COMPASS SURVEYING

Compass surveying is defined as the survey which is done to observe magnetic bearing of each and every station during reconnaissance and exploratory surveys, and to locate other points by measuring the directions with reference to a given point (or) line.

The direction of survey lines can be measured with the help of an instrument known as Compass.

Application and uses of compass survey:1. To find out the magnetic bearing of a line2. To fill in details of a survey operation.3. To find out the direction using night marching.4. Tracing streams5. Plotting irregular shore lines6. Reconnaissance survey7. Clearing in roads

The magnetic poles keep on changing with time and thus the magnetic bearings also change and are therefore not reliable. The observed magnetic bearing therefore be converted to true bearings; the true meridian is invariant.

Important definitions

Magnetic bearing: It is defined as the horizontal angle which a line makes with the magnetic meridian. Magnetic meridian: It is the direction indicated by a freely suspended and balanced magnetic needle unaffected by local attractive

forces. Magnetic declination: It is defined as the difference of angle between true meridian and magnetic meridian. Meridian: It is the fixed direction in hitch the bearings of survey lines are expressed. Bearing: It is the horizontal angle between the reference meridian and the survey line measured in clockwise or anticlockwise

direction. It is described either from north (or) south and the angle described is either east (or) west. True meridian: The true meridian passing through a point on the earth’s surface is the line in which a plane passing through the

given point and the geographic (true) north and south poles, intersects the surface of the earth. It represents the true north-south direction at that point.

True bearing: The horizontal angle measured clockwise between the true meridian and the line is called true bearing of the line. Grid bearing: The horizontal angle which a line makes with the grid meridian is called grid bearing. Grid meridian: It is the reference meridian for a country on a national survey map. The vertical grid lines on a national survey map

indicate the direction of grid north. For a country, the true meridian of the central place is regarded as the reference meridian. Arbitrary meridian: It is any convenient direction, usually from a survey station to some well-defined permanent object. The first

line of survey at times is also taken as arbitrary meridian. Arbitrary bearing: The horizontal angle measured with respect to the arbitrary meridian is known as arbitrary bearing. Azimuth: An azimuth is an angular measurement in a spherical coordinate system. The vector from an observer (origin) to a point of

interest is projected perpendicularly onto a reference plane; the angle between the projected vector and a reference vector on the reference plane is called the azimuth.

Nadir The nadir is the direction pointing directly below a particular location; that is, it is one of two vertical directions at a specified location, orthogonal to a horizontal flat surface there. Since the concept of being below is itself somewhat vague, scientists define the nadir in more rigorous terms. 

Zenith: The zenith is an imaginary point directly "above" a particular location, on the imaginary celestial sphere. "Above" means in the vertical direction opposite to the apparent gravitational force at that location. The opposite direction, i.e. the direction in which gravity pulls, is toward the nadir.

Types of compass

1. Trough Compass2. Tubular Compass3. Prismatic Compass4. Surveyor’s Compass

Most commonly used are prismatic and surveyor’s compass. Prismatic compass is considered to be more widely used in comparison with the later.

Prismatic Compass

It is a device used to measure directions of line (or) a point. It consists of a circular box of about 100mm in diameter. There is a broad magnetic needle balanced on a hard steel pointed pivot. An aluminium ring, graduated to degrees and half degrees is attached to the needle. A prism is provided on the observer’s side

to read the bearings. The ring is graduated from the south end of the needle. The observations run clockwise round to 360 o

with zero placed at south.When the needle is balanced on the pivot, it orients itself in the magnetic meridian and the north and south ends of the ring face

the N-S direction.The object vane carries a vertical hair of fine silk thread attached to a suitable frame.The sight vane consists of a vertical slit cut into the upper assembly of the prism. The two vanes are hinged at the box in

diagonally opposite directions.The object vane is sometimes provided with a hinged mirror which can be raised upward and downward and can also be slided,

to sight the objects too high or too low.Sunglasses are provided on the prism to sight luminous objects.The inverted figures in the graduated ring below the prism can be read erect after being reflected from the hypotenuse side of

the prism, when the observer looks horizontally into the prism.The two perpendicular faces of the prism are made convex, so that it also acts as magnifier.There is a breaking pin, provided at the base of the object vane, which is used to dampen the oscillation of the needle to

facilitate the reading.A prismatic compass reads the whole circle bearing of the line of objects, directly.

