An Introduction to the Mechanics of the Lasso

Duration: 33 mins 20 secs

Share this media item:

Embed this media item:

<iframe width="_width_" height="_height_" src="https://sms.cam.ac.uk/media/2620753/embed" frameborder="0" scrolling="no" allowfullscreen></iframe>

Choose size:

About this item

Available Formats

About this item

Description:	Ribe, N Thursday 30th November 2017 - 16:00 to 16:30


Created:	2017-12-04 08:41
Collection:	Growth form and self-organisation
Publisher:	Isaac Newton Institute
Copyright:	Ribe, N
Language:	eng (English)


Abstract:	Co-authors: Pierre-Thomas Brun (Dept. of Chemical Engineering, Princeton University, Princeton, NJ USA), Basile Audoly (Laboratoire LMS, Ecole Polytechnique, Palaiseau, France) Trick roping evolved from humble origins as a cattle-catching tool into a sport that delights audiences with its complex patterns or ‘tricks’. Its fundamental tool is the lasso, formed by passing one end of a rope through a small loop (the honda) at the other end. Here, we study the mechanics of the simplest rope trick, the Flat Loop, in which the rope is driven by the steady circular motion of the roper’s hand in a horizontal plane. We first consider the case of a fixed (non-sliding) honda. Noting that the rope’s shape is steady in the reference frame rotating with the hand, we analyse a string model in which line tension is balanced by the centrifugal force and the rope’s weight. We use numerical continuation to classify the steadily rotating solutions in a bifurcation diagram and analyse their stability. In addition to Flat Loops, we find planar ‘coat-hanger’ solutions, and whirling modes in which the loop collapses onto itself. Ne xt, we treat the more general case of a honda that can slide due to a finite coefficient of friction of the rope on itself. Using matched asymptotic expansions, we resolve the shape of the rope in the boundary layer near the honda where the rope’s bending stiffness cannot be neglected. We use this solution to derive a macroscopic criterion for the sliding of the honda in terms of the microscopic Coulomb static friction criterion. Our predictions agree well with rapid- camera observations of a professional trick roper and with laboratory experiments using a ‘robo-cowboy’.

Abstract:

Co-authors: Pierre-Thomas Brun (Dept. of Chemical Engineering, Princeton University, Princeton, NJ USA), Basile Audoly (Laboratoire LMS, Ecole Polytechnique, Palaiseau, France)

Trick roping evolved from humble origins as a cattle-catching tool into a sport that delights audiences with its complex patterns or ‘tricks’. Its fundamental tool is the lasso, formed by passing one end of a rope through a small loop (the honda) at the other end. Here, we study the mechanics of the simplest rope trick, the Flat Loop, in which the rope is driven by the steady circular motion of the roper’s hand in a horizontal plane. We first consider the case of a fixed (non-sliding) honda. Noting that the rope’s shape is steady in the reference frame rotating with the hand, we analyse a string model in which line tension is balanced by the centrifugal force and the rope’s weight. We use numerical continuation to classify the steadily rotating solutions in a bifurcation diagram and analyse their stability. In addition to Flat Loops, we find planar ‘coat-hanger’ solutions, and whirling modes in which the loop collapses onto itself. Ne xt, we treat the more general case of a honda that can slide due to a finite coefficient of friction of the rope on itself. Using matched asymptotic expansions, we resolve the shape of the rope in the boundary layer near the honda where the rope’s bending stiffness cannot be neglected. We use this solution to derive a macroscopic criterion for the sliding of the honda in terms of the microscopic Coulomb static friction criterion. Our predictions agree well with rapid- camera observations of a professional trick roper and with laboratory experiments using a ‘robo-cowboy’.

Available Formats

Format	Quality	Bitrate	Size
MPEG-4 Video	640x360	1.93 Mbits/sec	483.71 MB	View	Download
WebM	640x360	729.42 kbits/sec	178.17 MB	View	Download
iPod Video	480x270	522.25 kbits/sec	127.50 MB	View	Download
MP3	44100 Hz	249.78 kbits/sec	61.04 MB	Listen	Download
Auto *	(Allows browser to choose a format it supports)