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Geodesy, GPS and GIS
Assist. Prof. Dr. Himmet KARAMAN
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Chaining
Electronic Distance Measurement
GPS and other space techniques
Distance Measurement
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Chaining
In many instances, it is easiest to simply measure the horizontaldistance by keeping both ends of the chain (steel tape) at the sameelevation. This is not difficult if there is not a big elevation change
between points.
When the difference in elevation along the measurement becomes toogreat for level chaining, other methods are called for. One option,
break chaining, involves simply breaking the measurement intotwo or more measurements that can be chained level. This works wellfor measurements along a gentle slope where a reasonable distancecan be measured between break chaining points.
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Electronic Distance
Measurement (EDM)INTRODUCTIONElectronic distance measurement instruments (EDMI) determine
lengths using phase changes that occur as electromagnetic energy
of known wavelength travels from one end of a line to the other
end and returns.
The first EDM instrument was developed in Sweeden in 1948,
which was called geodimeter (geodetic distance meter) based on amodulated light beam. The second one was designed in South
Africa in 1957, called tellurometer employs modulated
microwaves.4 Istanbul Technical University
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Modern EDMs display distances in digital form, and many have
microcomputers which calculate horizontal (DX & DY) and vertical
components (DH) of measured slope distances.
EDMs are now being incorporated with theodolites having automaticangle readout capabilities to create, so called total station
(electronic tacheometers). These systems are also called field-to-
inish systems. They can simultaneously and automatically measure
both distances and angles. They record field notes electronically and
transmit them to computers, plotters and other office equipment for
processing.
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CLASSIFICATION OF EDM INSTRUMENTS
They are mainly two types of EDM instruments:
Electro-optical instruments : They transmit light havingwavelengths in the range of 0.7 to 1.2 micrometers within or
slightly beyond the visible region of the spectrum.
Microwave instruments : They transmit microwaves with
frequencies in the range of 3 to 35 GHz corresponding to
wavelengths of about 1.0 to 8.6 millimeters.
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FUNDAMENTAL PRINCIPLE OF EDMI OPERATION
Electromagnetic energy propogates through to atmosphere in
accordance with the following equation:
V = f.
Where V is the velocity of electromagnetic energy, in meters per
second; f the modulated frequency of the energy, in hertz; and
the wavelength, in meters. This propogation can be represented by
the sinusoidal curve illustrated in the following figure, which
shows one wavelength or cycle . Portions of wavelengths or the
positions of points along the wavelength are given by phase
angles .
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FIG. A wavelength of electromagnetic energyillustrating phase angles
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The generalised procedure of measuring distance electronically is
shown in the following figure. An EDM device, centered by means oa plumb bob or optical plummet over station A, transmits to station
B a carrier signal of electromagnetic energy on which a reference
frequency has been superimposed or modulated . The signal isreturned from B to the receiver, so its travel path is double the slope
distance AB . In the following figure, the modulated electromagnetic
energy is represented by a series of sine waves, each having
wavelength .
EDM devices in surveying are operated by phase shift measurement.9 Istanbul Technical University
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A
B
SA,B, HORZ
SA,B, SLOPE
Z
Reflector
EDM
Instrument
Electromagnetic wave
Generalized EDM procedure10 Istanbul Technical University
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Prisms
The reflector, or prism, is a corner cube of glass in which thesides are perpendicular to a very close tolerance. It has the
characteristic that incident light is reflected parallel to itself,thus returning the beam to the source. This is called aretrodirective prism or retro reflector .
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These reflectors have a so-calledeffective center . The location of thecenter is not geometrically obvious
because light travels slower throughglass than air. The effective center will
be behind the prism itself and isgenerally not over the stationoccupied. Thus there is a reflector constant or prism constant to besubtracted from the measurement.Some manufacturers shift the center of the EDM forward the same amount asthe prism offset to yield a zeroconstant.
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ERRORS IN EDMsTotal error = Constant (+5 mm) + 5 ppm ppm = part per million ppb = part per billion
Constant error is negligible for long baselines, but is significant for short baselines. The proportional part varies depending on thedistance measured.
The errors in EDM can be summarised as follows:ersonal errors
inaccurate setups of EDMs and reflectors over stations.
faulty measurements of instrument and reflector heights. errors in determining atmospheric pressures andtemperatures (and humidity if microwaveinstruments are used).
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nstrumental errors
calibration.they become maladjusted from time to time, andgenerate errors in frequencies.
errors in reflectors (especially corner cube reflectors).constant offsets between electrical center and effectivecenter in both instruments and reflectors.
atural erros
atmospheric variations in temperature, pressure andhumidity.multiple refraction of signals ( ground swing ).
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FIG Reduction of EDM slope distance to horizontal
COMPUTATIONS HORIZONTAL LENGTHS FROMSLOPE DISTANCES
hr
he
elev A
elev BDatum
d
hr -he
S
L
B
A
t
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FIG. Correction for vertical offset between theodolite and EDMImounted on standards
v
Horizontal
Lv
m
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1. Reduction of short lines by elevation differences
d = (elev A + h e) - (elev B + h r ) S L d 2 2
2. Reduction of short lines by vertical angles
rad sec/ * Lcos )hh(
" t er 265206
3. Considerations for different theodolite mounts
rad sec/ * Lcosv m"
v 265206
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4. Reduction of long lines to horizontal
755
)(5.0
10
359474.0)068.08864.4
604.287(
2.27310..5026.1
2.27310..
1
''
)6609.03.237
57'
42
56
'
'
P t t E e
E
N
t e
t P N
n
t
t .(
GR
GR
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where
no : refractive index of light or microwaves(given bymanifacturer)P : pressure (measured)t : dry temperature (measured)t' : wet temperature (measured)e : partial pressure of water vapour (computed)E' : saturation pressure of water vapour (computed)
N GR : group refractive index (computed)n : refractive index in other conditions (computed)
Other parameters
D' : distance (measured)he : height of instrument (measured)ht : height of reflector (measured)HA : height of point A (known)HB : height of point B (known)R : earth radius of curvature (6373394 m)
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Computations
H 1 = H A+h e H 2 = H B+h t DH = H 2 - H 1
Velocity correction (K 1) K 1 = D' (n o-n)Corrected slope distance (D) D = D'+K o+K 1 (K o is
the zero constant)Distance on mean sea level (S)
= D / (R+H 1)
S R DH
D DH
22 1
22( cos( ))
Projection correction ( ds ) dsS
RY Y Y Y
A B A b 6 2
2 2( )
Distance on projection s = S+ds20 Istanbul Technical University
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EXAMPLE
Refractive index of the instrument n = 1.0003108Group refractive index N GR = 107.925Zero constant K o = 0.124 m.Height of instrument (tripot) h e = 0.320 m.Height of reflector h t = 0.450 m
R = 6373394 m.
Meteorological ObservationsInstrument Reflector Mean
Wet temperature 22 o.2 21 o.5 21 o.85Dry temperature 16 o.9 15 o.5 16 o.20Pressure 773.5 757.4 765.45
E' = 13.81589692, e = 13.81215662, n = 1.000279287Velocity correction (K 1) = D' (no-n)=0.232 m.Corrected slope distance (D) = D'+K o+K 1=7357.823
MeasuredLengths7357.473 467
465 474468 470462 470
472 467469 459468 463462
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Electro-optical EDM instruments
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Total Stations
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Total stations with data collectors
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Single Reflectors
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Multiple reflectors
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