Below are the replies along with my initial question about turn performance.
I did find the following two references which I plan on getting.

1. J Biomech 20(7) 667-680, 1987 Sprinting on banked turns, PR Greene
2. J Biomech Eng 107(2), 96-103, 1985 Running on flat turns, PR Greene

Also looked at the example given in Beer and Johnston. Not exactly
what I'm looking for, no friction terms.

Thanks for the feedback

Larry Wellman
******************************** Initial Question ******
Subject: Impact or Turns on Running Performance
In-Reply-To: Message of 9 Oct 1997 16:10

I'm looking for information about the impact of turn radius and bank
angle on running performance. I would like the equations instead a
reference. In reviewing mens indoor and outdoor world records there
is about a 3 percent difference below 400m and only about 1-2 percent
at distances greater then 800m. Is there a max. speed on turns?

Date: Thu, 9 Oct 1997 17:27:50 +0100
From: Jim Martin
Subject: Re: Impact or Turns on Running Performance

I'd also be interested to read this, any chance of replying to the list?

Jim Martin.

@ @
* *
* Jim Martin *
* *
* Flight Mechanics Laboratory *
* School of Biological Sciences *
* The University of Bristol *
* Woodland Road *
* Bristol *
* BS8 1UG *
* *
* Tel: +44 01179 289000 ext. 3794 *

Date: Thu, 9 Oct 1997 12:26:02 -0400 (EDT)
From: Jason Michael Blank

You probably already know this but. . .
Be careful of attributing the entire difference in indoor/outdoor
performances to the track. World-class athletes usually center their
training around the summer grand-prix season and put much less emphasis
on the indoor season.
Of course, if you've ever watched an indoor track meet, you know
that the turns are much harder on the sprinters than the distance
runners because of the difference in speed. Another factor is that the
400m is run in lanes outdoors but is a bit of a free-for-all indoors.

Jason Blank

Date: Thu, 9 Oct 1997 09:36:08 -0700 (PDT)
From: Douglas Chang
Subject: Re: Impact or Turns on Running Performance


I don't have any data for you, but as an indoor and outdoor runner there
is another important consideration besides simple kinematic equations. The
indoor season tends to be in winter whereas the outdoor season occurs
after that in the Spring/Summer.

In addition to the turns, we runners felt that the increased conditioning/
training as well as the psychological feeling of being unbounded and un-
imprisoned contributed to the increased speeds of the outdoor season.


From: (Young Hui Chang)
Subject: Re: Impact or Turns on Running Performance

hi larry,
i don't mean to get your hopes up (b/c unfortunately i don't have
any answers for you!). but i am interested in getting a list of the
reponses you get to your question about max. speed in running around
curves. i've had some interest in rotational movements in locomotion
(including curve running) and would enjoy hearing what people have to say
about it. thanks.

Young Hui Chang

Young Hui Chang, M.S.
(it's pronounced "young-hee")


snail-mail: 3060 VLSB
Locomotion Lab
Dept. of Human Biodynamics
University of California
Berkeley, CA 94720-3140

Phone: 510-642-8662
Fax: 510-643-6264

---------"Learning how animals get from here to there."---------

Date: Mon, 13 Oct 1997 15:10:30 +0100
From: Neil Smith
Subject: Impact or Turns on Running Performance -Reply

I would be interested to hear any findings you gain into the banking problem.
Could you please mail me with any replies you get.

Cheers in advance
Neal Smith
Sports Biomechanics Laboratory
Chichester Institute

Date: Mon, 13 Oct 1997 22:19:41 -0400
From: "D. Gordon E. Robertson, Ph.D."
Subject: Re: Impact or Turns on Running Performance

There is a sample problem in Beer and Johnston's Vector Mechanics
for Engineers: Dynamics that shows how to compute the banking for cars.
Look in the index under "banking of curves."
May the moment of force be with you.

D. Gordon E. Robertson, Ph.D.
Associate Professor of Biomechanics

Date: Tue, 14 Oct 1997 09:15:44 -0700
From: (Devin Jindrich)
Subject: Re: Impact or Turns on Running Performance

Dear Mr. Wellman --

Did you ever receive any references in response to this post? If so, I
would be very interested if you could pass them on to me. I am studying
turning in insects and have references for insect turning (few with
equations, however), but have not been able to find too many references for
turning in other animals.

Thank you very much in advance,

Devin Jindrich

__________________________________________________ _______________________
Devin L. Jindrich
Department of Integrative Biology
University of California, Berkeley PH: 510-643-5183
Berkeley, CA 94720-3140 FAX: 510-643-6264
__________________________________________________ _______________________
From: "Doug McClymont"
Date: Wed, 15 Oct 1997 09:03:45 +1200
Subject: Re: Impact or Turns on Running Performance


You will get some interesting detail from Hugh Morton at:


Doug McClymont
(senior lecturer in Physical Education)
Christchurch College of Education
P.O.Box 31-065
New Zealand