In Greek mythology Clotho or Klothó was the youngest sister of the Fates –the daughters of Zeus and Temis-, the dread goddesses who were assigned to the target individual and non-transferable for each individual.
Clotho is the “spinner”, who is in charge of weaving the thread of life, from the moment of birth until death. The mathematicians decided to be baptized as clotho –derived Clotho - curve-flat, spiral-type, which joins a line with a circle.
This type of curve made its appearance in the decade of the thirties of the last century on the roads of north american and German and, since then, has not ceased to be present in our driving.
knots of freeways
The curved clotho –also called the spiral of Euler or spiral of Cornu - it is widely used in highways to join straight sections with curved sections, for example, that there is in the transitions between two roads, or two sections circulars which have curvatures different.
The start of the clotho is situated at the end of the straight section and develops until it appears the circular section, to connect it with the new line uses a curve clotho inverted.
The most important feature and crucial to driving safely is that the radius of curvature decreases inversely proportional to the distance traveled on it.
This uniqueness allows the driver to adapt smoothly to the change of trajectory and obtain a greater visibility. From the point of view of efficiency in the clotho produces less tire wear, lower fuel consumption and brake, since it is not necessary to stop the vehicle before reaching the curve.
amusement parksThe clotho is also present in amusement parks, specifically in the Russian mountains. His peculiar way of changing the curvature makes it especially suitable for the loops vertical.
The design of the rails of this attraction need to have sequences of curves that are united in a gentle way, and that their parameterization facilitates the study of their properties.
the loops of The coasters are formed by two arches of the clotho united states, which translates into a lower centripetal acceleration in the loops circular and a minor overclocking.
mathematical SolutionThe clotho is also the solution found by the engineers of the airports to design in an optimum way the conveyor belts of baggage. Basically, these devices generally consist of a pair of straight sections that move in opposite direction linked by semicircunferencias that link the changes of sense.
The clotho is a curve that is relatively easy to calculate. From the mathematical point of view, the radius of curvature “R” decreases proportionally to the length of the development “L”, from a radio infinity –in the beginning of the curve - up to a radius finite.
At any point of the curve it can be verified that L x R = A x A. where “a” is a constant, the parameter of the clotho, which defines the size of the curve.
Who was going to say to the greeks of antiquity, and is one of the Fates –equivalent to the Fates of roman - was going to be so present in our travel by road and air?
Pedro Gargantilla is a internist in the Hospital of El Escorial (Madrid), and author of several popular books.
Date Of Update: 21 September 2019, 11:01
