Fore bearing and back bearing are two measurements taken along the same path at back and forth direction.
Fore bearing refers to the measurement of the bearing from one station to the next adjacent station in the direction of the traverse. On the other hand, the back bearing denotes the measurement of the bearing from one station to the previous adjacent station in the opposite direction of the traverse. It is important to note that the fore bearing and back bearing of a line exhibit a difference of 180°.
Every individual survey line in a traverse is formed by two stations, and we need to determine the bearing of this in both forward and backward direction which forms the fore bearing and back bearing. This helps us to determine the included angles of the traverse that will help in calculating the areas in surveying.
In this article, we will explore in detail how fore bearing and back bearing are calculated and related surveying calculations.
Fore Bearing (FB) and Back Bearing (BB)
Fore bearing and back bearing can be expressed either in a
whole circle bearing (WCB) or reduced bearing (RB) system. If we have a survey line AB, and we place a bearing measuring instrument on A and find the bearing facing B, we call in fore bearing (FB). If we place the instrument on B and take the measurement towards A the bearing we get is the back bearing of line AB. This is shown in the figure below.

Fig.1. Fore Bearing (FB) and Back Bearing (BB) in Surveying 
 A → B Fore Bearing (FB)
 B → A Back Bearing (BB)
Calculation of Fore Bearing (FB) and Back Bearing (BB)
The surveying starts from one point and ends at another point until the area underconsidered is measured, also called as
traversing. Throughout this, a combination of lines forms formed by several stations ( the lines AB, BC, and CD; stations A, B, C, and D). We will consider line AB and determine its fore bearing and back bearing.
It has to be noted that the fore bearing and back bearing of a line can be expressed either in a whole circle bearing (WCB) or reduced bearing (RB) system.

Fig.2. FB and BB Calculation 
In Whole Circle Bearing (WCB) System
 If FB is less than 180 degrees ( Fig.2.(a))
 FB at A = Î¸;
 BB from B to A = Î¸ + 180 degrees;
 If FB is greater than 180 degrees (Fig.2.(b))
 FB at A = Î¸;
 BB from B to A = Î¸180 degrees;
In Quadrantal Bearing (QB)/Reduced Bearing (RB) System

Fig.3. Fore Bearing and Back Bearing in Quadrantal BeARING (QB) System 
 Consider Fig.3.(a)
 FB=NÎ¸E , then BB=SÎ¸W
 FB = SÎ¸W, then BB=NÎ¸E
 Consider Fig.3(b)
 FB = NÎ¸W and BB = SÎ¸E
 FB =SÎ¸E and BB = NÎ¸W
Example Problem
Convert the following quadrantal bearings into whole circle bearings and find their back bearings: N 67 E, S 31 E, N 26 W, and S 43 W.
Solution: Referring to Fig.4, we can easily find whole circle bearings to the given quadrantal bearing and back bearings.

Fig.4 
Sr.
No.

QB

WCB

BB

(i)

N 67 E

67°

67° + 180 = 247°

(ii)

S 31 E

180  31 = 149°

149 + 180 = 329°

(iii)

N 26 W

360  26 = 334°

334  180 = 154

(iv)

S 43 W

180 + 43 = 223°

223  180 = 43°

Computation of Angles from Bearings
If the bearings of two lines at a point (fore bearing or back bearing) is given, then the included angles formed between the two lines can be found easily. Included angles are most considered for the
computation of area. Let's see an example problem.
Question 2: Given are the observed bearings of a traverse, and the interior angles are given in fore bearing. We need to determine the included angles at each point.
Solution: First, we must use the given data to draw the traverse which will be approximately as shown in Fig. 5.
(i) Determination of Included Angle A
Given the bearing of line EA = 310 30'
Then from the figure, FB of line AE = 310 30' 180 = 130 30'
∠A = Difference in bearings of AE and AB = 130 30'  64 30' = 66 degrees
(ii) Determination of Include Angle B
∠B = Difference in bearings of BA and BC
Bearing of BA = bearing of AB + 180 = 64 30' +180 = 244 30'
Therefore,
∠B = 244 30'130 = 114 30'
(iii) Determination of Included Angle C
∠C = Bearing of line CB  Bearing of line CD
= ( 130 + 180)  (47)
= ( 263 degrees, which forms an exterior angle
(iv) Determination of Included Angle D
∠D = Bearing of line DC  Bearing of line DE
∠D = (47 +180)  210 30' = 16 30'
(v) Determination of Included Angle E
The bearing of line ED = (210 30' 180) = 30 30'
Exterior angle at E = 310 30' 30E 30' = 280 degrees
The included angle ∠E = 360  280 = 80 degrees;
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