| description abstract | The theory to predict cable pulling forces during installation in pipes has already existed for 7 decades. Here, gravity and capstan friction are ruling, and analytical equations are used for straight (sloped) sections and for horizontal and vertical bends. In this study, the theory is expanded to three-dimensional bends. They are entirely determined by the horizontal bend angle and inclination angles of the straight sections before and after the bend. Analytical solutions are given for the geometry of the bends, but pulling forces need to be calculated numerically. These calculations exactly match analytical solutions for the horizontal and vertical extremes. They also match analytical solutions for vertical bends with large bend radius, or for pushed cables, where the cable (partly) follows the outside facing wall of the pipe, for which the theory is also derived. The discussed software, which was developed using three-dimensional (3D) bends as input, can be used for pulling cables into pipes, but also for techniques like pushing, blowing, floating, water-push-pulling, and free-floating, although the latter techniques are not fully treated in this study. | |
