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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