The field operations in the interior angle method of traversing consist of occupation of the successive stations and a transit or theodolite is being used to measure horizontal angle. At each station the vernier is set at zero, and a backsight to the preceding station is taken. The instrument is then turned on its upper motion until the advance station is sighted and the interior angle is observed. All interior angles is generally observed twice, once with telescope direct and other with the telescope reversed. Immediately after completion of observation, an arithmetical check on the angular error of closure should be performed to detect any blunder or excessively large error in angular measurement.

Figure 28.6 shows an interior-angle closed traverse that originates at point A lying on the line PQ having a known azimuth of 42° 00' 00" as determined from a previous survey. In this traverse, point A was occupied first and an angle was observed between line PQ and traverse line AB. The angle is observed to be 18° 00' 00". After the interior angle at A was observed, points B, C, D and E were occupied and interior angles was observed by method of repetition (at least twice) at each traverse station. Directions for the traverse sides are reckoned using the angle QAB turned from the line of known azimuth PQ to line AB. Thus, the azimuth of line AB is 42° 00' 00" + 18° 00' 00"= 62° 00' 00".

To check the angular closure, azimuths are calculated from previously known azimuth of a line. The azimuth of each succeeding traverse line is computed by adding the clockwise interior angle or subtracting the anti-clockwise interior angle to the back azimuth of the preceding line. Thus,

W.C.B. of a traverse line = Back W.C.B. of the preceding line ± included angle --------------------- (Equation 28.2)

where + for clockwise interior angle and - for anti-clockwise interior angle. Further, 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.

The azimuth of each succeeding traverse line is then calculated by using Eq 28-2 and are as shown in column (3) of Table 28.4.

In this method also there are two ways for finding the error of closure in a traverse observation. These are

• Azimuth adjustment method
• Interior angle adjustment method

In azimuth adjustment method, the computed azimuth of the starting side is checked with its priori observed value. If both the values agrees, there is no error in the measurements for traverse. Otherwise there is error in measurement. To remove the error, a correction equal in magnitude but opposite in nature to the error of closure is distributed to the computed azimuth to find corrected azimuth.

Figure 28.7 illustrates the computation of azimuths using interior angles. It can be found that the calculated azimuth of AB (62° 01' 40") fails to agree with its previously observed value (62° 00' 00"). Thus, there is an error of angular closure by 1' 40" for the traverse. Since five interior angles are measured, the correction to each angle is - 20". The azimuth of BC receives a - 20" correction [column (4) of Table 28.4], since this azimuth has been obtained by considering only one measured angle; azimuth of CD receives a -40" correction, since this azimuth has been obtained by considering two measured angles and so on. The correction to the last azimuth is 5 X (-20") = -1' 40", since this azimuth has been obtained by using all five measured included angles. Finally, the adjusted value of azimuth is then found [column (5) of Table 28.4].

In interior angle adjustment method, the algebraic sum of the interior angles is being computed and needs to be (2n - 4) X 90° where n is the number of sides in the traverse. If there is no difference, no error is associated with the observation. Otherwise there is an error in observation of interior angles. The amount of error is distributed equally among all the interior angles to find their corrected values. Then, azimuth of the line are computed using the adjusted interior angles.

In any case, the sum of the interior angles of a traverse should not deviate from (2n - 4) X 90° by more than the square root of the number of instrument setups times the estimated standard deviation in observing the angles. 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 misclosure is within the permissible limit, it is to be adjusted. However, if it is large, the error should be located and corrected before leaving the field. If necessary the whole work should be repeated.

In the closed loop traverse, although the calculated azimuths are internally consistent, the absolute orientation is based entirely on one angle observed between the known azimuth line and the side of a traverse. This is a weakness in close loop method of traversing. To eliminate the weakness, another angle should be observed from some other traverse point to another independent line of known azimuth.

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