LINEAR MEASUREMENT

Content

1.  Introduction & Principle
2.  Slope, Horizontal, vertical distance
3.  Direct & Indirect linear measurement method
4.  Optical Distance Measurement (ODM)
5.  Electronic Distance Measurement (EDM)
6.  Linear survey (Chain Survey)
7.   Field procedure & plotting
8.  Obstacles in linear survey and their solution
9.  Error in linear measurement

1.   Introduction and principle

Linear Measurement

 

Chain survey is branch of surveying in which the distances are measured with a chain and tape and the operation is called chaining. chain Surveying is that type of surveying in which only linear measurements are made in the field. This type of surveying is suitable for survey of small extent on open ground having few simple details. 

The principles of chain surveying are triangulation. As we know triangle is the simplest 2D figure whose area can be calculated easily and it is only the figure which can be plotted without any angle. According to this principle the area of surveying is divided into number of small triangles which should be well conditioned. In chain survey sides of triangles are measured directly on the field and no angular measurements are taken. the exact arrangement of triangles will depend upon the extent and type of the area to be surveyed.

 

2.   Slope, Horizontal, vertical distance

Linear measurement includes the measurement of following units:

1.  Horizontal distance:

It is the distance between two vertical line (plumb line) on two points to be measured in a horizontal plane.

 

2.   Vertical distance:

It is the vertical difference (elevation difference) between two points measured in vertical plane between two horizontal lines touching two points whose vertical distance is required to measure. 

 

3.   Slope distance:

Slope distance is the length of slope from the top to the bottom of slope and is larger than H.D & V.D. Slope distance can be calculated when the vertical height and the horizontal distance of right angle are known. There is right angle if the vertical & horizontal distances are 'True’ to the vertical and horizontal, respectively.

# Relations between Horizontal, vertical & Slope distance: 

BC= vertical distance (V.D) =(h)

AC = Horizontal distance (HD)  =(D)

AB= slope distance (SD) =(ℓ)

If any two distances are known, then third distance can be calculated

(slope distance)² = (Horizontal distance)² + (vertical distance)² 

.: (S.D.) ² = (H.D.)² + (V.D)²

.: S.D. = √((HD)²+(VD)²)

.: H.D. = √((SD)²-(VD)²)
.: V.D. = √((SD)²-(HD)²)

Distance measurement of sloping Nature ground: - 

 Chaining or Tapping on the surface of a sloping ground gives the sloping distance. But, we need the horizontal distance for plotting work of the survey. Therefore it is necessary to reduce the sloping distance and made equivalent to the horizontal distance or to measure the horizontal distance between any two point by any method. 

Generally there are two methods of measuring sloping  ground 

1) Direct Method

       a) Stepping

2) In direct Method

       a) slope angle method 

       b) Height difference method

       c) Hypotenusal allowance 

1.  Direct Method

On the ground we can measure the horizontal distance directly by measuring the distance of short interval of ground. In this method full length of chain or tape not came to in use, it depends upon the steepness of the ground. Direct method is also known as "Stepping method"

1.a.  Stepping:

In this method the follower holds the zero end of the tape/chain at the top portion of ground while the leader selects suitable length l, of the tape and moves forward along the chain line. Follower should directs the leader for correct ranging. The leader used to pull the tape and stretches it horizontally to the ground at a convenient height that should be less than 1.8 m. The point vertically below a definite chainage used to marked , is accurately located on the ground by suspending a plumb bob or by dropping arrow. or for the less accuracy point can be transferred on to the ground by dropping a pebble. After that follower comes to the marked point and the process is continued until the entire length of the sloping ground, is measured. If d1,d2,d3,d4,........dn are the tape lengths measured from top to bottom than, the total horizontal distance between the two stations, is equal to the sum of the lengths of the steps i.e. d1+d2+d3+d4+........+dn

 

Following precautions are taken during stepping:

(1) Surveyor should direct the leader himself and also check either tape/chain is stretched horizontally or not.

