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Stadia & EDM
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Stadia Principles
Stadia is a tachometric form of distancemeasurement that relies on a fixed-angle
intercept to optically measure the distancealong the site path.
Stadia is used on topographic surveys wherelimiting accuracy of 1/400 will be acceptable.
The transit cross-hair has in addition to thenormal cross hair two additional horizontalhairs.
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Stadia Principles
The distances can be determined simply bysighting a rod with the telescope level and
determining the rod interval.
D = 100S
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Stadia Principles
Elevation can be determined by stadia in themanner illustrated in figure 7.4
Elevation of station A () + hi RR =
elevation of point B (rod)
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Stadia Principles
Figure 7.4
Stadia Principles.
(a) Stadia hairs.
(b) Distancedetermination
(c) Elevationdetermination
(d) Angle
determination
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Inclined Stadia
Measurements 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 sighthad been perpendicular to the rod.
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Figure 7.5 illustrates the previous twoconsiderations. The value of hi and the
rod reading (RR) have been madeequal to clarify the sketch
Inclined Stadia
Measurements
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The geometric relationships are as follows: (1) S is the rodinterval, (2) S is the rod of angle when the line of sight isinclined by angle .
D = 100S (7.1) (Figure 7.4b)
S = S cos (7.3) (Figure 7.5)
D = 100S cos (7.4) [from eqs. (7.1) and (7.3)]
H = D cos (7.5) (Figure 7.5)
H = 100S cos2
(7.6) [from eqs. (7.4) and (7.5)]V = D sin (7.7) (Figure 7.5)
D = 100 S cos (7.4)
V = 100 S cos sin (7.8) [from eqs. (7.7) and (7.4)]
Inclined Stadia
Measurements
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Some theodolites will only read zenith angels(90-), making it necessary to modifyeqs.(7.6) and (7.8).
H=100S Sin**2(90-)V= 100S Sin(90-) cos(90-)
Equations (7.6) and (7.8) can be used incomputing the horizontal distance anddifference in elevation for any inclinedstadia measurement.
Inclined Stadia
Measurements
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Inclined Stadia Measurements
Figure 7.6 shows the general case of aninclined stadia measurement which can bestated as follows:
Elevation() station k= vRR= elevation(rod) point M (7.9)
The relationship is valid for every stadiameasurement. If the hi and RR are equal
Eq. (7.9) becomesElevation station K = V = elevation (rod)
point M (7.10)
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Examples of stadia Measurements
There are three basic variations to astandard stadia measurement:
1. The rod reading is taken to be thesame as the hi.
2. The rod reading is not the same as
the hi
3. The telescope is horizontal
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Precision of stadia Measurements
Normal field practice permits accuraterod 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 becomputed to the closest 1ft or 0.3m.
The maximum relative accuracy of1/300 to 1/400
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Precision of stadia Measurements
Consistent reasoning indicates thatdifferences in elevation (v) can be
realistically computed to the closest0.1ft or 0.03m
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Establishing control by stadia methods
Stadia method can be used to establishsecondary points or to establish closed
traverses that will be used for topographicstadia control
The double readings provide an increase inprecision which permits stations so
established to be used as control for furtherstadia work
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Establishing control by stadia methods
Figure 7.12 illustrates as extension ofprimary control to the secondary
control point K. With the transit at 0+ 40 a horizontal
angle is turned (and doubled) on topoint K.
The hi, VCR, and rod interval aredetermined in the usual manner.
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Electronic surveying measurement
Electronic distance measurement(EDM) first introduced in the 1950s
Current EDM instrument use infraredlight laser light or microwaves
See figure 7.1
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Electronic angel measurment
The electronic digital theodolite firstintroduced 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 instruments operating status andmanages built in surveying programs and a
data collector that stores and processesmeasurements and attribute data (totalstation)
Figure 7.2
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EDM Instrument characteristic
Expensive instrument have longerdistance ranges and higher precision
Distance range 800m to 1km
Short range EDM can be extended to1,300 m using 3 prism
Long range EDM can be extended to15 km using 11 prism
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EDM Instrument characteristics
Accuracy range +(-) (15mm +5ppm)For short-range 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)
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Prisms
Prisms are used with electro-optical EDMinstruments to reflect the transmitted signal(figure 7.3)
A single reflector is a cube corner prism thathas the characteristic to reflecting light raysprecisely back to the emitting EDMinstrument
The quality of the prism is determined bythe flatness of the surface and theperpendicularity of the 90 surface
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Prisms
Prisms can be tribrach-mounted on a tripod,centered by optical plummet or attached toa prism pole held vertical on a point with
the aid of a bulls-eye level In control surveys tribrach-mounted prisms
can be detached from their tribrachs andthe interchanged with theodolite
This interchangeability of prism andtheodolite speeds up the work because thetribrach mounted on the tripod is centeredand leveled only once
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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
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EDM instrument operation
2.Aim
The EDM is aimed at the prism by using either thebuilt-in sighting devices on the EDM
Telescope (yoke-mount EDMs) will have the opticalline of sight a bit lower than the electronic signal
When the cross hair is sight on target the electronicsignal will be maximized at the center of the prism
Set the electronic signal precisely on the prismcenter
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EDM instrument operation
3. Measure The slope measurement is accomplished by simply
pressing the measure button
The displays are either liquid crystal (LCD) or lightemitting 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 prismconstant corrections
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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 byall relevant atmospheric and instrumentalcorrection factors
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