Surveying: Errors and Mistakes

• Study notes on mistakes, errors, most probable value

Errors

• Defined as the difference between the true value and the measured value of the quantity.
• Possible causes include the type of equipment being used or imperfections of the person undertaking the measurement.
• A surveyor must understand that errors are always present, and should be aware of the different types to select proper tools and instruments.

Mistakes

• Defined as inaccuracies in measurements due to carelessness, inattention, poor judgment, and improper execution.
• A large mistake is referred to as a blunder.

Types of Errors

• Systematic
• Accidental

Systematic Errors

• Always exhibits the same sign and magnitude as long as field conditions remain constant and unchanged.
• Changes in field conditions will cause a corresponding change in the magnitude of error.
• Separable and conform to mathematical and physical laws.
• Effects can be computed and eliminated by applying corrections, proper techniques in the use of instruments, or adopting a field procedure.

Accidental Errors

• Purely accidental in character.
• Occurrence relies on chance.
• Caused by factors beyond the surveyor's control.
• Present in all surveying measurements.
• Remains after mistakes and systematic errors have been eliminated.

Sources of Errors

• Instrumental Errors are due to imperfections of the instruments.
• Measuring with a steel tape of incorrect length.
• Using a leveling rod with painted graduations not perfectly spaced.
• Determining the difference in elevation with an instrument whose line of sight is not in adjustment.
• Sighting on a rod which is warped.
• Improper adjustment of the plate bubbles of a transit level.
• Natural Errors are caused by variations in the phenomena of nature.
• Changes in magnetic declination, temperature, humidity and curvature.
• Natural errors are beyond control.
• Effect of temperature variation on steel tape length.
• Error in magnetic needle readings due to variations in magnetic declination.
• Deflection of the line of sight due to atmosphere.
• Error in the measurement of the line with a tape being blown by wind.
• Error in the measurement of a horizontal distance due to slope or uneven ground.
• Personal Errors happen due to the limitations of the human senses.
• Determining a reading on a rod when it is out of plumb during sighting.
• Calculating a vertical angle when the cross hairs of the telescope are not positioned correctly on the target.
• Estimating the pull on a steel tape during measurement.

Accuracy vs Precision

• Accuracy indicates how close a measurement is to the absolute or true value of the quantity measured.
• Precision refers to the degree of refinement and consistency by which any physical measurement is made.

Theory of Probability

• Defined as the number of times something will probably occur over the range of possible occurrences.
• Useful in indicating the precision of results that are affected by accidental errors.
• Small errors occur more often than large ones they are more probable.
• Large errors happen infrequently and are therefore less probable.
• For normally distributed errors, unusually large ones may be mistakes rather than accidental errors.
• Positive and negative errors of the same size happen with equal frequency.
• The mean of an infinite number of observations is the most probable value.

Most Probable Value

• Arithmetic mean or the average of a group of repeated measurements.
• mpv = X = ∑X / n = (X1 + X2 + ......+ Xn)/n