Comparison of surveyor compass and prismatic compass

S.No. Item Surveyor’s Compass Prismatic Compass

1. Magnetic needle The needle is of edge bar type. The needle is a broad needle.

2.

Graduated ring The graduated ring is attached to the box and rotates along with line of the sight.The graduations are engraved erect, since the graduated ring is read directly.The graduations are in quadrantal bearing system.

The graduated ring is attached with the needle and does not rotate with the line of sight.Graduations are engraved inverted since the graduation ring is read through the prism.The graduations are in whole circle bearing system.

3. Reading system

The readings are taken directly by seeing through the top of the box glass.Sighting and reading cannot be done simultaneously.

The readings are taken with the help of a prism provided at the eye vane.Sighting and reading can be done simultaneously.

4. Tripod The instrument cannot be used without a tripod.

The instrument can be held in hand also while making the observation.

5. Vanes The eye vane consists of small vane with a small slit.

The eye vane consists of a metal vane with a large slit.

Temporary adjustments of compassThe adjustment required to be made every time the compass is set up are called its temporary adjustments.

1. Centering: A tripod is placed over the station with its legs spread well apart so that it is at a workable height. The compass is fixed on the tripod. It is then centered over the station where the bearing is to be taken with the help of a plumb bob.

2. Leveling: The compass is levelled by eye judgment. This is essential so that the graduated ring swings freely.3. Focussing the prism: This adjustment is done only in a prismatic compass. The prism is moved up or down till the figures

and graduations are seen clearly.

Designation of bearingsThere are two systems commonly used to express bearings.

WHOLE CIRCLE BEARING QUADRANTAL BEARING SYSTEM

In this system, the bearing of a line is always measured clockwise from the north point of the reference meridian towards the line right round the circle. The angle thus measured between the reference meridian and the line is called the whole circle bearing of the line. It will have the values between 0-360 degrees.

In this system, the bearings of lines are measured clockwise (or) anticlockwise from the north (or) south, whichever is nearer to the line.

Examples

Reduced bearing: When the whole circle bearing of a line exceeds 90o, it must be reduced to the corresponding angle less than 90 o

and the value recorded along with the quadrant in which its value will fall. This angle is known as reduced bearing.

S. NO. W.C.B. Q.B.S.

1 56O20’ N56O20’E

2 170O05’ S9O55’ES. NO. Q.B.S. W.C.B.

1 N10 O00’E 10 O00’

2 S02O10’W 182O10’

CASE W.C.B. between R.B. QUADRANT

1 0-90 W.C.B. NE

2 90-180 180O – W.C.B. SE

3 180-270 W.C.B. – 180O SW

4 270-360 360O-W.C.B. NW

Fore bearing: The bearing of a line in the direction of the progress of the survey is called the fore or forward bearing.Back bearing: The bearing of a line in the opposite direction of progress of the survey is called back or reverse bearing.

W.C.B. SYSTEM Q.B. SYSTEM

Back bearing = Fore bearing + 180o…..when fore bearing < 180o

Back bearing = Fore bearing - 180o…..when fore bearing > 180oFB = N 40O E BB= S 40O W

Angle remains the same, N is replaced by S or vice versa; E is replaced by W or vice versa.

Calculation of included angles from bearings

WHOLE CIRCLE BEARING

Fig. 1 Fig. 2

TRAVERSING DIRECTION- CLOCKWISEIncluded angle at B = FB of the forward line – BB of the previous line= β – α = -ve θ (interior angle)……….. Fig. 1(For getting exterior included angle add 360o.)= α – β = θ1 (exterior angle) …………. Fig. 2

TRAVERSING DIRECTION- ANTICLOCKWISEIncluded angle at B = FB of the forward line – BB of the previous line= α – β = θ (interior angle)…………Fig. 1= β – α = -ve θ1(exterior angle)……..Fig. 2(For getting interior included angle add 360o.)

