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DEPARTMENT OF CIVIL ENGINEERING Surveying-2 Field Book of Group-04 Prepared By: Gulfam akram 2013-CIV-336 0346-7473080 U NIVERSITY OF ENGINEERINGAND TECHNOLOGY LAHORE ( NAROWAL CAMPUS )

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Page 1: Surveying and leveling-2

DEPARTMENT OF CIVIL ENGINEERING

Surveying-2 Field Book of Group-04

Prepared By: Gulfam akram 2013-CIV-336

0346-7473080

U N I V E R S I T Y O F E N G I N E E R I N G A N D T E C H N O L O G Y L A H O R E ( N A R O W A L C A M P U S )

Page 2: Surveying and leveling-2

Job # 1

Title: Study of Topcon Theodolite

Objective: To get knowledge about transit theodolite and study about its

different parts.

Apparatus:

i) Transit Theodolite ii) Tripod iii) Plumb Bob

Related theory:

Definition:

A theodolite is a precise instrument for measuring angles in the horizontal and vertical

planes. A theodolite enables angles to be accurately measured in both the horizontal and

vertical planes. How accurately this can depend partly on the quality of the instrument, and

partly to the competence and experience of the Surveyor.

Basic Types: In 19th century, On the basis of movement of telescope it has been divided into two main types.

1-Transit theodolite 2- Non- transit theodolite In first one telescope can be revolved up to 180° i.e., Transit but in second one

telescope can’t revolve up to 180°. It featured a telescope that could flip over to allow easy back-sighting and doubling of angles for error reduction.

Description of Components: Following are the parts of Theodolite which are discussed as

follows:

1-Telescope: In theodolite, it is used to view our target/object that is actually to measure the

angles which need for complete description of land that is between two station points .It has eye-piece and object glass. On it, screws are present to adjust circle for centering as well as to see the cleared image in object glass by finishing blurredness.

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2-LCD & Keyboard:

As theodolite gives digital reading that has been displayed on LCD. Along

with LCD, there has been keyboard having different controls/buttons to attain different modes/target. On keyboard there are six buttons that are used for different purposes. These

are given below i- Power Button ii-Function iii-R/L

iv- V% v- Zero Set vi-Hold

Note:

Face left: The theodolite position in which the vertical circle is on the viewer's left while he looks into

the telescope.

Face right: The theodolite position in which the vertical circle is on the viewer's right while he looks into

the telescope.

Telescope

Sighting

collimator

Lifting handle

Vertical

circle

Optical

plummet

Base plate

Vertical

clamp

Operating

buttons

LCD

screen

Leveling

screws

Vertical

slow motion

srew

Page 4: Surveying and leveling-2

3- Vertical Scale (or Vertical Circle): It is known as graduated circle. It is a full 360° circle. It has been kept standard to decide the face of theodolite. If vertical circle is at left side of Surveyor while taking observations then that will be the face either left or right.

4- Vertical clamp / Tangent screw: In order to hold the telescope at a particular vertical angle a

vertical clamp is provided. This is located on one of the standards and its release will allow free transiting of the telescope. When clamped, the telescope can be slowly transited using another fine adjustment screw known as the vertical tangent screw.

5-The Horizontal clamp and Tangent screw: Th horizontal clamp is provided to clamp the horizontal circle. Once the clamp is released

the instrument is free to traverse through 360° around the horizontal circle. When clamped, the instrument can be gradually transited around the circle by use of the horizontal tangent screw.

6-Bubble tube, Leveling screws and circular bubble: All these are the parts of theodolite that is helpful in setting the theodolite. Leveling of instrument is done by leveling screws and

circular bubble must be in center for correct setting of theodolite. Note: circular bubble is also known as pill bubble and bull’s eye.

7-Slow-motion screw: The fine adjustment screw used to translate the theodolite in the horizontal or vertical plane

when the horizontal or vertical clamp is tightened.

Setting of a Theodolite:

1-Tripod Setup: Following steps are involved in setting up a

tripod.

a) Place the tripod over the positioning mark, setting the legs

at a convenient height, and roughly center and level the

tripod head by naked eye

b) Firmly fix the tripod feet in position. If necessary, adjust

the heights of the tripod legs to re-center the tripod.

2- Theodolite Setup (Centering & leveling):

Page 5: Surveying and leveling-2

a) Place theodolite on tripod and fix it on tripod.

b) Looking through the optical plummet, focusing

the centering index mark. Slide the theodolite on

tripod until the reference mark is centered in the

optical plummet.

c) Fully tighten the centering screw. Look through

optical plummet we may adjust the theodolite

foot screws for alignment with reference mark.

d) By adjusting the length of two tripod legs at a

time while keeping the other one still, the

circular bubble can be leveled without causing

disturbance to the previously accomplished centering (check the optical plummet to

see this is true).

e) Rotate the theodolite until its plate bubble is parallel to any two foot screws, and then

adjust these screws to center the bubble. Now rotate the theodolite body by 90, and

center the bubble with the third foot screw only.

Repeat this procedure for each 90 revolution of the

instrument until the bubble is centered for all four

positions. Now check the optical plummet: adjustment

of the foot screws has probably disturbed the

centering.

f) Loosen the tripod screw, and slowly translate (do not

rotate) the theodolite around until it is exactly centered

over the survey point, then tighten the screw.

3-Packing Up:

(a) Turn off

theodolite

(c) Align the theodolite as it was before packing

(d) Bring the theodolite foot screws to the center of

their travel

(e) Holding the theodolite handle

with one hand, undo the centering

screw with the other.

(f) Put the theodolite back in the box in its original position and close the clasps.

(g) Being careful not to disturb the positioning mark, lift the tripod

Page 6: Surveying and leveling-2

away , collapse it, and put it away.

Precautions:

Set the instrument carefully

Use theodolite carefully

Bisect the target with accuracy

Unclamp before attaining required movement.

COMMENTS:-

The station points are not visible from other stations.

The poles are not placed at the stations to locate only one station.

The center of plumb bob and optical plummet was not same.

Page 7: Surveying and leveling-2

Job # 02 Title: Measurement of Base Line by Manual Method Objective: To find out the length of base line with complete accuracy by Applying all

Corrections.

Apparatus:

I. Theodolite

II. Auto level

III. Thermometer

IV. Spring balance

V. Supporting stands

VI. Mallet & Pegs

VII. Steel tape

VIII. Fiber glass tape

IX. Leveling staff

Related Theory:

Base Line:

In triangulation the base line is of prime importance (b/c). It is the only for distance to measured. It should be measured

very accurately since the accuracy of the computed sides of triangulation system depends on it. Length of base line

varies from a fraction of (0.5-10) km and a fraction of a mile to 10 miles.

