Сoncept of back azimuths

BACKGROUND

Complex mapping skills are needed by workers in a wide range of occupations, including soil scientists, bedrock and surficial geologists, surveyors, mining companies, and land use planners of all types. These skills become critical in field situations where an immediate decision has to be made before some other activity can take place.

This activity develops the concept of back azimuths; that is, taking an azimuth and proceeding exactly (180 degrees) in the opposite direction. Triangulation extends azimuths from known points into back azimuths such that the azimuth - back azimuth line connects two margins of the map; where three such lines, from three separate points meet you have located, indirectly, a fourth (or unknown) point.

To determine the back azimuth for any given azimuth one does the following. If the original azimuth is less than 180 degrees, you ADD 180 degrees to the original azimuth. If the original azimuth is 180 degrees or more you SUBTRACT 180 degrees from it. This is shown on Figure 1.

Using back azimuths allows a person in the field to precisely back off from washed out roads, flooded areas, defunct bridges, and similar obstacles while maintaining the accuracy of direction needed for subsequent movements. For example, a person walking a proposed traverse for an oil company pipeline encounters a swamp, the person establishes a back azimuth, moves over a given distance to avoid the swamp (90 degree angle), and goes back to his original azimuth on a parallel line which lets him continue in the same direction while avoiding the swamp (Figure 2).

Triangulation involves plotting 2 or more lines from known azimuths and derived back azimuths and using the point of intersection to determine the position. Triangulation can be used in the field to find one's location with reference to visible landmarks; the field exercise is much easier if students have done triangulation on paper first. This is a good chance to reinforce the practical aspects of geometry with your students. In setting up map triangulations you take the coordinates of at least two known points and extend the azimuth from each point across the map. A back azimuth is established from the original point and a line extended across the rest of the map. When azimuth/back azimuth lines have been drawn for all points, the place where these lines intersect will be the coordinates of the unknown location. Since the triangulation lines may be quite long it is very important that they be plotted from the azimuths/back azimuths as accurately as possible. Note that an azimuth - back azimuth combination always forms a STRAIGHT line. If you wind up with a triangle on the map, the larger the triangle, the greater degree of error in plotting one or more of the lines. A typical triangulation diagram could look like Figure 3.

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