Bearings & Azimuths in Surveying | Calculation & Conversion of Bearings and Azimuths | Example

Bearings & Azimuths in Surveying

Angles and lengths are the basic measurements in surveying. Angles in surveying are classified as either horizontal or vertical, based on the plane in which they are measured. Horizontal angles are the elementary observations required for determining bearings & azimuths. Determining the positions of points and orientations of lines often depends on the observation of angles and directions. In surveying, directions are recorded using bearings and azimuths.

Bearings & Azimuths
Bearings & Azimuths

What is Bearing of a Line?

Bearing of a line is the angle measured from either the north or south end of a reference meridian. The angle is observed from north or south towards the east or west, to give a reading less than 90°. Bearing is represented by the letter N or S preceding the angle. The E or W succeeding it demonstrates the appropriate quadrant.

A properly expressed bearing contains quadrant letters and an angular value. Since bearing is with reference to N-S line angles, they are measured clockwise in the 1st and 3rd (NE and SW) quadrants and it is measured anticlockwise in 2nd and 4th quadrants (NW and SE). This is also known as quadrant bearing.

When bearings are measured with reference to true meridian it is called as true bearing. If the bearing is from magnetic meridian, it is magnetic bearing and when from a grid it is grid bearing. Figure 1 and table 1 shows the examples of bearings and calculation of bearings.

Fig.1 Bearing of a Line
Fig.1 Bearing of a Line

Table 1: Calculation of bearings

What is Azimuth of a Line?

The azimuth of a line is defined as the horizontal angle, measured clockwise, from a base direction to the given line. They are usually measured from the north and vary from 0° to 360° and so they do not require letters to categorize their quadrant. They are also called as whole circle bearing.

In the case of plane surveying these azimuths are normally observed from north, but astronomers and the military have used from south direction. National Geodetic Survey have used south as its reference direction for The North American Datum (NAD) of 1927 and north as the reference direction for NAD-1983. Figure 2 and table 2 shows the examples and calculation of azimuths. Here north direction is taken as the reference meridian.

Fig 2. Azimuth of a Line
Fig 2. Azimuth of a Line

Table 2: Calculation of Azimuths

Conversion of Bearing and Azimuths:

N.E. Direction (I Quadrant): Bearing equals Azimuth

S.E. Direction (II Quadrant):  Bearing = 180° – Azimuth

Azimuth = 180° – Bearing

S.W. Direction (III Quadrant):  Bearing = Azimuth – 180°

Azimuth =Bearing + 180°

N.W. Direction (IV Quadrant): Bearing = 360° – Azimuth

Azimuth = 360° – Bearing

Forward and Back Bearings

The bearing of a line in the direction in which a survey is progressing is called the forward bearing. The bearing of the line in the direction contrary to that of progress is called back bearing. In plane surveying, forward bearings can be calculated to back bearings and in return.

The value of both forward bearings and back bearing will be same but the direction will be opposite. The direction will be changing from N or S to S or N and E or W to W or E. For example, from Fig.1 forward bearing OA = N60°E will changes to AO = S60°W in case of back bearing.

Forward and Back Azimuths:

Forward direction of the line in which survey is progressing is forward azimuth and the reverse direction is backward azimuth. Here, in case of azimuth, the value of forward azimuth and backward azimuth will be different. Backward azimuth and forward azimuth can be calculated by adding or subtracting 180°.

If the forward azimuth is less than 180°, backward azimuth is addition of 180° with forward azimuth. If the forward azimuth is greater than 180°, backward azimuth is obtained by subtracting 180°. From Fig.2 backward azimuth for AO is 240° (OA=60° so 180°+60°) and for CO is 39° (OC=219° so 219°-180°)