And selecting site for a base line, the following requirement should be considered:

1. The site should be fairly leveled or uniformly sloping or gauntly undulating.

2. Should be free from obstructions throughout the entire length. 3. Ground should be firmed and smooth. 4. The site should be such that the whole length can be laid out the extremities of the line being visible at ground

level. 5. The site should be such that well shaped triangle can be obtained in connecting the end stations of the base line

to the main triangulation stations.

Theodolite:

A theodolite is a precision instrument for measuring angles in the horizontal and vertical planes. Theodolites

are mainly used for surveying applications. A modern theodolite consists of a movable telescope mounted within two

Page 8: Surveying and leveling-2

perpendicular axes—the horizontal or trunnion axis, and the vertical axis. When the telescope is pointed at a target

object, the angle of each of these axes can be measured with great precision, typically to seconds of arc.

Least count: Its L.C. is 5”. But 1” L.C. is also available.

Auto level:

Auto level, leveling instrument, or automatic level is an optical instrument used to establish or check points

in the same horizontal plane. It is used in surveying and building to transfer, measure, or set horizontal levels.

Thermometer:

A thermometer is a device that measures temperature or temperature

gradient using a variety of different principles. A thermometer has two important

Eye piece

Focusing screw

Telescope

Object glass

Leveling screws

Circular bubble

Slow motion

screw

Base plate

Page 9: Surveying and leveling-2

elements: the temperature sensor (e.g. the bulb on a mercury thermometer) in which some physical change occurs with

temperature, plus some means of converting this physical change

into a numerical value (e.g. the scale on a mercury thermometer).

Least count: Its L.C. is 1 degree.

Spring Balance:

A spring balance apparatus is simply a spring fixed at one

end with a hook to attach an object at the other. It works by Hooke's

Law, which states that the force needed to extend a spring is

proportional to the distance that spring is extended from its rest position.

Therefore the scale markings on the spring scale are equally spaced.

Before using this instrument we should check its zero error.

It may be of two types:

i. +ve zero error

ii. -ve zero error

+ve error is subtracted and –ve error is added in the measurement taken.

Supporting stands:

Supporting stand/wooden tripod/ trussles are the tripod stand which we have used to divide the line into the

length less than the 30 m tape length and for the line along the actual base line.

Mallet & Pegs:

Mallet & Pegs were used to mark the station point.

Steel tape:

It is 30 m length tape made up of steel. This was used to

measure the length of line in the pull applied condition.

Least count:Its least count is 1 mm.

Page 10: Surveying and leveling-2

Fiber glass tape:

It is also a 30 m length tape made up of fiber glass. This was not used in full condition because it would

elongate with full of 5 kg.

Least count:

Its least count is 1 mm.

Leveling staff:

A level staff, also called leveling rod, is a graduated wooden or aluminum rod, the use of which permits the

determination of differences in elevation. It is of 5 m length.

Least count:

Its least count is 0.005 m.

Ranging Rod:

This is 2 m length iron rod divided into many parts which are colored red and

white or white and black. This has one end which can be screwed or the station. This

used where we cannot see the station base.

Procedure:

There are so many method for accurate measurement of base line but the

method we are doing is

Manual method

Select the base line namely as AB.

Set the theodolite at A (initial point) after doing the temporary adjustment

(centering, leveling & focusing) sight the point B (end point of base line).

Divide the base line into lines of length less than the 30 m we which is the length of the tape marks these point

temporary with the pegs.

Set the trussles on these points. These points should be in a line this can be done by the theodolite which is sighting

the point B.

Mark the line of sight on the disk of the trussles. This can be done by a following simple method.

Page 11: Surveying and leveling-2

o One person is holding the theodolite at A sighting the point B.

o One person is at the point on trussle. He should move the pensile on the disk of the trussle in

such this is across the line of sight.

o The 1st person will guide the 2nd which way he should move that he can be in the line f sight.

o If he find the line of sight the mark the point on that point.

o In this way find another point on the disk and mark it.

o Join these two points to make the line.

o You can check this put the pensile on the line if this is in the line of sight then the marked line

will be correct.

Find the distance between the point A (base of the point) and the 1st trussle (on the disk).

Apply pull in this length measurement pull should be of 5 kg by the spring balance.

Temperature should also measure during this measurement. Thermometer should be hanged on point (under the

theodolite and trussles).

Set the auto level at a point from where all the point of the line are visible.

After the temporary adjustment (centering, leveling & focusing) find the levels of all points by setting the leveling

staff on each point.

Put all measurements in the table.

Formulas used for correction:

Ct = α(Tm-To) L Temperature Correction

CP = (P - PO) L/AE Pull Correction

CSP = - h2 / 2L Slope Correction

CS = - w2 L3 / 24 P2 Sage Correction

Cmsl = - HL / R Mean Sea Level Correction

Where

L = Measured length of the base (in meter)

α= Coefficient of thermal expansion (0.000011 / 0C)

Tm = Mean Temperature during measurement (0C)

P = pull applied during measurement (kg)

Po = Standardized Pull = 2 kg

A = Area of X-Section of Tape (0.0193 cm3)

Page 12: Surveying and leveling-2

E = Modulus of elasticity of tape (21 x 106 Kg/cm2)

H = Difference of elevation between two point (in meter)

W = Weight of tape per unit = o.o10193 Kg / m

H = Mean height of base above sea level = 1180 m

R = Mean radius of earth = 6367 Km

SCHEME USED:

A C F

UMER HALL GROUND

B D E

G

Comments:

In triangulation the base line is of prime importance (b/c). it is the only horizontal distance to measured. It should be

measured very accurately since the accuracy of the computed sides of triangulation system depends on it. Length of

base line varies form a fraction of (0.5-10) km and a fradion of a mile to 10 miles.

MAIN BLOCK

AYESHA HALL

Page 13: Surveying and leveling-2

Job # 03 Title: MEASUREMENT OF BEARINGS BY PRISMATIC COMPASS

Objective: To find out the bearings with complete accuracy by Applying all Corrections.

Apparatus:

Prismatic Compass

Tripod Stand

Ranging Rods

Pegs

Mallet

Related Theory:

Introduction to prismatic compass & its parts:

The 'Prismatic Compass' was invented by the maker Charles Schmalcalder and patented in 1812.

Radius of prismatic compass is 40mm.

Parts:

Compass box:

It is a circular metallic box of diameter 8 to 10 cm. A pivot with a sharp point is provided at the

centre of the box.

Magnetic needle:

It is made of broad magnetized iron bar &it is attached to a gruated aluminum ring. The ring is

graduated from 0 ˚to 360˚ clockwise & graduation begins from the south end of needle. Thus

zero is marked at the south, 90˚ at the west, 180˚ degree at the north & 270˚ degree at the east.

