updated: 30-May-2011

 Copan Lite for Windows

Bearing Expressions

A fairly sophisticated set of options exists for entering bearings (headings or azimuths) into Copan.

You can enter bearings explicitly, in whole-circle format or in quadrant format, or implicitly as being the bearing between two specified coordfile points. You can even include a + or operator in an expression to add a correction or turned angle to, or subtract from, a bearing. A correction, turned angle, or whole-circle bearing is always positive clockwise and negative anticlockwise. Finally, unless the appropriate Program Settings are made, angle units are degrees-minutes-seconds, and bearings are north-based (i.e., north=0).

(Note that while lay people may know bearings as directions, in surveying, a direction usually means an arbitrary angle reading, where an angle is the difference between two directions. Even so, we use cardinal direction below to have the common meaning.)

Syntax

If you measure angles in degrees-minutes-seconds (i.e., 1 circle = 360°), when entering bearings or angles, always use the format dd.mmss. For example, you must enter 24°52'10.5" as 24.52105 and you must enter 30' as 0.30 (or just .3).

If you measure angles in gons or grads (i.e., 1 circle = 400g), just enter bearings or angles as is (e.g., enter 24.82105g as 24.82105).

In these quasi-formal syntax definitions, a defined term (outdented) is followed by its definition (indented), with alternative definitions on separate lines or separated by vertical bars. Puzzled? See the Examples.

bearing-expression
bearing
bearing   operator   angle
implied-bearing [. 1 | 2 | 3]     (where .1, .2 or .3 means add ¼, ½ or ¾ circle)
bearing
[operator] angle
quad-bearing
implied-bearing
angle
ddd.mmsss
ggg.ggggg
quad-bearing
N | S | E | W | NE | SE | NW | SW
N | S   acute-angle   E | W     (where acute-angle is ≤ ¼ circle)
operator
+ |
implied-bearing
from-point-number   ,   to-point-number
,   to-point-number     (valid if the from-point-number is already entered in an appropriate from-point field)

Examples

In the following tables, note that case doesn't matter and that spaces are not required. Also, the bearings are north-based.
Table 1:   Degrees-Minutes-Meconds Bearing Expressions.

For the lower half of the table, assume that point 102 is at a bearing of exactly 035° from point 101.

Expression Bearing Explanation
210.5613 210°56'13" explicit whole-circle bearing
-10 350° negative bearing, normalized
24 - 2 022° bearing, plus correction or turned angle
s 180° cardinal direction
E - 10 080° cardinal direction, plus correction or turned angle
w+5 275° cardinal direction, plus correction or turned angle
n 35 W 325° explicit quadrant bearing
s 3 e +0.38 177°38' quadrant bearing, plus correction or turned angle
s 4 w 184° quadrant bearing
sw 225° cardinal direction
101, 102 035° implied bearing from point 101 to point 102
101, 102 .1 125° implied bearing from point 101 to point 102, plus 090°
101, 102 .2 215° implied bearing from point 101 to point 102, plus 180°
101, 102 .3 305° implied bearing from point 101 to point 102, plus 270°
101, 102 + 10 045° implied bearing from point 101 to point 102, plus 10°
101, 102 - 15 020° implied bearing from point 101 to point 102, minus 15°
, 102 035° implied bearing from point 101 to point 102
, 102 .2 215° implied bearing from point 102 to point 101

For the last two expressions, assume that 101 is already in an appropriate from-point field.

Table 2:   Gons (or Grads) Bearing Expressions.

For the lower half of the table, assume that point 102 is at a bearing of exactly 035g from point 101.

Expression Bearing Explanation
210.5613 210.5613g explicit whole-circle bearing
-10 390g negative bearing, normalized
24 - 2 022g bearing, plus correction or turned angle
s 200g cardinal direction
E - 10 090g cardinal direction, plus correction or turned angle
w+5 305g cardinal direction, plus correction or turned angle
n 35 W 365g explicit quadrant bearing
s 3 e +0.38 197.38g quadrant bearing, plus correction or turned angle
s 4 w 204g quadrant bearing
sw 250g cardinal direction
101, 102 035g implied bearing from point 101 to point 102
101, 102 .1 135g implied bearing from point 101 to point 102, plus 100g
101, 102 .2 235g implied bearing from point 101 to point 102, plus 200g
101, 102 .3 335g implied bearing from point 101 to point 102, plus 300g
101, 102 + 10 045g implied bearing from point 101 to point 102, plus 10g
101, 102 - 15 020g implied bearing from point 101 to point 102, minus 15g
, 102 035g implied bearing from point 101 to point 102
, 102 .2 235g implied bearing from point 102 to point 101

For the last two expressions, assume that 101 is already in an appropriate from-point field.

updated: 30-May-2011