TRIGONOMETRIC LEVELLING Base of the object is not accessible. (Expression for R. L. of top of the object)

Roll No. Group Members. Enroll. No. 42 Jubin Tamakuwala 130030106108

SURVEYING (2130601)

Trigonometric leveling. Definition: “ Trigonometric levelling is the process of determining the differences of elevations of stations from observed vertical angles and known distances. ” The vertical angles are measured by means of theodolite. The horizontal distances by instrument Relative heights are calculated using trigonometric functions. Note : If the distance between instrument station and object is small. correction for earth's curvature and refraction is not required.

Method of Observation. Direct Method: Where is not possible to set the instrument over the station whose elevation is to be determined. Combined correction is required. 2) Reciprocal method: In this method the instrument is set on each of the two station, alternatively and observations are taken.

METHODS OF DETERMINING THE ELEVATION OF A POINT BY THEODOLITE: Case 1. Base of the object accessible A = Instrument station B = Point to be observed h = Elevation of B from the instrument axis D = Horizontal distance between A and the base of object h1 = Height of instrument (H. I.) Bs = Reading of staff kept on B.M. = Angle of elevation = L BAC => h = D tan 

Case 2. Base of the object inaccessible, Instrument stations in the vertical plane as the elevated object.

Case 3. Base of the object inaccessible. Instrument stations not in the same vertical plane as the elevated object.

Procedure. Set up the instrument at P and measure the horizontal angle QPR’(1). Measure the vertical angle 1. Take the staff reading h1 at the BM. Shift the instrument to Q. Set it up and measure the horizontal angle PQR’(1). Measure the vertical angle 2. Take the staff reading h2 on the BM. Measure the Horizontal distance d between the instrument stations(P and Q).

In triangle PQR’ L PR’Q = 180 – ( 1 + 2 ) = 3 By the sine rule,

Knowing horizontal distances D1 and D2, the vertical components H1 an H2 are calculated as under: Now, H1 = ST = P’T tan 2 = PR’ tan2 [since P’T=PR’] And H2 = SR” = tan2 = QR’ tan2 [since Q’R’’=QR’] R.L. of S = R.L. of B.M. + h1 + H2 Also R.L. of S = R.L. of B.M. + h2 + H2