Linear Measurements

Linear MeasurementsLecture Notes

Unit-I Linear Measurements

Syllabus • Different types of ranging, tapes,

chains, linear measurements, approximate, direct, optical and electronic methods, Chain Surveying, Minor Instruments for setting out right angle.

Ranging• When a survey line is longer than a

chain length, it is necessary to align intermediate points on chain line so that the measurements are along the line. The process of locating intermediate points on survey line is known as ranging. There are two methods of ranging viz., direct ranging and reciprocal ranging.

Ranging

Direct Ranging

• If the first and last points are intervisible this method is possible.

• Stations A and B in which an intermediate point C is to be located. Point C is selected at a distance slightly less than a chain length. At points A and B ranging rods are fixed. The assistant holds another ranging rod near C. Surveyor positions himself approximately 2 m behind station A and looking along line AB directs the assistant to move at right angles to the line AB till he aligns the ranging rod along AB. Then surveyor instructs the assistant to mark that point and stretch the chain along AC.

Direct Ranging

Direct Ranging

Direct Ranging

Direct Ranging

Direct Ranging

Direct Ranging

Direct Ranging

Direct Ranging

Indirect or Reciprocal Levelling

• Due to intervening ground, if the ranging rod at B is not visible from station A, reciprocal ranging may be resorted. Figure shows this scheme of ranging.

• It needs two assistants one at point M and another at point N, where from those points both station A and station B are visible. It needs one surveyor at A and another at B. To start with M and N are approximately selected, say M1 and N1. Then surveyor near end A ranges person near M to position M2 such that AM2N1 are in a line. Then surveyor at B directs person at N, to move to N2 such that BN2M2 are in a line. The process is repeated till AMNB are in a line.







Linear Measurements• The determination of the distance

between two points on the surface of the earth is one of the basic operation of surveying. Measurement of horizontal distances or measuring linear measurement is required in chain surveying, traverse surveying and other types of surveying.

Linear Measurements• Methods of making linear

measurements• Direct methods• Optical methods• E.D.M methods

Linear Measurements• In the direct method, the distance is

actually measured during field work using a chain or a tape. This is the most commonly used method for linear measurements.

• In the optical methods, principles of optics are used. The distance is not actually measured in field but it is computed indirectly. The instrument used for making observations is called tacheometer.

Optical Methods

Linear Measurements• Electronic Distance Measuring (E.D.M)

instruments have been developed quite recently.

• These are practically replacing the measurement of distances using chains or tapes. There is a large variety of such instruments and depending upon the precision required the instruments should be used.

Electronic Distance Measuring (E.D.M)

EDM

l l l

l

l

llP

Linear MeasurementsApproximate methods• The methods given below may be used in

reconnaissance or for detecting major mistakes in linear measurements obtained with a chain or a tape.

Pacing• A distance between two points can be

approximately be determined by counting the number of paces and multiplying it with average length of the pace.

Pacing

Pacing

Linear MeasurementsPassometer:• It is a small instrument which counts

the number of paces.Pedometer:• This instrument directly gives the

distance by multiplying the number of paces with the average pace length of the person carrying the instrument.

Passometer

Pedometer

Pedometer

Linear MeasurementsOdometer• An odometer is a simple device

which can be attached to the wheel of a bicycle or any such vehicle. The odometer registers the number of revolution made by the wheel. The distance covered is equal to the product of the number of revolutions and the perimeter of the wheel.

Odometer

Linear MeasurementsSpeedometer• This is used in automobiles for measuring

distances.

Measuring Wheel• It is a wheel fitted with a fork and handle.

The wheel is graduated and shows a distance per revolution. There is a dial which records the number of revolution. Thus the distance can be computed.

Speedometer

Measuring Wheel

Measuring Wheel

Instruments Used in Chaining

• The following instruments are used while chaining.

