Closed/open traverse, consecutive, independent coordinates

Closed and open traverse

• 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.

Consecutive and independent coordinates

Consecutive (dependent) coordinates: the latitude and departure of a line, i.e. the coordinates of its end point measured from the preceding station taken as origin. Example: line AB with $L=100$ m and bearing $60^\circ$ gives $\Delta N=100\cos 60^\circ=+50$ m and $\Delta E=100\sin 60^\circ=+86.6$ m from A.

Independent (total) coordinates: the northing and easting of a station measured from one common origin (the reference station or a national grid). They are the algebraic sum of consecutive coordinates from the origin. Example: if A is $(1000,\,1000)$, then B is $(1050,\,1086.6)$, and C is B plus the consecutive coordinates of BC.

Independent coordinates are used for plotting because all stations refer to one origin, so plotting errors do not accumulate.

Worked example

Take A = (1000.00 N, 1000.00 E) and the consecutive coordinates (latitude, departure) of the lines:

Each independent coordinate is the sum of A's coordinates and all consecutive coordinates up to that station. For example $N_C=1000+85.20+30.10=1115.30$ m.