ACCURACY, PRECISION & ERRORS IN SURVEYING

 ACCURACY, PRECISION & ERRORS

SUBJECT: SURVEYING

CIVIL ENGINEERING

Below are the topics covered in this post

• Introduction
• What is Accuracy and Precision
• Sources of Errors
• Types of Errors

INTRODUCTION

Surveying deals with the measurement of distances and angles. The true value of such quantities is never known. The true value of a quantity is a value which is absolutely free from all types of errors. The true value cannot be determined because some errors always creep in the measured quantities. The errors occur because an instrument cannot be absolutely perfect. Moreover, a surveyor cannot take the observations correctly because of human limitations. Further, a change in climatic conditions also limits the accuracy of the measurement.

The fact that the true value of a measured quantity cannot be determined, can be illustrated with an example. If a student is asked to measure the width of his desk with a ruler (measuring scale) graduated in decimetre, he may report the width as, say, 4 decimetres. If he were asked to use a ruler graduated in centimetres, he may find the width as 41 cm. If the ruler were graduated in millimetres, he may measure more accurate width as 41.3 cm. If a scale with graduations of 0.1 mm were available and the student could use a microscope to take readings, he could probably estimate the width more closer to the true value. With a still better ruler and a better microscope, he could estimate the width further closer to the true value. As there is no end to such refinements, he will never be able to determine the true value.

The difference between a measured value and the true value is the true error. The true error cannot be determined as the true value is never known. However, using theory of probability, it is possible to determine a value called most probable value which is close to the true value. The most probable error and the standard error can also be determined. The surveyor must know various types of errors occur and how these can be controlled. The surveyor must have the skill and the judgement to keep the errors within the limits and to make reasonably accurate measurements.

ACCURACY AND PRECISION

Accuracy denotes the closeness of a measurement to its true value. If the measured value is very close to its true value, it is very accurate. Accuracy, therefore, indicates nearness to the true value. It is degree of perfection achieved in measurement.

Precision of a measurement denotes its closeness to another measurement of the same quantity. If a quantity is measured several times and the values obtained are very close to one another, the precision is high. However, it does not necessarily mean that accuracy is high, because the values though close to one another may not be close to the true value.

The reader should clearly understand the difference between accuracy and precision. Precision denotes the degree of agreement between several measures of a quantity. Precision reflects the degree of perfection used in the instrument, the observations and the methods. Accuracy is the degree of perfection achieved. For example, a distance may be assured very precisely with an invar tap to the nearest millimetre, but still it may not be accurate if the tape has the erroneous length of 30.10 m instead of the nominal length of 30.0 m. The measurement done with such a tape may be quite precise but they will not be accurate. To elaborate it further, let us consider the following example.

Below figure shows shots fired by a rifleman into bull's eye indicated by the inner circle. Figure (a) shows good precision, but poor accuracy because the average value of the shots is away from the bull's eye, Figure (b) shows poor precision as the shots are quite spread, but accuracy is good as the average value is in bull's eye, Figure (c) shows good precision and good accuracy, as the shots are close to one another and also the average vale is in bull's eye.

To illustrate the difference further, let us consider the measurements taken of the same line by two survey parties.

First party

73.590 m; 73.580 m; 73.570 m; 73.575 m; 73.585 ;

Average Value = 73.580 m.

Second party

73.569 m; 73.567 m; 73.569 m; 73.568 m; 73.568 m;

Average Value = 73.568 m.

If the true value of the line is 73.579 m, the measurements taken by the first party are more accurate but less precise. On the other hand, the measurements done by the second party are more precise but less accurate. The reason for the lower accuracy may be that the tape used was not properly calibrated or any other such cause.

A good surveyor should always try to achieve both precision and accuracy. It is possible if the measurements are taken carefully using the precise instruments and correct methods and all the mistakes and errors are eliminated or corrected. Proper choice of instruments and methods of operation will reduce the possibility of errors. A measurement that is precise will also be accurate if it contains no error. To obtain high precision and high accuracy, take all the measurements precisely and eliminate or minimize all errors.

Unfortunately, the cost of the survey work increase rapidly with an increase in accuracy. It requires more time, effort and money. It requires costly instruments. The degree of accuracy necessary for a particular work will depend upon the purpose of the survey. To achieve an accuracy higher than that required is wastage of time, effort and money. The surveyor should take measurements which are correct to a certain degree which is good enough for the purpose of a particular survey.

SOURCES OF ERRORS

Depending upon the source, the errors can be classified under the following three types:

• Instrumental Errors
• Personal Errors
• Natural Errors

Instrumental Errors

The instrumental errors occur due to imperfection or maladjustment of the instrument used. For example, if the tape used in measuring the distance is actually 29.95 m long whereas the nominal length is 30 m, the instrumental error occurs because of the imperfect tape. Generally, the instrumental errors can be eliminated or minimized by adopting suitable procedures and by applying corrections and adjustments.

Personal Errors

The personal errors occur due to human limitations, such as sense of sight and touch. The errors occur for want of perfection of human sight while taking observations or for want of perfection of touch while manipulating the instrument. For example, when measuring the distance with a tape marked in centimetres, one cannot estimate the fractional part in millimetres exactly. A distance may be estimated either too larger or too small of the exact value. For example, a distance of 1.576 m may be estimated as 1.577 m or 1.575 m.

