Compass Surveying


Chain surveying can be used when the area to be surveyed is comparatively small and is fairly flat. When large areas involved, methods of chain surveying is not sufficient. In such cases it is required to use some angle measuring instruments for the survey lines to be observed.

Definition: Compass surveying may be defined as that branch of surveying in which the position of an object is determined by angular measurement using compass.

Instruments for the direct measurement of directions:

  1. Surveying’s compass
  2. Prismatic compass

Instrument for measurement of angles

  1. Sextant
  2. Theodolite

Bearing and angle:

The direction of a survey line can either be established

  1. with relation to each other
  2. with relation to any meridian


bearing of a line is its direction relative to a given meridian ie. true, magnetic and arbitrary meridian

  1. True meridian: True meridian through a point is the line in which a plane, passing that point and the north and south pole and intersects with surface of the earth.
  2. True bearing: True bearing of a line is the horizontal angle which it makes with the true meridian (through one of the extremities of the line). Since the direction of true meridian remains fixed hence the true bearing of a line is constant.
  3. Magnetic meridian: Magnetic meridian through a point is the direction shown by a freely floating balanced magnetic needle free from all other attractive forces. The direction of magnetic meridian can be established by magnetic compass.
  4. Magnetic Bearing: The magnetic bearing of a line is the horizontal angle which it makes with magnetic meridian. The magnetic compass used to measure it.
  5. Arbitrary meridian: it is any convenient direction towards a permanent and prominent mark or signal such as church spire, top of chimney, light horse etc.
  6. Arbitrary Bearing: Arbitrary bearing is a line is the horizontal angle which it makes with any arbitrary meridian a theodolite is used to measure.

Systems of bearing:

There are two types of bearing system

1) Whole circle bearing system (W.C.B) or azimuthal system

In this system the bearing of a line is measured with magnetic north (or with south) is clock wise direction. the value of the bearing thus varies from 00-3600. Prismatic compass is graduated on this system.

From figure

This WCB of AB = θ1, of AC is θ2 of AD = θ3 of AF = θ4

2) The Quadrantal bearing system: (Reduced bearings)

In this system the Bearing of a line is measured eastward or westward from north or south whichever is nearer. The direction can be either clock wise or anticlockwise depending upon the position of the line. By surveyor’s compass. This system can be observed.

The QB of line AB is α and is written as NαE, the bearing is measured W.R.T, north meridian (since it is nearer) towards east.

Conversion of bearing from one system to the others:

Conversion from WCB to RB

Line WCB BETWEEN Rule For R.B Quadrat




0 and 900

900 and 1800

1800 and 2700

2700 and 3600


RB = 1800 – WEB

RB = WCB – 180o

RB = 3600 – WCB





Conversion from RB to WCB










WEB= 1800 – RB

WCB= 180o+RB

WCB= 3600 –RB

0 and 900

900 and 1800

1800 and 2700

2700 and 3600

Fore bearing (FB) and back bearing (BB):

The bearing of a line whether expressed in WCB or in QB system, differs according to the observation is made from one end of the line or from the other.

Eg: if the bearing of a line AB is measured from A towards B, if is known as fore bearing as forward bearing. If the bearing of the line AB is measured from ‘B’ towards ‘A’, it is known as back bearing or backward bearing.

In the WCB system the back bearing of a line many be obtained from the fore bearing by

BB= FB 1800

Use + sign if the given fore bearing is less than 1800 and use ‘-’ sign is exceeds 1800.

In QB system the FB and BB are numerically equal but with opposite letters. The BB of a line may therefore obtained by simple substuting N for S and S for N and E for W and W for E. thus, if the fore bearing of line CD is N400251E the back bearing of CD is S400 251W.

Calculation of angles from bearing:

Case I: when the bearing of two lines measured from the point of intersection of the line are given

Rule FB of one line – FB of other

Case II: when bearing of 2 lines are given

= (180 + θ1) – θ2

= BB of previous line – FB of next line


The prismatic compass:

The prismatic compass is the most convenient and portable form of magnetic compass which can either be used as a hand instrument or can be fitted on a tripod.

