3 levelling and applications

8/3/2019 3 Levelling and Applications

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3 Levelling and Applications

Level Line

Level surface:

It is any surface parallel to the mean spheroidal surface of the earth e.g. surface of a still

lake. Since the earth is a oblate spheroid, a level surface may be regarded as a curved

surface, every point on which is equidistant from the center of the earth. It is normal to the

plumb line at all points.

Level line:

It is line lying in a level surface. It is therefore, normal to the plumb line at all points.

There are three fundamental lines in a level instrument . These are

Vertical axis

Axis of the level tube

Line of sight

Fig 3. 1 Fundamental Lines in a Level

In a properly adjusted dumpy level, desired relations among fundamental lines are


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1. Axis of the level tube is perpendicular to the Vertical axis

2. Horizontal cross hair should lie in a plane perpendicular to the Vertical axis, so that itwill lie in a Horizontal plane when the instrument is properly leveled.

3. The Line of sight is parallel to the axis of the level tube.

Also, the optical axis, the axis of the objective lens and the line of sight should coincide.

Fig 3. 2 Desired Realations between Fundamental lines

Horizontal Line

Horizontal plane:

It is a plane tangential to the level surface at that point. It is perpendicular to direction of gravity

(plumb line).

Horizontal line:

It is any line lying in the horizontal plane. It is a straight line tangential to a level line.

Levels & Staves

A schematic diagram of an engineer's level is shown in Figure 3.3. An engineer's level primarily

consists of a telescope mounted upon a level bar which is rigidly fastened to the spindle. Inside

the tube of the telescope, there are objective and eye piece lens at the either end of the tube. Adiaphragm fitted with cross hairs is present near the eye piece end. A focussing screw is attached

with the telescope. A level tube housing a sensitive plate bubble is attached to the telescope (orto the level bar) and parallel to it. The spindle fits into a cone-shaped bearing of the leveling

head. The leveling head consists of tribrach and trivet with three foot screws known as leveling

screws in between. The trivet is attached to a tripod stand.


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Fig 3. 3 Schematic diagram of Engineer's level

Telescope : used to sight a staff placed at desired station and to read staff reading distinctly.

Diaphragm : holds the cross hairs (fitted with it).

Eye piece : magnifies the image formed in the plane of the diaphragm and thus to read staffduring leveling.

Level Tube : used to make the axis of the telescope horizontal and thus the line of sight.

Leveling screws : to adjust instrument (level) so that the line of sight is horizontal for anyorientation of the telescope.

Tripod stand : to fix the instrument (level) at a convenient height of an observer.


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Levelling Staff

It is a self-reading graduated wooden rod having rectangular cross section. The lower end of the

rod is shod with metal to protect it from wear and usually point of zero measurement from which

the graduations are numbered. Staff are either solid (having single piece of 3 meter height) ( Fig

3.4(a) ) or folding staff (of 4 meter height into two or three pieces) ( Fig 3.4(b)). The least countof a leveling staff is 5 mm.

Fig 3. 4 (a) Sinfle Piece 3 m staff (b) Folded staff

Spirit Level

A spirit level or bubble level is an instrument designed to indicate whether a surface is horizontal

(level) or vertical (plumb). Different types of spirit levels may be used by carpenters, stone

masons, bricklayers, other building trades workers, surveyors, millwrights and other

metalworkers, and in some photographic or videographic work.

Tilting level, dumpy level or automatic level [1] are terms used to refer to types of leveling

instruments as used in surveying to measure height differences over larger distances. It consists

of a spirit level in the above sense, mounted on a telescope containing cross-hairs, itself mounted

on a tripod. The observer reads height values off two staffs, one 'behind' and one 'in front', to

obtain the height difference between the ground points on which the staffs are resting. Starting
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from a point with a known (absolute) elevation, by repeating 'behind', 'front' and intermediate

'front' readings, (relative) height differences can be measured cumulatively over large distances

and elevations can be calculated of intermediate points

An engineer's spirit level is generally used to level machines, although they may be used to level

large workpieces on machines such as planers. Spirit levels are also used in buildingconstruction, by carpenters and masons.

The upper image is a plain precision level used in the engineering field to level machines or

workpieces, the lower image shows an adjustable precision level that has an accuracy of

1:10000. The adjustable nature of this level can also be used to measure the inclination of an

object.

The accuracy of a spirit level can be checked by placing it on any flat surface, marking the

bubble's position and rotating the level 180. The position of the bubble should then be

symmetrical to the first reading.

Both levels have a "vee" groove machined along the base which enables the level to sit on a

round bar while remaining parallel with the bar's axis. They also have a smaller cross level to

enable the second axis to be roughly checked or corrected.

Sensitiveness

Definition

The sensitivity of a level is defined as the change of angle or gradient required to move the

bubble by a set distance (usually 2mm). If the vial has graduated divisions then the sensitivity

refers to the angle or gradient change required to move the bubble by one of these divisions

(often spaced at 2mm).

