Calculation of the deflection in the lemniscate of Bernoulli. Application to railway transfer curves

Authors

DOI:

https://doi.org/10.46583/nereis_2020.12.523

Keywords:

Lemniscate, transfer curves

Abstract

Analytical expressions are deduced to calculate the deflection between a chord and a lemniscate curve. In railways, the interest of these expressions is that lemniscates are used as transfer curves between a straight and a circular section. Moreover, according to the regulations, the deflection that separates a wagon from the track must not exceed a certain amount, so that the expressions deduced are very useful in routine checks of railway tracks.

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References

Blanch L, Checa E, Marín J. Una aproximación a la curva de transición Clotoide vista desde Mathematica. Modelling in Science Education and Learning. 2013;6:105-19.

Spiegel MR. Handbook of Mathematical Formulas. New York, USA: Schaum-McGraw Hill, 1968.

Oldham KB, Myland J, Spanier J. An atlas of functions: with equator, the atlas function calculator. Springer Science & Business Media, 2010.

Published

2020-06-26