(ii) Error due to sag is proportional to (Weight/Tension)², therefore lighter in weight chain or tape, should be used with a maximum pull.

(iii) Short steps used to taken if the chain is heavy or the slope is steep. It's not necessary to keep the steps length uniform. step length is inversely proportional to the steepness of the slope and the weight of the chain or tape.

(iv) It is easy to run chaining work higher portion to lower portion of grounbd rather than lower to higher portion.

 

V=should be not excessed to 1.8m

 

Total HD = d1+d2+d3+d4+d5

 

2. Indirect Method.

The horizontal distance between two stations on a sloping ground may be obtained by any one of the following methods :

2.i.       By Measuring slope angle (Inclination or declination) :- 

The distance along the slope is measured and then the angle of Slope i.e. angle between the sloping ground and the horizontal surface is found with the help of Abney's level, clinometer or precisely with theodolite.

 

Here, 

AC = ℓ = slope distance

α = slope angle

AB = HD = Horizontal distance = ℓ * Cos α

 

 

 2.ii.    By Measuring differences of levels: - 

The distance along the slope is measured with chain and the difference in elevation between the first and the end station is found with the help of levelling Instrument

 

 ℓ= slope distance

Δh = difference of levels

HD = d = Horizontal distance

HD =√(ℓ^2 - h^2 )

2.iii.   By Hypotenusal allowance

For locating a number of intermediate points by applying a correction for each chain length, this method is commonly preferred. Hypotenusal allowance foe each chain length can be computed as follow:

let,

 α = the angle of slope of the ground

AD=AB= 1 chain = 100 links. 

Then AC = 100 Sec α links      &

BC = AC-AB = 100 (sec α -1) links. 

BC = hypotenusal allowance.

Comparison between the direct and indirect method:

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3.  Direct and indirect linear measurements methods:

The various method of measuring the distance directly are as follows:

1) Eye survey 

2) Pacing 

3) Passometer 

       4) Odometer / Speedometer 

5) Pedometer

6) Chaining 

7) Tapping

 

2. Pacing: - 

This method consists of counting the number of paces (steps) taken to reach from one point to another point. The length of the line can be computed by knowing the average length of the pace. The length of the paces varies with the individuals, and also with the nature of  the ground. if the pacing is carried out by experience surveyor than the accuracy of measurement is 1:50 to 1:100. two pace is equal to one stride. generally 1 pace =80cm, therefore, 1 stride = 160cm.

 Distance = No. of paces (steps) * pace factor.

 pace factor → distance covered by 1 pace of a surveyor.

 

 

3. Passometer:- 

It is an instrument shaped like a watched and is carried in pocket or attached to one leg. The mechanism of the instrument is operated by the motion of the body and it automatically registers the number of paces. The number of paces registered by the passometer can then be multiplied by the average length of the pace to get the distance. It is also used for rough and preliminary survey. Its accuracy is also 1:50 to 1:100.

 

 

4. Pedometer: - 

It is device similar to passometer. The length of the pace of a person carrying it was adjusted in it and it register the total distance covered by any number of paces. It avoids the monotony and strain of counting in case if Surveyor forgot to counting of paces (steps). Its accuracy is 1:50 to 1:500.It is also used for rough and preliminary survey.

Distance = No. of paces (steps) * length covered by 1 pace.

 

5. Odometer / speedometer: - 

The odometer is an instrument for registering the number of revolutions of a wheel. The well-known speedometer work on this principle. The odometer is fitted to a wheel which is rolled along the line whose length is required. The number of revolutions registers by the odometer Multiplied by the circumference of the wheel to get the distance of the route is smooth. It can be used for approximate distance measurement but not accurate reading obtained on undulating ground. Its accuracy is nearly 1:200. It is also used for rough and preliminary survey.

