## Bearing and types of bearing in Compass Surveying and Questions

Bearing and types of bearing in Compass Surveying and Questions Embark on a compass-guided exploration as we unravel the intricate world of bearings in Compass Surveying. In this comprehensive guide, we not only delve into the fundamentals of bearings but also navigate through different types, accompanied by challenging questions designed to sharpen your surveying skills.

## bearing:

### what is bearing?

**Bearing: **The horizontal angle made by the traverse line with reference line/meridian is termed as a bearing.

Depending upon the reference line selected, these bearings are of following types:

- True Bearing
- Magnetic Bearing
- Grid Bearing
- Arbitrary Bearing

### Representation/Designation of bearing:

Bearing of traverse line can be designated by following two systems

**a)** Whole Circle Bearing System **(WCB)****b) **Quadrantal Bearing System **(QB)**

**a)** Whole Circle Bearing System **(WCB)**:

- In this system bearing of a line is the horizontal angle between the line and the north end of the reference meridian.
- It is measured in clockwise direction.
- The WCB of a line varies from 0 - 360°.
- It is also termed as AZIMUTH if the reference is true north.
- It is measured with the help of "PRISMATIC COMPASS"

**b) **Quadrantal Bearing System **(QB)**:

- Quadrant bearing (Q.B.) a line is the acute angle, which the line makes with the reference meridian.
- It can be measured from north or south point, whichever is closer.
- It is measured in both clockwise and anticlockwise directions.
- It varies in range the of 0 - 90°.
- It is measured with the help of "Surveyor's compass".

**QB is reported as follows:**

i) Firstly, the letter N or S representing north or south point is mentioned.

ii) Mention the angle of the bearing.

iii) Lastly, E or W representing east or west point is reported.

Line | QB | WCB | WCB Range |

OA | N α E | QB | 0^{0} - 90^{0} |

OB | S β E | 180^{0} - QB | 90^{0} - 180^{0} |

OC | S θ W | QB + 180^{0} | 180^{0} - 270^{0} |

OD | N Φ W | 360^{0} - QB | 270^{0} - 360^{0} |

**Table - Conversion of Q.B into W.C.B**

Line | WCB Range | QB | Quadrant |

OP | 0^{0} - 90^{0} | WCB | NE |

OQ | 90^{0} - 180^{0} | 180^{0} - WCB | SE |

OR | 180^{0} - 270^{0} | WCB + 180^{0} | SW |

OS | 270^{0} - 360^{0} | 360^{0} - WCB | NW |

**Table - Conversion of W.C.B into Q.B**

**NOTES**

When a line points towards north, south, east and west it is reported as due north, due south, due east and due west, respectively.

**SO° : Due SouthNO° : Due NorthN90°W or S 90°W : Due WestN90°E or S 90°E : Due East**

### Fore Bearing (FB) and Back Bearing (BB):

**Fore Bearing:**The bearing of a line in the direction of the progress of the survey is called fore bearing (FB).**Back Bearing:**The bearing of a line in the direction opposite to the progress of survey is called back bearing (BB).

Line | FB | BB |

AB | α | β |

BA | β | α |

FB and BB of a line differ by an angle of 180°.

i) If FB < 180°, BB = FB + 180°

IF FB > 180°, BB = FB - 180°

Hence if bearing of the line is reported in WCB system then BB = FB ‡ 180°.

ii) If the bearing of a line reported in QB system, then

Back bearing angle = Fore bearing angle

But N → S and E → W and vice versa.

### important questions

**Q 1)** Fore bearing of different lines are given, compute the corresponding back bearing of the lines.

a) 26° 45'

b) 340°

c) S40° 40'W

d) N37°W

**Sol: a)**

FB = 26^{0}45' (FB < 180)

BB = 26^{0}45' + 180^{0} = 206^{0}45'

**b)**

FB = 340^{0} (FB > 180)

BB = 340^{0} - 180^{0} = 160^{0}

**c)**

FB = S40^{0}40' W

BB = N40^{0}4OE

**d)**

FB = N37^{0}W

BB = S37^{0}E

**Q 2)** Convert the following quadrantal bearing to whole circle bearing.

i) S30°36'E

ii) N6°40'W

**Sol: i)**

QB = S30°36'E

It lies in second quadrant.

So, WCB = 180° - 30°36'

WCB = 149°24'

**ii)**

QB = N6°40'W

It lies in a IV quadrant

So, WCB = 360° - 6°40'

WCB = 353°20'

## included angles:

- When two lines meet at a point, the angle enclosed between them is termed as an included angle.
- Included angle may either be an interior or exterior angle.
- In surveying, included angle is defined as the angle measured in clockwise direction from the preceding line to the forward line.

**Case I:** If the traverse runs in a clockwise direction, included angles are exterior angles.

**Case II:** If the traverse runs in an anticlockwise direction, included angles are interior angles.

### Calculation of included angles from bearing:

**Case I: When QB of lines are given:**

a) When bearings are measured on the same side of the common meridian.

θ = β - α,

θ is the included angle.

b) When bearings are measured on the opposite side of the common meridian.

Interior angle = θ = α + β

c) When bearings are measured on the same side of the different meridian.

Interior angle = θ = 180^{0} - (α + β)

d) When bearings are measured on the opposite side of the different meridian.

θ = 90^{0} - α + 90^{0} + β

θ = 180^{0} + β - α

**Case iI: When wcB of lines are given:**

a) The traversing is done in a clockwise direction OPQO, OP is forward line and QO is previous line

Included angle = FB of forward line - BB of previous line

θ = α - β**Note:** If α - β is (-) ve, add 360° to get the included angles, which will be an exterior included angle.

b) The traversing is done in anticlockwise direction OQPO, 0Q is forward line and PO is previous line.

Included angle = FB of forward line - BB of previous line

θ = β - α (interior included angle)

#### Calculation of bearing from included angle:

By knowing the included angle of traverse and bearing of a line, the bearings of other lines can also be computed.

Fore Bearing of next line = Fore Bearing of Previous line + Included Angle

Note:

a) If this sum is more than 180°, subtract 180°.

b) If this sum is less than 180°, add 180°.

c) If this sum is more than 540°, subtract 540°

## previous year's question in compass surveying:

#### Q 1) Traversing is carried out for a closed traverse PQRS. The internal angles at vertices P, Q, R & S are measured 92°, 68°, 123°, 77° respectively. If fore bearing of line PQ is 27°, then fore bearing of line RS (in degree, in integer) is.____?

**(GATE-2021, SET-I)**

#### Q 2) The following bearings were observed for a closed traverse

Line | AB | BC | CD | DE | EA |

FB | 140^{0} 30' | 80^{0} 30' | 340^{0} 0' | 290^{0} 30' | 230^{0} 30' |

#### Q 3) The following angles were observed in clockwise direction in an open traverse. If the magnetic bearing of line AB is 242° and interior angles are given as ∠ABC = 125°15', ∠BCD = 146°30', ∠CDE = 104°, ∠DEF = 100°15', ∠EFG = 210°45'. What would be the bearing other lines?

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