Sight vane & prism:

Site vane & reflecting prism are fixed diametrically opposite to the box. Site vanes are hinged

with metal box & consist of wire or hair at the center.

Dark glasses:

Two dark glasses (blue & red) are provided with the prism. Red is use for sighting luminous

object at night & blue for reduction of sunlight.

Page 14: Surveying and leveling-2

Brake pin:

It is provided at the base of sight vane & it stops the movement of ring.

Lifting pin:

It is below sight vane & it lifts the magnetic needle out of the pivot point to prevent damage the

pivot head.

Glass cover:

It is provided at the top of box to protect the aluminum ring from the dust.

Some Important Terms:

Bearing: Bearings are angle measured with reference to north.

Fore bearing: Bearing measured in the direction of progress of survey.

Back bearing: Bearing measured in the direction opposite to the progress of survey.

True bearing: A true bearing is measured in relation to the fixed horizontal reference plane of true north,

that is, using the direction toward the geographic North Pole as a reference point.

Magnetic bearing: A magnetic bearing is measured in relation to magnetic north, that is, using the direction

toward the magnetic north pole (in northeastern Canada) as a reference.

Grid bearing: A grid bearing is measured in relation to the fixed horizontal reference plane of grid north,

that is, using the direction northwards along the grid lines of the map projection as a reference point.

Magnetic Declination: It is a horizontal angle between true meridian and magnetic meridian.

There are 2 types of declination.

I-East declination II-West declination

Errors In Compass Observations:

The errors may be classified as

Instrumental errors

Personal errors

Errors due to natural causes

Instrumental Errors:

They are those which rise due to the faulty adjustments of the instruments. They may be due to the following reasons:

The needle not being perfectly straight.

Page 15: Surveying and leveling-2

Pivot being bent

Sluggish needle

Blunt pivot point

Improper balancing weight

Plane of sight not being vertical

Line of sight not passing through the center of graduated ring.

Personal Errors:

They may be due to the following reasons:

Inaccurate leveling of the compass box.

Inaccurate centering.

Inaccurate bisection of signals.

Carelessness in reading and recording.

Natural Errors:

They may be due to following reasons:

Variation in declination

Local attraction due to proximity of local attraction forces.

Magnetic changes in the atmosphere due to clouds and storms.

Irregular variations due to magnetic storms etc.

Procedure:

The compass centered over station A of the line AB and is leveled.

Having turned vertically the prism and sighting vane, raise or lower the prism until the graduations on the rings

are clear and look through the prism.

Turn the compass box until the ranging rod at the station B is bisected by hair when looked through the prism.

Turn the compass box above the prism and note the reading at which the hair line produced appears to cut the

images of the graduated ring which gives the bearing of line AB.

Page 16: Surveying and leveling-2

Adjustments Of Prismatic Compass:

The following are the adjustments usually necessary in the prismatic compass:

Centering

Leveling

Focusing the prism.

Centering: The center of the compass is placed vertically over the station point by dropping a small piece

of stone below the center of the compass, it falls on the top of the peg marking that station.

Leveling: By means of ball and socket arrangement the Compass is then leveled the graduated ring swings

quite freely. It may be tested by rolling a round pencil on the compass box.

Focusing: The prism attachment is slid up or down focusing till the readings are seen to be sharp and

clear.

Page 17: Surveying and leveling-2

Calculation & Observation

Line FB BB Difference Correction Corrected

FB

Corrected

BB

Remarks

AB 351˚00’ 172˚30’ 01˚30’ +00˚45’ 351˚45’ 171˚45’

No

Point

Is

Free

From

Local

attraction

BD 261˚30’ 80˚00’ 01˚30’ -00˚45’ 260˚45’ 80˚45’

DC 168˚30’ 349˚30’ 01˚00’ -00˚30’ 169˚00’ 349˚00’

CA 71˚30’ 250˚30’ 01˚00’ +00˚30’ 71˚00’ 251˚00’

DE 260˚30’ 79˚30’ 01˚00’ -00˚30’ 260˚00’ 80˚00’

EF 165˚45’ 347˚30’ 01˚45’ -00˚52’ 166˚37.5’ 346˚37.5’

FG 335˚00’ 154˚30’ 00˚30’ -00˚15’ 334˚45’ 154˚45’

GE 104˚00’ 285˚00’ 01˚00’ -00˚30’ 104˚30’ 284˚30’

Comments:

Local attraction was present near the station points.

Some station points were free from Local attraction so the difference of forbearing and back bearing at that points is exactly zero.

The Fore bearing is measured in the direction of survey and back bearing is measured opposite to that. For temporary adjustments of prismatic compass we performed following steps.

Fixing the compass with tripod stand.

Centering of the compass by dropping pebble. Levelling by ball and socket arrangement of tripod stand.

Adjusted the prism to see the graduated ring clearly.

Page 18: Surveying and leveling-2

Job # 04 Title: Measurement of Horizontal Distance By Tacheometry

Objective: To learn the method of measuring horizontal distance by tacheometry.

Apparatus:

1. Theodolite

2. Leveling staff

Related Theory:

Tacheometry is a branch of surveying in which horizontal and vertical distances are determined by taking

angular observations with an instrument known as tacheometer.

Theodolite:

A theodolite is a precision instrument for measuring angles in the horizontal and vertical planes. Theodolites

are mainly used for surveying applications. A modern theodolite consists of a movable telescope mounted within two

perpendicular axes—the horizontal or trunnion axis, and the vertical axis. When the telescope is pointed at a target

object, the angle of each of these axes can be measured with great precision, typically to seconds of arc.

We have used theodolite of least count 5” as a tacheometer. It is nothing but a transit theodolite fitted with a

stadia diaphragm and an anallatic lens.

Least count: Its L.C. is 5”. But 1” L.C. is also available.

Page 19: Surveying and leveling-2

Leveling staff:

A level staff, also called leveling rod, is a graduated wooden or aluminum rod, the use of which permits the

determination of differences in elevation. It is of 5 m length.

Least count:

Its least count is 0.005 m.

Telescope

Sighting collimator

Lifting handle

Vertical circle

Optical

plummet

Base plate

Vertical clamp

Operating buttons

LCD screen

Leveling screws

Vertical slow motion

srew

Page 20: Surveying and leveling-2

Characteristics of Tacheometer:

(a) The value of multiplying constant (f/i) should be 100.

(b) The telescope should be powerful, having magnification of 20 to 30 diameters.

(c) The aperture of objective should be of a 35 to 45 mm for there to be a bright image.

