Introduction to Surveying PDF - Errors & Most Probable Value

9/3/2023 Technological Institute of the Philippines Civil Engineering department Introduction to Surveying Engr. Harvey Ian P. Aquino, M.Sc. Instructor 1 ERRORS An error is defined as the difference between the true value and the measured valu...

9/3/2023 Technological Institute of the Philippines Civil Engineering department Introduction to Surveying Engr. Harvey Ian P. Aquino, M.Sc. Instructor 1 ERRORS An error is defined as the difference between the true value and the measured value of a quantity. It is a deviation of an observation or a calculation from the true value and is often beyong the control of the one performing the operation Errors are inherent in all measurements and result from sources which cannot be avoided. In any surveying operation the surveyor is continuously dealing with errors. 2 1  9/3/2023 MISTAKES Mistakes are inaccuracies in measurements that occur because some aspect of a surveying operation is performed by the surveyor with carelessness, inattention, poor judgment. If careful attention is given to the execution of any surveying operation, mistakes can be avoided. The various types of mistakes, however, can only be corrected if discovered. Their detection can be made by systematic checking of all work, making a common sense estimate and analysis, or by making a duplicate measurement. 3 TYPES OF ERRORS Civil Engineering CE 010 FUNDAMENTAL OF SURVEYING PRELIM 4 2  9/3/2023 TYPE OF ERRORS In surveying, errors in measurement are either systematic or accidental. There are defined in terms of theris behavior as to sign and magnitude and the conditions prevailing during the measurement. Systematic Error - This type of error is one that will always have the same sign and magnitude as long as field conditions remain constant and unchange. A systematic error will repeat itself in other measurements, still maintaining the same sign, and thus will accumulate. Ex. In making a measurement with a 30-m tape which is 5 cm too short, the same error is made each time the tape is used. Systematics error conform to mathematical and physical law. Such error can be computed and their effects eliminated by applying corrections. 5 TYPE OF ERRORS In surveying, errors in measurement are either systematic or accidental. There are defined in terms of theris behavior as to sign and magnitude and the conditions prevailing during the measurement. Accidental Errors - These are errors are purely accidental in characted. The occurence of such errors are matters of chance as they are likely to be positive or negative, and may tend in part to compensate or average out according to law of probability. Accidental errors are caused by factors beyond the control of the surveyor and are present in all surveying measurements. In comparison to systematic errors, accidental errors are usually of minor importance in surveying operations since they are variable in sign and are of a compensating nature. This characteristic usually tends to balance out in the final results. 6 3  9/3/2023 SOURCES OF ERRORS Civil Engineering CE 010 FUNDAMENTAL OF SURVEYING PRELIM 7 SOURCES OF ERRORS The sources of errors in surveying measurements are classified under the following three groups. Instrumental Errors - These errors are due to imperfections in the instruments used, either from faults in their construction of from improper adjustments between the different parts prior to their used. Natural Errors - These errors are caused by variations in the phenomena of natures such as changes in magnetic declination, temperature, humidity, wind, refraction, gravity, and curvature of the earth. Natural errors are beyond the control of man. Personal Errors - These errors arise principally from limitations of the senses of sight, touch and hearing of the human observer which are likely to be erroneous or inaccurate. 8 4  9/3/2023 ACCURANCY AND PRECISION Civil Engineering CE 010 FUNDAMENTAL OF SURVEYING PRELIM 9 ACCURANCY AND PRECISION Accurancy and precision are two terms which are constantly used in surveying, however, their correct meaning are often misunderstood. While accurancy may be synonymous with precision, the two should not be used interchangeably. The surveyor always attempt to obtain measurements which are not only accurate but also precise. Accurancy indicated how close a given measurement is to the absolute or true value of the quantity measured. It implies the closeness between related measurements and their expectations. Precision refers to the degree of refinement and consistency with which any physical measurement is made. It is portrayed by the closeness to one another of a set of repeated measurements of a quantity. 10 5  9/3/2023 ACCURANCY AND PRECISION A method frequently used to define and distinguish between accurancy and precision is illustrated below: 11 THEORY OF PROBABILITY The theory of probability is based upon the following assumptions relative to the occurrences of errors: Small errors occur more often than large ones and that they are more probable Large errors happen infrequently and are therefore less probable; for normally distributed errors, unusually large one may be mistakes rather than accidental errors. Positive and negative errors of the same size happen with equal frequency; that is, they are equally probable. The mean of an infinite number of observations is the most probable value. 12 6  9/3/2023 THEORY OF PROBABILITY Probability is defined as the number of times something will probably occur over the range of possible occurrences. It is very much involved in games of chance, such as throwing a dice, and tossing a coin. Things do happen randomly or by chance and these are proven by principles of mathematics commonly referred to as probability. Accidental errors exist in all surveying measurements and their magnitude and frequency are governed by the same general principles of probability. The theory of probability is useful in indicating the precision of resulty only in so far as they are affected by accidental errors. 13 MOST PROBABLE VALUE Civil Engineering CE 010 FUNDAMENTAL OF SURVEYING PRELIM 14 7  9/3/2023 MOST PROBABLE VALUE From the theory of probability a basic assumption is the the most probable value (mpv) of a group of repeated measurements made under similar conditions is the arithmetic mean or the average. Most probable value refers to a quantity which, based on the available data, has more chances being correct than has any other. There is only one correct value that should be considered and it is determined by using the following equation: 15 MOST PROBABLE VALUE Example 1: A surveying instructor sent out six groups of students to measure a distance between two points marked on the ground. The students came up with the following six different values: 250.25, 250.15, 251.04, 250.50, and 251.22 meters. Assuming these values are equally reliable and that variations result from accidental errors, determine the most probable value of the distance measured. 16 8  9/3/2023 MOST PROBABLE VALUE Example 2: The angles about a point Q have the following observed values 130°15'20", 142°37'30", and 87°07'40". Determine the most probable value of each angle 17 MOST PROBABLE VALUE Example 3: The observed interior angles of a tri-angle are A = 35° 14' 37", B = 96° 30' 09", and C = 48° 15' 05". Determine the discrepancy for the given observation and the most probable value of each angle. 18 9