Tacheometric survey

SHREE SA’D VIDYA MANDAL

INSTITUTE OF TECHNOLOGY

DEPARTMENT OF CIVIL

ENGINEERING

Subject:-Advanced Surveying

Topic:-Tacheometric Surveying

Presented by:-

Name

Arvindsai Nair

Dhaval Chavda

Nirmal Patel

Rupesh Patel

Saptak Raval

Enrollment no.

130454106002

130454106001

140453106009

140453106010

140453106015

Contents

Topics Slides

1. Tacheometric survey(intro)……….....05

2. Fixed hair method…………………..…06

3. Stadia constant…………………....……30

4. Movable hair method…………….........34

5. Tangential method……………………..39

6. Anallatic lens……………………….…...50

7. Subtense bar…………………………....53

8. Field work in tacheometric survey…57

Tacheometric survey

Tachometry is a method of measuring both

horizontal distance and vertical elevation of

a point in the distance, without the use of

sophisticated technology, such as electronic

distance measurement (EDM) or satellite

transmissions.

Fixed hair method

Fixed hair method• This is a method of finding the distance and elevation of staff from the theodolite (Tachometer).

•Different formulas are used in finding distance for different cases.

•Some cases are discussed as follows:-

Case 1 : When line of sight is

horizontal and staff is held

vertically.

Where,

A,B =Point on staff cut but upper and lower hair

a,b=upper and lower cross hair

ab=i=Stadia interval

AB=S= staff intercept

D=distance from axis of tachometer to staff

D=distance between optical center and axis of tachometer.

Proof:

From Similar triangle ABf and a’b’f

we get,

( f0=f ; AB=S;

a’b’=i)

Now total distance(D)=fC+f+d

+f+d

Now as i ,f and d are constants we can write that the total horizontal distance

i.e. D= K.S + C

where ,

K= =Multiplying constant

C=f+d= Additive constant

Here, vertical distance is zero.

Case 2: When line of sight is

inclined but staff is held

vertically.

C

A

O’

DO

A`

B

C`

P

P’

h

V

Ө

α

(a) Angle of elevation {+}

α

S

Line of axis

Horizontal distance (D)=

Formula for horizontal

distancecos.L

cos)cos.( CsKD

coscos. 2 CsKD

Vertical distance (V)=

Formula for vertical distance

sin2

2Sin . CsKV

sin)cos .( CsKV

sin.L

Reduced level of Q = Reduced level of

H.I. + V -h

Formula for elevation of staff

station

D

Line of

Axis

A

B

C’

C

V

h

P’

P

O

θ

O’

(b) Angle of Depression {-}

Horizontal distance (D)= L.


distance

coscos2 CKSD

cos)cos( CKSD

sin2

2Sin S K. CV

Vertical distance (V)= L.


sincossin S K. CV

Reduced level of P = Reduced level of

H.I. -V -h


station

Case 3: When line of sight is

inclined but staff is held normal

to the line of sight.

(a) Angle of elevation {+}

C

A

O’

DO

A`

B

C`

P

P’

h

V

Ө

αα

S

Line of axis

h c

os

θ

h sin θ

L cos θ

Horizontal distance (D)


distance sincos. hL

sincos).( hCsK

sincoscos. hCsK

Vertical distance (V)


sinL

sin).( CsK

sinsin. CsK


H.I. + V -h


station

cos

(b) Angle of Depression {-}

Line of

Axis

A

B

C

V

h cosθ

P P1

O

θO’

DL cos θ

L

h

sinθ

Horizontal distance (D)


distance sincos. hL

sincos).( hCsK

sincoscos. hCsK

Vertical distance (V)


sinLsin).( CsK

sinsin. CsK


H.I. -V -h


station

cos

STADIA CONSTANTS

STADIA CONSTANTS

Stadia or tacheometric constants are:-

1. Multiplying constant

where,

f =focal length of the

lens

i =stadia intercept

The value of multiplying constant is

generally 100.

i

fA

2. Additive constant

B=(f+d)

where,

f=focal length of the lens

d= horizontal distance between instrument axis to optical centre of a lens

The value of additive constant. varies from 0.15 m to 0.60 m.