(d) The telescope should be fitted with an anallatic lens to make the additive constant(f+d) exactly equal to zero.

(e) The eyepiece should be of greater magnifying power than usual, so that it is possible to obtain a clear staff

reading from a long distance.

Principle of tacheometry:

The principle of tacheometry is based on the property of isosceles triangle, where the ratio of the distance of

the base from the apex and the length of the base is always constant.

Page 21: Surveying and leveling-2

In figure shown below, triangles o1a1a2, o1b1b2 and o1c1c2 are all isosceles triangles where D1, D2 and d3 are

the distances of the bases from the apices and S1, S2 and S3 are the lengths of the bases(staff intercept).

So, according to the stated principle,

D1/S1=D2/S2=D3/S3=f/i

The constant f/i is known as the multiplying constant,

Where f= focal length of objective and i= stadia intercept

Methods of Tacheometry:

Tacheometry involves mainly two methods:

1. The stadia method

2. The tangential method

1. The stadia method:

In this method the diaphragm of the tacheometer is provided with two stadia hairs (upper and lower) . The

difference in upper and lower reading gives the staff intercept. To determine the distance between the stations

and the staff, the staff intercept is multiplied by the stadia constant (i.e. multiplying constant , 100) . The stadia

method may, in turn, of two kinds.

(a) The Fixed hair Method

(b) The Moveable Hair Method

2. The tangential method:

Page 22: Surveying and leveling-2

In this method, the diaphragm of the tacheometer is not provided with stadia hair. The readings are taken by

single horizontal hair.

We have used FIXED HAIR METHOD.

Fixed Hair Method:

There are three cases in fixed hair method.

Case 1:

When line of sight is horizontal and staff is held vertically.

The equation for distance is given by

D= (f/i) S+ (f+d)

Case 2:

When the line of sight is inclined, but staff is held vertically.

Here, the measured angle may be the angle of elevation or that of depression.

Page 23: Surveying and leveling-2

D= (f/i) S cos^2 Ѳ+ (f+d) cosѲ

Case 3:

Line of sight inclined, but staff normal to it.

D= (f/i) cosѲ+(f+d) cosѲ-hcosѲ

Procedure:

First of all, we made the temporary adjustment of the instrument at point A.

Page 24: Surveying and leveling-2

We bisected the leveling staff at point B.

After this ,we noted the upper(U) and lower readings(L) of leveling staff at point B, and got staff intercept (S)

by taking their difference.

Staff intercept=S=upper reading –lower reading= U-L

Multiplying staff intercept with multiplying constant, we got distance D between the stations

D= S * 100

We repeated the above procedure for the whole scheme and calculated all the distances.

SCHEME USED:

A C F

UMER HALL GROUND

B D E

G

MAIN BLOCK

AYESHA HALL

Page 25: Surveying and leveling-2

No.

of

obs.

Inst.

Station

Staff

station

Hair readings (m)

Staff

Intercept

(S=U-L)

Vertical

angle

(degrees)

Length

of line

(m)

Upper Middle Lower

1 A B 1.60 1.00 0.260 1.34 0 134

2 A D 2.750 2.480 1.75 1.00 0 100

3 B C 1.8 1.11 0.55 1.25 0 125

4 C E 1.650 1.040 0.45 1.20 0 120

5 G E 1.840 1.520 1.395 0.45 0 45

6 E F 1.90 1.350 0.70 1.20 0 120

7 G F 1.95 1.25 0.6 1.35 0 135

8 D C 5.65 4.70 3.9 1.75 0 175

Comments:-

The method we use consists of using a level, theodolite or specially constructed tachometer to make cross hair

intercept readings on a leveling staff. As the angle subtended by the crosshairs is known, the distance can be

calculated.

Page 26: Surveying and leveling-2

Job # 05

Title: TO SET OUT REVERSE CURVE

Objective: The object of this survey is to design and set out a reverse curve.

Apparatus:

1. Theodolite

2. Leveling staff

Related Theory:

Reverse Curve:

These are two simple curves with deflections in opposite directions, which are joined by a

Common tangent or relatively shorter distance. OR

A reverse curve consists of two circular arcs of equal or different radii turning in opposite directions with a common

tangent at the junction of the arcs.

Elements of a Reverse Curve:

PQ & RS are the two parallel lines at a distance “Y” apart. The angle of deflection =Ф1=Ф2=Ф. Ф is the angle subtended by the curve.

T1 is the tangent point for 1st curve.T2 is the tangent point for 2nd curve. C is the point of tangency or point of reverse curvature.

Distance salong long chord. T1T2 is the length of the line joining tangent points T1 & T2. X is the perpendicular distance between tangent point T1 & T2. Y is the perpendicular distance between tangent PQ & RS.

Design Parameters of a Reverse Curve:

Long chord for 1st curve T1C= 2Rsin Ф/2

Long chord for 2nd curve T2C= 2Rsin Ф/2

Tangent distance=T1T2= 2Rsin Ф/2+ 2Rsin Ф/2

Total Tangent distance= 4Rsin Ф/2

T1T2= 2√R√Y

As in Triangle

Cos Ф= O1A/O1C

Cos Ф= O1A/R

Page 27: Surveying and leveling-2

So R Cos Ф= O1A

From the fig (1)

T1A= O1T1-O1A

T1A=R-R Cos Ф

Y=T1A+T2B

Y=R(1- Cos Ф)+R(1- Cos Ф) :T2B=R(1- Cos Ф)

Y=2R(1- Cos Ф)

From the triangle

Sin Ф= CA/R

R sin Ф=CA

Similarly from the fig (1) for X

X=CA+CB

X=R sin Ф+ R sin Ф :CB=R sin Ф

X=2 R sin Ф

Length of curve Lc= πR Ф/180˚

Chainage of T1= Chainage of C- Length of Curve

Chainage of T2= Chainage of T3+ length of Curve

REVERSE CURVE

Page 28: Surveying and leveling-2

Setting out of Reverse Curve:

Apparatus:

Theodolite

Ranging Rods

Pegs

Mallet

Tripod stand

Wooden pegs Tripod stand

Theodolite

Page 29: Surveying and leveling-2

The lengths of the reverse curve are normally small. So the curve may be set out by taking offsets from (i) the long

chord or (ii) the chord produced. If the length of the curve becomes large and chaining along it difficult, the curve may

be set out by the deflection-angle method (Rankine’s Method).

All the necessary data for setting out of the curve are calculated in usual manner. The setting out table is prepared.

