Node network

In geodesy, the nodal network is that part of a larger surveying network where numerous measuring lines or triangular chains converge and can be mathematically replaced by a compact, local network.

A very stable geometry with numerous over-determinations can be built up through dense node networks on the one hand , which on the other hand can act as a stabilizer within the framework of a geographically extensive network. Thus it was in the 1920s to the 1940s possible to calculate very large-scale triangulation theory exactly, without the self-evident today automatic computing resources of the computer .

For example, with the Bowie method , with which the entire western half of the USA was geodetically uniformly calculated around 1925 , a system of intersecting meridians and parallel circle chains is built up. At each intersection, a network of nodes ( junction fogure ) is detached from these chains , which ideally forms a square from which four "connecting chains " ( section of an arc ) radiate out. If more than four such connecting chains (also called traverses in German ) meet in the knot , it becomes all the more stable and precise; A further increase in accuracy is possible through a precise astronomical orientation at a Laplace point , as well as through a separate, scaling baseline in each node network.

The individual nodal networks can then be subjected to an immediate and definitive adjustment - regardless of their wider surroundings, which do not have to be measured with such high precision . When they are later combined to form an overall network, the nodal networks can remain unchanged thanks to their geometric stability, which reduces the computational effort to a tenth or less.

So was z. As the entire western United States (about 2,000 × 2,000 km) with about 10,000  survey points to 26 knots networks at distances of some 500 kilometers compacted and could in a cast with about 100  unknowns are calculated. The solution of such a matrix of normal equations 100 × 100 was just possible at that time (without a computer). In contrast, the original network would have had around 20,000 unknowns, which is still difficult with today's mainframes.