levelling

Levelling

Prepared by: Ms. Nitika Kabra 1

LEVELLING

Introduction Levelling is a branch of surveying the object of which is:

1. To find the elevations of given points with respect to a given or assumed datum 2. To establish points at a given elevation or at different elevations with respect to a given

or assumed datum.

The first operation is required to enable the works to be designed while the second

operation is required in the setting out of all kinds of engineering works. Levelling deals

with measurements in a vertical plane.

The information obtained by the process of levelling proves very much useful in the initial

stages of design of the project as well as during the execution of various units of the project.

The process of levelling involves the operation of making linear measurements in the

vertical plane and it is because of the measurements in the vertical plane that the levelling

differs both in the methods and instruments of the measurements.

For engineering projects, the levelling is required for various purposes such as for

estimating the reservoir capacities, for setting out grades for sewers, for calculating depth of

cuttings, etc.

Definitions of some common terms in levelling:

Bench Mark: It is a relatively permanent point of reference whose elevation with respect to

some assumed datum is known.

Datum: Datum is any surface to which

elevations are referred. The mean sea level

affords a convenient datum world over, and

elevations are commonly given as so much

above or below sea level. It is often more

convenient, however, to assume some other

datum, especially if only the relative

elevations of points are required.

Horizontal Plane: The horizontal plane is

defined as the plane which is normal to the

direction of gravity at every point. The operations of chain survey, theodolite traverse

survey and plane table survey involve measurements in the horizontal plane.

Horizontal Line: It is the straight line tangential to the level line at a point. It is the line in a

horizontal plane.

Vertical Line or Plumb Line: The line normal to the level line at a point is known as a

vertical line or a plumb line. It is the line normal to a level surface.

Vertical Angle: The angle formed by the intersection of two lines in a vertical plane is

known as the vertical angle.

Level Line: It is the line drawn on a level surface. It is, therefore, normal to the plumb line

at all points.

Level Surface: A level surface is defined as a curved surface which at each point is

perpendicular to the direction of gravity at the point. This is a surface on which all the

points are equidistant from the centre of earth. As earth is a sphere, a level surface will be a

curved surface. The surface of a still water is a truly level surface.

Mean Sea Level: The average height of the sea for all stages of the tides is known as mean

sea level or M.S.L.

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Reduced Level: The elevation of a point or its vertical distance above or below the datum is

known as its reduced level or R.L.

Elevation: The vertical distance of a point with respect to a given datum, either positive or

negative, is known as the elevation of that point. The difference in elevation between two

points is the vertical distance between the two level surfaces in which the two points lie.

Line of Collimation: The line joining the intersection of cross-hairs and optical centre of the

object glass and its continuation is known as the line of collimation. It is also sometimes

referred to as the line of sight.

Station: The point whose elevation is to be ascertained or the point that is to be established

at a given elevation is known as the station and it thus indicates the point at which the staff

is held and not the point at which the level is set up.

Height of Instrument: The elevation or R.L. of the line of collimation, when the instrument

is correctly levelled, is known as the height of instrument or the height of plane of

collimation. Or the height of instrument is the elevation of the plane of sight (line of sight)

with respect to an assumed datum. It may be noted that the term height of instrument does

not mean the height of the centre of the telescope above the ground where the level is set

up.

Back Sight: It is the sight taken on a rod held at a point of known elevation, to ascertain the

amount by which the line of sight is above that point and thus ascertain the height of

instrument. Back Sighting is equivalent to measuring up from the point of known elevation

to the line of sight. It is also known as plus sight as the back sight reading is always added

to the datum to get the height of the instrument. The object of back sighting is therefore to

ascertain the height of the plane of sight.

Fore Sight: It is the sight taken on a rod held at a point of unknown elevation, too ascertain

the amount by which the point is below the line of sight and thus obtain the elevation of the

station. Fore sighting is measuring down from the line of sight. It is also known as minus

sight at the reading is always subtracted from the height of instrument to get the elevation of

the point. The object of fore sighting is to ascertain the elevation of the point.

