TACHEOMETRY (2)

8/10/2019 TACHEOMETRY (2)

1/35

GEOMATICS ENGINEERING

TACHEOMETRY


2/35

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


3/35

Figure 1 shows the set-up of a tachymetric measurement.


4/35


5/35

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.


6/35

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
http://c/Documents%20and%20Settings/dr.zaki/top03-04-07.htmlhttp://c/Documents%20and%20Settings/dr.zaki/top03-04-07.html


7/35

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)


8/35

Tacheometry: Stadia

L1

d1

L2

d2)tan(0.5

0.5Ld 11

)tan(0.5

0.5Ld 22


9/35

Stadia Readings

Middle Hair

Upper Hair

Lower Hair


10/35

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


11/35

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


12/35

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


13/35

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


14/35

S

D

V

hi

hL

A

B

Case of inclined sights

Vertical elevation angle:

L


15/35

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


16/35

hi

D

S

V

hL

A

B

Vertical depression angle:


17/35

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


18/35


19/35

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


20/35

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.


21/35

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(


22/35

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(


23/35


24/35

Inclined line of sight :

S

D D

1

2

1

2

D = S / ( tan 2tan 1)


25/35

Subtense bar system

1 m 1 m


26/35

2 mtheodolite

Subtense bar

plan

D = cot( / 2 )

For distance up to 80 m


27/35

1 2

D1= cot (1/2) D2= cot (2/2)

D = D1+ D2

For distance 80160 m


28/35

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



29/35


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


30/35

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.


31/35

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.


32/35

reflector

HI

D

S

Hr V

S = D cos

R.L.of point A = R.L.of point B + HI + V - Hr

B

A


33/35

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).


34/35

Error Sources

There are 4 main sources of error: Staff Readings

Tilt of the Staff

Vertical Angle

Horizontal Angle


35/35

TACHEOMETRY (2)

Documents

Transcript of TACHEOMETRY (2)