Units

The sensitivity can be defined as an angle or a gradient.

As an angle, the standard units are degrees(), minutes(') and seconds(). 1 degree = 60minutes and 1minute = 60seconds. (1 = 60' and 1' = 60").

As a gradient the standard units are mm/m (millimetres per metre), although sometimes

inches/10 inches or a simple number gradient is used. For example a gradient of 1mm/m isthe same as 0.01"/10 inches which is the same as 1:1000.
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Principals

For all spirit levels the sensitivity

specification is determined by the sensitivity

of the vials that are used. The sensitivity isdetermined by the radius of curvature of the

vials which the bubble moves across. Eventhough it cannot always be seen, all spirit

level vials are curved. The principal of

operation is that the bubble will move to thehighest point of the radius as gravity acts on

the liquid inside the vial.

See the picture to the right for a clearer

explanation.See the range ofbubble level vialsproduced

by Level DevelopmentsSee the range ofcircular levelsproduced by

Level Developments

Example

If we assume that the bubble in this picture

has moved 2mm off centre then we would

say that this vial has a sensitivity of 5 degreesper 2mm bubble movement. This can also

be expressed as a gradient where 5 degrees

corresponds to a gradient of 87mm/m

(millimetres per metre). That is to say that ifthis vial was placed on a 1 metre long beam,

and one end was lifted by 87mm, this would

create an angle of 5 degrees and would thus

move the bubble by 2mm.

Relationship Between Radius and Sensitivity

The sensitivity is directly related to the radius

of curvature of the vial; the longer the radius,

the more sensitive the vial will be; the shorter

the radius, the coarser the vial will be. Wemanufacture vials with radiuses from 30mm

to 100 metres to suit a wide range of

applications. On the right is a table showingthe relationship between the radius of the vial

and it's sensitivity. In this table we have

represented degrees in decimal, and indegrees, minutes and seconds. Use the boxes

at the bottom of the table to put in your own

Radius

mm

Sensitivity per 2mm bubble movement

Deg Deg Min ' Sec " mm/m

30 3.8200 3 49 12 66.62

60 1.9100 1 54 36 33.33

120 0.9550 0 57 18 16.67

240 0.4775 0 28 39 8.33

480 0.2388 0 14 20 4.17

960 0.1194 0 7 10 2.08

1920 0.0597 0 3 35 1.04

4000 0.0287 0 1 43 0.50

8000 0.0143 0 0 52 0.25

16000 0.0072 0 0 26 0.13

32000 0.0036 0 0 13 0.06
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figures for conversion.

Deciding Which Sensitivity

In order to determine which sensitivity is best

for a particular application, it is firstnecessary to decide how level the product

needs to be. Another way of looking at this isto consider what is the maximum angle off-

level that the product will still work

correctly.

Lets say for this example that the product

needs to be level within 0.1 (or 6). The nextassumption we need to make is how

accurately the user can centre the bubblebetween the divisions on the vial. We would

normally assume that this is possible towithin 0.5mm although in some applications

it may be more or less than this. Based onthese figures, we need a vial that will give at

least 0.5mm bubble movement for a 0.1 (6)

change in angle. This corresponds to 0.4

(24) for a 2mm bubble movement, so wewould say that we need a vial with a

sensitivity of 24minutes per 2mm bubble

movement.

64000 0.0018 0 0 6 0.03

100000 0.0011 0 0 4 0.02

Bench Marks

The term bench mark, or benchmark, originates from the chiseled horizontal marks thatsurveyorsmade in stone structures, into which an angle-iron could be placed to form a "bench"

for aleveling rod, thus ensuring that a leveling rod could be accurately repositioned in the same

place in future. These marks were usually indicated with a chiseled arrow below the horizontal

line.

The term is generally applied to any item used to mark a point as an elevation reference.

Frequently, bronze or aluminum disks are set in stone or concrete, or on rods driven deeply intothe earth to provide a stable elevation point.

The height of a benchmark is calculated relative to the heights of nearby benchmarks in anetwork extending from a fundamental benchmark, a point with a precisely known relationship

to the level datum of the area, typically mean sea level. The position and height of each

benchmark is shown on large-scale maps.
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The terms "height" and "elevation" are often used interchangeably, but in many jurisdictions they

have specific meanings; "height" commonly refers to a local or relative difference in the vertical(such as the height of a building), whereas "elevation" refers to the difference from a nominated

reference surface (such as sea-level, or a mathematical/geodetic concept near sea level known as

the geoid). Elevation may be specified as normal height (above a reference ellipsoid),

orthometric height, ordynamic heightwhich have slightly different definitions.

Temporary and Permanent Adjustments

At each set up of a level instrument, temporary adjustment is required to be carried out prior toany staff observation. It involves some well defined operations which are required to be carried

out in proper sequence.

The temporary adjustment of a dumpy level consists of Setting , Leveling and Focusing .

