Tacheometry
Muhammad Nadeem Amin Khokar H.O.D Civil Technology API Khudian Khas Kasur
Tacheometry
Tacheometry (/ˌtækiˈɒmɪtri/; from Greek for "quick measure"), is a
system of rapid surveying, by which the
horizontal and vertical positions of points on the earth's surface relative to
one another are determined without using a chain or tape, or a separate
levelling instrument. Instead of the pole formerly employed to mark a point, a
staff similar to a level
staff is used. This is marked with heights from the base or foot,
and is graduated according to the form of tacheometer in use.
A tachymeter or tacheometer is a type of theodolite used for rapid measurements and determines, electronically or electro-optically, the
distance to target. The principles of action are similar to those of rangefinders.
Stadia measurements
Other forms of tacheometry in
surveying include the use of stadia rods with theodolites or plane-table alidades.[1] These use stadia marks on the instrument's reticle to measure the distance between
two points on the stadia rod (the stadia interval). This is converted to
distance from the instrument to the stadia rod by multiplying the stadia
interval by the stadia
interval factor. If the stadia rod is not at the same elevation
as the instrument, the value must be corrected for the angle of elevation
between the instrument and the rod.
The
formula most widely used for finding the distances is:
d = k ×
s + c
Here, s
is the stadia interval (top intercept minus bottom intercept); k and c are
multiplicative and additive constants. Generally, the instrument is made so
that k = 100 and c = 0 exactly, to simplify calculations.
Subtense bars
Another device used in
tacheometry is the subtense
bar.[1] This is a rigid rod, usually of
a material insensitive to change in temperature such as invar,
of fixed length (typically two metres). The subtense bar is mounted on a tripod
over the station to which the distance is desired. It is brought to level and a
small telescopeon the bar enables the bar to be
oriented perpendicular to the line of sight to the angle measuring station.
A
theodolite is used to measure the angle between indicators on the two ends of
the subtense bar. The distance from the telescope to the subtense bar is the
height of an isosceles triangle formed with the theodolite at the upper vertex
and the subtense bar length at its base, determined by trigonometry.
Formula to carry out calculation works:
Case:
(a) Staff held vertical:
D = (f/i).s+ (f+d)
where, f/i = multiplying constant
s = staff
intercept between the bottom and top hair
f+d =
Additive constant
D = Horizontal
distance between the staff station and the observer's position
(b) Inclined sights staff held vertical:
D = (f/i).s. cos^2A + (f+d) cosA
V = {(f/i).s.}
.[{sin(2A)}/2] + (f+d) sinA
Where A
is the angle of elevation or angle of depression.
(c) Inclined sights upwards, staff held normal:
D = [(f/i).s+ (f+d)]cosA - h.sinA ;
V= [(f/i).s+ (f+d)].sinA
h= central hair reading.
R.L. of staff = H.I. + [(f/i).s+ (f+d)].sinA - hcosA
(d) Inclined sights downwards, staff held normal:
D = [(f/i).s+ (f+d)]cosA - h.sinA ; V=
[(f/i).s+ (f+d)].sinA
R.L. of staff = H.I. + [(f/i).s+ (f+d)].sinA -
hcosA
(B)Tangential Method:
In Tangential method only central hair reading is noted down and
generally two angular observations are taken to calculate the horizontal and
vertical distances.
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