New Findings on the Calculation of the Catenary

Since the end of the 17th century, science and technology have known how to calculate the shape of the catenary line. The formulas refer to a key parameter, the "scaling factor". As a theoretical calculation value, this factor however can only be determined on real chains to a limited extent by using currently known measurement technology methods. The findings presented here make it possible to calculate this key parameter from simple, angle-based measurements on a real suspended chain with high precision. The classical chain mathematics assumes a symmetrically suspended chain with mirror-image branches of equal length. This paper however shows for any suspension - regardless of symmetry, asymmetry, real or virtual low point - the derivation of a generally valid measurement calculation formula of the scaling factor.