Errors in Surveying occurs as survey work involves various measurement of angles and distances in the field. In dealing with measurements in surveying and the associated surveying errors, the following terms should be carefully studied.
Terms Used For Errors in Surveying
In surveying, observation is defined as the numerical value of a quantity measured in the field. When the magnitude of a measured quantity is taken directly in the field, the observation is known as the direct observation, e.g. measuring an angle by a theodolite or measuring the length of a line by a chain in the field but calculated from other measurements, the observation is said to be an indirect observation, e.g. height of tower.
Independent and Dependent Quantities
A quantity is said to be independent when its value does not depend upon any other quantity. An independent quantity bears no relation with any other quantity under consideration, i.e. the elevation of a point or the length of a line. A quantity is said to be dependent when its value bears certain relation with the value of other quantity or quantities, i.e. the angle of a triangle. The equation
is a conditional equation. If <A and <B are independent, <C is a dependent quanity.
Weight of an observation
The weight of an observation is a factor depending on the importance attached to the observation. It actually give an indication of the precision and trustworthiness of the observation when making a comparison between several quantities of different worth.
True Value of a Quantity
The value of a quantity which is absolutely free from any error is called the true value. It can never be found out and the true value of a quantity is indeterminate.
Observed Value of a Quantity
The value of a quantity which is obtained from field measurement after applying correction for all the errors related to the observation is called the observed value.
Most Probable Value of a Quantity
The most probable value of a quantity is one which is most likely to be true value than any other values. This is most likely to be free, but not likely to be absolutely free, from errors. In case of direct observations of equal weight, the most probable value is the arithmetic mean. In case of direct observations of unequal weights, the most probable value is the weights; the most probable value is the weighted arithmetic mean.
Accuracy and Precision
Accuracy is the degree of perfection obtained, whereas precision is the degree of perfection used in the instruments, the methods and the observations. Accuracy depends on (i) precise instruments, (ii) precise methods, and (iii) good planning. The use of precise instruments or reduces the effect of all types of errors. Good planning saves time and reduces the possibility of errors.
Error and Discrepancy
Error in any measured quantity may be defined as the difference between the observed and the true values of that quantity. If L is the true length of a line and L¢ is the observed length, then error = L¢–L. Discrepancy is the observed difference between two like measurements each of which may contain an error. If L1 is the length of a line in the first measurement and L2 is the length in the second measurement, then discrepancy = L1 ~ L2. A discrepancy is not an error. It may be small, yet the error may be great if each of the two measurements contains an error that may be large.