Unit I Tachometric Surveying
Tacheometer
Tacheometer is transit theodolite fitted with stadia diaphragm, and
analltic lens
Anallatic lens: Additional convex lens is provided between the eye piece
and the object glass at a fixed distance from the object glass. The
purpose of providing anallatic lens is to make additive constant (f+d)
exactly zero.
Tacheometry
 Anallatic lens is provided in external focusing telescope, not required in
internal focusing telescope.
 Advantage
 it simplifies the calculation by making the additive constant ‘0’.
 Therefore, there is only one constant which is multiplying constant.
 Distances are directly calculated by multiplying the difference of stadia
hair readings by 100.
 Disadvantage
 Brightness of the image is much reduced due to absorption of light.
Principle of tacheometry
• The principle of techeometry is based on property of
isoscales triangles, where the ratio of distance of the
base from apex and length of the base is always
constant.
• D1/S1=D2/S2=D3/S3=f/I
– F= focal length of object and
– i= stadia intercept
(multiplying constant)
Theory of stadia Tacheometery
STADIA METHOD
• The stadia readings with horizontal sight on a vertical
staff held 50 m from a tacheometer were 1.285 m and
1.780 m. the focal length of the object glass was 25 cm.
the distance between the object glass and the vertical
axis of the tacheometer was 15 cm. calculate the stadia
interval.
Theory of anallatic lens
Notation
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S = staff intercept CD1
O= Optical centre of object glass
A= Optical centre of anallatic lens
V= vertical axis of inst.
P= Principal focus of the anallatic lens
f1 and f2= conjugate focal lengths of the
object glass
f= focal length of object glass
f’= focal length of the anallatic lens
K= distance between object glass and
anallatic lens
d= distance between optical centre of object
glass and vertical axis of instrument
M=distance between optical centre of object
glass and real image dc
i= length of real image dc, when anallatic
lens is provided
I’= length of real image d3c3, when anallatic
lens is not provided
D= distance between vertical axis of
instrument and the staff
• Home assignment (no need to submit):
– How does the an anallactic lens work to
reduce the additive constant to zero?
– Illustrate the working of anallactic lens by a
neat diagram and discuss the effect on
constants using appropriate expression?
– Derive the distance and elevation formulae for
following cases of tachometry.
• Inclined sight and staff vertical (for angle of
elevation and depression both)
• Inclined sight and staff normal (for angle of
elevation and depression both)
SANTOSH PATASKAR
• FUTURE PM OF INDIA
• (09098445611)
• pataskarsantosh@gmail.com