• Chains• Tapes• Arrows• Ranging rods and offset rods• Laths & Whites• Pegs• Plumb bob• Line Ranger


Chains• Various types of chains used in

surveying are• Metric Chain• Gunter’s Chain or Surveyor’s Chain• Engineer’s Chain• Revenue Chain• Steel Band or band chain


Metric Chain• Normally this chain consists of galvanized

mild steel wire of 4 mm diameter known as link. The ends of the links are bent into loop and connected together by means of three oval rings which provide the flexibility to the chain and make it less liable to kinking. Both ends of the chain have brass handle with swivel joint so that the chain can be turned round without twisting

Metric Chain• In a metric chain at every one meter interval

of chain, a small brass ring is provided. Brass tallies are also provided at every 5.0 m length of chain. Each tally has different shape which indicates 5 , 10, 15m from any one side of the chain, metric chains are available in 20 m and 30 m length.

• A 20 m chain has 100 links each of 20 cm and 30 m chain has 150 links. Length of chain is embossed on the brass handles of the chain.

Metric Chain


Günter's chain• A 66 feet long chain consists of 100

links each of 0.66 ft it is known as Gunter’s Chain

• Here, 10 sq chain are equal to 1 acre,• 10 chains= 1 furlong and 8 furlongs

= 1 mile• This chain is suitable for taking

length in miles and areas in acres.

Günter's Chain

Günter's Chain


Engineer’s Chain• A 100 ft chain of 100 links each of 1

foot is known as Engineer’s chain. Brass tags are fastened at every 10 links. This chain is used to measure length in feet and area in square yards.

Engineer’s Chain

Engineer’s Chain


Revenue Chain• Revenue chain is 33 ft long chain

consisting of 16 links. This chain is used for distance measurements in feet & inches for small areas.

Revenue Chain


Steel Band or Band Chain• Steel bands are preferred than chains

because they are more accurate, but the disadvantages is that they get broken easily and are difficult to repair in the field. They are 20 and 30 m long, 12 to 16 mm wide and 0.3 to 0.6 mm thick. They are numbered at every metre and divided by brass studs at every 20 cm

Steel Band or Band Chain

Steel Band or Band Chain

Testing and Adjustment of Chain

• During continuous use, the length of a chain gets altered. Its length is shortened chiefly due to the bending of links. Its length is elongated either due to stretching of the links and joints and opening out of the small rings. For accurate work it is necessary to test the chain time to time. The chain can be thus tested by a steel tape or by a standard chain. Sometimes, it is convenient to have a permanent test gauge established where the chain is tested.


• When the length of a chain is measured at a pull of 8 kg at 20 0C the length of the chain should measure 20 m ± 5 mm and 30 m ± 8 mm for 20 m and 30 m long chain shall be accurate to within 2 mm. Following measures are taken to adjust the length of a chain.



If chain is found to be too long• It can be adjusted by;• Closing up the joints of the rings if

found to be opened out• Reshaping damaged rings• Removing one or more small rings• Adjusting the links at the end.


• If the chain is found to be too short• Straightening the bent links• Opening the joints of the rings• Replacing one or more small circular

rings by bigger ones.• Inserting new rings where necessary.• Adjusting the links at the end.

Measuring Tapes• Tapes are used for more accurate

measurement. The tapes are classified based on the materials of which they are made of such as:

• Cloth or linen tape• Fibre Tape• Metallic Tape• Steel tape• Invar Tape

Measuring Tapes

Measuring TapesCloth or linen Tape• Linen tapes are closely woven linen

and varnished to resist moisture. They are generally 10 m, 20 m, 25 m and 30 m long in length and 12 to 15 mm wide. They are generally used for offset measurements. These tapes are light and flexible.

Cloth or linen Tape

Measuring Tapes• Fibre Glass Tape• These tapes are similar to linen and plastic

coated tapes but these are made of glass fibre. The tapes are quite flexible, strong and non-conductive. These can be used in the vicinity of electrical equipment. These tapes do not stretch or shrink due to changes in temperature or moisture. These tapes are available in length of 20 m, 30 m and 50 m length.

Fibre Glass Tape

Measuring Tapes• Metallic Tape• A linen tape reinforced with brass or copper

wires to prevent stretching or twisting of fibres is called a metallic tape. As the wires are interwoven and tape is varnished these wires are visible to naked eyes. This is supplied in a lather case with a winding device. Each metre length is divided into ten parts (decimetres) and each part is further sub-divided into ten parts. It is commonly used for taking offset in chain surveying.

