Closed/open traverse, transit rule

Closed and open traverses

• Closed traverse: a traverse that ends where it began (a closed loop) or that starts and ends on stations of known position (a closed link/connecting traverse). It gives a mathematical check on the field work.
• Open traverse: a traverse that starts at a known station and ends at a point of unknown position, so there is no closing check. It is used for roads, canals, pipelines and similar route surveys, and the angles and lengths must be checked by repeat measurement.

Transit rule

Transit rule: the total error in latitude (or departure) is distributed in proportion to the latitude (or departure) of each line, taken without sign.

$$C_L=-\Sigma L_{at}\times\frac{|\text{lat of line}|}{\Sigma|\text{lat}|},\qquad C_D=-\Sigma D_{ep}\times\frac{|\text{dep of line}|}{\Sigma|\text{dep}|}$$

It is used when angles are measured more precisely than lengths (for example with a precise theodolite and ordinary taping). The assumption is that the error in a line's latitude depends on the latitude itself, so a line running mainly north-south gets a large latitude correction and a small departure correction. It is used less often than Bowditch's rule because its corrections depend on the directions of the lines relative to the reference axes, so the result changes if the axes are rotated.

Example

For the traverse with the latitudes and departures below, $e_N=+0.26$ m, $\Sigma|\text{Lat}|=230.34$ and $e_E=-0.13$ m, $\Sigma|\text{Dep}|=398.33$. The correction to the latitude of AB is $-(+0.26)\times85.20/230.34=-0.096$ m.

The corrected latitudes and departures sum to zero. Note that the lines with larger latitudes or departures get the larger corrections.