Aim: to give a description of the sources and significance of errors and an understanding of accuracy and precision of measurements.

Transcription

1 ACET108 SURVEYING I Sources of errors Precision and Accuracy Trigonometry A. Sources of Errors Aim: to give a description of the sources and significance of errors and an understanding of accuracy and precision of measurements. (a) Measurement is the main concern of the surveyor. In practice: no measurement is absolutely exact every measurement contains error the true value is never known the exact error is always unknown the true value of the quantity measured is determined statistically after repeated measurements are taken. In the simplest case, the true value for a distance id taken as the mean value for a series of repeated measurements. (this will be covered in subject Surveying II). (b) Types of Measurement Horizontal distances Vertical distances Slope distances Angle measurements (c) Mistakes Mistakes are observer blunders, usually caused by misunderstanding the problem, carelessness, fatigue (tiredness), missed communication and poor judgment. A common mistake is when you record a measured distance as instead of Another mistake is when you transport a number maybe from a field book to a clean paper and instead of the correct number which is you write They can occur at any stage and can have a damaging effect if left uncorrected. Independent checks should be made at each stage (d) Sources of errors All measurements contain errors. What are the sources of these errors? The sources of errors can be categorized as follows: Natural errors: they are caused by natural phenomena (wind, temperature, humidity etc). An example is a steel chain which changes length with the change of the temperature. 1

2 Instrumental errors: they are related to the construction and adjustment of instrumentation or movement of the different parts of an instrument. Personal errors: they are related to the human limitations of sight of the person reading the measurements. (e) Types of errors There are two types of errors as follows: Systematic errors: they are defined as the errors whose magnitude and algebraic sign can be determined. Systematic errors can be determined and therefore corrected. They result from factors that comprise the measuring system and include the environment, the instruments and the observer. As long as the measuring system remains constant, the systematic errors remain constant. If the conditions change, the magnitudes of the systematic errors will change. An example is the error due to the temperature effects which changes the length of a steel tape. If the temperature is known, the change in length of the steel tape (shortening or lengthening) can be determined. Because systematic errors tend to accumulate, they are also called cumulative errors. Random errors: they are the errors remaining after mistakes and systematic errors are eliminated. They are due to the eliminations of the observer and the instruments. Smaller errors occur more frequently than larger ones, while +ve and ve errors are equally likely to occur and balance each other. Ransom errors are also called accidental errors. B. Precision and Accuracy In Surveying, it is important that the surveyor makes measurements that are both accurate and precise. Accuracy and Precision are explained below: (a) Accuracy Accuracy is the absolute proximity of the observed value to the true measurement. In other words, it shows how close a measurement is, to the true value. Precision: the degree of refinement of the measuring process and the ability to repeat the same measurement with consistently small variations i.e. how close is one measurement to another. 2

3 This is explained with the following examples: 1. Example with target: High precision High accuracy High precision Low accuracy Low precision High accuracy Low accuracy Low accuracy High accuracy Low precision High precision Low precision 2. Example with distance measurement A known distance of 100m (i.e. true value) was measured three times by a surveying student as 99.12m, 99.10m and 99.08m. This measurement is precise but not accurate. 3

4 C. Trigonometry 4

5 5

6 SIMPLE GEOMETRY RULES SIMILAR TRIANGLES A E D B C A D E B C The following relationship (or similar) are valid: AB AC =, etc. AD AE 6