Speaker
Description
The rope curve or catenary line is a mechanical problem that has been solved since the 17th century. The cosine hyperbolic curve as a form of the rope curve is the subject of many mechanics textbooks. Nevertheless, it is worth taking another look at the chain line because technical applications, e.g. cable cars or suspension cables, have different boundary conditions which require different approaches to the calculation. The equations of the catenary are usually non-linear and in some cases cannot be solved analytically, which means that there are always steps in the calculation process that have to be solved numerically. In the first part, a numerically robust solution scheme is presented for the case of the rope with a given rope length between two fixed suspension points. The main focus here is on the simple determination of initial values for the non-linear equations to be solved, taking extreme cases into account. In the second part, a rope is considered in which one suspension point can be moved horizontally and a counterforce acts there. This case occurs, for example, with loop-shaped supply cables on cranes. Finally, the third part looks at the case that occurs with ropeways, in which the rope is held at a suspension point with a constant rope force. This can be achieved using a tensioning weight, for example. This case leads to ambiguous solutions. In addition, a universal constant can be derived here, which can be used to determine the minimum force required to hold a suspended rope at one end.