Natural Errors

The natural errors are caused by changes in natural phenomena, such as temperature, wind, humidity, refraction, magnetic field. For example, if a tape has been calibrated at 20°C, but the field temperature is 30°, there will be a natural error due to temperature variation. Generally, it is not possible to remove the causes of natural errors. However, the natural errors can be minimized by using good judgements and by applying corrections.

TYPES OF ERRORS

A thorough knowledge of different types of errors, their sources, characteristics and behaviour is essential for a good surveyor. It would help him in assessing the standard of accuracy of the work, and in selecting suitable methods and techniques. As far as possible, the surveyor should avoid errors. If the errors are unavoidable, their effects should be studied and proper corrections should be applied. The errors in surveying can be broadly classified into the following three types:

• Mistake
• Systematic Errors 
• Accidental Errors 

Mistakes

Mistakes occur in measurements due to carelessness, inattention, inexperience or poor judgement of the surveyor. Mistakes are quite common in a careless work done by an inexperienced person. For example, if the surveyor reads 16 m on a tape as 19 , it would be a mistake. Likewise, if the surveyor calls out 7 m but it is booked as 11 m, it would be a mistake. Mistakes are also called blunders or gross errors. Fortunately, large mistakes can be easily detected if suitable check measurements are taken in the field. An undetected mistakes may cause a very serious inaccuracy in the measurement and may lead to a faulty survey.

Mistakes can be eliminated by adopting standard methods of observation, booking and checking. The work should be organised in such a way that it is self-checking, as far as possible. Each measurement should be checked by some other independent method. The work should be done very carefully to avoid mistakes.

Mistakes are random in nature, as they do not follow any fixed pattern. The mistake may be positive or negative. A positive mistake makes the result too great, whereas a negative mistake makes the result too small. Although large mistakes can be easily detected, it is very difficult to detect small mistakes. In fact, some mistakes merge into random errors or accidental errors.

Systematic Errors

Systematic errors follow some well-defined mathematical or physical law or system. These errors have some well-defined pattern. The magnitude and the sign of the systematic errors can be determined and a suitable correction can be applied to the measured quantity. The surveyor must have the full knowledge of various systematic errors in the survey being conducted by him.

A systematic error will always have the same sign and magnitude under the same conditions. For example, if a 30 m steel tape has been standardised at a temperature of 20° but the field temperature is 30°, the tape will be about 3.5 mm too long. It would measure 3.5 mm less for each tape length. In other words, when the measured distance is 30 m, the actual distance is 30.0035 m. There is a systematic error of -3.4 mm in every 30 m tape length. The sign of correction is always opposite to that of the error. In this case, the correction would be +3.5 mm. The error follows the physical law of change in length due to an increase in temperature. If the field temperature is 40°C, the error will be -7.0 mm. The sign of the error will change if the field temperature is less than 20°C.

The systematic errors are cumulative in nature. For example, if in the above case the total distance is 300 m (i.e., 10 tape length), the total systematic error will be -35 mm for field temperature of 30°C.

Accidental Errors

Accidental errors are random in nature. These are, therefore, also known as random errors. These errors do not follow any fixed pattern or law. These errors can be positive or negative. Accidental errors are generally of small magnitude and they tend to distribute themselves equally on both sides of the true value. These errors tend to cancel themselves in a series of measurements, and are, therefore also called compensating errors. Accidental errors occur due to

• imperfection in the instruments
• human limitation 
• change in atmospheric conditions.

Accidental errors are small unavoidable errors which cannot be detected by the surveyor because of human limitations. For example, while marking a point below a plumb bob may cause an accidental error. The point marked may not be exactly below due to endless swinging of the plum bob. It may be slightly away from the true point on one side or the other. As another example, let us consider the case when a surveyor interpolates the distance in millimeters on a scale marked in centimeters. The surveyor may interpolate either slightly less or slightly greater of the true value.

For example, a distance of 145.3 m may be interpolated as 145.4 cm or 145.2 cm. The error is due to limitation of eye judgement and limited precision of the tape. However, with more precise instruments and better methods, the accidental errors may be minimised. While taking measurements with a steel tape, if there is a slight momentary change in atmospheric temperature, it will cause an accidental error.

Errors which remain in the measured quantities after mistakes and systematic errors have been eliminated or corrected are generally the accidental errors. Accidental errors are not of much significance for ordinary surveys. However, these are quite important in precise, control surveys. Accidental errors are directly proportional to N, where N is the number of observations made. As the accidental errors are random in nature, they follow the laws of change. The theory of probability is used to estimate these errors. To achieve high accuracy, all the mistakes should be eliminated, all the systematic errors be corrected the random errors should be minimised.

Discrepancy

A discrepancy is the difference between two measured values of the same quantity. A small discrepancy indicates that the mistakes and random errors are small. It does not guarantee that the systematic errors will also be small, because both the measured values may have large equal systematic errors. Precision is revealed by repeated measurements and by observing the discrepancies.