Stadia & EDM
Stadia Principles
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Stadia is a tachometric form of distance
measurement that relies on a fixed-angle
intercept to optically measure the distance
along the site path.
Stadia is used on topographic surveys where
limiting accuracy of 1/400 will be acceptable.
The transit cross-hair has in addition to the
normal cross hair two additional horizontal
hairs.
Stadia Principles

The distances can be determined simply by
sighting a rod with the telescope level and
determining the rod interval.
D = 100S
Stadia Principles
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Elevation can be determined by stadia in the
manner illustrated in figure 7.4
Elevation of station A (Λ) + hi – RR =
elevation of point B (rod)
Stadia Principles
Figure 7.4
Stadia Principles.
(a) Stadia hairs.
(b) Distance
determination
(c) Elevation
determination
(d) Angle
determination
Inclined Stadia
Measurements
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The distance from the instrument to
the rod must be reduced from slope to
horizontal
The rod interval of a sloped sighting
must be reduced to what the interval
would have been if the line of sight
had been perpendicular to the rod.
Inclined Stadia
Measurements
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Figure 7.5 illustrates the previous two
considerations. The value of hi and the
rod reading (RR) have been made
equal to clarify the sketch
Inclined Stadia
Measurements
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The geometric relationships are as follows: (1) S is the rod
interval, (2) S’ is the rod of angle when the line of sight is
inclined by angle θ.
D = 100S
S = S’ cos θ
D = 100S’ cos θ
H = D cos θ
H = 100S’ cos2 θ
V = D sin θ
D = 100 S’ cos θ
V = 100 S’ cosθ sinθ
(7.1)
(7.3)
(7.4)
(7.5)
(7.6)
(7.7)
(7.4)
(7.8)
(Figure 7.4b)
(Figure 7.5)
[from eqs. (7.1) and (7.3)]
(Figure 7.5)
[from eqs. (7.4) and (7.5)]
(Figure 7.5)
[from eqs. (7.7) and (7.4)]
Inclined Stadia
Measurements
Some theodolites will only read zenith angels
(90-θ), making it necessary to modify
eqs.(7.6) and (7.8).
H=100S’ Sin**2(90-θ)
V= 100S’ Sin(90-θ) cos(90-θ)
Equations (7.6) and (7.8) can be used in
computing the horizontal distance and
difference in elevation for any inclined stadia
measurement.
Inclined Stadia Measurements
FIGUER 7.5
Inclined Stadia Measurements
Figure 7.6 shows the general case of an
inclined stadia measurement which can be
stated as follows:
 Elevation(Λ) station k= v –RR= elevation
(rod) point M (7.9)
 The relationship is valid for every stadia
measurement. If the hi and RR are equal
Eq. (7.9) becomes
Elevation Λ station K = V = elevation (rod)
point M (7.10)
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Examples of stadia Measurements
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1.
2.
3.
There are three basic variations to a
standard stadia measurement:
The rod reading is taken to be the
same as the hi.
The rod reading is not the same as
the hi
The telescope is horizontal
Precision of stadia Measurements
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Normal field practice permits accurate
rod reading of 0.01 ft or 0.003 m for
distance of 300ft or 100m.
If rod intervals are read accordingly
,horizontal distances (100s) can be
computed to the closest 1ft or 0.3m.
The maximum relative accuracy of
1/300 to 1/400
Precision of stadia Measurements
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Consistent reasoning indicates that
differences in elevation (v) can be
realistically computed to the closest
0.1ft or 0.03m
Establishing control by stadia methods
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Stadia method can be used to establish
secondary points or to establish closed
traverses that will be used for topographic
stadia control
The double readings provide an increase in
precision which permits stations so
established to be used as control for further
stadia work
Establishing control by stadia methods
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Figure 7.12 illustrates as extension of
primary control to the secondary
control point K.
With the transit at 0+ 40 a horizontal
angle is turned (and doubled) on to
point K.
The hi, VCR, and rod interval are
determined in the usual manner.
Electronic surveying measurement
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Electronic distance measurement
(EDM) first introduced in the 1950s
Current EDM instrument use infrared
light laser light or microwaves
See figure 7.1
Electronic angel measurment
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The electronic digital theodolite first
introduced in the late 1960s
When the electronic theodolite is used with
built in EDM or an add on interfaced EDM
A microprocessor automatically monitors in
the instrument’s operating status and
manages built in surveying programs and a
data collector that stores and processes
measurements and attribute data (total
station)
Figure 7.2
EDM Instrument characteristic
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Expensive instrument have longer
distance ranges and higher precision
Distance range 800m to 1km
Short range EDM can be extended to
1,300 m using 3 prism
Long range EDM can be extended to
15 km using 11 prism
EDM Instrument characteristics
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Accuracy range +(-) (15mm +5ppm)For shortrange EDM
+(-) (3mm+1ppm) for long – range EDM
Slope reaction manual or automatic
Average of repeated measurements available on
some models
Battery capability 1,400 to 4,200 measurements
Temperature range -20c to +50c
Nonprism ,measurements available on some models
distances from 100 to 350 m (3 to 5 km with prism)
Prisms
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Prisms are used with electro-optical EDM
instruments to reflect the transmitted signal
(figure 7.3)
A single reflector is a cube corner prism that
has the characteristic to reflecting light rays
precisely back to the emitting EDM
instrument
The quality of the prism is determined by
the flatness of the surface and the
perpendicularity of the 90˚ surface
Prisms
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Prisms can be tribrach-mounted on a tripod,
centered by optical plummet or attached to
a prism pole held vertical on a point with
the aid of a bull’s-eye level
In control surveys tribrach-mounted prisms
can be detached from their tribrachs and
the interchanged with theodolite
This interchangeability of prism and
theodolite speeds up the work because the
tribrach mounted on the tripod is centered
and leveled only once
EDM instrument operation
1.Set up
 EDM instruments are inserted in to the
tribrach
 Set over the point by means of the optical
plummet
 Prisms are set over the remote station point
 The EDM turned on
 The height of the prism and the EDM should
me measured
EDM instrument operation
2.Aim
 The EDM is aimed at the prism by using either the
built-in sighting devices on the EDM
 Telescope (yoke-mount EDMs) will have the optical
line of sight a bit lower than the electronic signal
 When the cross hair is sight on target the electronic
signal will be maximized at the center of the prism
 Set the electronic signal precisely on the prism
center
EDM instrument operation
3. Measure
 The slope measurement is accomplished by simply
pressing the measure button
 The displays are either liquid crystal (LCD) or light
emitting diode (LED)
 The measurements is shown in two decimals of a
foot or three decimals of a meter
 EDM with built in calculators can now be used to
compute horizontal and vertical distances,
coordinate, atmosphiric,curveture and prism
constant corrections
EDM instrument operation
4. Record
 The measured data can be recorded in the
field note format
 Can be entered manually into electronic
data collector
 The distance data must be accompanied by
all relevant atmospheric and instrumental
correction factors