 Distance = Circumference of wheel * No. of revolution

 

6. Chaining: - 

Chaining is the term or concept which is used to denote measuring distance with the help of  chain. It is the more accurate method of making direct measurements than previous all instrument for work of ordinary precision. From this method we can achieve better accurate result having precision from 1:500 to 1:2000. there are different types of chain which are used,  (i.e. Gunter's chain, Engineer's chain, Metric chain)

 

7. Tapping: - 

It is quite similar to the chaining. in this method we use tape instead of chain to measure distance between any two point. Its accuracy is also same of chaining or better than that. In sloping ground tapping is prefer than of chaining. In sloping nature of ground stepping method used while tapping.While carrying stepping we have to run the work from top hill to down hill.

point to be observed during chaining 

following point to be observed during the process of chaning:

1.  Folding  and Unfolding of Chain:

The chain should be carefully folded and unfolded. Generally, to handles are kept in right hand and the chain is thrown by followers. Then, the leader takes one of the handle and start moving.

 

2.  Number of Arrows:

The leader inserts the arrow in the end of the measured chain length and the follower collect the arrow thus, inserted by leader. Hence the sum total of arrows held by follower and leader should always be equal to the arrows taken in the beginning by the leader which is usually 10. Thus the arrows possessed by leader and the follower provide useful check during chaining.

 

3.  Reading the Chain:

The fraction of chain should be read very carefully as there are identical tags for 1m and 9m; 2 m and 8 m; 3 m and 7 m; 4 m and 6 m. hence, it should be seen whether the tag is in front or on the back of the central tag.

 

4.  Testing and Adjustment of Chain:

The chain should be tested and adjusted for correct length before starting the chaining. if it is found afterwards that the length was measured by a wrong chain, the correction should be applied in following manner.

 

            Ca  =  (C*L)  / l

where,     

Ca = Correction for absolute length
C = correction to be applied to the tape 
L = Measured length of the line(m)
l = Nominal length of the tape (m)  

 

 Error in measurement with incorrect tape or chain

True length of line = L1 / L * measured length of line 
True area = (L1 / L)² *  measured length of line  
True volume =  (L1 / L)³  *  measured length of line

where,
L =  True length of chain 
L1 =  Incorrect length of chain 
    = L ± e
* e  =  error (+ve if the chain is too long and -ve if the chain is too short) 

The method of direct distance measurement is unsuitable in difficult terrain and sometimes Impossible when obstructions occurs. on that condition Indirect Method comes in use.

Subtense bar (Horizontal stave) :

Subtense bar is a distance measuring instrument. This is a rigid rod, usually of a material insensitive to change in temperature such as invar, of fixed length (typically 2m). The Subtense bar is mounted on a tripod over the station to which the distance is described. it is bought to level and small telescope on the bar is enables the bar to be oriented perpendicular to the line of sight to the angle measuring station. 

A theodolite is used to measure the angle between Indicators on the two ends of the subtense bar. The distance from the telescope to the subtense bar is the height of an isosceles triangle formed with the theodolite at the upper vertex and the subtense bar length at its base, determined by trigonometry. 

Note:

1. In subtense bar method, Horizontal angle can't be change.
2. It always gives horizontal angle (in m).
3. accuracy of Horizontal distance & horizontal angle  depend up on angular measurement 

• 

 

4.  Optical distance measurement (ODM): - 

In the optical methods, observations are taken through the telescope and calculation are done for the distances.It term as ODM because in this method  we use the optical properties of lens to carried out the distance from one station to another. such as in tacheometry, horizontal subtense method or telescopic alidade using optical wedge attachments. Its range is limited up to 150m and the accuracy obtained is 1 in 1000 to 1 in 10000.

