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LECTURE №6

TACHEOMETRY

6.1 Introduction
The stadium (Tacheometry) is a rapid and efficient way of indirectly measuring
distances and elevation differences. The accuracy attainable with stadia is suitable
for lower order trigonometric leveling, locating topographic details for mapping,
measuring lengths of back sights and fore sights in differential leveling, and
making quick checks of measurements made by higher order methods.

6.2 Principles of Stadia
In addition to the center horizontal cross hair, a theodolite or transit reticles for
stadia work has two additional horizontal cross hairs spaced equidistant from the
center one. With the line of sight horizontal and directed towards a graduated rod
held vertically at a point some distance away, the interval appearing between two
stadia hairs of most surveying instruments is precisely 1/100 of the distance of the
rod.

Fig 6.1 Horizontal stadia measurement

The stadia method is based on the principle that in similar triangles,
corresponding sides are proportional. In the figure 5.1 depicting a telescope with a
simple lens, light rays from points A and B passing through the lens center from a
pair of similar triangles AmB and amb. Here AB = I is the rod intercept (stadia
interval), and ab=I is the spacing between stadia hairs.

Standard symbols used in stadia measurements and their definitions are as
follows:
f = focal length of lens

i = spacing between stadia hairs

f/I = stadia interval factor, usually 100 and denoted by K
I = rod intercept, also called stadia interval

c = distance from instrument center (vertical axis) to objective lens center.
C = stadia factor=c+f

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