Safe 219 Safe landings Chad t kishimoto Justin C. Kao Jeffrey A. edlund California Institute of Technology Pasadena, California 91125 Advisor: Darryl H. Yor Abstract We examine the physical principles of stunt crash pads made of corrugated cardboard boxes and build a mathematical model to describe them. The model leads to a computer simulation of a stunt person impacting a box catcher. Together, the simulation and model allow us to predict the behavior of box catchers from physical parameters and hence design them for maximum safety and minimum We present two case studies of box-catcher design, a motorcyclist landing after jumping over an elephant and David Blaine's televised Vertigo stunt. These demonstrate the ability of our model to handle both high-speed impacts and large weights. For each case, we calculate two possible box-catcher designs, showing the effects of varying design parameters. Air resistance is the dominant force with high impact speeds, while box buckling provides greater resistance at low speeds We also discuss other box-catcher variations Basic concept Requirements A falling stunt person has a large amount of kinetic energy To land safely, most of it must be absorbed by a catcher before the performer hits the ground. Therefore, following Newtons Second Law, the catcher must exert a force to decelerate the performer, dt The UMAP Journal 24(3)(2003)219-232. Copyright 2003 by COMAP, Inc. Allrights reserved Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial dvantage and that copies bear this notice. Abstracting with credit is permitted, but copyrights for components of this work owned by others than COMAP must be honored. To to republish, to post on servers, or to redistribute to lists requires prior permission from COMAP.Safe Landings 219 Safe Landings Chad T. Kishimoto Justin C. Kao Jeffrey A. Edlund California Institute of Technology Pasadena, California 91125 Advisor: Darryl H. Yong Abstract We examine the physical principles of stunt crash pads made of corrugated cardboard boxes and build a mathematical model to describe them. The model leads to a computer simulation of a stunt person impacting a box catcher. Together, the simulation and model allow us to predict the behavior of box catchers from physical parameters and hence design them for maximum safety and minimum cost. We present two case studies of box-catcher design, a motorcyclist landing after jumping over an elephant and David Blaine’s televised Vertigo stunt. These demonstrate the ability of our model to handle both high-speed impacts and large weights. For each case, we calculate two possible box-catcher designs, showing the effects of varying design parameters. Air resistance is the dominant force with high impact speeds, while box buckling provides greater resistance at low speeds. We also discuss other box-catcher variations. Basic Concept Requirements A falling stunt person has a large amount of kinetic energy, Us = 1 2 msu2 s . To land safely, most of it must be absorbed by a catcher before the performer hits the ground. Therefore, following Newton’s Second Law, the catcher must exert a force to decelerate the performer, F = m dus dt . The UMAP Journal 24 (3) (2003) 219–232.
c Copyright 2003 by COMAP, Inc. All rights reserved. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice. Abstracting with credit is permitted, but copyrights for components of this work owned by others than COMAP must be honored. To copy otherwise, to republish, to post on servers, or to redistribute to lists requires prior permission from COMAP