In this method horizontal and vertical distance is carried out by using following formula:

 d =k(t-b)sin²z + c sin z

Δh = k(t-b) sin z cos z + c cos z

 here, 

d= Horizontal distance 

Δ= difference in elevation 

 k = multiplying constant of the instrument(100)

c = additive constant of the instrument (0)

z = zenithal angle

t = top wire reading

b = bottom wire reading 

distances are measured with instruments that rely on propagation, reflection and subsequent repletion of either radio or light waves

 

 

 5.  EDM (Electronic Distance Measurement):

It is an electronic methods, which is based on generation, propagation, reflection and subsequent reception of electromagnetic waves. It is also known as Electromagnetic distance measurement. The various instruments that are used under the electronic methods are: Geodimeter, Tellurometer, The Decca Navigator, Distomats, The Lambda position fixing system.Geodimeter based on light wave & other all are on Radio wave.  It is recently developed surveying instrument which gives very high accuracy in distance measurement. An accuracy 1 in 100000 (which is ±5mm per km) can be Achieved for sight up to range of 100 km.

 

on the basis of carrier used in EDM, it can be classified into three categories :

1) light wave EDM (visible light EDM) :

Frequency = 5 x 10ˆ4 HZ  

Range = 2 to 3 km.  

Accuracy = ± 0.2 to 1 mm /  km  

          Instrument =  Geodimeter  

 →made by sweden country   

→can't work in night.

                                                                                           

2)  Infrared / laser EDM

frequency = 3 x 10˄8  to  6.7 x 10˄8 MHZ     

Range =  2 to 5 km   

Accuracy = ± 10 mm in respective of distance.  

 Instrument = HP (Hewlet packard) 380   &  wild Distomats 

                                                                                                                                       

 3)  Microwaves EDM

frequency = 3 to 30 GHz
 Range - 30 to 80 km
 Accuracy = ±  5 mm / km.
 Instrument =  Tellurometer

  →developed by South Africa   

→Invented in Telecommunication office 

→This instrument have no prism 

→ Both stations have instruments (total station) 

→ Generally, it needs two station i. p. master station & slave station. 

→ It is best for day & night work.

Working Principle of EDM

It was based on transmission of electronic wave from the instrument towards the reflector or object and  the reflector/object reflects the wave back towards the transmitting unit. The equipment on transmitting unit received the wave reflected back from the reflector since it also acts as receives. Now by recording the transit time of wave and knowing the velocity, the instrument  compute required distance and  display the required distance between the points/stations. The wave travels twice distance (Instrument to Reflector and reflector to Instrument).    

 therefore, D= Vt/2                                                                                                                        where    

 D = Distance between points. 

V = velocity of wave   

 t = total transit time (t2-t1)

                                                                                                                                                          

Characteristics and Application (use) of EDM 

1.  Geodimeter is first edition of EDM 
2.  Accuracy of EDM was in part per million (1/1000000)
3. visibility between Instrument & reflector required
4. It measure slope distance too
5. To measure baseline of Triangulation
6.  To measure traverse leg of larger area
7.  To establish CPs by Trilateration method. 
8. setting out part in different engineering work.
9.  The most common type of EDM now available is termed as Total station. 

Distance by EDM ( According to Topcon Company & EDM)

1. 1 prism  → up to 3 km. 
2. 3 prism → up to 4 km
3. 9 prism → up to 5 km. 
4. Mini prism  →  up to 1 km (sticker prism)

Total station

Total station is a combination of theodolite, level, EDM, microprocessor with a specific memory. Total station integrates the functions of a theodolite for measuring angles, an EDM for measuring distances, digital data & data recorder. From this instrument distance, angle, height difference, co-ordinate, area, bearing, perimeter etc. can be easily measured. Its accuracy was in part per million (ppm). It can measured slope distance directly. Topcon, sokia, pentex, Nicon, Leica, Stonex, etc. are the model of total station.

Features and Uses of Total station:

1. Total Solution for surveying work 
2.  Most accurate of user friendly 
3.  Gives position of point (X, Y, Z) W.R.T. known point 
4.  EDM was fitted inside Telescope 
5.  on board memory to store data
6.  Digital display 
7.  Compatibility with computers
8. can be used for curre layout
9. 
   

