Deflection Angle Traverse

In this method of traverse surveying, successive stations are occupied and deflection angles are measured by a transit or theodolite. At each station, a backsight is taken to the previous station with vernier A set at zero. The telescope is then reversed by plunging it. A foresight to the next station is then taken by turning the instrument about the vertical axis on its upper motion, and the deflection angle is observed. The angle is recorded as right R or left L, according to whether the upper motion is turned clockwise or counter clockwise. Usually, deflection angles are observed twice, once with the telescope in face left and the other in face right condition. Immediately after completion of traverse observation, an arithmetical check on the angular error of closure should be performed to detect any blunder or excessively large error in angular measurement.

To check the angular closure, azimuths are calculated from previously known azimuth of a line. The unknown azimuth of a line is computed by adding the right deflection angle and subtracting the left deflection angle with the forward azimuth of the previous line. Thus,

W.C.B. of a traverse line = Forward W.C.B. of the preceding line ± deflection angle.

360° needs to be subtracted from computed W.C.B., if it is more than 360° and to be added, if the computed value is negative. Figure 28.3 illustrates the computations of azimuth using deflection angles to the left and right.

The error of closure in a traverse observation can be determined by two ways. These are either based on the computed azimuth or on the observed deflection angles.

In the azimuth adjustment method, the computed azimuth of the closing line is compared with its previously observed value. If both the values agrees each other, there is no error of closure otherwise it exist. To remove the error, a correction equal in magnitude but opposite in nature to the error of closure is to be distributed among the observed deflection angles.

In the deflection angle adjustment method, the algebraic sum of the deflection angles is being computed taking the right deflection angles as positive and left deflection angles as negative. The general relation to compute the error of closure by this method is as follows:

Forward azimuth of the first side of traverse (at first station) + SR - SL = Forward azimuth of the last side of the traverse (at terminating station) + 360° ---- (Equation 28-1)

where SR is the sum of the right deflection angles and SL is the sum of the left deflection angles. If the computed value differs from the previously observed values, an error of closure exists in the measurements of traverse. To find adjusted azimuth of the sides of the traverse, first the deflection angles get adjusted by applying correction equal to the amount of error of closure and then adjusted azimuths are computed.

A deflection angle should never be measured without double centering the instrument, because the error caused by the line of sight not being normal to the horizontal axis of the instrument may be too large to be tolerated. Moreover, the angular error of closure should not exceed the estimated standard deviation for observing an angle from a single setup times the square root of the number of instrument stations. In practice, this estimated standard deviation in angular measurement is usually taken equal to 0.5 to 1.0 times the least count of the instrument used in measuring the angles. If the error exceeds the permissible limit, then observation should be repeated till permissible limit has been achieved.

Deflection angle method of traversing is being generally used for open looped closed traverse. It is most useful for the location survey of linear engineering works such as highways, railways, canals and pipelines etc.

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