In tachometric surveying, instrument used is known as a tachometer.

With the help of a tachometer observations (stadia readings and vertical angles) are taken and horizontal and vertical distances are determined by using formulae.

Before doing calculations we should known the values of two constants for a tachometer to be used for survey work.

Generally their values are mentioned in the catalogue supplied by the manufacturer.

Also the constants may be determined by:

1. Laboratory measurement

2. Field measurement

MOVABLE HAIR

METHOD

MOVABLE HAIR METHOD

In this method the staff intercept is kept constant, but the distance between the stadia hairs is variable.

This of theodolite is known type as substense theodolite.

The diaphragm consists of a central wire fixed with the axis of the telescope.

The upper and lower stadia wires can be moved by micrometer screws in a vertical plane.

The distance by which the stadia wires are moved is measured according to the number of turns of the micrometer screws.

Fig. A special type diaphragm of

a moving hair theodolite

The full turns are read on the graduated scale seen in the filed of view and the fractional part of a turn is of the read on the graduated drum micrometer screw placed one above and one below the eye piece.

The total distance through which stadia is the sum wires move, equal to of the micrometer readings.

If the distance between the instrument station and staff position is within 200 m, an ordinary leveling staff may be used and a full meter reading used for the purpose of observing a constant intercept.

For distances exceeding 200m it becomes

In such cases two vanes or targets fixed at a known distance apart on a staff, are observed.

A third target is fixed at the mid-point of the two targets.

For taking the observation, the middle target is first bisected by the central wire.

Then the micrometer screws are simultaneously turned to move the stadia wires until the upper and lower targets are bisected.

The readings are then noted.

Tangential Method

Tangential Method

No stadia hairs

Levelling staff with vanes or targets

at known distance

Horizontal and vertical distances are

measured by measuring the angles

of elevation or depression.

Some cases are discussed as

follows:-

Case 1 : Both Angles of target are

Angles of elevation.

O’

O

S

h

V

B

A

D

C1

C2

θ2θ1

O’ -Instrument axis

O – Instrument station

C1 – Staff station

V – vertical distance between lower vane and axis of instrument

S – distance between the targets

θ1 - vertical angle by upper targets

θ2 - vertical angle lower targets

h – height of lower vane above the staff station

From figure we can say that,

Formula

21

2

21

21

2

1

tantan

tan

tantan

)tan(tan

tan

tan

SV

SD

DS

DV

DSV

RL of station C1 = RL of instrument axis + V - h

Case 2 : Both angles of target are

Angles of Depression

V

S

h

θ1 θ2

C2

A

B

C1

O’

O

D










Formula

12

2

12

12

1

2

tantan

tan

tantan

)tan(tan

tan

tan

SV

SD

DS

DSV

DV

RL of station A = RL of instrument axis - V - h

Case 3 : One angle is angle of

elevation and the other is angle of

depression.









S

V

h

θ1

θ2

C2

C1

O’

O

D


Formula

21

2

21

1

2

tantan

tan

tantan

tan

tan

SV

SD

DVS

DV

RL of station A = RL of instrument axis - V - h

Anallatic lens

Anallatic lens

• It is an additional lens generally provided in the

external focusing tachometer between object

glass & eyepiece

• Advantages of anallatic lens:-

1) For calculation of horizontal & vertical distances

constant (f+c)=0, if tacheometer is provided with

anallatic lens.

2) Calculation becomes simple.

Disadvantages of anallatic lens :-

1. The anallatic lens absorbs some of the

incident light which consequently results in reduction

of the brightness of the image.

2. It also adds to the initial cost of the instrument

because of one extra lens

SUBTENSE BAR

SUBTENSE BAR

The subtense bar is an instrument used for

measuring the horizontal distance between the

instrument station and a station where the

subtense bar is to be set up.

Substense method is an indirect method of

distance determination.

This method essentially consists of measuring the

angle subtended by two ends of a horizontal rod of

fixed length, called a subtense bar.