Functions of Total station:

1. It simultaneously measures angle of distance  & record 
2.  Correcting the measured distance with.   

 prism constant
 Atmospheric pressure
 Temperature 
 curvature of earth   
 Refraction correction 

3.  Computing the point elevation   
4.  Comparing the coordinates of every point  
5.   Remote elevation measurement
6.  Remote distance measurement
7. Area calculation  
 8. Data transferring facility from instrument to computer and computer to       Instrument 
 9. Format of conversion of units.

Note : -    Non-prism Totalstation

• Low accuracy than prism total station. 
• Can't measure more distance (up to 2 km only)
  
  

Ranging

The process of establishing intermediate points on a straight line between two end points is known as ranging. It can be done either by using instruments or eye survey. If tape or chain length was smaller than that of, we have to measured then Ranging work carried out. 

 

Types of Ranging (Methods of Ranging)

I) Direct Ranging

2) Indirect Method (Reciprocal Ranging)

 

Direct Ranging:

It is done when the two ends of the survey lines are invisible. In such case, ranging can either be done by eye or through some optical instrument such as a line ranger or a theodolite. Considered two points x & y which are inter-visible to each other. In this method ranging rod is fixed at station x & y. suppose if we want to locate a point ‘z’ on ground which is in line with xy. The surveyor stands half a meter back side of ranging rod at x in line with x y. Assistant then move another ranging rod under the guidance of surveyor. in such a way that ranging rod hold by assistant is in the line xy at point z between x & y. Surveyors has to Guide assistant by using signals of hand so that ranging rod comes in the line. Other points can be located by similar way.

Indirect / Reciprocal Ranging:

This method is used when two ends of survey stations or survey line are not inter-visible either due to high intervening ground or due to long distance between them. In such a case, ranging is done indirectly by selecting two intermediate points M1and N1 very near to the chain line is such a way that from both points A & B should be visible.

a) Sectional view

 

Sectional view

 

 

b) Plan view

Plan view

 

Let A & B be the two stations which are not inter-visible. so, to proceed in straight line between A & B process of indirect ranging is applied. Two intermediate point M1 & N1 are located in such a way that person standing with ranging at N1 can see M1 and A, where as person with Ranging rod at M1 can see N1 and B. Now person at N1 will guide person at M1 to come in line with N1  & x on a new position of M2. Now the person at M2  will guide et person at N1 to come in line with M2 & Y on a new position N2. These points will keep changing until both M & N comes exactly in the line of xy.

6.  Linear survey (Chain Survey)

Instruments for chain survey

1)chain or Tape 

2) Arrows 

3) pegs 

4) Ranging rod

5) plumb bob.

6) optical square 

 7) offset rods

 

Sketch of chain survey

Terms used in chain surveying: -

1.Survey stations

              a. Main station

              b. Subsidiary station

       

 2. Survey lines

  a. Main lines 

  b. Baseline

  c. Check line

  d. Tie line

 

3. Offset 

  a. Perpendicular offset

  b. Oblique offset

 

 

Main stations: 

The prominent point on the chain line, either at the beginning of the chain line or at the end is known as Main stations. These are connected with survey lines to form the triangles. These stations are denoted by Δ with letter A, B, C, D ...

 Subsidiary station:

 The point (station) which can be located on the survey lines or any other line are known as subsidiary station. It is also known as tie & auxiliary station. These stations are taken to run subsidiary lines for dividing the area into triangles for checking the accuracy of triangles. These stations are denoted by O with letter S1, S2, S3, I1, I2, I3 

Main line: – 

The chain line joining the two main survey station is known as main survey line.

 

Base line: – 

The line on which the framework of the survey is built is known as base line. It is most important line of the survey. generally, the longest line of the survey lines is considered as the base line. 

 

Check line: - 

The line which is run in the field to check the accuracy of the work (framework of the triangles). It is not required for plotting the triangles. It is also known as proof line. Each triangle must have a check line.

