Contribution of instrument centring to the uncertainty of a horizontal angle

Abstract One of the sources of uncertainty in the measurement of a horizontal angle in surveying comes from the instrument centring. There are two ways of evaluating the uncertainty coming from this source. One is to assume that the instrument centring uncertainty is dependent on both directions in the angle. The second way is to assume that it is independent on each direction. In this study, the differences between both approaches are analysed and some examples are given. For lengths of sight longer than 100–150 m, these differences are minimal. For short sighting distances of 10 m and a 1 mm centring uncertainty, a maximum positive difference of 90 centesimal seconds (cc) (29·1'') is derived when the angle is close to 0 or 400 grads (360°), and a maximum negative difference of −40cc (−13'') when the angle equals 200 grads (180°). The differences increase as the instrument centring uncertainty increases. An accurate setting up of the instrument is, thus, important. When assessing the effect of the differences between both approaches on the uncertainty of a horizontal angle, other sources of uncertainty should also be taken into account, mainly reading and pointing, target centring and target levelling. As is shown in the examples, the differences between the two approaches become small once all components are considered. This study is relevant and useful for the uncertainty budget of any surveying task where the two approaches are applicable, e.g. traverses or the assessment of tolerances in straight line traverses between two points of known coordinates. In addition, it is useful to investigate whether the differences are relevant in least squares adjustment of survey networks of observed directions when compared to network adjustments of observed angles.