Tangent points T1 & T2 are marked on the ground. A theodolite is centred over T1 and done all permanent adjustments

related to theodolite. Theodolite is set at 0˚0’0”. Chord lengths are provided so we calculate angle of deflection. Then

length of the curve is calculated. Ranging rods are fixed at given chord length and bisect all the ranging rod with the

help of theodolite so the ranging rods come in a straight line. Tangent length is marked at the half of angle of

deflection.

Then theodolite is again set to zero. And then at initial sub chord the angle of deflection is set & measuring the length

or peg interval by tape set out the angles and fix the peg on the ground so that each peg will be bisteced properly by

theodolite. By marking pegs we reach at the pt. of tangency or pt. of reverse curvature. And then now same procedure

is adopted on the either side of curve. The angle of defection is noted down and pegs are marked so that we reach at

final point T2.

DATA:

Chainage of T1= 2727.27m

R1=90m

R2=70m

FT1=40m

Page 30: Surveying and leveling-2

FT2=30m

T1F=2R1 sin Ф1/2

T1F/2R1 = sin Ф1/2

Ф1/2= sinˉ1 (40/2*90)

Ф1/2= 12˚50’

Length of 1st curve=Lc1= πR1Ф/180˚*60

Lc1=40.3m

Chainage of F= Chainage of T1+ Lc1

Chainge of F= 2727.27+40.3

Chainage of F=2767.57m

T2F=2R2 sin (Ф2/2)

Ф2/2= sinˉ1 (T2F/2R2)

Ф2/2=12˚22’25.06”

Length of 2nd curve=Lc1= πR2Ф/180˚*60

Lc2=30.23m

Chainage of T2= Chainage of F+ Lc2

Chainage of T2=2797.8m

2 tables are set out 1st for from T1 to F & then F to T2. Chainage of T1= 2727.27m & that of F= 2767.57m

.Peg interval is taken as 5m.So initial sub chord is calculated by a chossing a suitable round decimal such as 2730m so

initial sub chord is 2.73m & normal chords will be of 5m and that of final sub chord will be 2.57m.

Deflection angle is measured by a formula=1718.9*chord length/(R*60)

Point Chainages (m) Original Deflection Total Corrected

Page 31: Surveying and leveling-2

length (m)

angle (DMS)

deflection angle

angle from theodolite 5”

T1 2727.27 - - - -

P1 2730 2.73 0˚52’8.4” 0˚52’8.4” 0˚52’10”

P2 2735 5 1˚35’29.67” 2˚27’38.07” 2˚27’40”

P3 2740 5 1˚35’29.67” 4˚3’7.74” 4˚3’10”

P4 2745 5 1˚35’29.67” 5˚38’37.41” 5˚38’40”

P5 2750 5 1˚35’29.67” 7˚14’7.08” 7˚14’05”

P6 2755 5 1˚35’29.67” 8˚49’36.75” 8˚49’35”

P7 2760 5 1˚35’29.67” 10˚25’6.42” 10˚25’05”

P8 2765 5 1˚35’29.67” 12˚0’36.09” 12˚0’35”

F 2767.57 2.57 0˚49’41.4” 12˚49’41.4” 12˚49’40”

For 2nd Curve when R2=70m

Point Chainages (m) Original length

(m)

Deflection angle

(DMS)

Total deflection

angle

Corrected angle from

theodolite 5”

F 2767.57 - - - -

R1 2770 2.43 0˚59’40.22” 0˚59’40.22” 0˚59’40”

R2 2775 5 2˚2’46.71” 3˚2’26.93” 3˚2’25”

R3 2780 5 2˚2’46.71” 5˚5’13.64” 5˚5’15”

R4 2785 5 2˚2’46.71” 7˚8’0.35” 7˚8’0”

R5 2790 5 2˚2’46.71” 9˚10’47.06” 9˚10’50”

R6 2795 5 2˚2’46.71” 11˚13’33.77” 11˚13’35”

T2 2797.8 2.8 1˚8’45.36” 13˚16’20.48” 13˚16’20”

Page 32: Surveying and leveling-2

Job # 06 Title: SETTING OUT OF COMPOSITE CURVE

Objective: To understand and earn the procedure of setting of circular curve

Apparatus:

Theodolite Tripod Stand

Ranging Rods Pegs Mallet

Related Theory:

Introduction to composite curve:

It consists of different types of curve. It is also known as combined curve.

For example: a simple circular curve along with two transition curves on both end is example of

composite curve

Setting Out of Transition Curves:

1. Introduction:

Transition curves, as their name suggests, are designed to allow a smooth transition from a straight section to a (circular) curve and to allow the gradual introduction of super-elevation (also known as “banking” on a racing circuit

and “cant” on a rail track). Setting out of transition curves is done using the same techniques as for circular curves (theodolite and tape or EDM/co-ordinates) and the purpose of these notes is to introduce the calculations required to produce the necessary setting out data.

2. Forces on vehicles moving round curves: A moving object will continue moving in a straight line at constant velocity unless acted upon by a force. If the force

acts in the same direction as the motion, then the object will accelerate or decelerate; if the force acts perpendicular to the line of motion, then the object will change direction. In order to turn a vehicle round a curve, it is therefore

necessary to apply a sideways force – this is done by turning the front wheels. There are two important considerations when designing roads (and railways):

Page 33: Surveying and leveling-2

Comfort of occupants: When the vehicle moves round the curve, the occupants feel the sideways force

because their bodies wish to continue moving in a straight line. If this force is too great (curve radius too tight) or it is applied too rapidly (moving from a straight to a sharp circular curve) then the occupants will feel discomfort.

Safety of vehicle: The sideways force is transmitted to the vehicle via the tyres at road surface level. If the force is too great for the grip of the tyres, skidding may occur. If the centre of gravity of the vehicle is high,

then overturning may occur.

The centrifugal force, acting outwards as a vehicle moves round a curve, is expressed as follows:

Figure: Centrifugal force exerted on a vehicle travelling round a curve.

P = W V2 centrifugal force g R

Or P = V2 centrifugal ratio

W g R = V2 with V in km/h

127 R R in m g = 9.807 m/s2

For practical purposes, a “comfort range” is adopted for values of the centrifugal ratio, P/W:

Roads: P/W between 0.21 and 0.25 (typically 0.22) Railways: P/W = 0.125

From this can be derived an expression for the minimum radius required for a particular design speed:

Minimum = V2

Radius (P/W) x 127

Velocity V

Centrifugal

force P

Radius R

Vehicle

Circular curve

R

W

P

Page 34: Surveying and leveling-2

This should be regarded as a minimum value; the actual radius adopted (which may be larger) may depend upon other

factors such as the overall alignment of the road.

