The charmed string: self-supporting loops through air drag

Abstract

The string shooter experiment uses counter-rotating pulleys to propel a closed string forward. Its steady state exhibits a transition from a gravity-dominated regime at low velocity towards a high-velocity regime where the string takes the form of a self-supporting loop. Here we show that this loop of light string is not suspended in the air due to inertia, but through the hydrodynamic drag exerted by the surrounding fluid, namely air. We investigate this drag experimentally and theoretically for a smooth long cylinder moving along its axis. We then derive the equations describing the shape of the string loop in the limit of vanishing string radius. The solutions present a critical point, analogous to a hydraulic jump, separating a supercritical zone where the wave velocity is smaller than the rope velocity, from a subcritical zone where waves propagate faster than the rope velocity. This property could be leveraged to create a white hole analogue similar to what has been demonstrated using surface waves on a flowing fluid. Loop solutions that are regular at the critical point are derived, discussed and compared to the experiment. In the general case, however, the critical point turns out to be the locus of a sharp turn of the string, which is modelled theoretically as a discontinuity. The hydrodynamic regularisation of this geometrical singularity, which involves non-local and added mass effects, is discussed on the basis of dimensional analysis.

Self-rotating string loop’s overall state in vacuum and microgravity

“…For the shape of the self-rotating string loop, literatures (Daerr et al 2019;Taberlet et al 2019) obtained the shapes under normal gravity and air pressure on the earth through the method of numerical integration of the equation of motion, which read…”

“…where 𝑔 ⃑ ⃑⃑ is the acceleration of gravity. By projecting the equation of motion onto the Frenet-Serret frame, reference (Daerr et al 2019) gives an system of equations as…”

“…Inspired by cowboys' use of soft ropes for horses (Brun et al 2014), flexible strings in motion seem to be easier to manipulate. The research on self-rotating string loops is traced back to 1949 (Gregory 1949), and they have also attracted the attention of many researchers (Daerr et al 2019;Taberlet et al 2019;Abello et al 2020) recently.…”

The ping-pong ball water cannon

“…In conclusion, we have exemplified here one particular physics project performed in the Phy Ex initially created by Yves Couder. Indicative of the fruitful proximity of this teaching to fullfledged research is that occasionally, a successful experiment leads to a publication of the group of students and their supervisors in a scientific journal [29]. More famously some research projects started in Phy Ex have lead to discoveries that spawned a whole research branch over the following years.…”

String Shooter’s overall shape in ambient air

“…A resolution of 10 −5 N was reachable with our equipment.Note added in the proofAfter the submission of this paper, we have become aware of two recently published papers on the same topic[12,13]. Furthermore, after the paper was accepted by the journal, we were informed of[14] which first theorised the behaviour of the String Shooter in 1949.…”