QUADRANT BEARING (a) When bearings are measured in the same side of the common meridian; θ = β – α

(b) When bearings are measured in the opposite side of the common meridian; θ = β + α

(c) When bearings are measured in the same side of the different meridians; θ = 180o – (α + β)

(d) When bearings are measured in the opposite side of the different meridians; θ = 180o- (α – β)

Calculation of bearings from included angles

F.B. of the next line = F.B. of the previous line + included angle measured clockwise

If , the sum > 180, deduct 180o

If , the sum < 180, add 180o

If , the sum > 540, deduct 180o

NOTE: If the traversing is done in anticlockwise direction, the observed included angle is interior angle; whereas it is exterior angle, if traversing direction is clockwise. Again, the included angles are measured clockwise from the preceding line to the forward line.

Magnetic declination: It is defined as the horizontal angle between true north and the magnetic north at the time of observation.

Declination is +ve in eastern side and –ve in western side.When true and magnetic meridian coincide, the declination is zero.

Variation of magnetic declination

The declination at any place keeps on changing from time to time. The variation are as follows:

1. Secular variation: The magnetic meridian swings like a pendulum. It swings in one direction for about 100-150 years, gradually comes to rest, and then swings in other direction. This is known as secular variation.

2. Annual variation: It is the change in the declination at a place over a period of 1 (one) year. Annual variation is in the range of 1-2 mins.

3. Diurnal variation: It is the change in the declination at a place in 24 hours. It is due to the rotation of earth about its own axis. It is depends upon:

a. geographical position of the place( lesser near equator and increases towards the pole)

b. the time of the day ( more in day)

c. season of the year (more in summers)

d. the year of the cycle of secular variation.

True bearing = Magnetic bearing +/- magnetic declination (E/W)

4. Irregular variation: the variation caused by the magnetic disturbances or storms are listed under irregular variation. The value is in the order of 1o.

Purpose of magnetic declination

Most of the original land survey has been in terms of magnetic bearings. Magnetic declination is hence required for:

Re-running the survey lines

In a future time, to check the accuracy of the work

To locate the direction

Isogonic lines: It is the loci of the points or places having equal magnetic declination.

Agonic lines: Lines joining the places of zero declination.

Dip: It is observed that in elevation, a magnetic needle in equilibrium is not in a horizontal plane, but in a plane inclined at a definite angle to the horizontal. The vertical angle made by the magnetic needle with the horizontal is known as dip or inclination of the needle. This is because in elevation the lines of magnetic earth are inclined downward towards north in northern hemisphere and also downward towards south in southern hemisphere.

Local Attraction: The compass contains needle, which aligns along the magnetic lines of force due to earth’s magnetism and points N-S direction. However, in the presence of magnetic materials, such as iron pipes, steel structures, cables, chains, arrows, etc., the needle is deflected from its original position. This effect is known as local attraction.

Isoclinic lines: Lines joining the loci of the places having same value of dip.

Aclinic: Lines joining the loci of places with no dip, such as Magnetic equator.

Detection of Local Attraction: The local attraction at any station is detected by observing the fore and back bearing of the line. If the difference between them is 1800, then both the end stations are considered to be free from local attraction, provided the compass is devoid of any instrumental errors.

Elimination of Local Attraction: There are two methods by which local attraction can be eliminated.

1. By calculating the local attraction at each station: Local attraction at each station is calculated and then the required correction is applied to the observed bearings. It is most suitable for an open traverse. The steps involved are:

Observe a line whose fore and back bearings differ exactly by 180o

The end stations of such a line are accepted free from local attraction and the bearings observed at such stations are taken to be correct.

The back bearing of the preceding line and the fore bearing of the next line will also be correct.

The correct fore bearing of the preceding line or the back bearing of the next line can be calculated by adding or subtracting 180o as the case may be.

If the observed bearing is more than the corrected reading determined in the previous step, error will be positive and correction will be negative and vice versa.

Correction will be done one by one.

*For example problem, refer class notes.

2. By included angles: This method is most suitable for closed traverse.

Calculate the sum of interior angles of the traverse= (2n ± 4) π/2. Calculate the error if any.

Distribute the error equally to all the angles.

Locate the line, whose fore bearing and back bearing differ by 180o.

Find out the correct bearing of the successive lines by using the relations;

Fore bearing of next line= Fore bearing of previous line + included angle.

