EDM

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SURE 110 - Fundamentals of Surveying
Electronic Distance Measurement 1
ELECTRONIC
DISTANCE
MEASUREMENT
Robert Burtch
Surveying Engineering Department
Ferris State University
AGA Geodimeter
NASM-2A
INTRODUCTION
Introduced in 1950s – evolved into
total stations today
Types
Infrared or laser light – utilize transmitter
at one end and reflecting prism at other
Some are reflectorless
Long range – 10-20 km
Medium range – 3-10 km
Short range – 0.5-3 km
Microwave – utilize receiver/transmitter at
both ends of line
SURE 110 - Fundamentals of Surveying
Electronic Distance Measurement 2
PRINCIPLES
Wave – travels along x-axis at velocity
of 299,792.5 ± 0.4 km/s
Frequency – time taken for one
complete wavelength
Relationship:
λ = wavelength in meters
c = velocity, in km/s
f = frequency, in hertz (one cycle per
second)
f
c
λ =
PRINCIPLES OF
EDM
MEASUREMENT
SURE 110 - Fundamentals of Surveying
Electronic Distance Measurement 3
PRINCIPLES
Modulated wave
leaves EDM then
reflected back to
instrument –
measures double
distance (2L)
Partial wavelength
measured from phase
delay between
transmitted and
reflected
meters
2

L
ϕ +
=
• nλ whole number of
wavelengths
• φ partial wavelength
PRINCIPLES
EDM can send 3-4 modulated waves
at different frequencies
Find n by substituting these into
distance equation
Some EDM use pulsed laser emissions
Require to determine distance by
measuring travel time to and from EDM
SURE 110 - Fundamentals of Surveying
Electronic Distance Measurement 4
PRINCIPLES
Velocity of light affected by
Temperature
Atmospheric pressure
Water vapor content
Correction determined using
nomograph or automatically in
automatic processor by inputting
temperature and pressure
ATMOSPHERIC CORRECTION
Atmospheric
correction graph
SURE 110 - Fundamentals of Surveying
Electronic Distance Measurement 5
ATMOSPHERIC CORRECTION
Insignificant for short-wave light-wave EDM
Important for long range, especially microwave
+7 at 20°C
+17 at 45°C
-0.05 1 mm Hg Partial water
vapor
pressure
+0.4 +0.4 +1mm Hg Pressure
-1.25 -1.0 +1°C Temperature
Microwave Light Wave Error Parameter
Error (Parts per Million)
EDM INSTRUMENT
CHARACTERISTICS
Distance range – 800 – 1,000m with average
atmospheric conditions and single prism
Short-range can be extended to 1,300m with 3
prisms
Long-range can be extended to 15 km with 11
prisms
Accuracy range
Short-range ±(15 mm + 5 ppm)
Long-range ±(3 mm + 1 ppm)
Measuring time - 1.5
s
short-range, 3.5
s
long-
range
Accuracy and time reduced when in tracking mode
SURE 110 - Fundamentals of Surveying
Electronic Distance Measurement 6
EDM INSTRUMENT
CHARACTERISTICS
Slope reduction – manual or automatic
depending on model
Average of repeated measurements – available
on some models
Battery capability – 1,400 – 4,200
measurements depending on size of battery
and temperature
Temperature range - -20°C - +50°C
Nonprism measurements – available on some
models
Distances from 100 – 350 m
EDM Prisms
Reflect transmitted signal back to
EDM
Retrodirect capabilities
Mounted on tripod or attached to
prism pole
Forced centering capabilities
SURE 110 - Fundamentals of Surveying
Electronic Distance Measurement 7
EDM INSTRUMENT ACCURACIES
Given in terms of constant error and
proportional term based on distance
Most fall in range:
Both EDM instrument & prism
corrected for off-center location
Usually determined by manufacturer
±(3 mm + 1 ppm) to ±(10mm + 10 ppm)
GEOMETRY OF EDM
Using EDM when optical target and prism
at same height
HR V HI Elev Elev
A B
− ± + =
SURE 110 - Fundamentals of Surveying
Electronic Distance Measurement 8
GEOMETRY OF EDM
EDM instrument mounted on theodolite and target located
below prism
∆hi ∆HR X − =
From which,
S
α cos X
∆α sin =
EXAMPLE
EDM has slope distance AB of 561.276 m.
EDM instrument is 1.820 m above station
A, and the prism is 1.986 m above station
B. The EDM is mounted on a theodolite
whose optical center is 1.720 m above the
station. The theodolite measured a vertical
angle of +6º 21’ 38” to target on prism
pole; the target is 1.810 m above station B.
Compute both the horizontal distance AB
and elevation of station B given an
elevation at A of 186.275 m.
SURE 110 - Fundamentals of Surveying
Electronic Distance Measurement 9
Data given in following figures
( ) ( )
0.076m
1.720m 1.820m 1.810m 1.986m
∆hi ∆HR X
=
− − − =
− =
06" 22' 6 α α
" 28 α
561.276m
21'38" 6 cos m 076 . 0
S
α cos X
∆α sin
k
° = ∆ + = α
= ∆
°
= =
( ) m 813 . 557 " 06 ' 22 6 cos m 276 . 561
α cos S H
k
= ° =
=
( )( )
m 336 . 248
m 986 . 1 " 06 ' 22 6 sin m 276 . 561 m 820 . 1 m 275 . 186
HR V hi Elev Elev
A B
=
− ° + + =
− + + =

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