Intermediate Sight: All sights taken between B.S. and F.S. are known as intermediate sights

or I.S. It may be noted that the word sight does not imply any direction, but it denotes the

reading.

Turning Point: It is also known as change point. It is the point on which both the minus

sight and the plus sight are taken on a direct line of direct levels. The minus sight is taken

on the point in one set of the instrument to get the level while the plus sign is taken on the

same point in other set of instrument to establish the new line of sight.

Intermediate Station: It is a point intermediate between two turning points, on which only

one sight (minus sight) is taken to determine the elevation of the station.

Parallax: The term parallax is used to indicate the apparent movement of the image with

respect to the cross hairs and it occurs when the plane of image does not coincide with the

plane of cross hairs. It can be eliminated with the process of focussing.

Focussing: It is used to indicate the operation or process by which the clear image of the

object is brought in fixed plane of cross hairs. The process of focussing can be carried out

either by adjusting the eye-piece or the objective.

It involves two processes:

i. Focussing the eye-piece: The eye-piece unit is moved in or out with respect to the

cross-hairs so that the latter are clearly visible.

ii. Focussing the objective: The purpose of focusing the objective is to bring the image

of object in the plane of cross-hairs which are clearly visible. The focusing can be

done externally or internally.

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Methods of levelling:

Three principal methods are used for determining difference in elevation. They are:

1. Barometric levelling: Barometric levelling makes use of the phenomenon that difference in elevation between two points is proportional to the difference in

atmospheric pressures at these points. A barometer, therefore, may be used and the

readings observed at different points would yield a measure of the relative elevations of

those points.

At a given point, the atmospheric pressure does not remain constant in the course of the

day, even in the course of an hour. The method is, therefore, relatively inaccurate and

is little used in surveying work except on reconnaissance or exploratory surveys.

2. Trigonometric Levelling (Indirect levelling): Trigonometric or Indirect levelling is the process of levelling in which the elevations of points are computed from the vertical

angles and horizontal distances measured in the field, just as the length of, any side in

any triangle can be computed from proper trigonometric relations. In a modified form

called stadia levelling, commonly used in mapping, both the difference in elevation

and the horizontal distance between the points are directly computed from the

measured vertical angles and staff readings.

3. Spirit Levelling (Direct Levelling): It is that branch of levelling in which the vertical distances with respect to a horizontal line (perpendicular to the direction of gravity)

may be used to determine the relative difference in elevation between two adjacent

points. The method is also known as direct levelling. It is the most precise method of

determining elevations and the one most commonly used by engineers.

Levelling Instruments

The instruments commonly used for direct levelling are:

1. A level 2. A levelling staff

1. Level: The purpose of a level is to provide a horizontal line of sight. Essentially, a level

consists of the following four parts:

a. A telescope to provide line of sight b. A level tube to make the line of sight horizontal c. A levelling head (tribrach and trivet stage) to bring the bubble in its centre of run

d. A tripod to support the instrument. 2. Levelling Staff: A levelling staff is a straight

rectangular rod having graduations, the foot

of the staff representing zero reading. The

purpose of a level is to establish a horizontal

line of sight. The purpose of the levelling

staff is to determine the amount by which the

station (i.e., foot of the staff) is above or

below the line of sight. Levelling staves may

be divided into two classes:

a. Self-reading staff: It is the one which

can be read directly by the instrument

man through the telescope.

The graduations are inverted so that

they are seen in erect position when

looked through the telescope.

It is of three types:

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i. Solid staff

ii. Folding staff

iii. Telescopic staff

b. Target staff: It contains a moving target against which the reading is taken by

staff man. A target is provided on the staff and under the instructions received

from the surveyor, the target is moved by the person holding the staff. The target

is clamped and the reading is then recorded by the staff-man. The target is

provided with a vernier and it helps in taking very accurate readings. This type of

staff is useful when the distances for taking readings exceed 100 m.

