Unit 2 :- Accuracy and Errors

Accuracy

Accuracy refers to the closeness of a measured value to a standard or known value. It depends on three factors:

• Precise instrument
• Precise method
• Good planning

The degree of accuracy in chaining is expressed as a ratio called the chaining ratio. For example, if there is an error of 0.05 meters during the measurement of a total length of 500 meters, the chaining ratio is calculated as follows:
\[
= \frac{{0.25 m}}{{500 m}}
= \frac{{25 m}}{{50000 m}}
= \frac{{1}}{{2000}}
\]

Some permissible limits of errors:
For measurement with a steel band: ±8/1000
In normal conditions with a tested chain: ±8/1000
For rough work: ±8/50

 Precision: Precision refers to the closeness of two or more measurements to each other. It is independent of accuracy and is often considered a degree of perfection.

Discrepancy: This term represents the difference between two major measured values or quantities.

Errors: Errors arise from the difference between a measured value and the actual value. These errors can be caused by variations in temperature, pull, or defects in the measuring instrument. There are two types of errors:

Compensating errors: These occur in both positive and negative directions and tend to balance out when summed up over a series of measurements.

Cumulative errors: These errors accumulate and can impact the overall measurement. In survey work, compensating errors are proportional to the square root of the total number of measurements, where L represents the length of the line.These errors occur in the same direction and tend to accumulate over time.

They significantly affect the accuracy of the work.
The magnitude of cumulative errors is proportional to the length of the line (L).
These errors can be either positive or negative.

(I) Positive errors:
Positive errors occur when the measured length (Ls) is greater than the actual length (Lo).
For example:
When the chain is too short.
Slope correction not being applied.
Correction for sag not being made.

(II) Negative errors:
Negative errors occur when the measured length is less than the actual length.
For instance:
Due to the opening of chain joints.
When the applied pull is much greater than required.

 Sources of Errors in Surveying:

Errors in surveying can be classified as natural, instrumental, and personal.

Natural Errors:

These result from factors like temperature variations, magnetic declination, refraction, and obstacles during measurement.
For example, the length of a steel tape varies with changes in temperature.
While these errors are beyond the control of surveyors, precautionary measures and suitable methods can help contain them within permissible limits.

 Instrumental Errors: 

These errors arise due to imperfect construction and adjustment of instruments. For example, incorrect graduation of a steel tape or improper adjustment of a plane table or a level machine can lead to instrumental errors. However, most of these errors can be mitigated by applying proper correction methods.

Personal Errors: 

Personal errors result from limitations in human senses, such as sight, touch, and hearing. An example of a personal error is improperly bisecting an object while fixing the line of sight on a transit during angle measurements.

  Mistakes:

 Mistakes often arise from misunderstandings, carelessness, or poor judgment. They are a common occurrence, especially among individuals who are inexperienced or lack robust problem-solving skills. However, mistakes can be mitigated and even prevented by adopting standardized methods of observation and checking to ensure accuracy and precision in every task