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Pace and critical gradient for hill runners: an analysis of race records
journal contributionposted on 2014-12-12, 13:39 authored by Anthony Kay
Route choice through mountainous terrain requires a knowledge of how pace (the reciprocal of speed) varies with gradient of ascent or descent. To model this variation for runners, we analyse record times for 91 uphill and 15 downhill races or race stages. The pace is modelled as a nonlinear function of gradient and a linear function of race duration, using ordinary least squares to obtain a best fit. For the gradient-dependence, six functional forms are compared, of which a quartic is found to fit the data best; however, at steep gradients the quartic model is unrealistic and it may be argued that a linear model is more appropriate. Critical gradients, at which a runner's vertical speed (uphill or downhill) is maximised, may be calculated from a nonlinear model, although it appears that there is no uphill critical gradient within the range of our dataset. © 2012 American Statistical Association.
- Mathematical Sciences
Published inJournal of Quantitative Analysis in Sports
CitationKAY, A., 2012. Pace and critical gradient for hill runners: an analysis of race records. Journal of Quantitative Analysis in Sports, 8 (4).
PublisherDe Gruyter / © American Statistical Association
- VoR (Version of Record)
Publisher statementThis work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/
NotesThis article was published in the serial, Journal of Quantitative Analysis in Sports [De Gruyter / © American Statistical Association]. It is also available at: http://dx.doi.org/10.1515/1559-0410.1456