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Representing the direction of a line with bearings is a long-standing tradition that continues today on plats, legal descriptions, site plans, and other documents. Calculating the direction of a line by using bearings is also a longstanding tradition. However, some surveyors have realized that calculating the direction of a line is much easier when using azimuths and then converting the azimuths to bearings for representation on documents. I find while presenting training seminars that many people do not know how to calculate directions with azimuths as they have never seen it done. In this article, I will present what azimuths are and how they are calculated.
Comparison between Azimuths and BearingsAzimuths are measured clockwise from North and vary from 0Â° to 360Â°. They require only a numerical value (35Â°, 145Â°, 215Â°, etc.).
Azimuths may be referenced to true North, to magnetic North, to an azimuth taken from plans, or from an assumed direction. In addition, azimuths may be forward or backward.
After traverse angles have been adjusted to represent a closed geometric figure and a starting direction has to be determined or assumed, the direction of each line can be calculated. As noted, this is accomplished using either azimuths or bearings. It is purely a matter of personal preference because they both represent the same thing—a direction. However, as stated earlier, azimuths are much easier to calculate. Since they are easier, fewer mistakes in calculations generally occur. It will also be shown how bearings can easily be obtained by converting from azimuths.
Determining the QuadrantBy observation of the value of the azimuth, the surveyor should be able to instantly visualize where the azimuth is located.
Whether it is in the Northeast quadrant, Southeast, Southwest, or Northwest.
Obtaining a Back AzimuthTo calculate azimuths about a traverse, it is necessary to obtain the back azimuth of a line. To calculate a back azimuth, simply add 180Â° to the azimuth of the line.
Back Azimuth = Forward Azimuth + 180Â°
For example, if a line has an azimuth of 75, its back azimuth would be 255Â°. If a line has an azimuth of 150, its back azimuth would be 330.
Calculating Directions Clockwise or Counter-ClockwiseDirection calculations can be performed in either a clockwise or counter-clockwise manner about a traverse. There are specific rules for calculating in either direction.
To calculate azimuths clockwise around a traverse: Subtract the interior angle from the back azimuth of the preceding line.
To calculate azimuths counter-clockwise around a traverse: Add the interior angle to the back azimuth of the preceding line.
Step-by-step Procedure for Calculating DirectionsThe following is the step-by-step procedure for calculating azimuth of line BC for the figure shown in Steps 1 through 4.
Step 1Plan and prepare. Determine a known azimuth. In this case, it is shown to be 45 and the direction that the calculation will proceed (clockwise or counterclockwise). In this case, we are going to calculate clockwise from A to B to C. List the adjusted interior angle draw a sketch of the entire traverse. Be sure your sketch is reasonably accurate (that is, angles and distances should be close to scale). Label the points, the starting direction, and the interior angles. Orient the drawing properly to North.
Step 2Perform the calculation. Start by writing down the starting azimuth. Add 180Â° to obtain the back azimuth. Subtract the interior angle to obtain the azimuth of the next line. If the result is greater than 360, subtract 360. Write down the azimuth on the sketch.
Step 3Repeat the calculation for each line of the traverse. That is, add 180Â° and subtract the interior angle.
Step 4Check the calculations by using the last interior angle to recalculate the starting azimuth.
For the figure below, calculate the direction of each line and provide a check. Proceed clockwise about this traverse. The calculations are shown in a tabular form for ease of understanding along with a sketch of the calculation of each line.