Fore Bearing and Back Bearing  in Surveying

Bearings measured in the direction of progress of the survey are known as fore bearing and bearings measured opposite to the direction of the survey are known as back bearing.

The bearing of a line is the direction with respect to a given meridian; Meridian is a fixed reference line. While setting out a survey line, the bearing readings are necessary.

Simply,

• Fore Bearing - Bearing measured in the direction of progress of the survey
• Back Bearing - Bearing measured opposite to the direction of survey

Fore bearing and Back bearing of Survey Line

Hope you are pretty familiar with bearing, types of bearing and some of the related terms.

In the figure below, OA is the survey line to be set out.

• Fore Bearing (FB) of OA = θ1
• Back Bearing (BB) of OA = θ2

Relation Between Fore Bearing and Back Bearing

We will have two cases here:

• Case 1(Fore Bearing is less than 180 degrees)
• Case 2(Fore Bearing is more than 180 degrees)

Case 1(Fore Bearing is less than 180 degrees)

Let OA be the survey line.

According to the definition of fore and back bearing, in the figure:

θ1 is the fore bearing of OA

ϕ1 is the back bearing of OA

Using fundamental geometry, we can write-

ϕ1 = θ1 + 180 degrees

So, Back bearing = Fore bearing + 180 degrees

Case 2(Fore Bearing is more than 180 degrees)

Let OB be the survey line.

According to the definition of fore and back bearing, in the figure:

θ1 is the fore bearing of OB

ϕ1 is the back bearing of OB

Using fundamental geometry, we can write-

θ1 = ϕ1 + 180 degrees

So, Fore bearing = Back bearing + 180 degrees

This is all about the concept of fore and back bearing. The next thing we are going to see, how we can convert an angle to bearing and vice versa.

Finding Internal Angles from Bearing

Let us take AB and BC are two survey lines, and we are asked to find out the internal angle ABC.

θ1 is the fore bearing of line AB and θ2 is the fore bearing of line BC.

Using Geometry,

The internal angle ABC = Back Bearing of line AB - Fore Bearing of line BC(θ2)

Again, the beck bearing of line AB = its forebearing + 180 = θ1 + 180

Hence, Internal angle ABC = θ1 + 180 - θ2

Finding Bearing from Angle

Let us take AB and BC are two survey lines, and we are asked to find out the fore bearing of line BC(θ2), provided the fore bearing of AB is θ1.

Here, the internal angle is α; which is the central angle from the back station.

Fore bearing of BC = Fore bearing of AB + α ± 180

If, (Fore bearing of AB + α) < 180, then use the plus sign in the above formula

If, (Fore bearing of AB + α) > 180, then use the minus sign in the above formula

Before you solve any problem, I suggest you convert the Reduced Bearing to Whole Circle Bearing. If you are very confused with this, better draw the diagram and then start solving it.