Accuracy & Errors in Surveying

 

GENERAL

In dealing with measurements. it is important to distinguish between accuracy and precision. Precision is the degree of perfection used in the instruments, the methods and the observations. Accuracy depends on (1) Precise instruments, (2) Precise methods and (3) Good planning. The use of precise instruments simplify the work, save time and provide economy.The use of precise methods eliminate or try to reduce the effect of all types of error

   The difference between a measurement and the true value of the quantity measured is the true e"or of the measurement. and is never known since the true value of the quantity is never known.A discrepancy is the difference between two measured values of the same quantity; it is nor an error. A discrepancy may be small, yet the error may be great if each of the two measurements contains an error that may be large.

 1.1  SOURCES OF ERRORS

Errors may arise from three sources:-

• Instrumental Error
• Personal Error
• Natural Error

1) Instrumental Error :-   Error may arise due to imperfection or faulty adjustment of the instrument with which measurement is being taken. For example, a tape may be too long or an angle measuring instrument may be out of adjustment.

2) Personal Error :-  Error may also arise due to want of perfection of human sight in Observing and of touch in manipulating instruments. For example. an error may be there in taking the level reading or reading an angle on the circle of a theodolite.

3) Natural Error :-  Error may also be due to variations in narural phenomena such as temperarure. humidity, gravity, wind, refraction and magnetic declination. If they are not  properly observed while taking measurements, the results will be a mpe may be 20 metres at 20'C but its length will change if differenrnt.

1.2  KINDS OF ERRORS 

Ordinary errors met with in all classes of survey work may be classified as :

• Mistakes
• Systematic Errors (Cumulative Errors)
• Accidental Errors ( Compensating Errors)

1)  Mistakes  :-  Mistakes are errors which arise from inattention, inexperience, carelessness and poor judgment or confusion in the mind of the observer. If a mislake is undelected, it produces a serious effect upon the final result.

2) Systematic Errors (Cumulative Errors) :-  A systematic error or cumulative error is an error that, under the same conditions, will always be of the same size and sign. A systematic error always follows some definite mathematical or physical law. and a cOrrection can be determined and applied. Such errors are of constam character and are regarded as positive or negative according as they make the result too gr;at or too small. E.g :- if a tape is P crn shan and if it is stretched. N times. the total error in the measurement of the length will be P.N em.

3) Accidental Errors ( Compensating Errors) :-  Accidental errors or compensaJing errors are those which remain after mistakes and systematic errors have been eliminared and are caused by a combination of reasons beyond the ability of the observer to control. An accidental error of a single determination is the difference between (1) the true value of the quantity, and (2) a determination that is free from mistakes and systematic errors. Accidental errors represent the limit of precision in the determination of a value.

1.3 THEORY OF PROBABILITY

Investigations of observatioru of various types show that accidental errors follow a definite law, the law of probability. The most imponanr features of accident!l (or compensating) errors which usually occur. are :-

1. Small errors tend to be more frequent than the large ones; that is. they are
   more probable.
2. Positive and negative errors of the same size happen with equal frequency ;
   that is they are equally probable.
3. Large errors occur infrequently and are improbable.