Angle Measurement

Courses > Surveying > Horizontal and Vertical Angles, Azimuths, Traverses, Closure Error > Angle Measurement


Angles and directions are a fundamental part of surveying information. We must learn the various systems for measuring directions (horizontal angles, azimuths, bearings, and so forth) as well as the field procedures for making such measurements.

Surveying is the science of determining relative positions of points or objects on or near the earth's surface. From the study of geometry, it is evident that a point can be located by measuring only the distance from two known points. Surveyers find occasions when these two-distance method is very practical and even highly desirable. However, in many procedures which require locating a point, surveyers use a distance from two known points. The discussion of angles and directions in this chapter is simlified in most instanes to stay within the scope of plane survering.

Concepts and Formulas

Kinds of Horizontal Angles

Station Angle

When teo points of known positions are interversible (for example, Z and A in the following figure) and the survey starts from one of those points (from A in our example), the instrument is set up at A and backsighted on Z as the zero direction. The angle is turned to point B, the first point of the new line. As discussed, the angles is normally turned and read clockwise (to the right. This angle is refered to as the station angle.

Deflection Angle

Some surveyors use deflection angles in their computations. These can be computed from the station or ecplement angles, or they can be turned directly by using transit or -minute theodolite. The instrument is set up at A (Above figure), and a backsight is made on Z as is done for station angles. The telescope is pluged first instead of being rotated horizontaly. The angle to B is turned to the left. This is called a left deflection angle. It is recorded with an L or minus sign in front of the angular value. Above figure shows a left deflection angle to B and a right deflection angle to C, if C were the required point.

Interior and Exterior Angles

Some surveyors follow the border of a figure or area and close (tie in) to the starting point. The angles which are inside the figure are refered to as the interior angles, which their explements  are called,  exterir angles. Depending on the direction in which the survey is run, either the interior or exterior angles may be read as the direct or station angles. The other (exterior or interior) are then explement angles. Interior and exterior angles are not recorded in surveys; angles are read and recorded as direct and reverse directions.

Azimuth Angles

One way to describe directions in surveying is by using azimuth. The azimuth of a line is the horizontal directions measured clockwise from a zero direction which points north from the station occupied. Every line has two azimuth, dependimg on observer's position. For example in the following figure a survey is progressing from A toward B. Angle a is the forward azimuth for this line. To designate the direction from B to A, angle b is known as the back azimuth of the line. In plane surveying, the forward and back azimuth of a line always differ by exactly 180°. The zero azimuth line can be based on true, grid or magnetic north. Forward azimuths are converted to back azimuths, and vice versa, by adding or substrating  180°.

Bearing Angle

The use of bearings in measurements automatically keeps the angles below 90° ( see the following figure). The bearing of a line is its direction (within a quadrants) with reference to a meridian (that is north or south line). Bearings are measured clockwise or counterclockwise, depending on the quadrant, from eaither the north or the south line.


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