Metallic Tape

Measuring Tapes• Steel Tape• The steel tape is made of steel

ribbon of width varying from 6 to 16 mm. The commonly available length are 10 m, 15 m, 20 m, 30 m and 50 m. It is graduated in metres, decimetres, and centimetres. Steel tapes are used for accurate measurement of distances.

Steel Tape

Measuring Tapes• Invar Tape• Invar tape are made of alloy of nickel

36 % and steel 64 % having very low co-efficient of thermal expansion. These are 6 mm wide and generally available in length of 30 m, 50m, 100m. It is not affected by change of temperature therefore, it is used when high degree of precesion is required.

Invar Tape

Arrows• Arrows are made of tempered steel

wire of diameter 4 mm. one end of the arrow is bent into ring of diameter 50 mm and the other end is pointed. Its overall length is 400 mm. Arrows are used for counting the number of chains while measuring a chain line. An arrow is inserted into the ground after every chain length measured on the ground.

Arrows

Arrows

Ranging Rods and Offset Rods

• Ranging rods are used for ranging some intermediate points on the survey line. Ranging rods are generally 2 to 3 m in length and are painted with alternate bands of black or white or red and white colour with length of each equalizing 20 cm. The location of any survey station can be known from long distances only by means of ranging rods. If the distance is too long, a rod of length 4.0 to 6.0 m is used and is called ranging pole.

• The offset rod is similar to ranging rod with the exception that instead of the flag, a hook is provided at the top for pushing and pulling the chain or the tape. It is also used for measuring small offsets

Ranging Rods

Ranging Rods

Offset Rods

Ranging Rods and Offset Rods

Laths & WhitesLaths• Laths are 0.5 to 1.0 m long sticks of soft wood. They

are sharpened at one end and are painted with white or light colours. They are used as intermediate points while ranging or while crossing depressions.

Whites• Whites are the pieces of sharpened thick sticks cut

from the nearest place in the field. One end of the stick is sharpened and the other end is split. White papers are inserted in the split to improve the visibility. Whites are also used for the same purpose as laths

Laths & Whites

Pegs• Pegs are made of timber or steel and

they are used to mark the position of the station or terminal points of a survey line. Wooden pegs are 15 cm long and are driven into the ground with the help of a hammer.

Wooden Pegs

Pegs

Plumb Bob• Plumb-bob is used to transfer points on

the ground. It is also used for fixing the instruments exactly over the station point marked on the ground by checking the centre of the instrument whether coincides with the centre of the peg or station not, by suspending the plumb-bob exactly at the centre of the instrument under it. Plumb bob is thus used as centring aid in theodolites and plane table.

Plumb Bob

Plumb Bob

Line Ranger• It is an optical instrument used

for locating a point on a line and hence useful for ranging. It consists of two isosceles prisms placed one over the other and fixed in an instrument with handle. The diagonals of the prisms are silvered so as to reflect the rays.

Ranging by Line Ranger

Line Ranger• Its advantage is it needs only one

person to range. The instrument should be occasionally tested by marking three points in a line and standing on middle point observing the coincidence of the ranging rods. If the images of the two ranging rods do not appear in the same line, one of the prism is adjusted by operating the screw provided for it.

Line Ranger

Line Ranger• To locate point C on line AB (ref. Fig.) the

surveyor holds the instrument in hand and stands near the approximate position of C. If he is not exactly on line AB, the ranging rods at A and B appear separated as shown in Fig. (b). The surveyor moves to and fro at right angles to the line AB till the images of ranging rods at A and B appear in a single line as shown in Fig. (c). It happens only when the optical square is exactly on line AB. Thus the desired point C is located on the line AB.

Line Ranger

Line Ranger

Chain Surveying• Chain surveying is the type of surveying in which

only linear measurements are taken in the field.• This type of surveying is done for surveying of

small extent to describe the boundaries of plots of land and to locate the existing feature on them.

• It is the method of surveying in which the area is divided into network of triangles and the sides of the various triangles are measured directly in the field with a chain or a tape and no angular measurements are taken.