Back bearing = Fore bearing ± 180o

*For example problem, refer class notes.

TheodoliteTheodolite is an instrument to measure horizontal and vertical angles. Because of its variety of uses such as

horizontal and vertical angle measurement,

prolonging a straight line,

measurement of bearings and measurement of vertical,

horizontal distances, and

determination of the direction of true north,

it is also referred as universal instrument.

Classification

Based on the facilities provided for reading of observation:

1. simple vernier Theodolite

2. micrometer Theodolite

3. optical (glass arc) Theodolite

4. electronic Theodolite

Based on the construction:

1. Transit Theodolite: The Theodolite, whose telescope can be revolved through 180o in a vertical plane about its horizontal axis, thus directing the telescope in exactly opposite direction, is known as transit Theodolite.

2. Non-transit Theodolite: The Theodolite, whose telescope cannot be revolved through 180o in vertical plane, is known as non-transit Theodolite.

Construction details

Alidade assembly: It is the top most assembly which includes a telescope supported by two standards of letter A forming an U-frame and the vertical circle. An altitude bubble is also attached to the standards.

Horizontal Circle assembly: It consists of two plates, the lower carrying the main scale and the upper carrying the vernier scale.

Levelling Head assembly: It is the bottom-most assembly which is screwed on to the top of the tripod. At its base is the tribach which contains three or four screws and a circular bubble.

Levelling screws: The levelling head consists of three or four screws. A four screw head is compact, but leads to uneven pressures on screws which results in excessive wear, whereas, a three screw head is free from such objections.

Plumb bob: A plum bob is suspended from the vertical axis of the Theodolite, to be centered over the station, from where the measurements are made.

Shifting center: Shifting center or movable head is provided for facilitating the operation of centering. It is placed immediately below the trivet stage, but sometimes it is placed above the tribach. The advantage of movable head is that the theodolite and the attached plumb line can be moved and clamped independent of the tripod, when the plumb line is exactly over the station mark.

Levelling tubes: Two level tubes are provided on the horizontal circle upper plate for levelling the theodolite. One of the two is placed parallel and the other at right angles to the line of sight. Usually, a small circular tube is fitted to the foot plate of the tribach to facilitate the setting up of the theodolite. A bubble tube is also attached either to the vertical vernier frame or to the telescope, which is known as the altitude bubble.

Circles: The size of the theodolite is defined by the diameter of the horizontal circle which varies from 8 to 25 cm. it is graduated from 0 to 360 degrees. The vertical circle is usually of the same diameter as the horizontal circle with graduation from 0 to 90 degrees.

Clamp and tangent screws: Two sets of clamp and tangent screws are provided on the horizontal circle to control the motion of the telescope about the vertical axis. One set of clamp and tangent screws is provided to control the movement of telescope about the horizontal axis of the theodolite. The tangent screws make possible slow movement for accurate settings after the clamps have been tightened. (No tangent screws will function, until the corresponding clamp screw has been set.)

Telescope: A telescope of either internal or external focusing type is provided. To facilitate transiting it is convenient to provide an internal focusing rather than external focusing. The magnification ranges from 15 to 30 diameters.

Reading a Theodolite

Below is an example of how to read scale of a theodolite. The main scale least count in the figure is 40 minutes and Vernier scale least count is 40 seconds.

Fig: Main scale with least count 40’ and Vernier scale with least count 40”

Original scale of a Vernier theodolite is shown the figure below. The least count of main scale is 20 minutes and that of Vernier scale is 20 seconds.

Fig; Original scale of theodolite with main scale least count 20’ and Vernier scale least count 20”

Changing Face

It is the operation of bringing the vertical circle of the theodolite to the left of the observer, if originally it was to the right, and the vice versa. If the vertical circle is on the left side of the observer, it is termed as the left face position of the theodolite and if it is on the right side of the observer, then it is termed as right face of the theodolite.

Main scale reading: 127o00”Vernier scale reading: 14’00”

Final reading: 127o00” + 14’00”

Final reading: 127o00” + 14’00”

The errors eliminated by changing face are as follows:

1. Errors due to line of collimation not being perpendicular to the horizontal axis.

2. Error due to horizontal axis not being perpendicular to the vertical axis.

3. Errors due to line of collimation not being parallel to the axis of the altitude level.

Temporary Adjustments (Same as the temporary adjustment done for dumpy level. Refer class notes for detail.)