The magnetic needle is attached to the circular ring made of aluminum a non-magnetic substance. When the needle is on the rivet, it will orient itself. In the magnetic meridian and therefore the north and south ends of the ring will be in this direction the line of sight is defined by the object vane and the eye slit, both attached to the compass box, the object vane consist of vertical hair attached to a suitable frame while the eye slit consist of a vertical slit cut into the upper assembly of the prism unit. Both being hinged to the box. When an object is sighted, the sight vanes will rotate W.R.T the N-S end of ring through an angle which the two line makes with the magnetic meridian. A triangular prism in fitted below the eye slit, having suitable arrangement for focusing to suit different eye sights. The 00 or 3600 reading is engraved on the south end of the ring. So that bearing of the magnetic meridians read as 00.

The reading increases in clockwise direction from 00 at south end to 900 at west end, 1800 at north end and 2700 at east end.

The greatest advantage of prismatic compass is that both sighting the object as well as the reading circle can be done. Simultaneously without changing the position of eye.

Adjustment of prismatic compass

  1. Temporary adjustments
  2. Permanent adjustment s

Temporary adjustment:

Temporary adjustment are those adjustment which have to be made at every set up of the instrument.

  1. Centering: Centering is the process of keeping the instrument exactly over the station. Ordinary prismatic compass is not provided with fine centering device as it is generally fitted to engineer’s theodolite. The centering is invariable done by adjusting the legs of the tripod. A plumb bob may be used to Judge the centering and if it is not available, it may be judge by dropping a pebble from the center of the bottom of the instrument
  2. Leveling: If the instrument is a hand instrument it must be held in hand in such a way that graduated disc is swinging freely and appears to be level. Generally a tripod is provided with ball and socket arrangement with the help of which the tap of the box can he levelled.
  3. Focusing the prism: The prism attachment is slided up or down for focusing till the reading are seen to the sharp and clear.

The surveyor’s compass:

In surveyor’s compass the graduated ring is directly attached to the box and not with needle. The needle freely floats over the pivot thus the graduated ring is not oriented in the magnetic meridian.

The object vane is similar to that of prismatic compass. The eye vane consist of a simple metal vane with fine slit. The objects is to be sighted first and the reading is then taken against the north end of the needle, by looking vertically through the top glass.

When the line of sight is in magnetic meridian the north and south ends of the needle will be over 00 N and 00 S graduations of the graduated card. The card is graduated in quadrantal system having 00 at N and S end and 900 at east and west ends.

Magnetic Declaration:

Magnetic declination at a place is the horizontal angle between the true meridian and the magnetic meridian shown by the needle at the time of observation.

If the magnetic meridian is to the right side or eastern side of the true meridian, declination is said to be eastern or +ve. If is to be the left side or western side the declination is said to be western or –ve

The lines drawn through the points of same declination are called isogonic line.

The line made up of points having zero declination are called agonic line.

Local attraction:

A magnetic meridian at a place is established by a magnetic needle which is uninfluenced by other attracting forces. However, sometimes the magnetic needle may the attracted and prevented from indicating the true magnetic meridian.

Local attraction is a term used to denote any inference, such as the attracting forces, which prevents the needle from pointing to the magnetic north is given locality.

Detection of local attraction:

The local attracting at a particular place can be detected by observing the fore and back bearing of each line and finding the difference. If the difference between fore and back bearing in 1800, it may the taken that both the station are free from local attraction, provided there are no observational and instrumental error.

Elimination of local attraction:

First method:

In the first method true included angle at the affected stations are computed from the observed bearing. Commencing from the in unaffected line and using these included angles, the correct bearing of the successive lines are competed.


2nd method: It is in most common use the included angles are not computed but the amount and direction of error due to local attraction at each of the affected station is found starting from bearing unaffected by local attraction, the bearing of the successive lines are adjusted by applying the correction to the observed bearing.

Co-ordinate method of platting for a froverse survey.

If the length and bearing of a survey line are known, it can be represented on plane by 2 rectangles co-ordinates. The axis of the co-ordinates are the north and south line and east and west line.

The latitude of survey line many be defined as its co-ordinate length measured parallel to the meridian direction.

The departure of the survey line may be defined as its co-ordinates length measured at perpendicular to the meridian direction.

