Rope coiling

We present the results of the combined experimental and theoretical investigation of rope coiling arising from the buckling instability. The shape of the rope is perfectly circular in the coiling region and is straight in the region below the feeding point. In between these two distant regions, the rope assumes a catenary-like shape in the limit of slow feeding velocity and a helix-like shape in the limit of fast feeding velocity. When there is an increase in the feeding velocity, the transverse displacement of deformation persists over the long distance far beyond the coiling region. The catenary is associated with the purely imaginary wave number and the helix is associated with the real wave number. The catenary-to-helix shape transition is particularly evident when the rope is fed from a large height.