The 'two century plus' history of the constant-tension catenary as applied to tall ship sails, paravane and other tows, oil slick catch booms and some buoy moors

摘要

The best known catenary, caused by gravity acting on a flexible rope, with tension varying and proportional to height above the directix, has been well chronicled historically for three centuries. This has not been the case for the "other" catenary (of constant unvarying tension) of equal oceanic importance, created because of the cross-flow square law when a neutrally-buoyant rope is in a uniform current; even worse, the synthetic history, obtained by tracing back thru referenced sources in the literature, is distorted, omissive and abbreviated. The constant-tension catenary was not first discovered by the aerodynamist Glauert in 1934 as referenced by Pode and many other authors in the nineteen thirties and nineteen forties. Rather it was discovered more than two centuries ago, probably by Leonard Euler, as a mathematical model for the large rectangular sails of tall ships. The simple mathematical relationship between the two catenaries is given.