Errors and their Adjustments
Source of Errors
Errors in surveying may arise from three main sources:
- Instrumental: Surveying 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. Such errors are known as instrumental errors.
- Personal: Error may also arise due to wanting 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 and angle on the circle of a theodolite. Such errors are known as personal errors.
- Natural: Error in surveying may also be due to variations in natural phenomena such as temperature, humidity, gravity, wind, refraction and magnetic declination. If they are not properly observed while taking measurements, the results will be incorrect. For example, a tape maybe 20 meters at 200C but its length will change if the field temperature is different.
Types of Surveying Errors
Ordinary errors in surveying met within all classes of survey work may be classified as:
- Accidental errors
- Systematic or cumulative errors
- Compensating errors
Mistakes: Mistakes are errors that 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.
Accidental Errors: Surveying errors can occur due to unavoidable circumstances like variations in atmospheric conditions which are entirely beyond the control of the observer. Errors in surveying due to imperfection in measuring instruments and even imperfection of eyesight fall in this category. They may be positive and may change sign. They cannot be accounted for.
Systematic or Cumulative Errors: A systematic 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 correction can be determined and applied. Their effect is, therefore, cumulative. For example, if a tape is P cm short and if it is stretched N times, the total error in the measurement of the length will be P´N cm.
The systematic errors may arise due to (i) variations of temperature, humidity, pressure, current velocity, curvature, refraction, etc. and (ii) faulty setting or improper leveling of any instrument and personal vision of an individual. The following are the examples:
- Faulty alignment of a line
- An instrument is not leveled properly
- An instrument is not adjusted properly
Compensating Errors: This type of surveying error tends to occur in both directions, i.e. the error may sometimes tend to be positive and sometimes negative thereby compensating each other. They tend sometimes in on direction and sometimes in the other, i.e. they are equally likely to make the apparent result large or small. The following are a few examples:
- The discrepancy between chain and tape measurements when both are used simultaneously.
- Inaccuracy in marking chain lengths on the ground.
- Inaccurate centering.
- Inaccurate bisection of an object.
Propagation of Errors
Measurements are used for the calculation of different parameters. As the measurements are fraught with errors, it is important to know how these errors combine in various mathematical operations.
Error Propagation in a sum or difference of measurements:
When two or more quantities are added or subtracted, the error in result (Es) is the square root of the sum of the square of the errors (e1, e2, .....) of the individual quantity i.e.,
Error Propagation in a product of measurements:
- When two or more quantities are multiplied, the error in result (Eproduct) is the square root of the sum of the square of the fractional errors of the individual quantity. Thus
where EA and EB are errors in observed values of A and B respectively.
For example: A rectangle is measured 160.881 ± 0.026 cm long and 75.007 ± 0.001 cm wide. The error in its area (12,067 cm2) is
Error Propagation in a division of measurements:
When two or more quantities are divided, the error in the result is the square root of the sum of the square of the fractional errors in the individual quantity.
For example: If the area of a rectangular plot is somehow known to be 49,650 ± 10 m2 and the width dimension measured several times found to be 175.66 ± 0.46 m, the calculated length dimension is
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