Tie line: 

Line which Joins subsidiary or tie station on the main line is known as tie line.it is also known as subsidiary or auxiliary line. The main objective of running a tie line is to take the details of nearby objects but it also serves the purpose of a check line.

Offsets: 

 An offset is the lateral distance of an object or ground features measured from survey line. By method of offsets, the point or object is located by measurement of a distance and angle. 

Perpendicular offset: 

An offsets line which is perpendicular to the survey line is known as perpendicular offset. It is also known as right offset or rectangular offsets (simple offset). If the details are nearby chain line, It is appropriate to plot the detail. optical square, prism square, cross staff, swing method, used to set Perpendicular offset.

 

Perpendicular Offset                                            Perpendicular with ties line

Oblique offset: 

Offset line which is not perpendicular to the survey line is known as oblique offset. It is also known as tie line offset. when the details are far from survey line, the oblique offset is used. It is more accurate than perpendicular offset. It can be used to check the accuracy of perpendicular offset.

 

Oblique Offset                                                Oblique with tie line

Conditions to be fulfilled by survey lines or survey stations: 

1)  The main station should be mutually inter-visible so that the ranging can be done easily.  

 
 2) Survey line should be as few as possible so that the framework of triangles can be plotted easily. 
 

3)The lines must be run through open & level ground as possible so that chaining can be done easily.  

 
4) The framework must have one or two baselines. If one base line is used, it must run along the length and through the middle of the area. if two  baselines are used, they must intersect in the form of letter X. 
 
5) The main lines should form well-conditioned triangles, with no angles less than 30° or more than 180° 
 

6) As far as possible, the survey lines should be selected such that there are no obstacles in chaining and ranging. 

 

7) The survey lines should be close to the details to avoid long offsets. 
 

8) If required, a number of tie stations should be selected and tie lines run to avoid long offsets.

 
 9) Each triangles should have check line to detect mistakes in measurements and plotting. 

 

 10) To avoid trespassing the main survey lines should fall within the boundaries of the property to be surveyed. 

 

11)  while selecting the main stations and survey lines, the basic principle of

surveying of working from the whole to the part should be followed. "The larger framework consisting of control triangles should be accurately surveyed fly first to fix control points. The smaller triangles can then be fitted in the larger triangles, if necessary.

7. Field Procedure and Plotting 

Field work in Chain surveying:

1) Reconnaissance

 2) Marking & fixing station

3) Running survey lines 

 

Reconnaissance:

 Reconnaissance is the preliminary inspection of the area to be surveyed to have some idea of the terrain and the principle features of the ground. The surveyor thoroughly examines the ground and then decides upon the best possible arrangement of triangles. suitable position of survey station & survey lines is selected & inter-visibility between selected station is checked. During reconnaissance, a reference sketch of the ground should be prepared and general arrangement of lines, principal features (Such as building, roads, boundaries etc.) should be shown. Investigation of various difficulties that may arise and thinking of their solutions also comes under this.

 

 

 Making station: 

After completing reconnaissance, the main stations are marked on the ground so that the stations can be readily located afterward, if required. In soft ground, wooden pegs are used to mark stations & name of stations written on top. If ground is hard, a portion may be dug and filled with cement mortar. In case of roads or streets nails used to mark the station, and if the station is required for very long period of time permanent signals are used to mark. Survey stations must be fixed with reference to two or three permanent objects and sketch of location are drawn in the field book. It helps us to re-establish the station if the station was lost

Running survey line: -

Ranging

chaining

offsetting 

Survey lines are run to measure the distance between main Stations and to locate the adjacent details by offsets. The Chaining is usually commenced from the baseline and continued to other survey lines.

Offsetting:

The process of taking the offsets is known as offsetting. The offsets are generally measured with a metallic tape in chain surveying. An offset rod can be used for taking short offsets, if tape is not available. If the plan is to be plotted on a large scale, a steel tape should be used for the measurement of offsets.

If length of offset is less than 15m termed as short offset 

If length of offset is more than 15m termed as long offset

 If length exceed 30m, a subsidiary line should run to take offset.