In fig the length of the line OA is given by l1 and bearing of line OA is θ1 then latitude L1 = +l1 cos θ1 and

D1 = l1 sin θ1

WCB RB and Quadrent Sign of
Latitude Departure
0 to 900

900 to 1800

1800 to 2700

2700 to 3600

N θ E I

S θ E II


N θ W IV





Omitted measurements:

In order to have a check on field work and in order to balance a traverse the length and direction of each line is generally measured in the field.

Sometimes when it is not possible to take all measurements due to obstacles or because of some over sights such omitted measurement or missing quantities can be calculated by latitudes and departure provided the quantities required are not more than two.

For closed traverse ƸL and ƸD are Zero

ƸL = l1 cos θ1 + l2 cos θ2 + 13 cos θ3 +……………….. = 0

ED = l1 sin θ1 + l2 sin θ2 + l3 sin θ3 + …………. = 0

Where l1, l2, l3…………. Are length of line and θ1, θ2, θ3………….. are reduced bearings.

Given Required Formula

l, θ

L1, D

L1, θ

D1, θ

L1, l


L, D



Tan θ



Cas θ

Sin θ


l = l cas θ

D = l sinθ

Tan θ = D/L

l = L sec θ

l = D cosec θ

Cos θ = L/l

Sin θ = D/l

l =

Cases of omitted measurement

Case I: Bearing or length or bearing and length of one side omitted

To calculate, bearing or length or bearing and length of line EA

Calculate ƸL1 and ƸD1 of the four known sides AB, BC, CD, DE then ƸL = Latitude of EA + ƸL1 = 0

ED = Departure of EA + ƸD1 = 0

Departure of EA = -ƸD1

Knowing the latitude and departure of the line EA the length and bearing are calculated

Case II: Length of one side and bears of another side omitted.

Let the length of DE and Bearing of EA be omitted join DA which become the closing line of the traverse ABCD is which all quantities are known.

Now Length and bearing can be calculated as in first case.

In ∆ADE, the length of sides DA and EA are known and angle ADE is known. The angle β and length DE can be calculated.

Sin B = sin and =180 – (B + )

DE = = DA

Knowing can be calculated

Case III:-

Length of two sides omitted:

Length DE and EA be omitted the length and bearing of the closing line can be calculated by the 1st case. The angle β, can be calculated by knowing bearing, length of DE of EA can be computed by ∆DEA

DE = x DA

EA = x DA

Errors in compass survey:

The errors may be classified as

  1. Instrumental error
  2. The needle not being perfectly straight
  3. Pivot being bent
  4. Sluggish needle
  5. blunt pivot point
  6. Improper balancing weight
  7. Plane of sight not being vertical
  8. Line of sight not passing through the center of the sight
  9. Personal errors:
  10. Inaccurate leveling of the compass box
  11. Inaccurate centering
  12. Inaccurate bisection of signals
  13. Carelessness is reading and recording
  14. Natural errors:
  15. Variation of dedication
  16. Local affection
  17. Magnetic changes in atmosphere due to clouds and storms etc.

Graphical method of adjusting compass traverse:

For a rough survey such as compass traverse the Bowditch rule may be applied graphically. According to the graphical method, it is not necessary to calculate latitude and departure etc. before plotting the traverse directly from the field notes, the angle or bearing may be adjusted to satisfy the geometric condition of the traverse.

In fig (a) polygon A B1 C1 D1 E1 A1 an unbalanced traverse having a closing error equal to A1A. The total closing error A1A is distributed linearly to all the sides in proportion to their length by a graphical construction shown in fig (b).

In fig (b) AB1, B1C1, C1D1, D1E1 etc. represents the length of the sides of the traverse either to the same scale as that of fig (a) or to a reduced scale. The ordinate aA1 is made equal to closing error A1A, by constructing similar triangle corresponding error bB1, cC1, dD1, eE1 are found. In fig (a), lines E1E, D1D, C1C, B1B are drawn parallel to the closing error A1A and made equal to eE1, dD1, cC1, bB1 respectively. The polygon ABCDE thus obtained represents the adjusted traverse. It should note that the ordinates bB1, cC1, eE1, aA1 in fig (b) represents the corresponding error in magnitude only but not in direction.


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