Let us solve an example to understand the calculation procedure of interior angles in a closed traverse.
The following bearings were noted down with a compass in a clockwise traverse. Calculate the interior angles of a closed traverse.
|
Line |
Fore bearing |
|
AB |
65°15 ' |
|
BC |
127°45' |
|
CD |
42° 0' |
|
DE |
217°30' |
|
EA |
295°0' |
Following are the 4 points or rules to be known before computing the interior angles.
1. For the clockwise traverse,
Included angle = [back bearing of the previous line - fore bearing of next line.]
2. If a back bearing is ＞180°, deduct 180° from the bearing.
3. If a back bearing is < 180°, add 180° to the bearing.
4. If the value of the included angle comes -ve, we have to add 360° to compute the angle in the whole circle bearing system.
The closed clockwise traverse is drawn for the given fore bearings as below.
For the clockwise traverse,
Included angle = [back bearing of the previous line - fore bearing of next line.]
Here, the back bearing is not given, so we have to calculate the back bearing with the help of fore bearings.
Note:
BB 👉 short form of back bearing.
FB 👉 short form of forebearing.
To understand A to Z of surveying, click here.
1. Angle A:
∠A = [BB of line EA - FB of line AB]
As fore bearing of EA > 180°, we have to deduct 180° from the FB.
BB of line EA
= [295° - 180° ]
= 115°
∠A = [115° - 65°15']
= 49°45'
2. Angle B:
∠B = [BB of line AB - FB of line BC]
As fore bearing of AB <180°, we have to add 180° to the FB
BB of line AB
= [65°15' + 180° ]
= 245°15'
∠B = [245°15' - 127°45']
= 117°30'
3. Angle C:
∠C = [BB of line BC - FB of line CD]
As fore bearing of BC <180°, we have to add 180° to the FB
BB of line BC
= [127°45' + 180° ]
= 307°45'
∠C = [307°45' - 42°]
= 265°45'
4. Angle D:
∠D = [BB of line CD - FB of line DE]
As fore bearing of CD <180°, we have to add 180° to the FB
BB of line CD
= [42° + 180° ]
= 222°
∠D = [222° - 217°30']
= 4°30'
5. Angle E:
∠E = [BB of line DE - FB of line EA]
As fore bearing of DE >180°, we have to deduct 180° from the FB
BB of line DE
= [217°30' -180° ]
= 37°30'
∠E = [37°30' - 295°]
= - 257°30'
In the whole circle bearing system, the angle cannot be -ve. In such cases, we must add 360° to the -ve angle.
∠E = [-257°30' + 360°]
= 102°30'
Check:
The total sum of interior angles
= [∠A +∠B + ∠C +∠D + ∠E]
= [49°45' + 117°30' + 265°45' + 4°30' + 102°30']
= 540°
The total value of the angle should be equal to [(2n -4) ✕90°], where n = no. of sides.
[(2 ✕ 5 - 4) ✕ 90°] = [6 ✕ 90°] = 540° ✔
Thank you for going through these calculation steps❤. Have a good day 😄.
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