During Setting, the tripod stand is set up at a convenient height having its head horizontal

(through eye estimation). The instrument is then fixed on the head by rotating the lower part ofthe instrument with right hand and holding firmly the upper part with left hand. Before fixing,

the leveling screws are required to be brought in between the tribrach and trivet. The bull's eye

bubble (circular bubble), if present, is then brought to the centre by adjusting the tripod legs.

Next, Leveling of the instrument is done to make the vertical axis of the instrument truly

vertical. It is achieved by carrying out the following steps:

Step 1: The level tube is brought parallel to any two of the foot screws, by rotating the upper part

of the instrument.

Step 2: The bubble is brought to the centre of the level tube by rotating both the foot screws

either inward or outward. (The bubble moves in the same direction as the left thumb.)

Step 3: The level tube is then brought over the third foot screw again by rotating the upper partof the instrument.

Step 4: The bubble is then again brought to the centre of the level tube by rotating the third footscrew either inward or outward.

Step 5: Repeat Step 1 by rotating the upper part of the instrument in the same quadrant of thecircle and then Step 2.

Step 6: Repeat Step 3 by rotating the upper part of the instrument in the same quadrant of thecircle and then Step 4.

Step 7: Repeat Steps 5 and 6, till the bubble remains central in both the positions.
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Step 8: By rotating the upper part of the instrument through 180 , the level tube is brought

parallel to first two foot screws in reverse order. The bubble will remain in the centre if theinstrument is in permanent adjustment.

Focusing is required to be done in order to form image through objective lens at the plane of the

diaphragm and to view the clear image of the object through eye-piece. This is being carried outby removing parallax by proper focusing of objective and eye-piece. For focusing the eye-piece,

the telescope is first pointed towards the sky. Then the ring of eye-piece is turned either in or outuntil the cross-hairs are seen sharp and distinct. Focusing of eye-piece depends on the vision of

observer and thus required whenever there is a change in observer. For focusing the objective,

the telescope is first pointed towards the object. Then, the focusing screw is turned until theimage of the object appears clear and sharp and there is no relative movement between the image

and the cross-hairs. This is required to be done before taking any observation.

The permanent adjustment of a level is tested by finding the relative position of fundamentallines.

Permanent Adjustment of Dumpy Level

If any fundamental relation is found to be disturbed in a dumpy level, the cross-hairs and leveltube are adjusted so that the fundamental relations get satisfied. The reference line for the

adjustments in dumpy level is the vertical line which remain fixed in direction, as it depends

upon the direction of gravity.

Axis of the Level Tube is Perpendicular to the Vertical axis

Test

After setting and leveling the level, turn the telescope through 180 about its vertical axis. If the

bubble remains central, the axis of the level tube is perpendicular to the Vertical axis. Otherwise,a displacement of the bubble from the central position indicates that the tube is not in adjustment.The amount of displacement is double the amount of error, by the principle of reversion (Fig

3.5).
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Fig 3. 5 Adjustment of axis of Level tube

Adjustment

Step 1: With the help of capstan screw, one end of the level tube is raised or lowered, as needed,so that the bubble is halfway back to the centre position.

Step 2: With the help of leveling screws, the other half of the displacement is moved further to

bring the bubble at centre.

The steps are repeated until the adjustment is perfected.

Horizontal Cross Hair Should Lie in a Plane Perpendicular to the Vertical axis

Test

A well-defined point is focused along the horizontal cross hair on one side of the field of view.

The instrument (telescope) is then rotated about its vertical axis. If the point appears to travel

along the horizontal cross-hair, the instrument is in adjustment i.e., the horizontal cross-hair liesin a plane perpendicular to the Vertical axis. Otherwise, there is a need for adjustment.

Let us rotate the instrument in such a way that the well defined point occupy a position on the

opposite side of the field of view, say X' (Figure 12.4). The cross hair ring is then rotated byloosening two adjacent capstan screws. Repeat the process until the point travels along the

horizontal cross hair
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The Line of Sight is Parallel to the axis of the Bubble Tube

Test

Two pegs are set at some distance (of about 60 to 90 m) on a fairly level ground. A dumpy level

is set up on a point which is equidistant from the pegs and preferably, in a line with the pegs.Staff readings are taken at the pegs, say the readings are a and b respectively. Then, the true

difference in elevation between the points is h = (a b). Now, the instrument is set on the line

oining the pegs near one of the pegs but opposite to the other peg, as shown in Figure 12.5. LetD1 and D2 are the distances of the near and far peg from the instrument position. Staff readings

are again taken at the pegs, say the readings are c and d respectively. Then, the apparent

difference in elevation between the points is h' = (c d). Now, if h' is found to be equal to h, the

line of sight of the level is parallel to the axis of the bubble tube. Otherwise, an adjustment of thebubble tube is required.