8. Different types of obstacles & its solution:

1. Obstacles in Ranging
2. Obstacles in chaining 
3. Obstacles in both Ranging & chaining

1. Obstacles in Ranging

Sometimes, there are obstacles, such as a forest or a hill, on a survey lines which obstruct ranging as both ends of the lines are not inter-visible.

 

case I: - The end stations may be visible from some intermediate points on the rising ground. In this case Reciprocal ranging can be done.

 

Case-II: - The end stations are not visible from intermediate points when Jungles area comes between the points.

 

Using Pythagoras theorem 

AB=√(AD^2 - BD^2 )

2.  Obstacles in chaining

Case  i: -   Chaining round the obstacles possible

Case  ii: -   Chaining round the obstacles not possible 

Case i :-Chaining round the obstacles possible, when obstacles is small lime pond, depression, etc.

 

Case ii :- Chaining round the obstacles not possible like long wide river, building etc.

 

3.  Obstacles in both ranging and chaining

 

 

 

 

 

 

9. Errors in linear Managements

A.   On the basis of source of error:

1.   Instrumental error
2.  Personal error
3.  natural error

1.  Instrumental error: 

Error which occurs due to faulty adjustment or imperfection of the instrument with which the measurement is being taken is known as instrumental error. It can be eliminated or minimized by adopting suitable procedures and by applying proper correction and adjustment. 

 

For Eg. :  If the tape used in measurement of distance is actually 30.10 m long where as nominal length is 30 m, the error occurs because of the imperfect tape called instrumental error.

 

2.  Personal error: 

The personal error occurs due to human limitation , fault such as sense of sight and touch.the errors occurs for want of perfection of human sight while taking observation or for want of perfection of touch while manipulating the instrument.

For Eg. : A distance of 1.444 m may be estimated as 1.445 m  or 1.443 m.

3.  Natural error: 

The error which arise due to variations in natural phenomena such as temperature, humidity, gravity, wind, refraction,and magnetic declination. If they aree not properly observed while taking measurements,the results will be incorrect.Generally it is not possible to remove the cause of natural errors. however, the natural errors can be minimized by using good judgement and applying corrections.

For Eg. : If tape was calibrated at 20  ͦ C. but the field temperature is 35  ͦ C, there will be natural error due to temperature variation.

B.   On the basis of nature of error:

1.  Cumulative error
2.  Compensating error 
3.  Blunder or mistake 

1.  Cumulative error:-

It is an error that, under the same conditions, will always be of the same size and sign.It follows some well-defined mathematical or physical law or system, and the correction can be determine and applied. This type of errors are of constant character and according to result too great and too small it regarded as positive or negative. It can be eliminated by applying required correction.

 

A. Positive Cumulative error:-

 

The error which makes the measurement more than the actual, is known as positive cumulative error.

 

The condition for occurring positive cumulative errors:

1. The  slope correction ignored while measuring along the sloping ground.
2. If sag correction is not applied when the chain or tape is suspended at its end.
3. Incorrect alignment / Bad ranging 
4. If chain or tape is not horizontal to the ground.
5. Measurement above the MSL.
6. The length of chain or tape becomes shorter than of its original standard length due to following reason: 
•  Due to shrinking of tape when moist.
• Due to bending of the chain links.
• Due to fall in temperature lower than that the tape was calibrated.

B. Negative cumulative error:

The error which makes the measurement less than the actual, is known as negative cumulative error. 

 

The condition for occurring negative cumulative errors:

1.  The length of chain or tape becomes longer than of its original standard length due to following reason:
• Due to flattening of the connecting rings.
• Due to opening of the ring joints.
• Due to rise in temperature higher than that the tape was calibrated.
• Tension applied is greater than the standard pull.

 

2. Compensating error:

The error which are likely to occur in either direction and tend to compensate are called compes\nsating error. It is also known as Accidental error. It can not be eliminated by applying any correction.

