Forced centering
The positive centering is a special method to assist in precision vermessungen the accuracy of the angle measurement to increase by small residual error in the centering largely eliminates the measuring instrument.
For the forced-centered measurement of a traverse , not only one tripod (for the theodolite ) is used, but three . In addition to the respective position, the target points (reflector or target mark) are also signaled on tripods with a fixed measuring base and not by a measuring stick . If the angle between the backsight and foresight is then measured with the theodolite , the instrument is transferred to the tripod of the previous foresight and the rearmost tripod moves forward to the next polygon or measurement point .
Greater accuracy
The occupation of all essential measuring points with a tripod instead of the measuring stick does not eliminate the inevitable small errors of the centering itself, but it does eliminate its error propagation . Firstly, the eccentricity is smaller and, secondly, it always has the same value when moving the devices. The last-mentioned aspect is the most important and ensures that the high accuracy of the direction measurement (about 2 "or 0.0005 °) is maintained in the sequence of the work:
Because if the centering over the respective ground point is, for example, 3 mm accurate with the conventional polygon (see optical plumb line ), this amounts to 6 angular seconds in the direction of a 100 meter long polygon side (significantly more than the actual measurement accuracy). At the next measurement point there is another such deviation, which statistically (with normal distribution ) adds up to about 30 "after 4 points of view. This means that the polygon is increasingly" pivoted "laterally. This so-called transverse error , which was barely 5 mm after 100 meters, increases approximately with the square root of the number of points and therefore after 1000 meters to about 2 centimeters. In contrast , the longitudinal error with modern distanceers remains in the range of a few millimeters, so that the accuracy of the measurement is inconsistent.
Approach and other methods
When using forced centering, the changing influence of the not completely centric setup can be kept below 0.1 mm. For this purpose, the theodolite is exchanged for the target mark and vice versa using several tripods and special bases .
The forced centering method was developed around 1930 and has contributed significantly to the high accuracy of today's engineering geodesy . It became particularly important for underground measurements ( tunnel construction , pressure tunnels , mines, etc.), where measurement is only possible from one side, or for periodic monitoring of large structures.
The repeated observation of long-range targets or a few solar azimuths has a similar stabilizing effect on error propagation , but the measurement effort is somewhat greater than when using forced centering.