Spinning flight: dynamics of frisbees, boomerangs, samaras, and skipping stones

369 Pages·2006·16.4 MB·English

by  Ralph D. Lorenz

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DynflmJG of rrulie«, Boomerangs,
Saii)0riis,flnil$liippin(i Stones
RAIPHD.IORENI
Sprriin ger
Ralph D. Lorenz
Lunar and Planetary Laboratory
University of Arizona
1629 E. University Blvd.
Tucson, AZ 85721-0092
USA
[email protected]
Library of Congress Control Number: 2005937515
ISBN-10: 0-387-30779-6
ISBN-13: 978-0387-30779-4
Printed on acid-free paper.
© 2006 Springer Science+Business Media, LLC
All rights reserved. This vvork may not be translated or copied in whole or in part without the
w^ritten permission of the publisher (Springer Science-I-Business Media, LLC, 233 Spring Street,
New York, NY 10013, USA), except for brief excerpts in connection with review^s or scholarly
analysis. Use in connection w^ith any form of information storage and retrieval, electronic adapta
tion, computer software, or by similar or dissimilar methodology now known or hereafter devel
oped is forbidden.
The use in this publication of trade names, trademarks, service marks, and similar terms, even if
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PrefoK
This book is about things that spin in the air or in space.
Specifically, it is about things that spin in the air and space that I
find interesting. I am by training an aerospace engineer, but v^ork as a
planetary scientist. Indeed, as an aerospace engineering undergraduate,
I regarded—unfairly in retrospect ^—my lectures in fluid mechanics and
aerod3niamics as only a necessary evil on the noble road to exploring
space Avhere such subjects tend not to apply. My main project during my
15-year career as engineer and scientist has been the Huygend probe. In
early 2005 this probe descended through the atmosphere of Saturn's
moon Titan, w^here as it turns out, these fields applied after all. In an
attempt to gain familiarity with the dynamics of a slowly spinning vehicle
like Huygend under its parachute, I began in 2002/03 some experiments
Spinning Flight
^th instrumented small-scale models. These little models recorded the
saving and spin w^ith small sensors, and provided me w^ith insights I
Avould not otherwise have gained, and not a little entertainment besides.
Some months after these experiments began, and as my instru
mentation became more compact, I had the idea (v^hile sitting on an air
plane, appropriately enough) that the instrumentation Avas compact
enough to install on a Frisbee without terribly altering its flight char
acteristics. I duly made such experiments, ^vhich introduced new chal
lenges in attitude determination and range instrumentation. I found
that there was in fact relatively little published w^ork on the subject
of Frisbee aerodynamics. I therefore had the opportunity to make some
genuinely new^ observations, w^hich have since been published in the
academic literature.
I also observed that almost everyone I spoke to (mostly scientists
and engineers, it must be conceded . . .) thought that these experiments
w^ere rather cool. It might be interesting to assemble my experiments
w^ith the modest body of scientific w^ork on the subject, although the
Frisbee research w^ould not be enough subject matter for a w^orth^^hile
book by itself.
How^ever, these investigations reactivated latent interests of mine
in many other areas. Like millions of other people, I have marveled at
how^ a boomerang flies, or how^ a stone skips across the surface of a
pond. And I realized that there w^as a common theme to these subjects —
that of spinning flight — and the idea emerged of compiling a book Avith
that theme. Thus motivated, I also began other experiments w^hich are
reported here.
Exploiting to the full one of the few^ privileges afforded to an
author, I have been liberal in my interpretation of the theme. Although
it w^as not in the project as originally conceived, I have interpreted
"flight" to include space, thereby encompassing certain dynamical
aspects of space probes, satellites, asteroids, and planets. I make no
apologies for this^—these cases are just as interesting as the more clas
sically "aeronautical,'' and many are more so. Similarly, my coverage of
Prefa
spinning disk-wings such as Frisbees stretched a httle to embrace radar
early-^varning aircraft with spinning disk antennae, and thence to
include a fe^v Avords and pictures on nonspinning disk-wings.
