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Groups search result 148 for group:rec.running author:Terry author:R. author:McConnell

Search Result 148
From: Terry R. McConnell (
Subject: Re: Adam Helmer, Indian Running, Group Pursuit
Newsgroups: rec.running
View complete thread (4 articles)
Date: 2000/06/08

In article <8hohgq$fk4$>,
John Pennifold <> wrote:
>Seems to me that this is what is done in marathons and bike races. One
>person takes the lead for a while then slowly drifts to the back. The person
>at the front is probably encountering the most wind resistance and the
>others follow  in the slipstream. Look at the Tour de France to see this in

This round-robin protocol is what is commonly referred to as "Indian running",
but it turns out that this is not exactly the way groups of indians tried
to run down opponents. Instead, they used the following rather clever
strategy: Each pursuer would start out at a different pace. One of them would
take off in a virtual sprint trying to catch the escapee quickly. The next
one would run a slightly slower pace so that if the first pursuer failed to
make the catch he would still have some endurance left. And so on. 

As shown by J.B. Keller in a recent article (Optimal Running Strategy to
Escape from Pursuers, Amer. Math. Monthly 107(2000), 416-421), this strategy
on the part of the pursuers is optimal in order to catch an opponent of 
equal ability who has a modest head start. Consider the plight of the
escapee. He must run quite fast to evade the first pursuer. When that pursuer
gives up, he must contend with another who has been running a steady (albeit
slower) pace, versus his own too fast early pace. Each subsequent pursuer
taxes the escapee in a different way. 

Keller also derives the optimal strategy for an escapee pursued by a possibly
infinite number of pursuers of equal ability. Perhaps surprisingly, the
escapee must not run even pace. He should run an even pace that is too fast
to sustain indefinitly for an initial time period. (The length of this
initial period depends on how much head start he has in a way too complicated
to reproduce here.) After the initial period, he essentially "hangs on,"
running an ever slower pace as exhaustion sets in. For details, consult the
article cited.

Terry R. McConnell   Mathematics/304B Carnegie/Syracuse, N.Y. 13244-1150                   

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