Principles of Chain Surveying


• The principle of chain surveying is to divide the area into a number of triangles of suitable sides. As a triangle is the only simple plane geometrical figure which can be plotted from the length of the three sides even if the angles are not known. A network of triangles is preferred to chain surveying.

• Triangulation is the principle of chain surveying. If the area to be surveyed is triangle in shape and if the lengths and sequence of its three sides are recorded, the plan of the area can be easily drawn.






Terms related to Chain Surveying

Survey Stations• Survey stations are the points at the

beginning and at the end of a chain line they may also occur at any convenient position on the chain line. Such station may be

• Main Stations• Subsidiary Stations• Tie Stations



• Main Station Stations along the boundary of an area as controlling points are known as ‘Main Stations’ The lines joining the main station are called ‘ Main Survey Lines’. The main survey lines should cover the whole area to be surveyed. The main stations are denoted by Δ.


• Subsidiary Stations: Stations which are on the main survey lines or any other survey lines are known as ‘ Subsidiary Stations’ these stations are taken to run subsidiary lines for dividing the area into triangles, for checking the accuracy of triangles and for locating interior details.


• Tie Stations:• These stations are also subsidiary

stations taken on the main survey lines. Lines joining the stations are known as ‘ Tie lines’ Tie lines are taken to locate interior details.


Main Survey Lines:• The line joining the main stations are

called main survey lines or chain lines.


• Base Line: The line on which the framework of the survey is built is known as ‘ Base line’. It is the most important line of the survey. Generally the longest of the main survey lines is considered as the base line. This lines should be taken through fairly level ground, and should be measured very carefully and accurately.


• Check Line• The line joining the apex point of a

triangle to some fixed points on its base is known as ‘ Check line’. It is taken to check the accuracy of the triangle. Sometimes this line helps to locate interior details.


• Tie Line• A line joining tie stations is termed as

a tie line. It is run to take the interior details which are far away from the main lines and also to avoids long offsets. It can also serve as check line.

Selection of Survey Station

• The following points should be considered while selecting survey stations:

• It should be visible from at least two or more stations.

• As far as possible main lines should run on level ground.

• All triangles should be well conditioned (No angle less than 30º).

• Main network should have as few lines as possible.

Selection of Survey Station

• Each main triangle should have at least one check line.

• Obstacles to ranging and chaining should be avoided.

• Sides of the larger triangles should pass as close to boundary lines as possible.

• Trespassing and frequent crossing of the roads should be avoided

Operation in Chain Surveying

• The following operations are involved in chain surveying.

• Chaining• Ranging• Offsetting• These three operations are done

simultaneously during chain Surveying.


ChainingChaining on Level Ground• The method of taking measurement with the

help of chain or tape is termed as chaining.Chaining involves following operations• Fixing the stations• Unfolding the chain• Ranging• Measuring the distance (Survey Line)• Folding the Chain


Fixing of Station• Stations are first of all marked with pegs

and ranging rods to make them visible.Unfolding of a Chain• To open a chain, the strap is unfastened and

the two brass handles are held in the left hand and the bunch is thrown forward with the right hand. Then one chainmen moves forward by holding the other handle until the chain is completely extended.

Fixing of Station

Unfolding of a Chain


Ranging• The process of establishing

intermediate points on a straight line between two end points is known as ranging. Ranging must be done before a survey line is chained

Ranging ( Code of Signals)

Sr. No.

Signal by the Surveyor Meaning of the signal to the assistant

1 Rapid Sweep with right hand

Move considerable towards left

2 Slow Sweep with right hand Move slowly towards left3 Right arm extended Continuously move towards

left4 Right arm up and move to

the rightPlumb the rod towards left

5 Rapid Sweep with left hand Move considerable towards right

6 Slow Sweep with left hand Move slowly towards right7 Left arm extended Continuously move towards

right8 Left arm up and move to

the rightPlumb the rod towards right

9 Both hand above head and brought down

Ranging is correct

10 Both arm extended horizontally and brought down quickly

Fix the ranging rod

Ranging


Measuring the distance (Survey Line)• Two persons are required in this operation,

i.e. Leader and Follower.• The chainman at the forward end of the

chain who drags the chain forward, is known as the leader

• The chainmen at the rear end of the chain, who holds the zero end of the chain at the station, is known as the follower.