3. Entry to a curve:

Centrifugal force leads both to passenger discomfort and to slipping/overturning forces on vehicles. On high-speed

roads, and on many modern medium-speed roads, this is counteracted by the application of super-elevation. This is the tilting of the road surface so that the resultant force of the weight of the vehicle and the centrifugal force is close to normal with the road surface. In railway engineering, this is known as “cant”; on a motor racing circuit it would be

called “banking”.

Figure: Super-elevation

The super-elevation angle, , is usually expressed as a gradient (e.g. 1 in 14) and is related to the velocity of the vehicle and the curve radius.

Clearly, this cannot be applied suddenly, but must be introduced gradually. Furthermore, sudden entry from a straight into a circular curve may result in “acceleration shock” to the passengers.

For both of the above reasons, it is preferable to change the radius of curvature gradually from the straight to the

circular curve steadily along a transition curve. Design of transition curves is based upon the change of curvature (the inverse of radius) at a steady rate from the

straight (curvature = 0) to the circular portion of the curve (curvature = 1/R). The rate of change of radial acceleration, q, must also be kept constant whilst the vehicle negotiates the transition curve at constant velocity over time t. This

results in the following relationships: time taken to travel t = L/V

along transition curve

radial acceleration aR = V2/R rate of change of q = aR / t

radial acceleration = (V2/R)/(L/V)

Road surface

W

P

Resultant

force

Page 35: Surveying and leveling-2

= V3/RL

i.e. L = V3

46.7 q R with V in km/h and R in m.

An acceptable value of q is found to be 0.33 m/s3. This gives an expression for the minimum length of transition curve

required. The actual length of transition used may also depend upon previous experience. The completed curve now consists of

an entry transition

a central circular portion

an exit transition

Both of the transitions will have identical geometry, but will be of opposite hand.

Shape of the transition To satisfy the criterion that rate of change of curvature must be constant along the transition curve, we must calculate

the shape of the curve as follows.

At a distance l into the transition, measured from the transition tangent point T1, the radius of curvature will be r. At l = 0, i.e. at the transition point, r is infinite, and reduces to the circular curve radius, R, at the circular curve tangent

point T1, where the transition curve joins the circular portion. This situation is shown in the diagram below:

Figure : Shape of the transition curve.

The radius is related to the length l by the equation derived above, i.e.

l = V3

46.7 q r

d

dl

T1

T1

R

l

Entry

tangent

Tangent to

circular

curve

Page 36: Surveying and leveling-2

which can be re-written l = K since velocity is

r constant

From figure 3, because angle d is small, we can write:

r d = dl

i.e. d = 1 dl = l dl

r K

This may now be integrated, inserting limits:

= l2 = l2

2 K 2 r l = l2

2 R L

or l = (2 R L )½

This is the equation of the clothoid or Euler spiral. It is regarded as the ideal shape for the transition curve. The

angle consumed by the transition curve, , is

= L (radians)

2 R

= L x 180 (degrees)

2 R

The clothoid is regarded as the “ideal” shape for a transition curve, as it satisfies our criteria for all values of . However, although it appears simple to write down, it is not easy to translate into a form that can be used readily for

setting out in the field.

Setting out the transition curve:

The curve that has now been formed is composite in nature, i.e. it contains a number of different curves, which are designed to fit together. There is a transition curve at each end and a central circular portion. As a whole, the

composite curve is symmetrical, though it should be remembered when setting out that, unlike a circular curve, transition curves are not themselves symmetrical – one end has a greater radius of curvature than the other, so they are not reversible!

Page 37: Surveying and leveling-2

A transition curve can be set out in exactly the same way as a circular curve, i.e. by setting up a theodolite at the tangent point, aligning the telescope with the Intersection Point, swinging through the appropriate angles and taping

chords between consecutive pegs. This is the simplest method, and the one on which the calculations are based. Other methods can be adopted, such as setting out using a Total Station set up off the curve, or from a point other than the

tangent point for some practical purpose; however, in each case the same initial calculations are made and then adapted to suit as required.

In order to derive suitable equations relating chord length and deflection angle, we must examine the shape of the transition curve. First, look at it in terms of orthogonal co-ordinates, using the tangent as a reference axis:

Figure: Co-ordinates of the transition curve. Imagine a point some distance, l, along the curve from the tangent point. It will have co-ordinates X and Y as shown in

figure 4 and the angle between the tangent and the line joining T1 and p is . Direct calculation of for specific values of l (i.e. chainages) requires the use of tables of standard data, though such calculations would be made now by

computer. For hand calculation, a series expansion of the clothoid is available:

X = l - l5 + l9 - l13 +….. 40(RL)2 3456(RL)4 599040(RL)6

Y = l3 - l7 + l11 -….. 6RL 336(RL)3 42240(RL)5

tan = + 3 - 5 + 7 -….

3 105 5997 198700

These are clearly impractical. However, for values of up to about 3, the higher order terms can be neglected,

resulting in simpler formulae from which setting-out data can be readily calculated:

Cubic Spiral: Y = l3/6RL = /3

Cubic Parabola: Y = X3/6RL = /3

These are sufficiently accurate for most applications where hand calculation is likely to be employed, and the following procedure is based upon the cubic spiral, which is a better approximation to the clothoid.

X

Y

p

T1 Entry

tangent

T1

Page 38: Surveying and leveling-2

3.1.1. Setting-out calculations for the cubic spiral

The equations in the above section allow us to calculate the deviation angle (i.e. the angle set on the theodolite when it is set up at the tangent point) directly. Note that, unlike the circular curve calculations, this is not cumulative.

Deviation angle = /3 = l2/6RL (radians)

i.e. = 180 l2

6 R L

The tangent length of the composite curve (i.e. transition + circular + transition) will be needed for setting out the first

tangent point, T1, and for calculation of the chainages of setting out points. It is obtained by first considering the

properties of an equivalent circular curve, which has the same centre as the circular portion of the curve to be set out, but has a slightly larger radius. The relationship between the two curves is shown in the following diagram:

Figure 5: Equivalent circle and shift for a composite curve.

It can be shown that the line OQ, from the centre of the circle to the tangent point of the equivalent circle, bisects the transition curve T1 T1 and that the shift, S, is

S = L2 / 24R

From the dimensions of the equivalent circular curve, we can obtain its tangent length, distance QI:

QI = (R + S) tan (/2)

Q

S

I

T2 T1 T1 T2

O

R

Page 39: Surveying and leveling-2

And, since length T1Q is half the length of the transition curve, we can write

T1I = L / 2 + (R + S) tan (/2)

This allows us to establish the chainage of the first tangent point T1 and hence the distance from the tangent point to

the chainage pegs along the transition curve as well as the chainage of the tangent point to the circular curve, T1.

