M e thod of li ne a r m easurement Indirect Measurement ...€¦ · theodolite Either: ... First...
Transcript of M e thod of li ne a r m easurement Indirect Measurement ...€¦ · theodolite Either: ... First...
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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
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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
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Temperature
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))((0000065.
/0000116.
/0000065.
))((
LTTC
C
Fk
LTTkC
st
st
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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
)(
s
PP
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
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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
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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
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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
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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.
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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.