signal is 115.7o determine the length of the

distance being measured.

2

pnL

Length p would be (115.7/360) x 20.000 =6.428 m

mL 214.93

2

428.6000.209

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Errors in the EDM measurements

1. Personal errors

Not Setting the instrument or reflector exactly over the point.

Not measuring the instrument height and weather conditions

perfectly.

2. Natural errors

Variation in temperature, humidity, and pressure.

For electro-optical instruments, correction for humidity can be

neglected.

Snow, fog, rain, and dust affect the visibility factor for EDMs.

3. Instrumental Errors

Very small if the equipment has been carefully adjusted and

calibrated.