Catenary

In physics and geometry, a catenary^[p] is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends. The curve has a U-like shape, superficially similar in appearance to a parabola, but it is not a parabola: it is a (scaled, rotated) graph of the hyperbolic cosine. The curve appears in the design of certain types of arches and as a cross section of the catenoid—the shape assumed by a soap film bounded by two parallel circular rings.

The catenary is also called the alysoid, chainette, or, particularly in the material sciences, funicular.

Mathematically, the catenary curve is the graph of the hyperbolic cosine function. The surface of revolution of the catenary curve, the catenoid, is a minimal surface, specifically a minimal surface of revolution. The mathematical properties of the catenary curve were first studied by Robert Hooke in the 1670s, and its equation was derived by Leibniz, Huygens and Johann Bernoulli in 1691.

Catenaries and related curves are used in architecture and engineering, in the design of bridges and arches, so that forces do not result in bending moments. In the offshore oil and gas industry, "catenary" refers to a steel catenary riser, a pipeline suspended between a production platform and the seabed that adopts an approximate catenary shape.

Catenary (disambiguation)

Catenary may refer to:

Overhead line

An overhead line or overhead wire is used to transmit electrical energy to trams, trolleybuses or trains. It is known variously as:

In this article the generic term overhead line is used, as used by the International Union of Railways.

Overhead line is designed on the principle of one or more overhead wires (or rails, particularly in tunnels) situated over rail tracks, raised to a high electrical potential by connection to feeder stations at regular intervals. The feeder stations are usually fed from a high-voltage electrical grid.

Overview

Electric trains that collect their current from overhead lines use a device such as a pantograph, bow collector or trolley pole. It presses against the underside of the lowest overhead wire, the contact wire. Current collectors are electrically conductive and allow current to flow through to the train or tram and back to the feeder station through the steel wheels on one or both running rails. Non-electric locomotives (such as diesels) may pass along these tracks without affecting the overhead line, although there may be difficulties with overhead clearance. Alternative electrical power transmission schemes for trains include third rail, ground-level power supply, batteries, and electromagnetic induction.