How to convert whole circle bearing to reduced bearing?/ Converting WCB to RB in surveying.

 Let us consider 4 lines in all 4 quadrants having whole circle bearing as given below.

Line	WCB
AB	65°15 '
BC	127°45'
CD	242° 0'
DE	305°30'

 

Let us convert the given WCB into reduced bearings.

Note: 

          WCB 👉 short form of whole circle bearing.

             RB 👉 short form of reduced bearing.

1. Line AB:

As you can observe in the above drawing, 

The given WCB of line AB=65°15' < 90°.

Therefore the line AB lies in the 1st quadrant.

So, RB = WCB = 65°15'

The line lies in the NE quadrant.

So, the quadrantal position reading for RB = N65°15'E

2. Line BC:

The given WCB of the line BC = 127°45' which is > 90° & < 180°

 Therefore the line BC lies in the 2nd quadrant.

So, RB θ2 =[180° - WCB]

            = [180° -127°45']

            = 52°15'

The line lies in the SE quadrant.

So, the quadrantal position reading for RB = S52°15'E

3. Line CD:

The given WCB of the line BC =242°which is  > 180° & < 270°

 Therefore the line BC lies in the 3rd quadrant.

So, RB θ3 =[WCB-180°]

            = [242° -180° ]

            = 62°

The line lies in the SW quadrant.

So, the quadrantal position reading for RB = S62°W

4. Line DE:

The given WCB of the line DE =305°30'which is  > 270° & < 360°

 Therefore the line DE lies in the 4th quadrant.

So, RB θ4 =[360° - WCB]

            = [360° -305°30' ]

            = 54°30'

The line lies in the NW quadrant.

So, the quadrantal position reading for RB = N54°30'W

To understand A to Z of surveying, click here.

Thank you for going through these calculation steps❤. Have a good day 😄.

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