In this method a staff or target rod is not necessary,

and the theodolite required is also of the ordinary

transit type.

SUBTENSE BAR

The subtense bar is a metal bar of length varying from 3 to 4 m.

There are two discs of diameter about 20 cm at both ends of the bar.

The discs are painted black or red in front and white on the other side.

The alidade is made perpendicular to the axis of the bar.

A spirit level is included for levelling. The bar is mounted on a tripod stand which contains a ball and socket arrangement for levelling.

FIELD WORK IN

TACHEDMETRY1. Suitability:- A tacheometric survey is

conducted mainly for preparing a contour

map of a reservoir site, alignment of

highways or railways, canals etc. It is

also suitable for carrying out traverses

and filling in detail in rough and rugged

terrain where direct chaining is very

difficult. By means of a tacheometer the

relative distances and RLs of different

points can be computed from the

instrument station by taking observations

(vertical angles and staff readings).

2. Reconnaissance:- Before starting the

survey work the area to be surveyed is

thoroughly inspected examined) and

the instrument stations are selected

according to the nature of the area. If

the survey is conducted along a

narrow belt. the stations are selected

along the centre line of the belt fie.

alignments of highways,railways,

canals, etc)

Procedure:-

The tacheometric survey should be

conducted in the following steps:-

1. The tacheometer is set at station. It is

centred up the starting and levelled with

respect to the plat bubble and altitude

bubble.The height of the instrument

(HI) is measured by leveling staff or

stadia rod or tape. (i.e. height from

ground to centre of the trunnion axis).

2. Set-up horizontal and vertical vernier to

zero. Sight the staff held on the nearby

bench mark and observe the vertical

angle (for inclined sight, and the

readings of the three hairs on staff held

vertically bench mark. If there is no

bench mark nearby, fly levelling may

be done from any nearby BM. To

establish another one near the site area

to know the RL of the starting station.

3. The instrument is oriented with

reference to any pre-determined station

by taking its magnetic bearing and

consider it as first ray at 0.

4. To cover the area (details) from the station, rays at 15

or 30 intervals are extended from the station The

overlap of the rays from nearby stations should be 10

to 15.Also the extension of rays depends on the

topography of the area of the station. Staff positions

on these rays depend on the slope of the ground.

Sight all the representive points from the starting

station and first must be extended up to the whole

length of the ray traverse leg (1e, A to E) to know the

length of the line. Observe the vertical angle and the

staff readings at the three hairs at each staff position.

This way take observations all rays and complete

the station. Take fare sight the traverse a station and

observe the vertical angle and the staff readings the

three wires. Also measure the horizontal angle

between the two traverse legs . Close the work the

BM. before shining the instrument on second station

get the check.

5. Shifting the instrument and set up at the second station.

it is centered and leveled. Measure the height of

instrument. Take the first reading from the BM and then

orient the telescope the first ray.First ray must be extended

to its fun length from B to A Sight all the representative

points on the rays observe vertical angles and staff

readings, and complete the station. Take a for sight on the

third station and observe vertical angle and staff readings.

Also measure horizontal angle between the two traverse

legs. Same way close the the work on the BM. to get the

check. All readings are recorded in the tachometric book.

6. Proceed similarly at each of the successive stations and

all the traverse stations are connected and the necessary

observations for all the points are taken from each station

and recorded clearly in the book.

7. From the metric book, the distances of the points from

the instrument stations and their respective RLs are

calculated by using tachometric table.

8. Since each station is sighted twice, the two values for

the length and elevation are obtained. If they are within

the limits of accuracy, the average of the two values

may be taken and if not work should be repeated.

9. The traverse is plotted to any suitable scale. Rays are

drawn from each station. The points are marked on

these rays considering their horizontal distances from

the station and RLs of the respective written. Then lines

may points are the contour be drawn by the method of

interpolation or by approximate method. North-line is

plotted considering the magnetic bearing of the first

traverse line. This way field work is carried out and

contour map is prepared.

Tacheometric survey

Engineering

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