Unit 4

UNIT-4
TACHEOMETRIC SURVEYING
D.Parthiban/Asst., Professor/Civil

Definition of Tacheometry
 Tacheometric surveying is a method of angular surveying in which the
horizontal distance & vertical distance from the instrument to the staff
stations are determined from instrumental observations only.
 Thus the chaining operations are eliminated.
 Field Work can be completed very rapidly.
 Tacheometry is mainly used for preparing the contour plans of areas.
 As chaining is avoided, as far as possible, this method of surveying is
best suited in broken and hilly areas, areas covered with stretches of
water, Swamps, etc. where chaining will become very slow, tedious
and inaccurate.
 Even though this method is not very accurate owing to the above-
mentioned advantages, it is employed in location surveys of lines of
communications such as roads railways, reservoirs, etc.

Principle of Tacheometry
• The main principle of Tacheometry is based on the basic
principle of isosceles triangle.
• It state that “Ratio of the perpendicular to vertex on their base
and their base is always constant in isoceles triangle”
• It means if object is far from vertex than it cover more area
and if it is near than it cover less area because ratio is constant

What is Tacheometer?
 A tacheometer is similar to an ordinary transit
theodolite fitted with stadia wires in addition to the
central cross-hairs.
 As accuracy and speed are necessary, the telescope
fitted with a tacheometer must fulfill additional
requirements. Also, the vertical circle should be more
refined.
 The telescope of the tacheometer is usually longer
than that of the Ordinary theodolite and has a higher
power of magnification.
 The object glass is of greater diameter, and the lens
system is of better quality.
 The magnification power should not be less than 20-
25.
 The effective aperture should not be less than 3.5-4.5
cm in diameter facilitating the obtaining of a bright
image.
 The multiplying constant of the instrument (f/I) is
generally kept as 100.
 Sometimes an additional pair of cross-hairs is
provided such that the multiplying constant (f/I) is 50.

Stadia Rod
• An ordinary levelling staff can be used if
the sights are short but in tachometry
since the sights are usually of much
greater length, therefore, an ordinary
levelling staff cannot serve the purpose.
• But a specially designed graduated rod
known as stadia rod is used.
• The stadia rod is transport, it may be
folding or telescopic.
• It is 3 to 4m long and 5cm to 15 cm
wide.
• The graduations are bold and clear with a
least count usually less than the least
count of an ordinary levelling staff, the
stadia rods should be as light as possible.
• Some common patterns of stadia rods are
shown in fig

Methods of Tachometry
• (i) The stadia system.
 In the stadia system, the observation are taken with the
stadia wires of the tacheometer
• (ii) The tangential system.
 In the tangential system the angles of elevation are
measured from instrument station to the points with a
theodolite and their tangents are used to determine the
horizontal of the telescope for necessary but the stadia
system needs only one and is more commonly used.

stadia system
In the stadia system of tachometrythere are two methods of surveying
(i) Fixed hair method, and
(ii) Moveable hair method.
https://www.youtube.com/watch?v=MA-l1DqRtjI
https://www.youtube.com/watch?v=Xo6cNTuMbDw

Moveable Hair Method
• In this methods, the stadia hair are not fixed but can
be moved by means of micrometer screws.
• The stall is provided with two vanes or targets fixed
at a known distance apart.
• The variable stadia distance is measured, and from
this value the required horizontal distance may be
found out.
• The method is now rarely used.

Tangential System of Tachometric Surveying
• This method is used when the telescope is not fitted with a stadia diagram.
• In this method, the telescope is directed towards the staff to which the
horizontal and vertical distances are to be measured and two vertical angles
to two vanes or targets on the staff at a known distance (S) apart are taken.
• https://www.youtube.com/watch?v=u5McIIB7Blk

Horizontal and vertical distances
Measurement
• Case1: When both the observedangles are angles of elevation

• Case II: Whenboth the observedangles are angles of depression

• Case III- Whenone of the observedangle is the angle of elevationand
the other an angle of depression

Anallatic Lens
 Anallatic lens is an additional lens used in the instrument.
 It is a special lens which is placed between the object glass
and the eyepiece of the telescope in order to eliminate the
additive constant (f+d).
 This is done to make the expression for the distance between
instrument station and staff position more simplified.
 The lens in only provided in an external focusing telescope but
not in the internal focusing.

Subtense Bar Measurements
• A subtense bar is a horizontal staff with targets fixed at a known distance
apart.
• It is about 4m long having a small spirit level and a quick levelling head.
• A sight rule, provided at its centre, can be placed along the line of sight by
viewing the telescope of the theodolite thought the vanes.
• The bar is mounted on a tripod and is placed at right angles to the line of
sight for making observations.
• After levelling and aligning, it is clamped by means of clamp screw

• The targets, made of discs of about 20 cm diameter are painted
red on one side, and white on the other.
• The centres of body the sides of the targets are painted black in
7.5 cm diameter.
• The targets are placed at a distance of 2.5 m and 3 m.
• When the targets are placed 2.5 m apart, the white faces are to
face the instrument and when they are placed 3m apart, the red
faces face the instrument.

https://www.youtube.com/watch?v=E
sO1LnvXq1Q
• The horizontal and vertical angles are
measured with a transit theodolite.
• For measuring vertical angles the method
will be similarly to the movable hair
method of stadia tachometry and the
distances are similarly deduced.
• For measuring horizontal angles,
subtended at the instrument station by the
two targets, the method of repetition is
used, the horizontaldistance.

Distance (D) between the instrument station and the
subtense bar station is found as follows

Errors and Precautions in Tachometric
Surveying
• The errors may be instrumental errors, due to manipulation
and sighting or due to natural causes.
• The instrumental errors may be due to imperfect permanent
adjustments in the instrument and due to incorrect graduations
on the stadia rod.
• When the instrument is in perfect permanent adjustment before
starting the work, the constants of the instrument given by the
manufacturer should be verified in the field by actual
observation.
• This is very necessary for important surveys where accuracy
(and not the time) is the main criterion.
• The graduations on the rod should be carefully examined, and
if any discrepancy is observed, suitable corrections should be
applied to the observed readings.

The errors due to manipulation and sighting depend on
the efficiency and skill of the surveyor.
• These are due to inaccurate centering and leveling of
the instrument and taking incorrect Stadia readings.
• To view the stadia rod clearly, there should be no
Parallax.
• While taking stadia hair readings, care should be taken
to see that the axial hair is not mistaken for a stadia
hair.
• The accuracy of the stadia hair readings may be
checked by seeing whether the mean of the stadia hair
readings is equal to axial hair reading.

• The errors due to natural causes may be due to wind,
unequal expansion of the instrument parts, and visibility and
unequal refraction.
• Out of these the last one is the most important.
• This happens due to unequal refraction of rays of light
When they pass through layers of air of different densities.
• Therefore, to avoid this error, taking readings in the mid-
day should be avoided as far as possible.
• Also, the lines of sight should not be within a meter from
the ground.
• The average permissible error in the distance is 1 in 500 to
1 in 900 and in elevations 0.08 to 0.10 m.
• The closing error in a tacheometry traverse should not be
more than 0. l√P,
• where p is the perimeter of the traverse in meters.

• https://www.facebook.com/civilengineeringvi
deo/videos/252457942017222/
• https://youtu.be/qsfQJLpPG4w

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