In the May 1990 issue of Kaskade (the European Juggling Magazine) Joerg Treiber of West Germany asks the following question: Where do the clubs have to be thrown between two parachutists who are passing while in free fall? Upwards, downwards, or straight across? I'll give my answer at the end of this column.
I continue to get mail from jugglers interested in communicating via electronic mail. The most promising response was from Emory Kimbrough (E-mail address 72777.1553@Compuserve.COM). Emory is a system operator of Compuserve's Science/Math Forum, and has offered to set up a message-board, library, and conference space on this forum if enough people are interested.
Other computing jugglers who wrote to me too late to get in last issue's column, along with their electronic mail addresses, are: Peter Lawson (lawson@astron.physics.su.OZ.AU), Eric Promislow (promislo@qucis.queensu.ca), David Ward (djward@chico.colorado.edu), and Mike Hojnowski (mqh@cornellc.cit.cornell.edu).
It would not surprise me if our juggling day survey found that approximately one percent of Americans know how to juggle. I base this guess on the fact that about one percent of all employed workers in the U.S. are computer programmers, and most programmers seem to know how to juggle! More seriously, since the juggling survey consisted of people who are interested enough in juggling to fill out the form, it will likely overestimate the true percentage of people who can juggle (statisticians call this type of problem "sample selection bias").
Why are so many jugglers also computer programmers? Juggling and computer programming have some similarities. They tend to be practiced alone or in small groups, they involve inventiveness within strictly defined limits (the hardware and the law of gravity), and they both consist of challenges to be mastered. Juggling is an offbeat, nonconformist thing to do, and programmers tend to be attracted to hobbies of that sort.
Why are so many jugglers also vegetarians? It's partly due to this same willingness to be different. Tolerance of nonconformity, of differences in views and beliefs, is almost required to take up something as unusual as juggling. These characteristics, and the generally peaceful nature of juggling itself, are generally consistent with liberal philosophy, which may explain the general tendency of jugglers to be politically left wing. As juggling becomes more common and less unusual, we should expect to see jugglers with more diverse and mainstream attitudes. Does this relate to the rise in popularity of combat juggling?
Answer to the parachute question: If there were no air resistance, the jugglers would throw the clubs straight across, exactly as if they were weightless in space. The situation would be the same as that experienced by Jake Garn when he juggled in the space shuttle. When the shuttle orbits the earth it is actually falling around it (without air resistance) and is weightless.
Given that air exists, assume that the parachutists had fallen for long enough to reach terminal velocity before they start passing. Terminal velocity is the speed at which the decelerating effect of air resistance exactly matches the acceleration due to gravity. Any dropped object will accelerate until it reaches its own terminal velocity, and then not go any faster. Generally, the more mass behind each square inch of surface area facing down, the greater is terminal velocity. If a juggler falling at her own terminal velocity lets go of a club, the hollow club will start decelerating (to get to its own, most likely slower, terminal velocity). Simply put, the club will be blown straight up by the wind from falling, more so than the juggler is. To compensate for having a lower terminal velocity, the jugglers will have to throw the clubs downwards.
After opening parachutes the answer changes. With a parachute open the juggler's terminal velocity is greatly reduced, to approximately 17 feet per second for an average parachute. The larger the parachute, the lower the terminal velocity, and hence the more likely that the jugglers will have to throw the clubs straight ahead or even upwards.
If any of you actually try this stunt you will need to find objects with terminal velocities similar to your own. In freefall you will probably need solid balls or weighted clubs. Passing with open parachutes might be physically easier, except for the problem of parachutes tangling. Given how much jugglers like a challenge, I'm sure we'll soon see a photo of parachuting jugglers in this magazine. Maybe I'll try juggling parachutes instead.
"The Academic Juggler" is an occasional feature of Juggler's World, and is devoted to all kinds of formal analyses of juggling. Anybody who has suggestions, comments, or potential contributions for this feature is encouraged to write to me (Arthur Lewbel, 3 Audubon Road, Lexington, MA 02173), or phone (617-862-3089), or E-mail (Bitnet address Lewbel@Brandeis)