Adjustment

Step 1: The amount of error (e) associated with the observation is determined from

e = h h ' = (a b)(c d)

Step 2: The error e occurs in a distance of D = D2 - D1. Assuming the error e is positive and the

line of sight is inclined upward, the error in distance D2

Step 3: Calculate the correct staff reading at the distant peg as

Step 4: The capstan screws at the top and bottom of the diaphragm ring is then loosened and thering is moved vertically so that the line of sight intersect the distant staff at d'.

Step 5: To check the adjustment, read the staff reading on the near peg and it should read

If the near staff reading is not c', then repeat Step 4 and till Step 5 is satisfied.

This method is known as two peg method. In this method, due account need to be taken about


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sign throughout the test.

Methods of Leveling

Direct Leveling : Direct measurement, precise, most commonly used; types:

Simple leveling : One set up of level. To find elevation of points.

Differential leveling : Numbers of set-ups of level. To find elevation of non-intervisible points.

Fly leveling : Low precision, to find/check approximate level, generally used duringreconnaissance survey.

Precise leveling : Precise form of differential leveling.

Profile leveling : finding of elevation along a line and its cross section.

Reciprocal leveling : Along a river or pond. Two level simultaneously used, one at either end.

Indirect or Trigonometric Leveling : By measuring vertical angles and horizontal distance;Less precise.

Stadia Leveling : Using tacheometric principles.

Barometric Leveling : Based on atmospheric pressure difference; Using altimeter; Very roughestimation.

Booking

A field book, also called level book is being used for taking down each staff reading duringleveling and subsequently, used for finding out the elevation of points/ stations. There are two

types of level books. Usually, level book contains columns of both the types together and it is fora surveyor to use only the relevant columns only.

Reduction

The observed staff readings as noted in a level book are further required to be manipulated to

find out the elevation of points. The operation is known as reduction of level. There are twomethods for reduction of levels:

1. Rise and Fall method and

2. Height of instrument method.

Rise and Fall method


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For the same set up of an instrument, Staff reading is more at a lower point and less for a

higher point. Thus, staff readings provide information regarding relative rise and fall ofterrain points. This provides the basics behind rise and fall method for finding out

elevation of unknown points.

Fig 3. 6 Differential Levelling

With reference toFig 3.6, when the instrument is at I1, the staff reading at A (2.365m) ismore than that at S1 which indicates that there is a rise from station A to S1 and

accordingly the difference between them (1.130m) is entered under the rise column inTable 3.1. To find the elevation of S1 ( 101.130m), the rise (1.130m) has been added to

the elevation of A (100.0m). For instrument set up at I2 , S1 has been treated as a point of

known elevation and considered for backsight (having reading 0.685m) . Foresight is

taken at S2 and read as 3.570m i.e, S2 is at lower than S1 . Thus, there is a fall from S1 and S2 and there difference (2.885m) is entered under the fall column in Table 13.1. To

find the elevation of S2 ( 98.245m), the fall (2.885m) has been subtracted from the

elevation of S1 (101.130m). In this way, elevation of points are calculated by Rise and

Fall method.

Staff Reading Difference in Elevation Elevation

Points B.S (m) F.S.(m) Rise (m) Fall (m) R.L (m) Remark

A 2.365 100.000 B.M.

S 1 0.685 1.235 1.130 101.130 T.P.1

S2 1.745 3.570 2.885 98.245 T.P. 2

B 2.340 0.595 97.650Table 3. 1 Level book note for Rise & Fall Method

Height of Instrument Method

In any particular set up of an instrument height of instrument, which is the elevation of the line

of sight, is constant. The elevation of unknown points can be obtained by subtracting the staffreadings at the desired points from the height of instrument. This is the basic behind the height of

instrument method for reduction of level.
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Fig 3. 7 Differential Levelling

With reference toFig3.7 andTable 3.2, when the instrument is at I1, the staff reading observed at

A is 2.365m. The elevation of the line of sight i.e., the height of instrument is 102.365m obtainedby adding the elevation of A (100.0m) with the staff reading observed at A (2.365m). Theelevation of S1 (101.130m) is determined by subtracting its foresight reading (1.235m) from the

the height of instrument (102.365m) when the instrument is at I1 . Next, the instrument is set up

at I2. S1 is considered as a point of known elevation and backsight reading ( 0.685m) is taken .The height of the instrument (101.815 m) is then calculated by adding backsight reading (

0.685m) with the elevation (R.L.) of point S1 (101.130m). Foresight is taken at S2 and its

elevation (98.245m) is determined by subtracting the foresight (3.570m) from the height of the

instrument (101.815 m). In this way, elevation of points are calculated by Height of instrumentmethod.

Staff Reading Height of Instrument(m)

R.L. (m) RemarksPoints B.S (m) F.S.(m)

A 2.365 102.365 100.000 B.M.

S 1 0.685 1.235 101.815 101.130 T.P.1

S2 3.570 98.245 T.P.2

B 2.340 97.650

Table 3. 2Level book note for Height of Instrument Method
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Curvature & Refraction

Curvature of the earth:

The earth appears to fall away with distance. Thecurved shape of the earth means that the level

surface through the telescope will depart from thehorizontal plane through the telescope as the line of

sight proceeds to the horizon.