S. No. Self Reading Staff Target Staff

1. The fineness of reading taken is less. The fineness of reading taken is more

than that of self reading staff.

2. The level-man records the readings in

case of self reading staff.

The staff-holder takes the readings in case

of target staff.

3. The staff man need not be a trained

person.

The staff-man should be a trained

person.

4. The readings from self-reading staff

can be taken easily and speedily

The taking of readings from target staff

takes time and is not easy.

Precautions to be taken while using a levelling staff:

a. Holding the staff: The level staff should be held truly vertical. b. Reading the staff: The reading to be taken on the staff depends on the manner in

which the figures arc written on the staff.

Essential parts of a level:

Any type of level contains the following three essential parts:

1. Bubble tube: This is also known as a level tube, and it helps in establishing a horizontal

plane. It is designed on the principle that any liquid surface at rest will always be

perpendicular to the direction of gravity.

2. Levelling head: It assists in bringing the bubble in the central position. It consists of

two plates which are held at a constant distance apart with the help of foot screws. The

bottom plate is known as foot plate and the hole in it is treaded so that the instrument

can be fixed on treaded tripod head to ensure stability. The top plate is known as bush

plate.

3. Telescope: It is the most important part of the level and it helps in taking the readings

from the levelling staff.

The telescope has four essential parts:

a. Objective: The objective is invariably a compound lens consisting of

i. The front double convex lens made of crown glass

ii. The back concavo-convex lens made of flint glass

The two being cemented together with balsm at their common surface. Such

compound lens is known as achromatic

lens, and two serious optical defects viz.,

spherical aberration and chromatic

aberration are nearly eliminated.

b. Eye Piece: It is also called as eye lens. It

is required to see the object and its size

corresponds to the size of human eye so

that other rays are avoided to see the

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object clearly. The eye piece may be of

erecting type or non-erecting type.

c. Diaphragm: The cross hairs, designed

to give a definite line of sight, consist

of a vertical and horizontal hair held in

a flat metal ring called reticule.

In modern instruments interchangeable

cross hairs are used and they are

carried in a cell or a capsule.

The cross hairs must be clean, fine,

opaque and without fringes. The cross

hairs are usually made up of spider's

web, silk web, lines on glass, fine

platinum wire, etc.

Cross hairs (a), (b) and (c) in the

diagram are used in levels.

d. Body and Focusing Device: The

focusing device depends upon whether

it is an external focussing telescope or

an internal focussing telescope.

i. External Focussing: The movement of the objective or eye-piece is carried

out externally and the body of telescope consists of two tubes, one capable

of sliding axially within the other, by means of rack gearing. The focussing

screw controls the gearing arrangement and it is moved in clockwise or

anticlockwise direction till the image falls at the plane of diaphragm. This

type of focussing is not favoured.

ii. Internal focussing: The objective and eye piece are kept fixed in position

and the focussing is achieved by moving an extra double concave lens

provided in the telescope between the objective and diaphragm hairs. Thus,

a short tube carrying the lens is moved along and inside the tube carrying

the objective by means of gearing arrangement. The modern instruments

contain internal focussing arrangement

Types of Levels

1. Dumpy Level: It is a very simple, compact and stable level. It can be used for rough

work. The telescope is rigidly fixed with the support and hence, it is not possible to

rotate it about its own axis.

The instrument gives fairly

accurate work and possesses

greater stability of

adjustments.

The modern form of dumpy

level has the telescope tube

and the vertical spindle cast in

one piece and a long bubble

tube is attached to the top of

the telescope. This form is

known as solid dumpy.

In some of the instruments, a

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clamp screw is provided to control the movement of the spindle about the vertical

axis. For small or precise movement, a slow motion screw (or tangent screw) is also

provided.

The levelling head generally consists of two parallel plates with either three-foot

screws or four-foot screws. The upper plate is known as tribrach and the lower plate

is known as trivet which can be screwed on to a tripod.

