Preamble:
In linear measurement works peculiar to surveying practice, twelve sources of error are usually encountered when making direct measurements. These errors must be examined for their cause and effect so that precautions may be taken to guard against unacceptable errors.
These twelve error sources are classified under three broad categories namely;
(a) Systematic or Cumulative Errors
(B) Compensating or Accidental Errors
(C) Gross Errors
Systematic or Cumulative Errors
These errors exist in any survey measurement and each individual measurement increases the effect of the errors. Such errors which may be either positive or negative can have an appreciable effect but this effect can be reduced as required by taking suitable field precautions or by correcting the observed measurements.
Sources of Systematic errors:
(1) Wrong length of tape (cumulative positive or negative): these errors are common with chains and fiber tapes and these should be tested frequently. For steel tapes, they are less likely to occur. However, steel tapes should also be tested for precise work or after repairs. If tape measurement was found in error, the following measures should be taken for corrections:
When area calculations have been made from measurements that are in error, they can be corrected using the formula:
(2) Poor ranging (cumulative positive): this usually gives rise to a relatively small error. If a whole length of tape deviates a distance, ‘d’ from the ranged straight, the error in length is d2/2l, where ‘l’ is the length of the tape. If the divergence is in the vertical plane of height, ‘h’, instead of the horizontal plane, the error in length would be h2/2l.
(3) Poor straightening (cumulative positive): if both ends of the tape are incorrect lines and the center is off by a distance, ‘d’, the effect is greater, being 2d2/l or twice the error rising in each half of the tape.
(4) Slope (cumulative positive): the effect of the slope is similar to that of poor ranging but in the vertical plane. It can be the source of quite large errors.
(5) Sag (cumulative positive): this often occurs when a tape is suspended as in step chaining or when measuring over rough ground. This occurs due to the unsupported part of the tape that would be giving large readings. The amount of error caused by sap is proportional to;
The errors increase as the cube of the suspended length.
(6) Temperature variation (cumulative positive or negative): the effect of temperature variation is negligible in work where a chain is used. For precise work with steel tape, temperature correction must be made.
Error due to temperature variation = l x c x t
Where,
l = measured length
c = coefficient of expansion (0.000011 per oC for steel)
t = temperature differences from standard
Compensating or Accidental Errors
Although every precaution may be taken, certain unavoidable errors always exist in any measurement. Such errors are usually less important than systematic errors. As they are sometimes positive and sometimes negative, they tend to cancel each other out in the long run.
Sources accidental errors:
(1) Holding and marking (compensating): when an untrained person holds a tape at zero against a point, and the length is read off against another point, an error will always occur.
(2) Variation in tension (compensating): the tension applied to a tape for correct measurement should be the same as that applied when testing the tape against a standard spring balance but this is not always the same and errors due to tension usually occurs due to variation in tensions. When using linen or plastic tapes, frequent light and hard pulling results in cumulative errors, and efforts should be made to guard against these errors.
Gross Errors
These errors arise from mistakes, carelessness, or lack of experience. They are quite random and allowance cannot be made for them.
Sources of gross errors:
(1) Displacement of arrows or station marks: If arrows, ranging rods, or pegs have been displaced accidentally by removal or been knocked over, they can be replaced with less accuracy.
(2) Miscounting tape lengths: when taking long lengths of measurement, care should be taken to ensure that lengths are not miscounted.
(3) Misreading tape: care should be taken to note unique points on the tape to avoid misreading that tape. Experts should be engaged in tape measurements.
(4) Wrong booking: even with correct tape measurement, there is the possibility of a wrong booking. The assistant should always call out the readings loudly to the Surveyor and repeated the same for accurate booking.
