2. Direction

A direction is angle from a meridian to a line. It is similar to a horizontal angle in a traverse except the backsight is always along the meridian, Figure C-3.

Figure C-3
Direction

 

There are two different ways to express line direction: bearing and azimuth.

a. Bearing

A bearing is an angle from the North or South end of the meridian turned to the East or West.  A bearing has three parts:

      • Prefix - N or S indicating which end of the meridian is turned from.
      • Angle
      • Suffix - E or W indicating turning direction from the meridian to the line.

N 66°40' E - from the North end of the meridian, turn 66°40' to the East.

Example

Bearing AB = N 66°40' E

Bearing AC = S 55°32' E

Bearing AD = S 44°21' W

Figure C-4
Bearings
 

 

A bearing falls in one of four quadrants so the angle does not exceed 90°. The angle is to the right (clockwise) in the NE and SW quadrants, to the left (counter-clockwise) in the SE and NW quadrants. A due North direction can be expressed as either N 00°00' E or N 00°00' W; due East as  N 90°00' E or S 90°00' E; similarly for dues South and West.

A back-bearing is reverse of a bearing, that is, Bearing BA is the back-bearing of Bearing AB. Because the meridians are parallel at both ends of the line, the bearing angle is the same but quadrant is reverse. This is true only when meridians are parallel. Where meridians converge, the forward and back bearing angles will differ by the total convergence. More on this later.

  

 

 

Bearing AB = N 66°40' E


Bearing BA = S 66°40' W

Figure C-5
Back Bearing
 

 

b. Azimuth

An azimuth is an angle to the right (clockwise) from the meridian to the line. In most cases the azimuth is turned from the north meridian end; earlier control surveys used the south end. An azimuth varies from 0° to 360°.

Example

Azimuth AB = 66°40'

Azimuth AC = 124°28'

Azimuth AD = 224°21'

Azimuth AE = 322°26'

Figure C-6
Azimuths
 

 

A back-azimuth is reverse of a azimuth: Azimuth CA is the back-azimuth of Azimuth AC. Because the meridians are parallel at both ends of the line, the back-azimuth and forward azimuth differ by 180°. As with bearings, this is true only when meridians are parallel. Where meridians converge, the forward and back azimuths will differ by (180° ± total convergence). More on this later.

Example

 

 

 

Azimuth AC = 124°28'

Azimuth CA = 124°28' + 180°00' = 304°28'

Figure C-7
Back Azimuth

 

 

c. Converting Between Bearings and Azimuths

Since Bearings and Azimuths are both referenced to a meridian it is simple to convert one to the other.

To convert from bearings to azimuths:

Table C-1
Quadrant From Bearing To Azimuth
NE N β E β
SE S β E 180° - β
SW S β W 180° + β
NW N β W 360° - β

Example

Azimuth AB = 66°40'

Azimuth AC = 180°00' - 55°32' = 124°28'

Azimuth AD = 180°00' + 44°21' = 224°41'

Azimuth AE = 360°00' - 37°34' = 322°26'

Figure C-8
Azimuths from Bearings
 

 

To convert from an azimuth, α, to a bearing:

Table C-2
Quadrant To Bearing

NE

N α E

SE

S (180° - α) E

SW

S (α - 180°) W

NW

N (360° - α) W

Example

Bearing AB = N 64°40' E

Bearing AC = S (180°00'-124°28') E = S 55°32' E

Bearing AD = S (224°21' - 180°00') W = S 44°21' W

Bearing AE = N (360°00' - 322°26') W = N 37°34' W

Figure C-9
Bearings from Azimuths

 

 

Rather then memorize tables, drawing a sketch will help determine correct conversion logic to use.

d. Bearing or Azimuth?

Which one should a surveyor use to express directions? It shouldn't matter as both express the same thing abeit using a different format.

The bearing's biggest advantage is that it's immediately recognizable as a dirrection: N 24°18'30"E, S 56°05'24"W. An azimuth, on the other hand looks like an angle (which it is) with no indication what it represents unless it's specifically called out as a direction: 242°45'36" vs 242°45'36" Az.

Bearings are a more traditional way of expressing directions, espacially in property surveys. Check any metes and bounds description or subdivision plats and chances are 10 times out of 9 the bearings will be used for directions.

Azimuths have a computational edge. Bearing angles are limited to a maximun of 90° and can be clockwise or counterclockwise measured from either end of the meridian. Azimuths always start from North and are clockwise. As we'll see shortly, that makes them easier to compute going around a traverse. And we'll see later how azimuths are a little more efficient for other traverse computations.

So which direction format to use is basically up to the surveyor.