This effect makes actual level rod readings too

large by:

where D is the sight distance in thousands of feet.

Effects of Curvature are:

Rod reading is too high

Error increases exponentially with distance

Atmospheric Refraction:

Refraction is largely a function of atmosphericpressure and temperature gradients, which may

cause:

the bending to be up or down by extremely

variable amounts.

There are basically three types of temperature gradient (dT/dh):

1. Absorption: occurs mainly at night when the colder ground absorbs heat from the

atmosphere. This causes the atmospheric temperature to increase with distance from the

ground and dT/dh > 0.2. Emission: occurs mainly during the day when the warmer ground emits heat into the

atmosphere, resulting in a negative temperature gradient, i.e. dT/dh < 0.

3. Equilibrium: no heat transfer takes place (dT/dh = 0) and occurs only briefly in theevening and morning.
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4. The result of dT/dh < 0 is to cause the light ray to be convex to the ground rather than

concave as generally shown.

This effect increases the closer to the ground the light ray gets and errors in the

region of 5 mm/km have resulted.

The atmosphere refracts the horizontal line of sight downward, making the level rod readingsmaller. The typical effect of refraction is equal to about 14% of the effect of earth curvature.

The combined effect of curvature and refraction is approximately

Fig 3. 8 Curvature & Refraction

The formula for computing the combined effect of curvature and refraction is:

C + R = 0.021K2


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Where C = correction for curvature

R = correction for refraction

K = sighting distance in thousands of feet

Correlations for various distances

Distance Correction

100' 0.00021'

200' 0.00082'

500' 0.0052'

700' 0.01'

1 mile 0.574'

How to eliminate error due to Curvature and Refraction

1. Proper field procedures (taking shorter shots and balancing shots) can practically reduceerrors

2. Wherever possible, staff readings should be kept at least 0.5 m above the ground,

3. Using short observation distances (25 m) equalized for backsight and foresight4. Air below is denser than air above Air below is denser than air above, Line of sight is

bent downward which Negates earth curvature error by 14%.

5. Simultaneous Reciprocal Trigonometrical Heighting

6. Observations made at each station at exactly the same time, cancels the effects ofcurvature and refraction

Reciprocal Leveling

This procedure is used for either differential or trigonometric leveling when along sight across a

wide river, ravine, or similar obstacle must be made. This long sight will be affected by

curvature and refraction and by any small error in aligning the line of sight with the bubble axis.

The alignment error can be minimized by balancing the long sight and computing the

curvature. The atmospheric conditions will vary so much over an open expanse that the

refraction correction will be quite erratic. Reciprocal leveling is desired to minimize the effect of

the atmosphere as well as the line of sight and curvature corrections. To do this, take the

following actions: 1. In reciprocal leveling, balance the BSs and FSs as carefully as possible

before you reach the obstacle. In figure 14-15, a TP, N, is selected close to the edge of the

obstruction so that it is visible from a proposed instrument location, B, on the other side. A

second rod is held on the other side of the obstruction at F. Point F should be selected so that
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the equivalent distances, AN and FB, and AF and NB, are almost equal. The instrument

is setup at point A and leveled carefully. A BS reading is taken on the N rod and an FS on the F

rod. These readings are repeated several times. The instrument is moved to point B, set

up, and carefully leveled. The rods remain at their stations. Again, a BS is taken on the N rod

and an FS on the F rod, and repeated several times. Since instrument leveling is especially

critical on reciprocal leveling, you need to check the bubble before each reading and center it

carefully. If it is off-center a slight amount, the procedure must be repeated. The

difference in elevation between N and F is computed from the readings at A setup and

from the readings at B setup separately. Because of the errors in the long sight, the two results

will have slightly different values. Note, however, that the long sight is an FS from A and a BS

from B. The true difference in elevation is the average of both values, since the errors have

opposite signs and will cancel each other.

2. For more accuracy, make several long sight readings for each short sight and average

them. You should use a target on the rod and reset it for each reading. Average each series of

long sights and combine this average with corresponding short sights for the

computations. 3. Changes in atmospheric density and temperature affect the refraction of

a line of sight. The longer the time interval is between reciprocal long sights, the greater the

chance of an atmospheric change and a variation in the refraction value. For this reason, you

should keep the time lapse between the long sights as short as possible. 4. An excellent method

of avoiding the time lapse problem is simultaneous-reciprocal observation. The object is to read

both long sight values at the same time. This requires two instruments and two observers and two

rods and two rodmen. Some method of communication or sequence of operationsmust be agreed upon. 5. The note keeping for reciprocal leveling is identical to

differential leveling. Take a series of either BS or FS readings on the far rod from one setup

and take only one sighting on the rear rod. Average the series of readings, and use a single value

to make the elevation computations

Longitudinal and Cross Section


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In many projects, terrain information transverse to the longitudinal section (through profileleveling) is also required such as for highways, railways, canals etc. In those cases, surveying iscarried out at right angle to the central line, generally, at regular interval is being carried out and

is termed as cross- sectioning. If, for any reason, a cross-section is run in any other direction, the

angle with the centre line is required to be noted. The observations are then recorded as being to

the left or right of the centre line. The notes of the readings are maintained as shown in Table 3.3for taking a cross-section along the stake point 4. Reduction of levels, Plotting etc. can be done

as in case of profile leveling. A plotting of the cross section at stake 4 is as shown in Figure 3.9.