 

The condition for occurring compensating errors: 

1. Incorrect  holding of the chain.
2. The chain is not uniformly calibrated throughout its length.
3. Refinement is not made in plumbing during stepping method. 

 

3.  Mistake / Blunder / Gross error:

Mistakes occurs in measurement due to carelessness, inattention, inexperience, poor judgement or confusion of the surveyor. It do not follow any mathematical rules and may be larger or smaller  and positive or negative. It can be eliminated by adopting standard methods of observation, booking and checking.

 

 

Errors in chaining and it's corrections -

1.      Error due to standardization

2.       Error due to non-horizontality (slope)

3.       Error due to variation in Temperature

4.       Error due to pull

5.       Error due to sag

6.       Error due to bad Ranging

7.       Error due to incorrect handling & marking

8.       Error due to displacement of arrow

9.       Error due to miscounting the chain / tape length

    10.  Error due to misrecording

 

1.  Error due to standardization: -

If the absolute length (actual length) of the chain/Tape is not equal to the nominal length, the measured distance will not be equal to the correct distance. Difference of correct distance and measured distance in this Condition termed as error due to standardization. It is an instrumental error and cumulative in nature.

 Correction 

(Cs) = { (ℓ' - ℓ)/ℓ } * L'

where, 

 ℓ' = actual length of tape 

ℓ = nominal length of tape

L' = length measured by tape on ground. 

If actual length is greater than the nominal length, the error is negative and correction is positive and vice-Versa 

corrected length (L) = measured distance ± correction

= L' ± C

 

2.   Error due to non-horizontality (slope)

If the slope is uniform, the Correction for slope can be computed. As the distance measured is always greater than its actual horizontal distance, the error is always positive, so it's correction is negative. Up to slope of angle 3ͦ, slope correction is generally neglected. before this correction for standardization should be applied. It's nature is  Cumulative nature of error.

                 Csl = L-(L^2 - h^2) ^1/2

3.   Error due to variation in Temperature

The correction for temperature is required if the tape temperature is different from the temperature at which it was standardised. the tape was usually calibrated at a temperature of 20  ͦ C or 27  ͦ C. It is cumulative in  nature. Rise in temperature occurs +ve error and -ve correction, and vice-versa.

 

Temperature correction (Ct) is given by:  

Ct  = α (T - T◦) L

Where,

 

 Ct = Correction for temperature

 α = Coefficient of linear expansion.

T = Mean temperature during survey.

T◦ = Standard temperature

4.  Error due to pull 

If the pull (tension)applied at the ends of tape during measurements in the field is different from the standard tension at which the tape was calibrated, a correction for pull is required.If the pull applied is greater than the standard pull, the actual length of the tape is greater than the  standard pull, the actual length of the tape is greater than nominal length so its correction is positive and error is negative, and vise versa.It is also cumulative in nature.

 

The correction for pull(Cp) is given by:

 Cp = (P - P◦)L / A E

 

Where,

P = Pulled applied during measurement(in Newton) 

P◦ = Standard pull (In Newton) 

A = Correctional area of tape (sq.cm) 

E = Young's modulus of elasticity (Kg/cm²) 

L = Measured length (In meter)

5. Error due to sag:

During the measurement tape or chain became sag and form shape of an arc due to the gravity of the earth termed as catenary. In this condition actual length is greater than nominal length so its error is +ve and correction is -ve. It is cumulative in nature.

 

                        Cs = L/24*(W/P)^2

where, 

Cs = correction for sag 

W =total weight of the tape between support(Kg) 

w = Weight per unit length of the tape(kg) 

f= Applied pull(kg)(If Newton F=p) 

L = Measured curved distance(m)  

 

 θ = Angle of inclination of the support stations. 

Cs' = Ordinary sag correction for zero(0) slope

6.  Error due to bad ranging; 

•  Measured length  is greater than original length
•  Cumulative in nature
•  +ve error and -ve correction
•  Careful ranging