Bowie method

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The Bowie method is a method of national surveying for the calculation of a very large surveying network , the processing of which takes place in regional (node ​​and line-shaped) parts, which are then put together to form a whole. The thrust is also Operate to process that significantly exceed the available computing capacity.

The method was developed in 1924 by the American geodesist William Bowie for the US Coast and Geodetic Survey ( USCGS ). The approximation method is based on a basic idea of Friedrich Robert Helmert , according to which one can replace individual triangular chains of a large-area triangulation with individual geodetic lines with only little loss of accuracy . This principle works with area networks as well as with grid-shaped frame or node networks and was used for large-scale national surveying of North America. As a result, the entire western United States (about 2000 × 2000 km) could be calculated in one go with less than 100 unknowns, although in the original it contains tens of thousands of unknowns and at the time was not computationally unsolvable.

Each of the sub-lines is defined by the geographical longitude and latitude difference of its endpoints, and the individual blocks are finally joined together by a field (main adjustment based on mediating observations). From today's point of view, the procedure contains a few weak points, but also basic ideas that have found their way into other methods of astro-geodetic network adjustment over the course of several decades .

The arithmetic operation according to Bowie consists of a system of intersecting meridians and parallel- circle chains. For these chains is at each intersection a " nodal network " ( junction figure ) dissolved out, which in the ideal case a quadrangle formed by the beam-like 4 "link string" ( section of an arc going out). Each nodal network should contain a Laplace point for precise orientation and a scaling baseline , which has been reduced from its sea ​​level to a mean earth ellipsoid . Every nodal network is subjected to an immediate and definitive adjustment , i. That is, it remains unchanged in the overall network that is subsequently assembled.

After all node networks have been calculated (in the case of the western half of the US, 26 subnetworks at intervals of around 500 km), the "connecting chains" (in German "Traverse") are provisionally calculated and their approximate coordinates are determined. Finally, the overall system is balanced using the least squares method , i.e. H. made as free of contradictions as possible . In the western United States, the 26 node and 42 interconnection networks gave a relative accuracy between 1: 300,000 and 1: 1.5 million; H. average about meter accuracy or 1 mm per kilometer. This corresponded to the state of the art at that time, but for an area at least ten times larger than was computationally possible up to now.

The Bowie method was used on a large scale - in a somewhat theoretically modified form - among other things for the Central European network (German army survey around 1940 and Bamberg Institute for Earth Surveying 1945-1947). Here, a strict adjustment would have required the simultaneous solution of 1300 conditions, which could be reduced to around 50 each by the subnetworks and could therefore still be solved without a computer . The final network quality was ± 1.3 "in the directions of the link chains. 1: 500,000 in total, an average of only 2 mm per kilometer That it was slightly below that of the US, was by the inconsistent (and sometimes inaccurate) triangulation in Eastern Europe due .

See also

Specialist literature