Fig 3. 9 Reduction Level

PegsDistance(m)DirectionStaff reading (m)

Difference in

elevation (m) H.I (m)R.L

(m)Remark

B.S. I.S. F.S. Rise (m) Fall (m)

A 3.005 108.620 105.615 B.M.

:

4 0+30 2.105 0.320 106.515 0m

1.850 106.770 2m left

1.725 106.895 4m left

1.680 106.940 6m left

1.985 106.635 2m right1.875 106.745 4m right

1.780 106.840 6m right

B 0+40 2.875 3.105 1.000 108.390 105.515 T.P.1

Table 3. 3 Feild book for reduction level


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Plotting

Plotting of profile leveling provides a graphical representation of the ground points on alongitudinal section along the alignment. It is being used to determine the depth of cutting or

filling on the proposed gradient (for highways, railways, canals, etc.), to study grade crossing

problems, to select appropriate grade, to locate depth of sewer, tunnels etc. In this, a datum lineis drawn along which distance of the stakes are marked and reduced levels are plotted along

vertical lines drawn on the marked points. Segmented straight lines joining the reduced levelpoints represent the longitudinal profile of the ground surface. Profile is generally drawn so that

the vertical scale is much larger than the horizontal scale in order to accentuate the differences of

elevations.

Fig 3.10shows the longitudinal section of the profile leveling (Fig 3.9). In this, the datum and

ground lines are drawn in black and the ordinates in blue. The value of the datum line is given

and the reduced levels are written against ordinates.

Fig 3. 10 Profile of Longitudinal Section

Contour

A contour is defined as an imaginary line of constant elevation on the ground surface. It can also

be defined as the line of intersection of a level surface with the ground surface. For example, theline of intersection of the water surface of a still lake or pond with the surrounding ground

represents a contour line.

A line joining points of equal elevations is called a contour line. It facilitates depiction of therelief of terrain in a two dimensional plan or map.


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Contour Interval

The difference in elevation between successive contour lines on a given map is fixed. This

vertical distance between any two contour lines in a map is called the contour interval (C.I.) of

the map.Fig 3.11(a) shows contour interval of 1m whereas Fig 3.11(b) shows 10m.

Fig 3. 11 Contour Lines Showing CI (a) 1 m (b) 10 m

The choice of suitable contour interval in a map depends upon four principal considerations.These are:

Nature of the Terrain

Nature of Terrain

The contour interval depends upon the nature of the terrain (Table 3.4). For flat ground, a small

contour interval is chosen whereas for undulating and broken ground, greater contour interval is

adopted.

Sl. No Purpose of survey Scale CI (m)

1 Building site 1/1000 or less 0.2 to 0.5

2Town planning,

reservoir etc.1/5,000 to 1/10,000 0.5 to 2

3Location Survey,

earthwork, etc.1/10,000 to 1/20,000 1 to 3

Table 3. 4 Contour Interval (CI) for different Types of Survey

Scale of the Map

The contour interval normally varies inversely to the scale of the map i.e., if the scale of map is

large, the contour interval is considered to be small and vice versa (Table 3.5).
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SI.NO Map ScaleType of

TerrainCI(m)

1

Large

(1:1000 or

less)

Flat 0.2 to 0.5

Rolling 0.5 to 1

Hilly 1 to 2

2

Intermediate

(1:1000 to

1: 10,000)

Flat 0.5 to 1.5

Rolling 1.5 to 2

Hilly 2 to 3

3

Small

(1: 10,000

or more)

Flat 1 to 3

Rolling 3 to 5

Hilly 5 to 10

Table 3. 5 CI for different Scales and type of ground

Accuracy

Accuracy need of surveying work also decide the contour interval. Surveying for detailed designwork or for earthwork calculations demands high accuracy and thus a small contour interval isused. But in case of location surveys where the desired accuracy is less, higher contour interval

should be used.

Time of Cost

If the contour interval is small, greater time and funds will be required in the field survey, in

reduction and in plotting the map. If the time and funds available are limited, the contour interval

may be kept large.

