ENGI 3703 Surveying and Geomatics

Transcription

1 Distance Measurement Errors (Chapter 6) We have reviewed at vertical distance measurement and identified errors associated with those. Now we turn to horizontal distance measurement. There are a number of methods to determine horizontal distance. In our field school we practiced: ii) pacing, ii) taping and iii) eletronic distance measurement. Beside these we can determine distance using iv) satellite (i.e. GPS) systems, v) air photos, iv) remote sensing imaging, and vii) triangulation. These will be discussed at greater length later in the course. Less common and outdated methods of viii) stadia, ix) subtense bar and x) optical rangefinder will be briefly mentioned here. Lect 6 - Sept 21/07 Slide 1 of 6

2 Relative Precision and Accuracy Ratio: Before describing these methods we should define a measure of precision and accuracy that we can use. Recall that accuracy was defined as relationship between the measured value and the true value. An accuracy ratio is a measure of difference between the true measurement and the actual measurement normalized by the true measurement: Accuracy Ratio = true distance - measured distance true distance = error truth This is often expressed in a form with a numerator of one and a denominator rounded to the nearest 100 units (e.g. 1/1132 = 1/1100). We will also encounter relative precision (section 10.6) later in the text. Recall that precision was defined as the degree of refinement with which a measurement is made. Hence the relative precision would refer to a ratio similar to the accuracy ratio but without specific knowledge that all systematic errors have been removed from the estimate of truth. Lect 6 - Sept 21/07 Slide 2 of 6

3 Pacing: (Section 6.3) Pacing may seem a crude form of distance measurement. However, it can be extremely valuable in many instances high accuracy is not required and in the discovery of mistakes from other methods with high precision. An average pace is somewhat less than 1 m. However, many surveyors train themselves to take giant steps of 1 m in practice. Knowing ones calibrated pace length is a useful tool for low accuracy measurement. Accuracy ratio 1/50 to 1/100 for distances greater than 30 m. Optical Rangefinders: (Section 6.5 and 4.2 ) Just as you adjust focus a 35 mm camera to manually improve the clarity of a photograph in older cameras, optical rangefinders use the same principle in determine distance. The operator adjusts the clarity of the image by changing the distance f 1 between the lens and image. The focus length f for give lens (i.e. the value of f 1 for an infinitely distant object, f 2 = lens is known. Since the system follows the relation: 1 f = 1 f f 2 f 2 f 1 by keeping a precise measurement of the distance f 1 in our rangefinder we are able to determine the the distance f 2 to the object once the image is in clear focus. Accuracy ratio 1/50 for distances less than 50 m. Lect 6 - Sept 21/07 Slide 3 of 6

4 Stadia: (Section 6.6) Also known as Tacheometry. Can be easily used with leveling instruments to determine the distance of foresight and backsight shots. The optic of the instrument are set such that the viewing angle between the top and bottom cross hairs are constant. The difference between the top and bottom rod reading when multiplied by a constant (typically 100) will provide the geometrically determined distance to the rod. Accuracy ratio 1/500 for reasonable leveling procedure distances. Lect 6 - Sept 21/07 Slide 4 of 6

5 Subtense Bar: (Section 6.7) is a tripod mounted bar with targets precisely m apart. The bar is set over a point (B), leveled and turned so that it is precisely perpendicular to a one-second minimum reading theodolite set at point A. The horizontal angle between the subtense bar targets is measured using the theodolite to determine the distance to the bar center and hence the distance AB. Accuracy ratio 1/3000 for distances of 150m or shorter. While accurate, this method is seldom used today. A m Distance AB = cot B 2 where: cot( ) = 1/tan( ) Lect 6 - Sept 21/07 Slide 5 of 6

6 Taping Errors: (Section ) Taping equipment and methods have been covered in the field school. However, it is useful to consider taping errors since taping is still used in practice. These consist of: 1) Incorrect Tape Length Correction 2) Temperature Correction 3) Pull Correction 4) Sag Correction 5) Alignment Error These sources of error tend to be systematic and can be eliminated with careful planning and technique. Accuracy ratio 1/10,000 can be obtained using taping. To obtain these accuracies we must use standardized equipment with published specifications. Lect 6 - Sept 21/07 Slide 6 of 6