Where I have dra^vn a hne — one must be drav^n some^vhere — is
before rotorcraft. Hehcopters have fascinating aerodynamics and gyro-
dynamics, and are magnificent machines. There are also many excellent
textbooks and more popular w^orks that cover them in detail ^—I cer
tainly have no significant insights of my ow^n to add. The one exception
is a class of rotorcraft ^rherein the w^hole body of the vehicle is spun up,
in addition to the rotor. Again, the criterion for inclusion has been that
I thought this Avas novel and interesting.
The book is not intended as a textbook, although students and
researchers in various fields may find ideas for many outstanding inves
tigations or problems, and I have tried to be rigorous in my use of ter
minology. Exjuations (simple ones) have been used in the text w^here
they are the most succinct ^way of expressing something, but I have no
Avish to deter the casual reader.
In the hope that readers may be motivated to pursue investigations
of their ow^n, I have included appendices Avith some technical details of
my o^vn experiments and have been fairly rigorous in including refer
ences to papers. None of the bibliographies can claim to be complete,
but should give ample starting material, and certainly are representa
tive of w^hat I have found to be the most recent, comprehensive, or
useful papers on the various subjects. Although it did not exist 15 years
ago, it barely needs stating now^ that the Internet is an enormous
resource for information. A ^veb search will rapidly bring far more
material than is in these pages.
The book before you is a little larger than the original outline pro
posed to the publisher, and I thank them for their indulgence in accom
modating the additional material. This is the first book I have w^ritten
myself (I have had the good fortune to write a couple of previous books
^th some excellent and experienced co-authors) and so in this case all
errors are entirely my ow^n responsibility.
Spinning Flight
As this book was being completed, the Huygeiu probe ended its
long journey, successfully parachuting dov^n to the surface of Titan. As
I and my colleagues try and understand the probe's behavior and its
environment, I have found the intellectual preparation deriving from
my experiments to have been quite useful. To play is to learn.
Harry Blom at Springer has been an enthusiastic supporter of this
project—his strong commitment from an early stage has been instru
mental in getting this book done. Some other editors, Ingrid Gnerlich
at PUP and Peter Gordon at CUP, have been kind enough to provide
early feedback on the idea.
Zibi Turtle, Joe Spitale, and Jess Dooley have all helped ^th
field experiments. Helen Fan and Melissa Myers have provided
much-needed help with digitizing data and dra^ving figures. Some of
this activity, together with digging reference material out of the excel
lent University of Arizona library, was supported by NASA through the
Arizona Space Grant Consortium. Melissa Myers also helped greatly
with some proofreading and editing.
Spinning Flight
I would never have started on all this without inspiration from the
comprehensive Avebsites on Frisbee dynamics by Jon Potts and Sarah
Hummel. Similarly, the excellent Wx-Bumms softw^are made available
on the web made boomerang simulation come alive easily.
I thank Erwan Reffet for dra^ving my attention to his w^ork
on balls on cylinders, and Kelly McComb for information on the
Turboplan. Raytheon Inc. provided information on the Whirl, and
Textron Systems Inc. was kind enough to review the text on Samaras.
Special thanks are due to Alan Adler for taking time to explain the
history of and providing material on the Aerobic and other toys. Ted
Bailey w^as generous w^ith his time in explaining some boomerang back
ground and photographing some of his boom collection. Mike Bird
explained much of the background to the Giotto encounter.
Obtaining permission to use graphic material is aWays something
of a chore for an author. Credits for images are given in the relevant
captions, but let me record here my appreciation for the prompt and
generous cooperation from the relevant parties.
Brian Riddle at the library of the Royal Aeronautical Society, and
Claudia Condry of the Imperial War Museum, both in London, are
thanked for their assistance in the archives.
Lastly I thank the friends and colleagues, and not least my ^vife
Zibi Turtle, for patiently tolerating my ranting about spinning things,
and indulging my experiments and writing.