Horizontal Equivalent

The horizontal distance between two points on two consecutive contour lines for a given slope isknown as horizontal equivalent. For example, inFigure 3.11 (b)having contour interval 10m, the

horizontal equivalent in a slope of 1 in 5 would be 50 m. Thus, horizontal equivalent depends

upon the slope of the ground and required grade for construction of a road, canal and contourinterval.
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The method of establishing / plotting contours in a plan or map is known as contouring. Itrequires planimetric position of the points and drawing of contours from elevations of the plotted

points. Contouring involves providing of vertical control for location of points on the contours

and horizontal control for planimetric plotting of points. Thus, contouring depends upon theinstruments used (to determine the horizontal as well as vertical position of points). In general,

the field methods of contouring may be divided into two classes:

Direct methods

In the direct method, the contour to be plotted is actually traced on the ground. Points which

happen to fall on a desired contour are only surveyed, plotted and finally joined to obtain the

particular contour. This method is slow and tedious and thus used for large scale maps, smallcontour interval and at high degree of precision. Direct method of contouring can be employed

using Level and Staff as follows:

Vertical control : In this method, a benchmark is required in the project area. The level is set up

on any commanding position and back sight is taken on the bench mark. Let the back sight

reading on the bench mark be 1.485 m. If the reduced level of the bench mark is 100 m, theheight of instrument would be 100 + 1.485 = 101.485 m. To locate the contour of 100.5 m value,

the staff man is directed to occupy the position on the ground where the staff reading is 101.485 -

100.500 = 0.985 m. Mark all such positions on the ground where the staff reading would be0.985 m by inserting pegs. Similarly locate the points where the staff reading would be 101.485 -

101 = 0.485 m for 101m contour. The contour of 101.5 m cannot be set from this setting of the

instrument because the height of instrument for this setting of the instrument is only 101.485 m.

Therefore, locating contours of higher value, the instrument has to be shifted to some other

suitable position. Establish a forward station on a firm ground and take fore sight on it. Thispoint acts as a point of known elevation, for shifting the position of the instrument to another

position, from where the work proceeds in the similar manner till the entire area is contoured.

Horizontal control : The horizontal control is generally provided by method of plane table

surveying or locating the positions of points by other details in which will be discussed in latermodule (Fig 3.12).


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Fig 3. 12 Direct Method of Contouring

Indirect methods

In this method, points are located in the field, generally as corners of well-shaped geometrical

figures such as squares, rectangles, and spot levels are determined. Elevations of desiredcontours are interpolated in between spot levels and contour lines are drawn by joining points of

equal elevation.

Indirect methods are less expensive, less time consuming and less tedious as compared to the

direct method. These methods are commonly employed in small scale surveys of large areas or

during mapping of irregular surface or steep slope. There are two different ways usuallyemployed for indirect method of contouring:
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Grid method

In this method, the area to be surveyed is divided into a grid or series of squares (Figure 17.12).

The grid size may vary from 5 m x 5 m to 25 m x 25 m depending upon the nature of the terrain,

the contour interval required and the scale of the map desired. Also, the grids may not be of the

same size throughout but may vary depending upon the requirement and field conditions. The

grid corners are marked on the ground and spot levels of these comers are determined byleveling. The grid is plotted to the scale of the map and the spot levels of the grid corners are

entered. The contours of desired values are then located by interpolation. Special care should betaken to give the spot levels to the salient features of the ground such as hilltops, deepest points

of the depressions, and their measurements from respective corners of the grids, for correct

depiction of the features. The method is used for large scale mapping and at average precision

Fig 3. 13 Contouring by Grid Method

Radial line method

In this method, a number of radial lines are set out at known angular interval at

each station and points are marked at the ground at convenient distance apart on the rays

that are set. Spot levels of these points are determined by leveling. The points are plottedto the scale of the map and spot levels are entered. The contours of desired values are

then located by interpolation. This method is convenient in hilly terrain with level

stations chosen at high points so as to command a large area from each. Horizontal

control may be obtained by taping


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Fig 3. 14 Contouring by Radial Line Method

Characteristics & Uses of Contours

The principal characteristics of contour lines which help in plotting or reading a contour map areas follows:

1. The variation of vertical distance between any two contour lines is assumed to be

uniform.2. The horizontal distance between any two contour lines indicates the amount of slope and

varies inversely on the amount of slope. Thus, contours are spaced equally for uniformslope (Figure 17.2); closely for steep slope contours (Figure 17.3) and widely for

moderate slope (Figure 17.4).3. The steepest slope of terrain at any point on a contour is represented along the normal of

the contour at that point (Figure 17.5). They are perpendicular to ridge and valley lines

where they cross such lines.4. Contours do not pass through permanent structures such as buildings (Figure 17.6)
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5. Contours of different elevations cannot cross each other (caves and overhanging cliffs are

the exceptions). (Figure 17.7)6. Contours of different elevations cannot unite to form one contour (vertical cliff is an

exception). (Figure 17.8)

7. Contour lines cannot begin or end on the plan.

8.

