Introduction to measurements Surveying is concerned with the measurements of quantities whose exact values may not be determined: distances, elevations, volumes, directions. With advanced equipment, close to the exact value can be estimated, but will never be able to determine the absolute value. No measurement is exact. Is accurate measurement in surveying is necessary? -Construction a long bridge -setting delicate machinery -Tunnels - tall buildings - Missile sites Example: a surveyor measured a distance thee times with a 100m steel tape and obtained the values 984.72, 984.69, and 984.73. he did very precise and very accurate job. If the tape found to be 100.30m long instead of 100m. The values not accurate although they are precise.

Accuracy: refers to the degree of perfection obtained in measurements Accuracy: refers to the degree of perfection obtained in measurements. It indicates how close a given measurement is to the true value of the quantity. Precision: is the degree of refinement with which a given quantity is measured. It indicates how close is one measurement to another.

Accuracy and precision Good precision Poor accuracy Poor precision Good accuracy Good precision Good accuracy

In measuring distance: Precision= Error/measured distance

Errors and mistakes: the differences between measured quantities and the true magnitudes of those quantities are classified as either mistakes or errors. A mistake is a difference from a true value caused by the inattention of the surveyor. -read number 9 as 6 - record wrong quantities in the field notes. So, mistakes are caused by the carelessness of the surveyor and can be eliminated by careful checking or comparing several observations of the same quantity. An error is a difference from a true value caused by imperfection of a person’s senses, by the imperfection of the equipment, or weather effects. Errors cannot be eliminated but can be minimised by correction.

Sources of errors: Personal errors Instrumental error Natural error - no surveyor has perfect senses of sight and touch (estimating a frictional part of scale?) Instrumental error - instruments cannot be manufactured perfectly. - instruments cannot be adjusted exactly. - The wear and tear of instruments caused additional errors. Natural error - temperature, wind, moisture, magnetic variations, and so on.

Systematic and Accidental or Random errors. Systematic errors: is one that , for a constant conditions, remains the same as to sine and magnitude. Accidental or Random errors: is one whose magnitude and direction is just an accident and beyond the control of the surveyor. Give examples

Measures of precision Probability curve Number of frequency of each measurement Measurement Residual or deviation 96.90 1 -0.04 96.91 2 -0.03 96.92 3 -0.02 96.93 5 -0.01 96.94 6 -0.00 96.95 5 +0.01 96.96 3 +0.02 96.97 2 +0.03 96.98 1 +0.04 Average=96.94 28

Probability Curves

General Laws of probability Small residuals (error) occur more often than large ones, that is they are more probable. Large error happen infrequently and are therefore less probable. For normally distributed error unusual large ones may be mistakes rather than random errors. Positive and negative errors of the same size happen with equal frequency.