Page 40: Surveying and leveling-2

The circular portion of the curve:

The central circular arc can be set out in exactly the same way as a purely circular curve, i.e. from the tangent point using theodolite and tape. The difference in the case of a composite curve is that the tangents to the circular arc are not

the same as the entry and exit tangents for the composite curve – the intersection angle will be lessened and the point at which they intersect will be closer to the curve than the point I, as shown in the diagram below.

Figure : Geometry of the circular portion of a composite curve.

It can be seen that the angle of the circular arc is

C = 2

Hence the length of the circular arc is

LC = R C

180

This allows the chainages of the two remaining tangent points, T2 and T2, to be calculated. After calculating the positions along the circular arc of the chainage pegs, (cumulative) deflection angles for the entry and exit sub-chords

and the standard chord are calculated in the usual way: d = 28.648 lC / R

The curve can now be set out by setting up the theodolite at T1 and taping between pegs. In order to do this we must

establish the orientation of the tangent, since we can no longer sight onto the Intersection Point, I. This can be done by looking at the geometry of the transition curve.

I

T2 T1 T1 T2

O

-

2

R

Page 41: Surveying and leveling-2

Figure 7: Transition curve and Back Angle.

From the properties of the cubic spiral, we know that

= / 3

and the back angle can therefore be calculated as

back = 2 / 3

angle

The theodolite can therefore be oriented at T1 by sighting back to T1 and turning the alidade through 180 + 2 /3

(clockwise). The telescope will then be facing along the tangent to the circular arc, ready to continue setting out.

Note that, for a left-hand curve, the alidade must be rotated through 180 - 2 /3 (clockwise). This is because all

of the curve angles will have been reversed, but the theodolite is still graduated in a clockwise direction.

The exit transition:

The entire circular curve has now been set out, assuming that there have been no obstructions, from one tangent point, usually the entry tangent point T1. However, because the transition curve is not symmetrical, the formulae used above

to calculate deviation angle are only valid for angles from the start of the transition, i.e. T1 or T2. We must therefore

move directly to T2 to set out the second transition curve. The position of T2 can be found by linear measurement

along the exit straight from the intersection point, and checked from T1 by measuring the angle between either straight

and the line T1-T2, which should be equal to /2.

Figure: Checking the position of the two tangent points.

It is important to remember that chainage is still running from T2 to T2, even though we are calculating deviation

angles from T2 to T2 and, in all probability, setting out from T2. Also worth checking in the field with the theodolite

T2 T1

I

required

orientation

Tangent to

circular arc

back

angle

T1

Entry

tangent T1

/

2

/

2

Page 42: Surveying and leveling-2

set up at T2, before the transition is set out, is the position of T2. The formula used to calculate deviation angles in the

second transition is exactly the same as before, except that it will be of the opposite hand.

Calculation & observation:

Radius of circular curve= 150m ∆= 48˚48’

C=.45m/s3

Ch. of I.P= 2575.37m Peg interval not greater then 10m

Design velocity = 60 km/hv = 60 * 1000 / 3600 = 16.67m/s

Computation:

Length of transition curve= L = V3/3π = 68.63m/s Xc= 68.03m Yc=L2/6R=5.23m

∆/2 = 24˚24’ Φc=L/2R rad. =1306’27”

Ϭ= L2/24R = 1.31 α = 155˚36’

center of circular arc = 22˚35’06” length of circular arc = π R(22˚35’06”)/180 = 59.3m

tangent length= Xc + ( R + Ϭ ) tan∆/2- R sin Φc = 102.65 ϴ = l2/6RL rad . when l is length along transition

Ditection of tangent at c1 NC1H = 360 – (1/2 central angle + α + 90) =103˚06’27”

Chainages:

Ch. of T1= 2575.37-102.65=2472.72m Ch. of C1= 2472.72+ L=2541.35m

Ch. of C2=2541+lg + circular arc=2600.48m Ch. of T2= 2600.48 + L=2669.11

Detail:

For circular curve each deflection angle = 1718.9 * C / R minutes AT1=Tangent length = 102.65 m T1T2 = (102.65/sin24˚24’) *sin 24˚28’ = 186.96 m

1. Table For Setting Out Transition & Circular Curve:

Page 43: Surveying and leveling-2

Procedure: 2. Set two points T1,T2 at 186.96 m apart. 3. Erect poles in direction from T1 to T2.

Transition T1C1 Circular arc C1C1 Transition T2C2

Ch

ain

ag

es

M

l

(m)

Total

def.

angle

Angl

e to

be

set

on

thed

olite

Chainages

(m)

Ch

or

d

(c)

(m

)

Each

def.

angle

Total

def.

Angle

Angl

e to

be set

on

thedo

lite

Chainages

m

l

(m)

Total

def.

Angle to

be set on

thedolite

24

72.72 (T

1)

0 0 0 254.31 (C1) 0 0 0 0 2669.11 (T2) 0 0 0

2480

(P1)

7.28 0˚2’57” 0˚2’55”

2550 (P1) 8.65

1˚39’7” 1˚39’7”

1˚39’5”

2660 (P1) 9.11

0˚4’37” 0˚4’35”

24

90 (P2)

17.28 0˚16’37” 0˚16

’35”

2560 (P2) 10 1˚54’36

3˚33’4

3”

3˚33’

45”

2650 (P2) 19.

11

0˚20’20” 0˚20’20”

25

00 (P3

)

27.28 0˚41’24” 0˚41

’25”

2570 (P3) ˶ ˶ 5˚28’1

9”

5˚28’

20”

2640 (P3) 29.

11

0˚47’10” 0˚47’10”

2510 (P4

)

37.28 1˚17’21” 1˚17’20”

2580 (P4) ˶ ˶ 7˚22’55”

7˚22’55”

2630 (P4) 39.11

1˚25’8” 1˚25’10”

2520

47.28 2˚4’24” 2˚4’25”

2590 (P5) ˶ ˶ 9˚17’31”

9˚17’30”

2620 (P5) 49.11

2˚14’14” 2˚14’15”

25

30 (P6

)

57.28 3˚2’37” 3˚2’

35”

2600 (P6) ˶ ˶ 11˚12’

7”

11˚12

’5”

2610 (P6) 59.

11

3˚14’28” 3˚14’30”

2540 (P7

67.28 4˚11’56” 4˚11’55”

2600.42 (C2)

0.48

0˚5’30” 11˚17’37”

11˚17’35”

2600.48 (P7) 68.63

4˚22’9” 4˚22’10”

25

41.35

68.63 4˚22’9” 4˚22

’10”

Page 44: Surveying and leveling-2

4. Start setting out from T1 for first transition curve. 5. Start setting out from T2 for 2nd transition curve.

6. Set out circular arc C1C2 using table of setting out for circular curve.

Page 45: Surveying and leveling-2

Job # 07

Title: To Design And Set Out Of A Vertical Curve

Objective: The objective of this survey is to design and set out a vertical curve.