• To chain the line, the leader moves forward by dragging the chain line and taking with him ranging rod and ten arrows. The follower stands at the starting station by holding the other end of the chain. When the chain is fully extended, the leader holds the ranging rod vertically at arms length.

• The follower directs the leader to move his rod to the left or right until the ranging rod is exactly in the line. Then the follower holds the zero end of the chain by touching the station peg.

• The leader stretches the chain by moving it up and down with both hands, and finally place it on the line. He then inserts an arrow on the ground at the end of the chain and mark it with cross.


• Again the leader moves forward by dragging the chain with nine arrows and the ranging rod. At the end of the chain, he fixes another arrow as before, As the leader moves further, the follower picks the arrow which were inserted by the leader. During chaining the surveyor or an assistant should conduct the ranging operation.

• In this way, chaining is continued, when all the arrows are inserted the leader has non left with him, the follower hands over to the leader.

• To measure the fractional length, the leader should drag the chain beyond the station and the follower should hold the zero end of the chain at last arrow, then odd links should be counted.



Folding of Chain• To fold the chain, a chainmen should move

forward by pulling the chain at the middle. Then the two halves of the chain will come side by side. After this, commencing from the central position of the chain, two pairs of links are taken at a time with the right hand and placed on the left hand alternately in both directions. Finally the two brass handles will appear at top. The bunch should be then fastened by the strap.

Folding of Chain


Chaining on Sloping Ground• The object of survey is to prepare a plan or a

map. In the plan or a map the distance plotted between any two points is always a straight line. Even if the chaining is done on a sloping ground, this sloping distance is converted into horizontal equivalent distance while plotting.

• There are two methods of finding out horizontal distance while on a sloping ground.

• Direct Method• Indirect Method


Direct Method• This method is also called method of stepping in this

method, the distance is measured in small horizontal stretches. A suitable length of chain or tape say l1 is taken. The follower holds the zero end of the tape at a point on the top of the hill or sloping ground. i.e. at point A. The tape is stretched horizontally from A at small length l1 of 3 to 5 m. The point at the end of the l1 is dropped and marked on the ground as a1. From a1, again tape is stretched exactly in a horizontal plane at a convenient step l2 and drop end of l2 on the ground as b1. Likewise entire length of line on the sloping ground is measured.

• Finally the total horizontal length of the line AB, i.e. D is obtained

• D= l1 + l2 + l3 + ……… ln

• Where ln= the last step for the given survey line







• Indirect Method• Indirect method involves calculation from the

directly measured length these methods are briefly explained here.

Method-1• Horizontal distance of the segment is calculated

by knowing sloping length of the segment and angle of inclination of that with horizontal.

• The angle of the sloping surface with horizontal can be known by a simple handy instrument called as abney’s level


• Total Distance D= ∑d = d1 +d2 +….dn, and

• d= l CosӨ for d1 = l1 Cos Ө1

Where, Ө = angle of sloping surface with

horizontal and l= sloping length.


Clinometer

Clinometer

Abney’s level

Abney’s level



Method 2• If elevation difference between two terminal

point and the sloping distance between the two terminal point is known, the horizontal distance H can be calculated as,

• H= l2 – D2

• Where, • l= sloping length• D= Elevation difference between two points



Method 3 • This method is also known as hypotenusal

allowance method. The chaining is done on the sloping ground, but instead of putting the end arrow at the actual end of the chain, it is put at some advanced distance and that point is considered as the end of one chain length.

• In this method, the chain of 20 m length ends at point B. Therefore, sloping length l = 20 m, but the actual horizontal length (H) is less than 20 m and calculation is required to calculate horizontal distance based on Ө. Angle of inclination of ground.


