tacheometry (2)
TRANSCRIPT
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GEOMATICS ENGINEERING
TACHEOMETRY
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What is tacheometry??
Easy and cheap method of collecting muchtopographic data.
Tachymetry (or tacheometry) also calledstadia surveying in countries likeEngland and the United States
means fast measurement; rapid andefficient way of indirectly measuring
distances and elevation differences
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Figure 1 shows the set-up of a tachymetric measurement.
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Stadia System
The theodolite/auto level is directed atthe level staff
the distance is measured by reading thetop and bottom stadia hairs on thetelescope view.
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Measurement
Electronic Tacheometry: Uses a total station which contains an
EDM, able to read distance by reflecting off
a prism.
Subtense Bar system:
An accurate theodolite, reading to 1" of
arc, is directed at a staff, two pointings
being made and the small subtended anglemeasured
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Equipment
Measurement can be taken withtheodolites, transits and levelsand stadiarods
While in the past, distancesweremeasured by thesurveyors chain ortape
This can be done easier and faster using a
telescope equipped with stadia hairlines incombination with a stadia rod (auto leveland staff)
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Tacheometry: Stadia
L1
d1
L2
d2)tan(0.5
0.5Ld 11
)tan(0.5
0.5Ld 22
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Stadia Readings
Middle Hair
Upper Hair
Lower Hair
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Stadia Principles
A,B rod intercepts
a, b stadia hairs
S = rod intercept
F = principal focus of objective lens
K d
D
i
c f
K = stadia constant
C = f/i = stadia interval factor
d = distance from focal point to rod
D = distance from instrument centerto rod
b
a a'
b'
F
B
A
S
f = focal length
i = stadia hair spacing
c = distance from instrumentcenter to objective lenscenter
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Stadia Equations
Horizontal sights
100SH
0K100,Cusually
KCSH
0V
100ScosH
KcosCScosH
2
2
sin2100SV
Ksinsin2CSV
21
21
Inclined sights
i
S
f
d
From similar triangles
KCSD KSSi
fd
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In practice, the multiplicative constant generallyequals 100 and the additive constant equals zero.
This is certainly the case with moderninstruments by may not always be so with olderTheodolites.
The values are usually given by the makers butthis is not always the case.
It is sometimes necessary to measure them in anold or unfamiliar instrument.
The simplest way, both for external and internalfocusing instruments, is to regard the basicformula as being a linear one of the form:
D = C.S + K
Constant determination
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For example:
D =C.S + K
30.00 = 0.300 * C + K
90.00 = 0.900 * C + Ktherefore C = 100 & K = 0
Any combination of equations gives the same result, showingthat the telescope is anallatic over this range, to all intents
and purposes.
Distance Readings Intervals
(m) upperStadia Centre LowerStadia upper lower total
30.000 1.433 1.283 1.133 0.15 0.15 0.30
55.000 1.710 1.435 1.160 0.275 0.275 0.55
90.000 2.352 1.902 1.452 0.450 0.450 0.90
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S
D
V
hi
hL
A
B
Case of inclined sights
Vertical elevation angle:
L
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L = C S cos + K ,
D = L cos
Then ;
D = CS cos2 +K cos ;
V = L sin = ( C S cos + K ) sin
= 1/2 C S sin 2 + K sin ;
L = h i+ Vh = R.L. of B - R.L. of A ;
Where : h is the mid hair reading
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hi
D
S
V
hL
A
B
Vertical depression angle:
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D = CS cos2 +K cos ;
= 1/2 C S sin 2 + K sin ;
L = - h i + V + h = R.L. of A - R.L. of B ;
Where : h is the mid hair reading ;
may be elevation or depression
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N
D
A
B
C
H1
H2
H3
1
2
Stadia readingsVerticalangles
bearingStaff
points
(1.10,1.65,2.20)5128530A
(2.30,2.95,3.60)012510B
(1.45,2.15,2.85)93010430C
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Solution
For line DAS1 = 2.20 1.10 = 1.10 m
H1 = 100 x 1.10 x Cos2 (+5o12) = 109.0964 m
V1 = 109.0964 x tan (+5o12) = + 9.929 m
R.L.of A = 150.10 + 1.40 + 9.929 1.65 =159.779m.
For line DB
S2 = 3.60 2.30 = 1.30 m.
H2 = 100 x 1.30 x Cos2 (+00.00) = 130 m.
V2 = 130 x tan (+00.00) = + 00.00 m.
R.L. of B =150.10 + 1.40 + 00.00 2.95 = 148.55 m.
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For line DC
S3 = 2.85 1.45 = 1.40 m.
H3 = 100 x 1.40 x Cos2 (+9o
30) = 136.186 m.V3 = 136.186 tan (+9o30) = + 22.790 m.
R.L. of C = 150.10 + 1.40 + 22.79 2.15 = 172.140m.
1 = 104o
30 85o
30 = 19o
002 = 125o10 104o30 = 20o40
= 19o00 + 20o40 = 39o40
From Triangle DAC
AC =
AC = 48.505 m
022 19cos186.136096.1092)186.136()096.109(
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From Triangle DCBBC=
BC= 48.133 m
From Triangle DAB
AB=AB= 83.471 m
0420cos186.136000.10302)186.136()000.130( 022
022 19cos096.109000.10302)096.109()000.130(
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Inclined line of sight :
S
D D
1
2
1
2
D = S / ( tan 2tan 1)
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Subtense bar system
1 m 1 m
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2 mtheodolite
Subtense bar
plan
D = cot( / 2 )
For distance up to 80 m
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1 2
D1= cot (1/2) D2= cot (2/2)
D = D1+ D2
For distance 80160 m
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Theodolite 1Theodolite 2
900
Auxiliary
base
x/2
x/2
x
X = ( 2D )
1/2 ;
X = cot ( /2 ) , D = X cot, D = X/2 cot /2
For distance 160350 m
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For distance 350800 m
D1 D2
X = 0.7( 2D )1/2;
X = cot ( /2 ) ,D = X ( cot 1+ cot 2) ,
D = X/2 [ cot (1/2) + cot (2/2) ]
1 2 x
x/21 2
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Electronic Tacheometry(Total Station)
The stadia procedure is used less and lessoften these days, more commonlygeomatic engineers use a combination
theodolite-EDM known in jargon as a totalstation.
Often these instruments are connected toa field computer which stores readings
and facilitates the processing of the dataelectronically.
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Electronic Tacheometry
This instrumentation has facilitated thedevelopment of this method of detail andcontour surveying into a very slickoperation.
It is now possible to produce plans oflarge areas that previously would havetaken weeks, in a matter of days.
The math's behind the operation is very
simple, it is in effect the same as thestadia formulae with the term for thedistance replaced by the measured slopedistance.
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reflector
HI
D
S
Hr V
S = D cos
R.L.of point A = R.L.of point B + HI + V - Hr
B
A
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Tacheometry Field Procedure
1. Set up the instrument (Theodolite) at areference point
2. Read upper, middle, and lower hairs.
3. Release the rodperson for movement tothe next point.
4. Read and record the horizontal angle(azimuth).
5. Read and record the vertical angle(zenith).
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Error Sources
There are 4 main sources of error: Staff Readings
Tilt of the Staff
Vertical Angle
Horizontal Angle
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