## 8. Summary

Converting between angles and directions isn't difficult, but there are a few things someone new to the computations needs to watch out for.

#### (1) Incorrect bearing quadrant.

This usually happens when the sketch isn't correctly drawn. In the diagram below, the surveyor assumed line JK was in the NE quadrant.

The bearing angle is the difference between the back bearing and the angle J. Based on his sketch, the surveyor recorded the bearing JK as S 8°19'15" E while it really is N 08°19'15" W. While a sketch helps, an incorrectly drawn one can lead to wrong answers.

#### (2) Bearing angle exceeds 90°

In this example, the surveyor computed the bearing angle as the sum of the back bearing angle and angle M, recording the bearing of line MN as N 91°05'45" E

When a bearing angle exceeds 90°, the line crosses into the adjacent quadrant. Line MN's correctly written bearing is S 88°54'15" E

#### (3) Confusing Directions and Back Directions

A number of Surveying textbooks use a tabular method to compute directions from angles. These are based on a systematic computation process like the *Azimuth from Deflection Angles* example in this section. While efficient, it may require flipping back and forth between forward and back directions depending on the direction type, which can lead to errors (like being exactly 180° off or flipped bearing quadrant). It requires the surveyor understand the systematic process that will be applied. Consider the *Azimuth from Deflection Angles* example in this section: it was for traveling counter-clockwise around the traverse. What changes in the computation process if travel ran clockwise?

The biggest drawback to a tabular method is there is no visualization. A sketch helps organize directions and angles allowing the surveyor to see the relationships. It's easier to spot a back bearing error on a sketch than in a table. Plus, as shown in the *Azimuth from Deflection Angles* example, using sketches for the first few computations helps identify the systematic process which can simplify subsequent calculations.

#### (4) Using the East-West line

Directions are always referenced to a meridian, a North-South line. When performing calculations, angles should *never* be computed from the East-West line as it may lead to confusion. Students working with directions early on tend to break up angles into smaller parts, often computing parts from the East-West line. For example, in the following sketch, an intermediate calculation may be:

Bearing line RS would is N 70°19'30" W from:

Using the East-West line adds another layer of calculations and potential error.

#### (5) Math mistakes

Most errors are mistakes made when adding or subtracting angles. This is generally because angles are a mixed unit system, deg-min-sec. Calculators which have built-in degree conversion or direct deg-min-sec manipulation capabilities help reduce the problem (providing the user knows how to use the calculator). In manual calculations, subtraction errors are generally more prevalent than addition errors, eg, 180°00'000" - 50°25'30"= 130°35'30".

For each example problem presented here, we identified and applied a math check. If a math check fails, it won't tell us where exactly the error(s) occurred, but it will let us know there *is* an error.

Always, *always*, apply an applicable math check.