A contour line must close itself but need not be necessarily within the limits of the map.9. A closed contour line on a map represents either depression or hill (Figure 17.9(a)). A set

of ring contours with higher values inside, depicts a hill whereas the lower value inside,

depicts a depression (without an outlet)Figure 17.9(b).10.Contours deflect uphill at valley lines and downhill at ridge lines. Contour lines in U-

shape cross a ridge and in V-shape cross a valley at right angles. The concavity in

contour lines is towards higher ground in the case of ridge and towards lower ground inthe case of valley (Figure 17.10).

11.Contours do not have sharp turnings.

Uses of Contours

Nature of Grounds

To visualize the nature of ground along a cross section of interest, a line say XY is being

considered through the contour map (Fig3.15). The intersection points between the line andcontours are projected at different elevations of the contours are projected and joined by

smooth curve. The smooth curve depicts the nature of the ground surface along XY.
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Fig 3. 15 Nature of Terrain From Contour Map

To Locate Route

Contour map provides useful information for locating a route at a given gradient such as

highway, canal, sewer line etc.Let it be required to locate a route from P to Q at an upward gradient of 1 in 100. The contourmap of the area is available at a contour interval of 5 meter at a scale of 1:10000. The

horizontal equivalent will therefore be equal to 100 meter. Then with centre at P with a

radius of 2 cm draw an arc to cut the next higher contour, say at q. With q as centre, mark the

next higher contour by an arc of radius 2 cm say at r. Similarly, other points such as s,t,u.etc are obtained and joining the points provides the location of route

Fig 3. 16 Contour Gradient on the Ground
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Intervisibility between Stations

When the intervisibility between two points can not be ascertained by inspection of the area,

it can be determined using contour map. The intervisibility is determined by drawing a line

joining the stations / points say PQ and plot the elevations of the points and contours

intersected by PQ as shown in Fig 3.15. If the intervening ground is found to be above A'B'line, the intervisibility is obstructed. In the figure, the ground is obstructing the line of sight.

To Determine Catchment Area or Drainage Area

The catchment area of a river is determined by using contour map. The watershed line which

indicates the drainage basin of a river passes through the ridges and saddles of the terrain

around the river. Thus, it is always perpendicular to the contour lines. The catchment area

contained between the watershed line and the river outlet is then measured with a planimeter(Fig 3.17).

Fig 3. 17 Shaded portion shows catchment area of a river

Storage capacity of a Reservoir

The storage capacity of a reservoir is determined from contour map. The contour line

indicating the full reservoir level (F.R.L) is drawn on the contour map. The area enclosedbetween successive contours are measured by planimeter (Figure 18.5). The volume of waterbetween F.R.L and the river bed is finally estimated by using either Trapezoidal formula or

Prismoidal formula
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Fig 3. 18 Contours showing storage capacity of a reservoir

Plotting

Points of desired elevation, at which contours are desired to be drawn, are interpolated inbetween observed points. Then, contours are drawn by joining points of equal elevation by

smooth curves keeping in mind the principal characteristics of contour. They are then inked in,preferably in brown to distinguish them from other features. The contour value is written down

in a gap in the line provided for the purpose. Every fifth contour is drawn bolder to make itdistinguishable from the rest.

In a hydro-electric project, the reservoir provides a storage of 5.9 million cubic meter betweenthe lowest draw down and the top water level. The areas contained within the stated contours andthe upstream face of the dam are as follows :

Contour (m) 200 195 190 185 180 175 170 165

Area (104

sq m) 44 34 28 23 20 16 11 8

If the R.L. of the lowest draw down is 167 m, find the reduced level of water at the full storage

capacity of the reservoir.

Solution :

The area contained in lowest draw down level i.e. at 167 m is as follows :

Given, contour interval = 5 m

The area contained between 165 m and 170 m level is (11 - 8) x 104 = 3 x 104 sq m

i.e., For a height of 5 m, difference in area = 3 x 104 sq m

Therefore between 165 m and 167 m, i.e. for a height drift of 2 m, the area difference


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= 1.2 x 104 sq m

The area contained in 167 m contour = (8 + 1.2 ) x 104 sq m = 9.2x 104 sq m

Now from given and calculated data and using trapezoidal rule

ContourArea contained

(104)

Volume contained

between (104)

Volume contained by

(104)

167 9.2

30.3

170 11.0 30.3

67.5

175 16.0 97.8

90.0180 20.0 187.8

107.5

185 23.0 295.3

127.5

190 28.0 422.8

155.0

195 34.0 577.8

195.0

200 44.0 772.8

So, at full storage capacity, the height of water level lies between 195 m and 200 m.

The volume of water beyond 195 m height is

(5.9 x 106 - 5.778 x 106) = 1.22 x 105 cu.m

Let h be the height of water level above 195 m height. Then area contained in (195 + h) mcontour is

= 34 x 104

+

The volume between 195 m and (195 + h) m contour is


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or, h2

+ 34 h -12.2 = 0

Solving, we get h = 0.355 m

Thus the reduced level of water at the full reservoir capacity is (195 + 0.355) = 195.355 m

3 levelling and applications

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