Consecutive, independent coordinates, plotting

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 the 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.

Plotting a traverse by grid coordinates

1. Choose a scale so that the whole traverse fits on the sheet (for example 1 cm = 10 m). Find the range of N and E, subtract the minimum values and divide by the scale to get the size needed.
2. Draw the grid of squares (the grid sheet) and label the grid lines with the independent northing (vertical axis) and easting (horizontal axis) values, choosing an origin near the south-west corner so that all coordinates are positive.
3. Convert each station's independent coordinates to plotting units. For example, with scale 1 cm = 10 m, a station at $(N, E)$ is at $(E-E_0)/10$ cm along the east axis and $(N-N_0)/10$ cm along the north axis from the origin.
4. Mark each station with a fine pencil dot by measuring its coordinates from the nearest grid lines with a scale (no protractor is needed), and circle it and write the station name.
5. Join the stations in order with thin lines and check that each plotted line length, measured with the scale, agrees with the field length. This is a check for blunders.
6. Plot details (offsets and radiations) from the stations, ink the map and add the title, scale, north arrow, legend and border.

Advantage: each station is located independently from its coordinates, so plotting errors do not accumulate and the plotted traverse closes exactly.