The advantages of the dumpy level over the Wye level are:

a. Simpler construction with fewer movable parts

b. Fewer adjustments to be made

c. Longer life of the adjustments

2. Cooke's Reversible Level: This level combines the advantages of dumpy level and V-

level. It contains the arrangements such that it can be rotated about its own axis in its

sockets and it can be removed and ends can be exchanged.

The telescope is supported by two rigid sockets into which the telescope can be

introduced from either end and then fixed in position by a screw. The sockets are

rigidly connected to the spindle through a stage. Once the telescope is pushed into the

sockets and the screw is tightened, the level acts as a dumpy level.

This type of instrument is heavy because there is an addition of an extra tube. There is

also possibility of the instrument being disturbed while changing the telescope end to

end.

3. Wye or Y-level: The

essential difference

between the dumpy level

and the Wye level is that in

the former case the

telescope is fixed to the

spindle while in the Wye

level, the telescope is

carried in two vertical 'Wye'

supports. It is a very

delicate instrument

consisting of various loose

parts. Hence, it requires

careful handling. The

telescope is put up on the supports having the shape of letter Y and it can be removed

and its ends can be exchanged. It thus grants the facility of carrying out the permanent

adjustments indoors. However, the adjustments soon get disturbed due to loose

supports and hence, it becomes necessary to check them quite often.

4. Cushing's level: In this type of level, the telescope is firmly secured in collars as in

case of a dumpy level. The ends of the telescope tube are enlarged to form two exactly

equal sockets, ground carefully to receive either the objective lens cell or the eyepiece

and diaphragm cell. It is thus possible to interchange objective for eye piece and

vice versa. This type of level is heavy due to the addition of the collar fittings.

5. Tilting Level: It is used for very precise work. A tilting screw is provided at the base

of telescope and at every observation; the line of collimation is made truly horizontal.

The line of sight can be tilted slightly without tilting the vertical axis. Thus, the line of

sight and the vertical axis need not be exactly perpendicular to each other. This

feature of this type of level helps in quick levelling.

The instrument is levelled roughly by the three-foot screws with respect either to the

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bubble tube or to a small

circular bubble, thus making

the vertical axis approximately

vertical. While taking the sight

to a staff, the line of sight is

made exactly horizontal by

centring the bubble by means

of a fine pitched tilting screw

which tilts the telescope with

respect to the vertical axis.

S. No. Dumpy Level Tilting Level

1. The vertical axis and the axis of bubble

are fixed rigidly at right angles to each

other and hence, when the bubble is in

the centre i.e. axis of the bubble is

horizontal; the vertical axis is truly

vertical.

The telescope and the bubble are

independent of the vertical axis and

as such, the line of sight and the axis

of the bubble can be made

horizontal without the vertical axis

being truly vertical.

2. The line of collimation may get tilted

upwards or downwards and in that

case, the line of collimation and the

axis of the telescope will not coincide.

Thus, the adjustment will have to be

carried out with the diaphragm screw.

In tilting level, the line of

collimation and the axis of the

telescope are made one and the

same.

3. Two permanent adjustments are

required.

Only one permanent adjustment is

required.

6. Gradientor or Gradiometer: In this level, the arrangement is made in such a way that

any desired gradient can be set up with the minimum interval of time. It thus

facilitates the measurement or setting out of long uniform gradients. It consists of a

level in which the telescope is so mounted that it may be set at various inclinations to

the horizontal and the gradient is registered on a drum.

Bench Marks

Following are the four types of bench marks:

1. Arbitrary bench marks: Some permanent objects are selected to serve the purpose of

bench marks and they are given some arbitrary value. Such objects are known as

arbitrary or assumed bench marks and they are used for small levelling operations.

2. G.T.S. bench marks: The survey department of Govt. of India has established all over

the country certain bench marks known as Great Trigonometrical Survey or G.T.S.

bench marks at intervals of about 100 km. These bench marks are established with

high precision and their positions and elevations are -published in catalogues or

shown on G.T.S. maps. The standard datum adopted for G.T.S. bench marks is the

mean sea-level at Karachi or Bombay.