Apparatus: 1. 5 sec Transit Theodolite

2. Ranging Rod

3. Tripod Stand

4. Automatic Level

5. Leveling stave

6. Pegs

7. Wooden Hammer

8. Measuring Tape

Related Theory:

1. Theodolite: It is an instrument which is used mainly for accurate measurement of horizontal and vertical angles. The least count of this theodolite (TOPCON DT-104) is 5” but can be changed by changing the settings.

2. Ranging Rod: It is a long metal or wood bar with noticeable markings and colors (usually it is painted in red and white stripes). In this

Experiment, it will be used to mark the station point and to make it easier for the station point to be sighted with the

prismatic compass.

3. Tripod Stand: It may be wooden or metallic. It is three-legged and the Prismatic Compass is fixed on it with the fixing knob. The

Prismatic compass is centered and levelled on the stand prior to sighting.

4. Automatic Level: This is also called as self-aligning level. This instrument is leveled automatically within a certain tilt range by mean of compensating device (The tilt compensator)

5. Leveling Stave:

Page 46: Surveying and leveling-2

The leveling stave is graduated rod used for measuring the vertical distance between the points on the ground and the line of collimation.

6. Pegs: It is used to mark point on the ground.

7. Wooden Hammer:

It is used to insert pegs into the ground.

8. Fiber Glass Tape: It can be graduated in different scale like meters or feet. It can be metallic or fiber glass tape. In our case it is fiber glass

tape. Its length is 30m or 100 ft.

Page 47: Surveying and leveling-2

Procedure: Set up theodolite at any point before station A, mark the calculated intervals in the line of peg A. Afterwards mark the next points at a distance x from the station A at 20m. Find the value of radius, chainages, and levels by using the

following formulas. Place the instrument level at any point a little away from the line of sight and find the values of level of all the stations. Then, find the MSL as shown in the table.

Chainages:

I= 2325.0 m A= 2325.0 – (127.84/2) = 2261.08 m

C= 2261 + 127.84 = 2388.92 m

Chainag

e x(m) Level on

Tangent

(Z)

y Level on

parabola (Z-

y)

MSL

2261.08 0 213.15 0 213.15 213.1

5

2280 18.92 213.72 .07 213.65 213.87

2300 38.92 214.32 .29 214.03 214.4

4

2320 58.92 214.92 .68 214.24 214.74

2340 78.92 215.52 1.22 214.30 214.5

4

2360 98.92 216.12 1.91 214.21 214.26

2380 118.92 216.72 2.76 213.96 213.77

2388.92 127.84 216.98 3.19 213.79 214.49

Precautions: Following precautions should be taken into account while performing the survey.

ld be accurate.

nt.

Page 48: Surveying and leveling-2

Job # 07

Title: To Design And Set Out Simple Circular Curve

Objective: The objective of this survey is to design and set out a vertical curve.

Apparatus:

1. 5 sec Transit Theodolite

2. Ranging Rod

3. Tripod Stand

4. Pegs

5. Wooden Hammer

Related Theory: 1. Theodolite:

It is an instrument which is used mainly for accurate measurement of horizontal and vertical angles. The least count of this

theodolite (TOPCON DT-104) is 5” but can be changed by changing the settings.

2. Ranging Rod: It is a long metal or wood bar with noticeable markings and colors (usually it is painted in red and white stripes). In this

Experiment, it will be used to mark the station point and to make it easier for the station point to be sighted with the prismatic compass.

3. Tripod Stand: It may be wooden or metallic. It is three-legged and the Prismatic Compass is fixed on it with the fixing knob. The Prismatic

compass is centered and levelled on the stand prior to sighting.

4. Pegs: It is used to mark point on the ground.

5. Wooden Hammer:

It is used to insert pegs into the ground.

Procedure: Mark a point on the ground with the help of peg and set up the instrument theodolite on it.

After centering, leveling and focusing of the theodolite mark point T2 at the specified distance.

Fix a ranging rod at I so that angle IT1T2 is Φ/2. Now bisect I and set the 1st small deflection

angle, rotate the theodolite and clamp the horizontal clamping screw, this will set the line of

sight, now measure length of first sub-chord and mark the peg by guiding it from the

Page 49: Surveying and leveling-2

theodolite. Swing till the rod bisected by the vertical hair of theodolite. Repeat the procedure

each time setting the deflection angle for each point and measuring the distance from the

previous point.

Steps For Curve Calculation Data:

Following formulas are used for setting out of curve.

Length of circular curve= πRΦ/180

Length of long chord= 2Rsin(Φ/2)

Tangent Length= Rtan(Φ/2)

Chainage of T1= Chainage of I – Tangent Length

Chainage of T2= Chainage of T1 + Length of circular curve

Length of initial sub-chord

Deflection angle for initial sub-chord= 1718.9(C)/R ; C=Peg Interval

Deflection angle for full chord=1718.9(C)/R ; C=Peg Interval

Deflection angle for last sub-chord=1718.9(C)/R ; C=Peg Interval

Observations table: Radius of curve= 120m

Φ= 40o

Chainage of I= 5755.67m

Point Chainage Chord Length

Deflection Angle for Chord

Total Deflection Angle

Angle to be set

Remarks

T1 5712 0 0 0 0 Starting point

P1 5720 8 1o54’35’’ 1o54’35’’ 1o54’35’’ 1st Peg P2 5730 10 2o23’14.5’’ 4o17’49.5’

’ 4o17’50’’ 2nd Peg

P3 5740 10 2o23’14.5’’ 6o41’4’’ 6o41’5’’ 3rd Peg P4 5750 10 2o23’14.5’’ 9o4’18.5’’ 9o4’20’’ 4th Peg P5 5760 10 2o23’14.5’’ 11o27’33’’ 11o27’35’

’ 5th Peg

P6 5770 10 2o23’14.5’’ 13o50’47.5’’

13o50’45’’

6th Peg

P7 5780 10 2o23’14.5’’ 16o14’4’’ 16o14’5’’ 7th Peg P8 5790 10 2o23’14.5’’ 18o37’16.

5’’ 18o37’15’

’ 8th Peg

T2 5747.77 5.77 1o22’39’’ 19o59’55. 19o59’55’ Ending

Page 50: Surveying and leveling-2

5’’ ’ point

Precautions:

Following precautions should be taken into account while performing the survey.

Calculations should be done with great care.

Centering, levelling and focussing of instrument should be accurate.

Peg should be inserted in the ground at the exact point.