Abstract
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.
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Brodtmann, N.L., Schilberg, D. (2021). New Findings on the Calculation of the Catenary. In: Ahram, T.Z., Karwowski, W., Kalra, J. (eds) Advances in Artificial Intelligence, Software and Systems Engineering. AHFE 2021. Lecture Notes in Networks and Systems, vol 271. Springer, Cham. https://doi.org/10.1007/978-3-030-80624-8_41
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DOI: https://doi.org/10.1007/978-3-030-80624-8_41
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