3. Permanent bench marks: The bench marks established as reference points on some

permanent objects between the G.T.S. bench marks by the state P.W.D. are known as

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permanent bench marks. The permanent objects chosen for this type of bench marks

include tops of culverts or bridge kilometre stones, pillars, railway platform, isolated

rock, etc.

4. Temporary bench marks: The bench marks established for short duration at the end of

day's work or for some break in the work are of temporary nature and hence, they are

referred to as temporary bench marks. The unfinished work is started again with

reference to these temporary bench marks. The permanent objects chosen for this type

of bench marks include floor or verandahs, roots of the trees, tops of parapet; gate

posts, etc.

Temporary Adjustments of Levels

Each surveying instrument needs two types of adjustments:

1. Temporary adjustments: These are also known as station adjustments and are those which are made at every instrument setting and are preparatory to taking observations

with the instrument.

2. Permanent adjustments: These need to be made when the fundamental relations

between some parts or lines are disturbed.

Temporary adjustments of a level consist of the following:

1. Setting up the level: It includes: a. Fixing the instrument on the stand

b. Levelling the instrument approximately by leg adjustment. The instrument is removed from the box. To fix the level on the tripod, the clamp is

released; the instrument is held in the hand and is fixed on the tripod by turning

around the lower part with the other hand. The tripod legs are so adjusted that the

instrument is at a convenient height. Any two legs of the tripod are fixed on the

ground by pressing with the hand. The movement of the third leg is made in such a

way that the bubble remains in the centre. Thus the tribach is made approximately

horizontal.

2. Levelling up: After having levelled the

instrument approximately, accurate

levelling is done with the help of foot

screws and with reference to plate

levels. The purpose of levelling is to

make the vertical axis truly vertical. The

manner of levelling the instrument by

the plate levels depends upon whether

there are three or four levelling screws.

For three-screw levelling head; the telescope is placed parallel to a pair of screws and

by turning these screws, inwards or

outwards, the bubble is brought at the

centre. The telescope is then turned

through 90 so that it now lies over the

third screw and centre of the line

joining the other two screws. By

turning the third screw, the bubble is

centred and then, the telescope is

brought in its original position. The

procedure is carried out till the bubble

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remains in centre for both the positions which are at right angles to each other. It

should be noted that the bubble will move in the direction of movement of the left

thumb. For four-screw levelling head, the telescope is placed parallel to two

diagonally opposite foot screws in both positions and the above procedure is repeated

till the bubble remains in centre for both the positions.

In modern instruments, three foot screw levelling head is used in preference to a

four foot screw levelling head.

3. Elimination of parallax: Parallax is a condition arising when the image formed by the

objective is not in the plane of the cross hairs. Unless parallax is eliminated,

accurate sighting is impossible. Parallax can be eliminated in two steps:

a. Focusing the eyepiece: point the eye piece unit towards the sky (or hold a sheet of paper in front of the objective) and move eye-piece unit in or out with

respect to the cross-hairs so that the latter are seen sharp and distinct.

b. Focusing the objective: The purpose of focusing the objective is to bring the

image of object in the plane of cross-hairs which are clearly visible. The

telescope is directed towards the staff and the focusing screw is turned till the

image appears clear and sharp.

Permanent Adjustment of Levels

Principles of Levelling

Some of the important principles which are to be observed in simple direct levelling are as

follows:

1. Change point: The intermediate staff should be carefully selected and it should be in

the form of firm point which can be easily located. The elevation of change point

should be carefully determined as a slight error in it will be reflected in the subsequent

readings. If convenient, a bench mark can be used as a change point.

2. Lengths of B.S. and F.S.: For accurate work, the lengths of B.S. and F.S. should be

maintained nearly equal. If this condition is satisfied, the error due to non parallelism

of the line of collimation and the bubble line will be reduced to a great extent. When

the bubble is in the centre of its 'run; the line of collimation is horizontal. . This is

only possible when the line of collimation and the bubble line are exactly parallel.

