Traverse Adjustment - Bowditch method

The software will handle almost any combination of closed and/or un-closed traverses, side-shots, loops which close back onto a previous section of traverse, or self-closing loops on the end of an open-ended traverse section, provided that the traverses are set out in an orderly, logical sequence. In a self-closing loop, the closing angle may be turned either onto a line within the loop, or onto a line on a previous section of the traverse leading into the loop. Refer to Traverse Types for diagrams of possible traverse configurations.

Any traverse, or a new section which does not commence at a point fixed in a previous section within the same set of data, must have at least one point (the first instrument station) specified as a fixed point (refer to the heading Fixed Points under Enter Points) and also close onto a fixed point in order that the section be able to be adjusted; if the start point is not fixed (or held fixed from a previous traverse section) the traverse will still compute but cannot be adjusted.

Subsequent traverse sections within the same set of data, which commence at points (either traverse stations or side-shot points, and either adjusted or not) computed in any previous traverse section, do not require that their start points be specified as fixed; in fact, the points should not be fixed if they are 'adjustable' points, as fixing will upset prior traverse adjustment.

When the start of a new traverse section is detected by the software, all points prior to the new start are held as fixed for the purpose of allowing the adjustment (if necessary) of subsequent sections - i.e., if a subsequent traverse section closes back onto a previous unclosed (and hence unadjusted) section, the points from the previous section will be held fixed even though they may not have been adjusted, and the current section will then be adjusted accordingly.

Adjustment is performed in this way :

  1. As calculation proceeds, each point is checked to determine if it is a fixed point. If the entire traverse is reduced and no fixed end-point is found, or if a new instrument station is found that was not the previous observed point, the traverse (or traverse section) is unclosed. All points (including any side-shots) have been calculated at this stage.

  2. When a point is observed that is a fixed point, the next observation in sequence is examined to determine if the next point is still on the current traverse section and is also a fixed point.
    1. If the current traverse section ends with 2 fixed points in succession, an angle closure was made and an angular adjustment is possible. The amount of angular misclose is determined by comparing the traverse bearing with the true bearing between the 2 fixed points. Where angular adjustment is possible, the average amount of adjustment made to each traverse angle is given by:

      However, in order to distribute the misclose more in keeping with the anticipated variable reliability of angle observations over lines of differing lengths, the amount of misclose adjustment applied to each angle is proportional to the sum of the inverse lengths of the backsight and foresight lines:

      where 'n' is the number of angles to adjust (including the closing angle).

      The current traverse section is re-run, applying the required correction to each traverse angle. (Angles observed to side points are not subject to adjustment).

    2. If the traverse or current traverse section ends with only 1 fixed point, or following angle adjustment as in (i) above, a Bowditch (Compass) adjustment is made to the points (now stored in the database) on the current section. An adjustment is also made to computed heights on the same proportional distances principle (see Vertical Adjustment), except where heights have already been supplied in the Manual Traverse ToRL field or where there was never a height value assigned to the start or end points of the current section - i.e. no height adjustment can be made if either of the start or end points has no height assigned. A search is made over the current traverse section, and any side-shots found are re-computed using the original angles and distances.

Enclosed area - If a traverse section is adjusted, a value will be calculated for the enclosed area. If the traverse is not a loop that closes back to the start, a closure back to the start is calculated to obtain the area - in such a case, Invalid if lines cross is printed in the Traverse Summary following the area value to indicate that the area relies upon the assumption that it is a valid enclosure. If the closing line or any other traverse line crosses over the traverse route, the area computed will be invalid.

Note : No variation to the method of linear adjustment is made for traverses computed on spheroid - it is considered that the method described is adequate for engineering-type surveys. If a more rigorous adjustment is required, then the Least-Squares Network adjustment is recommended.

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