Physics for Roping Technicians March 2018 Richard Delaney, RopeLab © RICHARD DELANEY, 2018 ROPELAB: PHYSICS FOR ROPING TECHNICIANS 2 © RICHARD DELANEY, ROPELAB,2018 This text has been developed to assist roping technicians in gaining an understanding of the fundamental principles of physics that underpin so many rope based activities. Some of us are fortunate enough to have had teachers and mentors who have managed to make mathematics and physics interesting. My high school maths teacher, the late Mr Kevin Garitty, was a unique individual and had a way of making us understand rather than learn. Through this approach I have managed to grasp and retain much. This stuff is not that hard, I suspect it’s just that not many people take the time to explain it well. The following is my effort to restate the basics and build to a place where some of the more common roping scenarios can be better understood. I have gained this knowledge and understanding through a lifetime of experience and having had the good fortune of working and playing alongside many very talented individuals who have happily shared their craft. In no particular order thanks must go to Glen Nash, Adam Darragh, William Proctor, Pat Rhodes, Dallas Atkinson, Robert Dunshea, Rob Stringer, Lucas Trihey and a host of others for their patience and sharing. Thanks must also go to my dear wife Sarah and our two sons, Tom and Ben, for their assistance, understanding, and patience over the years. At times they must have questioned my sanity and motivation for this work. Many of the illustrations in this text have been created with the vRigger software package. See www.vrigger.com for details. Unless otherwise credited, all text, drawings, and images © Richard Delaney 2016. All rights reserved for the contents of this publication. No unauthorised duplication or distribution by any means without the prior written permission of the author. For further information, please do not hesitate to contact me at [email protected] RopeLab, Blue Mountains, Australia © RICHARD DELANEY, 2018 ROPELAB: PHYSICS FOR ROPING TECHNICIANS 4 © RICHARD DELANEY, ROPELAB,2018 ROPELAB: PHYSICS FOR ROPING TECHNICIANS Contents Mass ................................................................................................................................................. 5 Force ................................................................................................................................................. 5 Weight .............................................................................................................................................. 6 Fall Factor ......................................................................................................................................... 8 Carabiner and equipment specifications ........................................................................................ 10 Direction of pull arrows .............................................................................................................. 10 30kN ........................................................................................................................................... 11 MBS & 3 sigma ............................................................................................................................ 11 Statistical example of Carabiner rating ...................................................................................... 12 Maximum acceptable load in normal use .................................................................................. 13 Design Factor .............................................................................................................................. 13 Safety Factor ............................................................................................................................... 13 WLL ............................................................................................................................................. 14 SWL ............................................................................................................................................. 14 Example ...................................................................................................................................... 14 Equipment inspection and logging ................................................................................................. 15 Why have formal inspections? ................................................................................................... 15 What should be recorded? ......................................................................................................... 16 The inspection ............................................................................................................................ 17 Case study: aluminium carabiner ............................................................................................... 17 Who does the inspection? .......................................................................................................... 18 Unique identifiers ....................................................................................................................... 19 Marking hardware ...................................................................................................................... 20 Marking software ....................................................................................................................... 21 The recording system ................................................................................................................. 22 Accessing records ....................................................................................................................... 24 Summary..................................................................................................................................... 24 Vectors ............................................................................................................................................ 25 Vector addition ........................................................................................................................... 25 Vector quiz .................................................................................................................................. 26 Vectors in rope systems ............................................................................................................. 26 Highlines ......................................................................................................................................... 28 Highline forces ............................................................................................................................ 28 Highline anchor load calculations during movement ................................................................. 33 Effect of pre-tension on Highlines .............................................................................................. 35 © RICHARD DELANEY, ROPELAB, 2017 1 ROPELAB: PHYSICS FOR ROPING TECHNICIANS Skate block ..................................................................................................................................... 36 Detailed analysis of the skate block ........................................................................................... 40 Mechanical Advantage (MA) .......................................................................................................... 42 Levers ......................................................................................................................................... 42 Pulleys ........................................................................................................................................ 43 Magic or physics? ....................................................................................................................... 44 The ‘T-system’ for calculating Mechanical Advantage .............................................................. 46 Mechanical Advantage examples .............................................................................................. 47 Mechanical Advantage Worksheets .......................................................................................... 49 Ideal, Theoretical, and Actual Mechanical Advantage ............................................................... 51 Friction ........................................................................................................................................... 52 Friction between flat surfaces ................................................................................................... 52 Friction: Same mass, different orientation ................................................................................ 53 Friction between curved surfaces .............................................................................................. 55 The Capstan Equation ................................................................................................................ 56 Measuring coefficients of friction .............................................................................................. 58 Real test results .......................................................................................................................... 60 Friction through Progress Capture Devices (PCDs) ...................................................................