Even if careful adjustments are performed, there are chances of not achieving the

absolute parallelism between the line of sight and the axis of the level tube. It will

naturally lead to an-error in the staff reading which is proportional to the distance

from the instrument to the staff. If the lengths of backsight and foresight are kept

nearly equal, the error due to non-parallelism of the line of collimation and the axis of

the bubble can be eliminated. This is known as balancing backsight and foresight

distances

If the back sight and the foresight distances are balanced, the difference in elevation

between two points can be directly calculated by taking the difference of the two rod

readings and no correction either for the inclination of the line of sight or for

curvature and refraction is necessary.

3. Position of level: As such, the level can be set up at any point. It is however desirable

to put the level on a firm spot from where maximum number of sights can be taken.

The selected spot for level should neither be too high nor too low and it should

preferably be located midway between the change points.

4. Starting and ending: The process of levelling at any point should start with backsight

or B.S. and it should end with foresight or F.S. Also, the process of levelling should

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always commence from a permanent Bench Mark or B.M. and end on a permanent

B.M.

Methods of Levelling

The levelling can broadly be divided into the following two categories:

1. Direct levelling or spirit levelling

2. Indirect levelling

1. Direct Levelling: It is the most commonly used method of levelling. The method

employs spirit level and telescope to measure vertical distances on the levelling staff

placed on various points. Various forms of direct levelling are as follows:

a. Simple levelling: This is used to find out the difference in elevations of two

points which are visible from a

single position of the level.

Following points should be noted:

i. If the point is situated at a

lower level, the staff

reading will be more and if

it is situated at a higher

level, the staff reading will

be less.

ii. It should be seen that the

bubble remains in its central position, when the readings are taken.

b. Differential levelling: The object of this method is solely to determine the

difference in elevation of two points regardless of the horizontal positions of the

points with respect to each other. It is also known as compound levelling or

continuous levelling, is resorted to under the following circumstances:

i. The points P and Q. are situated far away from each other.

ii. The difference in

elevations of

points P and Q is

too great.

iii. There is presence

of obstacles

between points P

and Q.

In this process, the

change points or C.P. are selected as required. The level is set up at O1 and with

the bubble in central position, the staff readings are taken for points P and first

C.P. The process is repeated at points O2 and O3 till the point Q is reached. The

difference in level of P and Q. can then be worked out by simple calculations.

Difference = (b1 a) + (c1 b2) + (b c2)

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If the difference works out to be positive, point Q is higher than point P and if it

works out to be negative point Q is lower than point P. It may be noted that the

readings at a change point are taken twice i.e. once before and the next after the

instrument is shifted. The location and situation of change point should be

carried out carefully. The positions O1, O2 and O3 of the instrument should be

selected in such a way that the level lies roughly midway between the points to

be read.

c. Reciprocal levelling: The

process of reciprocal

levelling is adopted to

calculate accurately the

true difference in levels

of two points which are

situated in such a way

that it is not possible to

set up the instrument at

any intermediate position

and from which the

lengths of the fore sight

and the back sight will be

even approximately

equal.

When this method is

adopted, the total error

due to curvature,

refraction and imperfect

collimation adjustment disappears.

It is carried out across a river, or a ravine or any obstale requiring a long sight

between two points.

d. Profile levelling: The process of levelling carried out along a given line to

determine the elevations of points at known distances is known as the profile

levelling or the longitudinal sectioning. It is done for short distances. It is done

in order to obtain a profile of the surface along a fixed line. The fixed line may

be a single straight line, or it may be composed of a succession of straight lines

or a series of straight lines

connected by curves. It is

also known as longitudinal

section. By means of such

sections the engineer is able

to study the relationship

between the existing ground

and the levels of the

proposed construction in

the direction of its length.

