Need for traversing, types, Bowditch rule

Necessity of traversing

Traversing is the quickest and cheapest way to provide horizontal control for surveys of long, narrow strips and of built-up and wooded areas, where triangulation is not practicable. It gives the coordinates of the stations, from which details are plotted and works are set out.

Types of traverse

• Closed traverse: closed loop (starts and ends at the same station) and closed link (starts and ends at known stations).
• Open traverse: starts at a known station and ends at an unknown one.
• By instrument and angle measurement: compass, chain, theodolite and plane table traverses; included angle, deflection angle and direct bearing methods.

Bowditch's rule

Bowditch (compass) rule: the closing error in latitude and departure is distributed among the lines in proportion to their lengths.

$$C_L=-\Sigma L_{at}\times\frac{l}{\Sigma l},\qquad C_D=-\Sigma D_{ep}\times\frac{l}{\Sigma l}$$

where $l$ is the length of the line and $\Sigma l$ the perimeter (or total length of the traverse).

Assumptions:

• Angular and linear measurements are of equal precision, and the errors are accidental (random) only.
• The error in the linear measurement of a line is proportional to $\sqrt{l}$, and the error in angular measurement is inversely proportional to $\sqrt{l}$. On these assumptions, the correction to the latitude and departure of each line works out to be proportional to its length.
• The angular misclosure has already been distributed among the angles before the rule is applied.

It is simple, and it is the most commonly used rule in plane surveying.