accuracy of measurements

El tElementary SurveyingSu ey g

Accuracy of Measurements

MeasurementsMeasurements

• Direct measurements– Using a tape to measure a line– Using a transit to measure horizontal and vertical anglesangles

– Using a protractor to determine the angle between two lines

• Indirect measurements– Summing up a series of tape measurements to measure the distance of a long linemeasure the distance of a long line

– Using the tachymetric methods in obtaining horizontal distances

3Prepared by: Andre‐Paul C. Ampong

Prepared by: Andre‐Paul C. Ampong 4

ErrorsErrors

• An error is defined as the difference betweenAn error is defined as the difference between the true value and the measured value of a quantityquantity– Cannot be determined exactly as the true value cannot be ascertainedcannot be ascertained

– Inherent in all measurements– Cannot be entirely avoided but may be minimized– Cannot be entirely avoided but may be minimized by careful work and applying corrections


MistakesMistakes

• Mistakes are inaccuracies in measurements which sta es a e accu ac es easu e e ts coccur because some aspect of a surveying operation is performed by the surveyor with

l d dcarelessness, inattention, poor judgment and improper execution

May also be caused by a misunderstanding of the– May also be caused by a misunderstanding of the problem, inexperience, or indifference of the surveyor

– A large mistake is called a blunderg– Are not considered errors; are usually so large in magnitude compared to errors


Frequently committed mistakesFrequently committed mistakes

• Reading the wrong graduation on the tapeReading the wrong graduation on the tape• Omitting a whole length of tape• Transposition (switching of positions) of figures• Transposition (switching of positions) of figures• Reading a scale backwards• Misplacing a decimal point• Incorrect recording of field notes• Adding a row or column of numbers incorrectly


Mistakes have no place in engineeringMistakes have no place in engineering and surveying works

Errors can only be minimized but notErrors can only be minimized but not entirely avoided

Mistakes can be detected and eliminated


Types of errorsTypes of errors

• Systematic errorSyste at c e o– Has a magnitude and sign that remains unchanged as long as field conditions remain constant and

h dunchanged– Repeats itself in other measurements and thus accumulates

– Also called cumulative error– Conforms to mathematical and physical laws– Can be computed and eliminated by applying corrections, using instruments properly and employing appropriate proceduresemploying appropriate procedures


Types of errorsTypes of errors• Accidental error

– Purely accidental in nature– May be positive or negative– Cannot be absolutely determined or eliminatedCannot be absolutely determined or eliminated– Caused by factors beyond the control of the surveyor– Present in all surveying measurementsR i f i k d i– Remain after mistakes and systematic errors are eliminated

– Usually of minor importance compared to systematic errors

– Tend to cancel each other out as more measurements are made


Sources of errorsSources of errors

• Instrumental errorsInstrumental errors– Due to imperfections in the instruments from:

• Faults in their constructionFaults in their construction• Improper adjustment of parts prior to use• Wear and tear

– Examples:• Measuring with a tape of incorrect length• Using rods with erroneous graduations



• Natural errorsNatural errors– Caused by variation in the phenomena of nature such as changes in magnetic declinationsuch as changes in magnetic declination, temperature, wind, refraction, gravity and curvature of the earth

– Examples:• The effect of temperature on the length of the tape• Deflection of the line of sight due to the earth’s curvature and atmospheric refraction



• Personal errorsPersonal errors– Arise from the limitations of the human sensesAre significantly reduced or eliminated through– Are significantly reduced or eliminated through constant practice and experience


Accuracy and precisionAccuracy and precision


Theory of probabilityTheory of probability

• Small errors occur more often than large gones and that they are more probable

• Large errors are less probable; large ll b i t k th therrors may well be mistakes rather than

accidental errors• Positive and negative errors of the samePositive 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 in the most probable value


Most probable valueMost probable value

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• In the case of related measurements taken under identical conditions where the sum should be equal to a mathematically exact quantity, the most probable values are the q y, pobserved values corrected by an equal part of the total error


ResidualResidual

xxv −= xxv −=


Probable errorProbable error

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• The probable error is a quantity which when• The probable error is a quantity which, when added to and subtracted from the most probable value defines a range within which there is 50value, defines a range within which there is 50 percent chance that the true value of the measured quantity lies inside the limits thus set


measured quantity lies inside the limits thus set

Relative (error) precisionRelative (error) precision

error of magnitudequantity measured of magnitude


Weighted observationsWeighted observations


accuracy of measurements

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