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DIN 18723 Specification for Theodolite Accuracy

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urveyors have seen the expression “per DIN 18723” associated with statements of accuracy of theodolites since the introduction of electronic theodolites. DIN stands for Deutsches Institut für Normung which loosely translates into the German Institute for Standards (English language website located at http://www2.din.de/index.php?lang=en). At the time the standard was first quoted by manufacturers (mostly from continental Europe) as an accuracy specification, it was actually a draft (~1983). However it has become widely accepted by manufacturers worldwide for specifying the accuracy of theodolites. It should be noted here that DIN accuracy cannot be inferred from the least count of a theodolite, which is the finest measurement or count that an instrument is able to make. In fact, with the advent of electronic instruments, reliance on the least count for anything but an estimate of precision achievable (not accuracy) is highly inadvisable. DIN Spec vs. Accuracy The standard is equally applicable to optical theodolites, and in fact has occasionally been used for that purpose. But whether the theodolite is optical or electronic, surveyors have tended to assume that a “5-second” theodolite measures angles with an accuracy of 5 seconds. This is rarely the case (except by coincidence). The specification is useful for comparing theodolites however, in that all theodolites classified as having a DIN accuracy of 3 seconds, for example, will be roughly equal in terms of angle measurement performance. For purposes of survey design, analyzing data after a survey, especially when trying to apply a weight to the accuracy of angle measurement, the DIN specification value must be interpreted in the light of how the instrument was used. If you read the fine print, you are likely to find text in manufacturer’s specifications that reads something like “standard deviation of the mean of a face I

. . . One needs to apply the rules for random error propagation, for the particular way you use your instrument. and a face II direction.” Understanding this is key to using the DIN specification value. If you take a theodolite or total station with an angle measuring “accuracy according to DIN” of 5 seconds, for example, and observe the horizontal circle reading to a precise target in face I (telescope in the direct position) and then invert the telescope and take another horizontal circle reading to the same target in face II (reversed position), the specification tells you that the standard deviation (that is, confidence level of ~68%) of the mean (or average) of the two directions is ±5 seconds. This however is not an angle as surveyors are used to thinking about. To measure a single angle, we are required to measure two directions (first a backsight, then a foresight). Using the equations for propagation of random error, the standard deviation of the angle, if measured in face I and face II and then averaged is 7 seconds! (Take the square root of the sum of the squares of the errors in each direction, which in this case simplifies to – √2 •5.) Thus the first lesson to be learned from this discussion is that one needs to apply the rules for random error propagation, for the particular way you use your instrument. For example, if you measure the angle twice in face I and twice in face II, the standard deviation of the angle will be 5 seconds. If, however, you only measure the angles in face I, you can expect the angles to have an uncertainty of 10 seconds. The second lesson, which may be the more important, is that the method of determining the accuracy of theodolites us-

DISPLAYED WITH PERMISSION • PROFESSIONAL SURVEYOR MAGAZINE • November 2002 •

ing DIN 18723 is actually one that measures precision. As with surveying, by accounting as well as possible for systematic errors, it is possible to arrive at an estimate for accuracy. Thus if the angles are not measured in face I and face II, if collimation has not been checked and adjusted, if the instrument has not been leveled properly, if the so-called “height of standards” adjustment is incorrect, and so on, then the “fundamental accuracy” of the theodolite as given by the DIN spec may not be true at all! Environmental Influences In addition to the above-mentioned sources of error resulting from practices and instrumentation, there are the influences of circumstances, mostly environmental (such as atmospheric disturbances) and the practices and adjustment (or lack thereof) of the accessories that will affect the accuracy that is achieved. Examples of these are: optical plummet(s) adjustment, whether the targets are prisms or precise traverse targets, whether these targets are mounted on tripods or on range poles, or whether the targets are subject to the problem of “phase” error, particularly if a pole or mini-pole is used as the target. In summary, DIN accuracy values indicated for instruments are not the values to be assumed that can be obtained when measuring angles. Depending on how the instrument is used (ignoring accessories and conditions), the angle accuracy may be higher or lower than the specified value. Once the correct value is computed, however, it must then be combined with knowledge of practices, instrumentation and conditions, including knowledge of the level of adjustment of all the component parts of the surveying system and accuracies. Note: Information for this article was compiled by the technical staffs of the GIAA members that manufacture theodolites and total stations. WWW.PROFSURV.COM

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