• Horizontal distance H= (l + a) Cos Ө ,Where,H is intended to make one chain length,• Therefore ,• H= (l + a) Cos ӨHere, AB= one chain length= l= H= 20 m• Therefore Put H= l= 20 m• 20= (20 +a) Cos Ө• 20 Sec Ө= 20 + a• a= 20 Sec Ө – 20• a= 20 (Sec Ө – 1)


• Where a hypotenusal allowance for 20 m chain

• For a chain other than 20 m length,• a= l (Sec Ө – 1) where l= length of

chain in m• Thus the arrow is inserted at (l+a)

distance on the ground instead of at the end of chain. Thus the horizontal distance of this sloping distance on ground is equal to one chain length.


Offsets• Lateral measurements to chain lines

for locating ground features are known as offsets. For this purpose

• perpendicular or oblique offsets may be taken . If the object to be located (say road) is curved more number of offsets should be taken. For measuring offsets tapes are commonly used.

OffsetsPerpendicular Offsets• The offsets which are taken

perpendicular to the chain line are termed as perpendicular offsets. These offsets are taken by holding zero end of the tape at the object and swinging the tape on the chain line. The shortest distance measured from object to the chain line is usually the perpendicular offset.

Perpendicular Offsets

OffsetsOblique Offset• Oblique distance is always greater

than perpendicular distance. All the offsets which are not taken at the right angle to chain line are known as oblique offsets.

Oblique Offset

Offsets

Offsets• For setting perpendicular offsets any

one of the following methods are used:

• (i) Swinging• (ii) Using cross staffs• (iii) Using optical or prism square.

Perpendicular Offset by Swinging

• Chain is stretched along the survey line. An assistant holds the end of tape on the object. Surveyor swings the tape on chain line and selects the point on chain where offset distance is the least.

• and notes chain reading as well as offset reading in a field book on a neat sketch of the object





Perpendicular Offsets Using Cross Staffs

• Three different types of cross staffs used for setting perpendicular offsets. All cross staffs are having two perpendicular lines of sights. The cross staffs are mounted on stand. First line of sight is set along the chain line and without disturbing setting right angle line of sight is checked to locate the object.

• With open cross staff (Fig(a)) it is possible to set perpendicular only, while with French cross staff

• (Fig(b)), even 45º angle can be set. Adjustable cross staff can be used to set any angle also, since there are graduations and upper drum can be rotated over lower drum.



Perpendicular Offsets Using Optical Square and Prism

Square• These instruments are based on the

optical principle that if two mirrors are at angle ‘θ’ to each other,

• they reflect a ray at angle ‘2θ’. Figure shows a typical optical square.

Perpendicular Offsets Using Optical Square and Prism Square

Optical Square and Prism Square

Optical Square and Prism Square







3-4-5 Method• AB is the chain line it is required to erect a

perpendicular at C of the chain line. Establish a pt D at 3 m distance. 5m & 6m marks are brought to gather to form a loop .The tape is stretched tight by fastening the end D and C. The point D is established such that DE = 5 m and CE= 4 m and CD = 3 m and DE2 = CD2 + DE2

• i.e. 5 2 = 3 2 + 4 2 = 25 thus Angle DCE = 90 0

• i.e. CE is perpendicular to chain line at C

3-4-5 Method

3-4-5 method

3-4-5 method

Field Book• All observations and measurements taken during chain

surveying are to be recorded in a standard field book. It is a oblong book, which can be carried in the pocket.

• There are two forms of the book • (i) single line and • (ii) double line. • The pages of a single book are having a red line along the

length of the paper in the middle of the width. It indicates the chain line.

• All chainages are written across it. The space on either side of the line is used for sketching the object and for noting offset distances. In double line book there are two blue lines with a space of 15 to 20 mm

• is the middle of each book. The space between the two lines is utilised for noting the chainages.

Field Book

Field Book

References

• “Surveying and Levelling” Vol I Kanetkar and Kulkarni (2011) Pune Vidhyarthi Griha, Pune

• “ Surveying and Levelling” N.N.Basak (2010) Tata Mcgraw Hill

• “ Surveying Vol- I Dr. B.C. Punamia Laxmi Publication

• Internet Websites• http://www.fao.org/docrep/r7021e/r7021e02.htm#

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Linear Measurements

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