Word Finder - catenaries

definition

The curve described by a flexible chain or a rope if it is supported at each end and is acted upon only by no other forces than a uniform gravitational force due to its own weight and variations involving additional and non-uniform forces.

definition

Any physical cable, rope, chain, or other weight-supporting structure taking such geometric shape, as a suspension cable for a bridge or a power-transmission line or an arch for a bridge or roof.

definition

The curve of an anchor cable from the seabed to the vessel; it should be horizontal at the anchor so as to bury the flukes.

definition

A cable, the segments of which between supports take a catenary geometric shape, supporting in turn an overhead conductor that provides trains, trams or trolley buses with electricity, or the combination of the conductor, the cable, and supports.

Again, if a chain pass over a perfectly smooth peg, the catenaries in which it hangs on the two sides, though usually of different parameters, wifi have the same directrix, since by (10) y is the same for both at the peg.

Since the tension is measured by the height above the directrix these two catenaries have the same directrix.

Every catenary lying between them has its directrix higher, and every catenary lying beyond them has its directrix lower than that of the two catenaries.

Now let us consider the surfaces of revolution formed by this system of catenaries revolving about the directrix of the two catenaries of equal tension.

Draw Pp and Qq touching both catenaries, Pp and Qq will intersect at T, a point in the directrix; for since any catenary with its directrix is a similar figure to any other catenary with its directrix, if the directrix of the one coincides with that of the other the centre of similitude must lie on the common directrix.

The catenaries which lie between the two whose direction coincides with the axis of revolution generate surfaces whose radius of curvature convex towards the axis in the meridian plane is less than the radius of concave curvature.

The catenaries which lie beyond the two generate surfaces whose radius of curvature convex towards the axis in the meridian plane is greater than the radius of concave curvature.