Stadia Surveying

STADIA SURVEYING Stadia survey is a tacheometric form of distance measurement measurement that relies on a xed-angle intercept. Tacheometry  is the procedure by which horizontal distances and dierence in elevations are determined indirectly using subtended intervals and angles observed with a transit or theodolite on a graduated rod or scale.  The equipment for stadia measurement measurement consists of a. a telescope telescope with with two horizonta horizontall cross cross hairs, called called upper upper and lower cross hairs, and b. a graduated graduated rod rod called called a stadia stadia rod or stadia stadia board. board.

HORIZONTAL SIGHTS  The principle of the stadia method method is based in igure igure !." shown, shown, wherein the line of sight of the telescope is horizontal and the rod is vertical. or the notation i # spacing between stadia hairs, c # distance from the instrument center to the ob$ective lens center, f # focal length %ob$ective lens to focal point&, d # distance from the focal point  to the face of the rod, ' # %f ( c& # stadia constant, for internal focusing telescope, ' # ).) and for external focusing telescope, ' # )." m * # %' ( d& # distance from the instrument center to the face of the rod, and + # stadia intercept or interval • •

graduated rod telescope B

S

i

c

f 

d

C

D Figure 2.3 The stadia method for horizontal sights. =

'onsidering ig. !.", by similar triangles, f i

d S

d = * S, K = but  The horizontal distance d, from focal point to the rod is f i

f i

therefore, d = K S,

where

Eq. (2.1)

 is the stadia interval factor %usually equal to )) for most instruments&

 The horizontal distance *, from instrument center to rod is D = K S + (f + c) D = K S + C

VERTIAL SIGHT

Eq. (2.2)

+/0123 1456230+ 1roblem  / survey party proceeded to do their stadia survey wor7 as follows the transit was set up at a point / and with the line of sight horizontal, too7 rod readings with the rod at points 6 and ', which were then measured to have taped distances from / to !))-m, and 8)-m respectively. 4od 6 4od ' +tadia 9nterval, + !.)) m ).8)) m  The distance from the center of the instrument to the principal focus was recorded as ).") m. Then they went on to survey other points, with some of the data recorded as follows with the transit at point *, two points 3 and  were sighted. 4od 3 4od  +tadia 9nterval !.!) m ".:8) m ;ertical /ngle ( -"=?> a. 'ompute the stadia interval factor. b. 'ompute the horizontal distances *3 and *. c. 'ompute the dierences in elevation between points * and 3 and points * and .

1roblem ! .

/ transit with a stadia constant equal to ).")m is used to determine the horizontal distance between points 6 and ', with stadia intercept reading of .@: m. The distance 6' is equal to @!.@? m. 'ompute the stadia interval factor of the instrument.

!. Asing the same instrument, it was used to determine the dierence in elevation between 6 and * having stadia intercept reading of !.