This process is useful for

getting the data for the

design of engineering

structures such as road,

railway, canal, sewer, water

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main, etc.

e. Cross sectioning: When the width of

the proposed project is not in the form

of a trip of small width, but exceeds

say 30m to 60m, it becomes necessary

to take levels in transverse direction

also. Such operation of levelling

carried out in the crosswise direction is

known as cross-sectioning and in most

of the cases, the cross-sections are

taken at right angles to the longitudinal

line as it is very easy to set up

perpendicular lines with the help of simple instruments like cross staff. The

cross-sections are usually run at constant distance along the centre line.

f. Precise levelling: For very accurate work, such as establishing bench marks,

extra-ordinary precautions are taken in the process of levelling to eliminate all

the possible errors.

The instruments used for such type of levelling are of the highest order and

perfectly in working condition. While working in the field, a high degree ofto

have any chance of error. For instance, the work of levelling is postponed on

rainy and windy days. No unnecessary haste is made to complete the work. The

check levels are taken in the opposite direction and preferably by another

surveyor.

g. Check levelling: The process of levelling carried out in the reverse direction i.e.

from end point to first point, just to check the difference in level between two

points, worked out previously, is known as check levelling. Many shortcuts may

be taken in check levelling as it is intended for checking the results of accurate

levelling done before hand.

h. Fly levelling: It becomes sometimes necessary to carry out levelling work along

two or three alternative routes of a proposed project. Hence, if accurate levelling

is adopted in such cases, it will take more time without any fruitful purpose.

Hence, to get in short time the rough idea about the nature of ground, the

levelling work is carried out speedily along each route. Such levelling is known

as fly levelling and the accuracy desired in the fly levelling is far less than that

in the check levelling.

2. Indirect Levelling: The relative levels of the points are found out by the indirect

observations and the following are the three forms of the indirect levelling.

a. Barometric levelling: The principle that atmospheric pressure varies inversely

with the altitude of a point is applied in case of barometric levelling. A

barometer is therefore used in this method and the readings observed at different

points give a measure of the relative elevation of those points. The process of

barometric levelling gives approximate results and it is therefore adopted in the

reconnaissance or preliminary survey.

b. Hypsometry: Init, the temperature at which water boils is taken as the basis for

determining the height of a point. As the altitude increases, the atmospheric

pressure decreases and due to this, the boiling point of water is lowered down.

c. Trigonometrical levelling: In case of trigonometrical levelling, the relative

elevations of different stations are worked out by taking the vertical angles and

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measuring or computing the horizontal distances. The vertical angles are

measured by means of a theodolite. The main advantage of this method is tha t it

brings down the number of change points to a minimum even though the

difference in level of two points is very great.

Entering the Staff Readings

Reduction of Levels

Levelling Problems

The following are some of the difficulties commonly encountered in levelling:

1. Levelling on steep slopes: When levelling is to be carried out, either uphill or down-

hill, care should be taken to avoid the errors due to the non verticality of the staff and

imperfect adjustment of the level. The former error is minimised by holding the staff

vertical and using a pendulum plumb bob. The latter error is minimised by equating;

as far as possible, the backsight and foresight distances. It is quite evident that while

levelling down hill, the foresights will be near the top of the staff and the backsights

will be near the foot of the staff. The reverse will be the case for levelling, uphill.

2. Levelling on summits and hollows: In levelling over summit, the level should be set

up sufficiently high so that the

summit can

be sighted

without extra

setting.

Similarly, in

levelling

across a hollow, the level should be set only

sufficiently low to enable the levels of all the

required points to be observed.

3. Taking level of an overhead point: When

the point under observation is higher than

the line of sight, staff should be kept

inverted on the overhead point keeping the

foot of the staff touching the point and

reading should be taken.

Such readings show the height of that

point above the line of sight and should be

added to the H.I. to get the R.L. of the

point.

4. Levelling ponds and lakes: When

the ponds and lakes are too wide

to be sighted across, advantage

may be taken of the fact that the

surface of still water is a level

surface.

