B. Angles and Directions

1. Take a Breath...

An angle is between two lines; a direction is similar except one of those lines is a meridian. An angle only relates one line to another; a direction relates all lines referenced to the same meridian. Directions are a fundamental concept in horizontal positioning.

Starting with a direction for one line, directions of other connected lines can be computed using the horizontal angles linking them. Directions and angles are added or subtracted dependent on the type of horizontal angle (interior, deflection, etc), turn direction (clockwise or counterclockwise), and direction type (bearing or azimuth).

We can also go at it in reverse: given line directions, compute the angle relating the lines (interior, left/righ, deflection, etc). This comes in handy when summarizing the results of a traverse adjustment which will be covered in a later topic.

Every surveyor should be able to convert between directions and angles. That sounds like an easy skill to master, however it does take some practice. A good approach for the beginning (and some seasoned) surveyors is to draw a sketch. This allows you to visualize what you are statring with, what you're solving for, and the correct math to connect the two.

When computing directions from angles or vice versa there are a few things to remember:

  • the releationship between forward- and back-bearings (same angle, opposite quadrant) and forward- and back-azimuths (±180°).
  • angles to the right are positive (added), left are negative (subtracted)
  • meridians are parallel at all points (plane surveying)

There are a few common pitfalls to avoid and they are coverd in the Chapter Summary after the examples problems. This is to give you an opportunity to expereince them.