Setting up the theodolite- centering and approximate levelling

Levelling up

Focussing- Focussing of the eyepiece and focusing the objective

Permanent adjustment

There are nos. of fundamental lines like vertical axis, the axis of plate levels, the line of collimation, the horizontal axis, and the bubble line of the altitude, of theodolite, which have interrelationship amongst each other. These relationships get disturbed over a period of time due to mishandling, which requires correction. These corrections (or) adjustments are known as permanent adjustments.

The desired relations are:

1. The axis of the plate levels must be perpendicular to the vertical axis.

2. The line of collimation must be at right angles to the horizontal axis.

3. The horizontal axis must be perpendicular to the vertical axis.

4. The axis of the telescope level must be parallel to the line of collimation.

The permanent adjustment of a theodolite consists of the following adjustments:

1. Horizontal plate level: the axis of the plate level is made perpendicular to the vertical axis of the theodolite.

2. Horizontal axis: Horizontal axis is made perpendicular to the vertical axis.

3. Telescope: Adjustment of horizontal and vertical hair.

4. Telescope level: Adjustment of level tube on the telescope.

5. Vertical circle index: Adjustment of altitude level and vertical index frame.

Order of permanent adjustment:

The permanent adjustments of a theodolite are carried out in such an arrangement that the next adjustment does not disturb the previous adjustment. The order of the tests and adjustments are as follows:

1. Plate level test: Make the plate bubbles central to their run when the vertical axis of the theodolite is truly vertical.

2. Cross-hair ring test: Make the vertical cross-hair lie in a plane perpendicular to the horizontal axis.

3. Collimation in azimuth test; Make the line of sight perpendicular to the horizontal axis.

A

B

C

Method of repetition

4. Spire test: Make the horizontal axis perpendicular to the vertical axis.

5. Bubble tube adjustment: Make the telescope bubble central when the line of sight is horizontal.

6. Vertical arc test: Make the vertical circle indicate zero when the line of sight is perpendicular to the vertical axis.

Measurement of horizontal angle

Horizontal angles are measured on the horizontal circle of a theodolite by operating the upper clamp, the lower clamp, and the upper and the lower tangent screws. A horizontal angle is measured either of the following methods.

Method of repetition

To measure an angle by repetition, between two stations, means to measure it two or more times allowing the vernier to remain clamped each time at the end of each measurement instead of setting it back to 0o every time when sighting at the previous station. Thus an angle is mechanically multiplied by the no. of repetitions. The value of the angle observed is obtained by dividing the accumulated reading by the no. of repetitions.

Advantages:

1. The errors of graduations are minimized by reading the angle on different parts of the graduated circle.

2. Personal errors of bisection are eliminated.

3. The errors due to eccentricity of the centers and that of the verniers are eliminated, by reading both the verniers.

4. Error due to the line of collimation not being perpendicular to the transverse axis of the telescope is eliminated as both the face left and face right readings are taken.

Method of reiteration

This method of measuring a horizontal angle is preferred when several angular measurements are to be made at a station. All the angles are measured successively and finally the horizon is closed. The final reading on vernier A should be same as the initial zero. If not, the discrepancy is equally disturbed among all the angles.

Note: This method is most commonly used in triangulation survey. For face left, the observation should be made in clockwise direction, whereas for face right, they should be made in the anticlockwise direction.

Measurement of vertical angle

A vertical angle may be defined as the angle subtended by the line of sight and the horizontal line at a station in the vertical plane.

If the point to be sighted is above the horizontal plane, the angle is called the angle of elevation (+) and if the point is below it, the angle is called the angle of depression.

Measurement of direct angle

An angle measured in clockwise from the preceeding line to the following line is called direct angle or angle to the right of azimuth. This method of measuring angles is generally adopted for closed traverses in theodolite traversing.

A C

B D

Measurement of deflection angle

A deflection angle is the angle, made by the prolongation of the preceeding line with the following line. When the angle is measured clockwise, it is called right deflection angle, whereas when measured anticlockwise, it is the left deflection angle. This method is useful in open traversing.