5. Levelling across river: If the

width of the river is less, the

method of reciprocal levelling is

Levelling


to be used. If the river is too wide to be sighted across, levelling may be continued

from one side to the other with little error, provided care is taken to choose the

comparatively still stretch and to see that the water levels are taken at points directly

opposite each other.

6. Levelling past high wall: The problem of crossing a high wall during the process of

levelling can be solved in one of the

following ways:

i. Two pegs P and Q may be

driven on either side of wall.

The R.L. of point P is obtained

by taking a F.S. on it. The

height of wall is measured and

R.L. of top wall is determined.

The distance between top of

wall and peg Q is measured and

subtracting this distance from

the R.L. of top of wall, the R.L.

of peg Q is obtained. Then, a

B.S. is taken on peg Q and a

new line of sight is worked out. The levelling work is then continued.

ii. The line of sight is made to cut at point A on wall and from this point A, the distance of top of wall is measured. The R.L. of top of wall is then worked out.

Now, the instrument is transferred on the other side of wall and line of sight is

made to cut the wall at point B. The distance between point B and top of wall is

measured and then, new H.I. is obtained by deducting this measurement from

the R.L. of the top of wall. The levelling is then continued.

7. Taking reading when B.M. or staff station is above the line of sight: It becomes

sometimes necessary to adopt the underside of a girder, a string course beam, lintel or

some such feature to adopt as a B.M. and the situation arises in which the point is

above the line of sight. A very simple operation is performed to overcome this

difficulty. The staff is held inverted on the point and the reading is taken and ids

designated as negative. It is treated either as negative F.S. or negative B.S., as the case

may be. A note stating, that the reading is taken by keeping the staff in inverted

position is entered in the remarks column.

As far as possible, the situation leading to the inverted staff reading should be

avoided.

Following are the disadvantages of holding the staff inverted:

i. In some cases, it may prove very difficult to keep the zero of the staff in line

with the point whose level is required.

ii. It is difficult to keep the staff truly vertical.

iii. The proper sign may not be given while booking the reading. iv. The staff may be read wrong.

8. Taking reading when the staff is too near the level: It is desirable to a void the

situation of holding the staff very near to the level. However, when it is not possible

to a void such situation, the staff reading can be taken directly by looking through the

object glass or by measuring the staff up to the centre of the object glass.

Alternatively, a piece of paper may be used to serve the purpose of a target and it

should be moved up and down the staff till its edge is bisected by the line of

collimation. The reading where the edge of paper cuts the staff is then noted.

Levelling


Errors in Levelling

The process of levelling is subject to various errors and suitable precautions should be taken

to see that these errors do not cause appreciable effect on the results of the levelling work.

The errors can broadly be divided into the following three categories:

1. Instrumental errors: The instruments used for the levelling work may not be of

adequate standard. The usual instrumental errors can be enlisted as follows:

a. Defective levelling staff with incorrect lengths of graduations

b. Faulty focussing arrangement;

c. Line of collimation not parallel to the bubble tube axis

d. Over sensitive or under-sensitive bubble tube

e. Rigid joints of the tripod

2. Natural errors: The usual natural errors caused by the natural external forces can be

enlisted as follows:

a. Error due to atmospheric refractions and their changes;

b. Error due to curvature of earth;

c. Error due to settlement of tripod or change points;

d. Error due to vibrations caused by wind and not permitting the staff to be held

vertical;

e. Error due to variation in temperature; etc.

3. Personal errors: The errors caused by persons carrying the levelling process are

serious in the sense that they can be easily avoided, if the work is done with due care.

They can be enlisted as follows:

a. Bubble not at the centre while taking reading

b. Careless levelling of the instrument

c. Entering wrong remark against a reading

d. Exerting pressure on the telescope while focussing

e. The eye-piece and objective

f. Improper sighting due to imperfect focussing of the eye-piece and objective

g. Incorrect holding of the staff

h. Mistake in taking the reading

i. Omitting the entry

j. Ordinary arithmetical mistakes

k. Reading wrong metre mark on the staff

l. Wrong booking of the reading