The document discusses various types of errors and mistakes that can occur when measuring distances using a chain or tape. It describes two types of errors - cumulative errors, which accumulate and affect accuracy, and compensating errors, which cancel out. Examples of each are provided. Mistakes are defined as errors from carelessness rather than instruments, and don't follow rules. The document also outlines corrections that must be applied to measurements for factors like slope, temperature, tension, and sag.

1. LECT#11
QUEST, CAMPUS
LARKANA
Errors and Mistakes in chaining

2. Errors
 Chain is standardized at 20 c temperature and 8 kg
tension(pull).
 So the error in chain may occur due to variation of
temperature and pull from standard value.
 Errors may also be due to defective instrument.
 So errors are related to instrument and its faults and
methods of measurement.
 There commonly two types of errors
 (1) Cumulative Error
 (2) Compensating error

3. (1) Cumulative Error
 Cumulative errors are said to be systematic errors or
instrumental errors as they are one-directional hence
keep on accumulating as the survey progresses.
 If not checked they have serious implications to the
accuracy of the survey. Errors in this class include
incorrect length of the tape, page of the tape or the
tape not being in line.
 Since the sources of these errors are known, they can
be eliminated.
 They are proptional to L

4.  They can either be positive or negative errors.
 Positive error
 These errors make the measured length more than
the actual length which results into wrong
calculations by the Surveyor.
 The following are some of the positive errors:
 The length of chain is shorter than the standard
length due to bending of links, removal of connecting
rings and knots in links.
 The temperature is lower than at which the tape was
calibrated.
 Not applying sag correction.
 Sag takes place due to self weight of the chain.
 Incorrect alignment

5.  Negative errors
 These errors make the measured length less than the
actual length.
 Following are some of the negative errors:
 Length of chain or tape greater than its standard
length due to flattening of rings, opening of ring
joints and temperature being higher than at which it
was standardized.
 Wearing of connecting rings
 Elongation of links

6. (2) Compensating error
 Compensating errors are said to be accidental errors
hence cancel out and does not pose serious problem
to the accuracy of the survey.
 They occur both direction positive and negative.
 These errors are proportional to square root of
L(length of chain)

7.  Following are some of the compensating
errors:
 1) Incorrect marking of the end of chain
 2) Fractional parts of the chain may not be correct
when the chain is corrected by adding or removing a
ring.
 3) Graduation in the tape may not be exactly of same
length throughout
 4) In the method of stepping horizontality and
verticality not properly maintained.
 Angles not accurately measured.

8. Mistakes:
 Mistakes are errors which arise from inattention,
inexperience, carelessness and poor judgment or
confusion in the mind of the observer.
 They do not follow any mathematical rule (law of
probability) and may be large or small, positive or
negative.
 They cannot be measured. However, they can be
detected by repeating the whole operation.

9.  If a mistake is undetected, it produces a serious effect
upon the final result.
 Hence, every value to be recorded in the field must be
checked by some independent field observation.
 The following are the examples of mistakes:
 Erroneous recording, e.g. writing 69 in place of 96
 Counting 8 for 3
 Forgetting once chain length
 Making mistakes in using a calculator.
 So mistake is related to human errors not instrumental
error.

10. CORRECTIONS IN
CHAINING

11. Corrections in chaining
 Whenever errors occur in chaining it becomes
necessary to apply correction.
 Remember that for every negative error correction is
positive and vice versa. Following corrections are
applied in a chain
 CORRECTION FOR SLOPE
 CORRECTION FOR TEMPERATURE
 CORRECTION FOR PULL
 CORRECTION OF SAG

12. CORRECTION FOR SLOPE
 If length measured ‘L’ and the difference in the levels
of first and last point ‘h’ are given then correction for
slope is,
 Chl=h2 /2L
 If θ and L are given, Chl=L (1-cosθ) This correction is
always subtractive.

13. CORRECTION FOR TEMPERATURE
 Temperature correction is necessary because the
length of tape or chain may increase or decrease due
to variation of temperature.
 Let
 α- Coefficient of thermal expansion of the material of
tape
 Tm – Mean temperature during measurement
 To - Temperature at which tape is standardized, and
L – Measured length
 Then temperature correction Ct is given by
 Ct=Lα(Tm-To)

14. CORRECTION FOR PULL
 Chain is standardized at 8 kg tension but at field pull may
be more or less than the standard pull and due to elastic
property of chain strain will vary according to pull applied
, for this pull correction are necessary.
 Let, E – Young’s modulus of the material of tape
 A – Cross – sectional area of the tape
 P – Pull applied during measurement
 P0 - Standard pull, and L – Measured length of chain
 Then, the correction for pull Cp is given by
 Cp= (P-P0) L/AE
 The above expression takes care of signs of the correction
also

15. CORRECTION OF SAG
• While taking reading, if the tape is suspended
between two supports, the tape sags under its own
weight.
• Hence, measured length is more than the actual
length. Hence, this correction is subtractive. This
correction is given by