Error in Chain Survey

 

Errors in linear Managements(Chain survey)

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 / Systematic error / Persistent errors
2.  Compensating error / Accidental error / Random error
3.  Blunder / Mistake / Gross error

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 compensating 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 judgment 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 3  ͦ, slope correction is generally neglected. before this correction for standardization should be applied. It's nature is  Cumulative nature of error.

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.

 

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