Calculation of the chord in Bernoulli's lemniscata. Application to railway transfer curves

Abstract

Analytical expressions are deduced to calculate the arrow between a chord and a lemniscate curve. In railways, the interest of these expressions is that lemniscatas are used as transfer curves between a straight and a circular section. Moreover, according to the regulations, the arrow 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.