Dear list member,
the next research seminar of The Open University Statistics Group will be held on Friday, October 14th at the following venue: Christodoulou Meeting Room 15 (CMR15), Walton Hall campus, Milton Keynes (MK7 6AA). The meeting will begin at 11 a.m., with tea and coffee available from 10.30 a.m., and usually finishes at approximately 12 noon. The meeting is free and open to all.
Professor Philip A. Scarf (Salford Business School, University of Salford) will be speaking on the topic of: "A statistical excursion in the isochronic hills".
Abstract:
The adventure racer, when competing in mountain navigation events, is often faced with an over-or-around route choice. Is it quicker to go over or around a hill when trying to get from a point A, on one side, to a point B, on the other? Route choice aesthetics are of no interest. The competitor wishes to get from A to B as efficiently as possible.
Naismith's rule can be used in these circumstances. This rule relates climb to distance, and implies that, in terms of time taken, 1 unit of distance vertically is equivalent to N units of distance horizontally.
Naismith in his original paper in 1892 implied that N=7.92. Now, if a route (from A to B) comprises a horizontal distance component of x units and a vertical distance component of y units, then x+Ny is the equivalent distance of the route. Given a choice between routes, the competitor should then ceteris paribus choose that route with minimum equivalent distance. This talk will consider a number of questions in this context: What are the origins of Naismith's rule? What is the connection between the rule, the treadmill crane at Harwich, and the Scottish Mathematician MacLaurin? What is the fastest mile ever run? Can N be estimated from data? Does N vary with age, that is, do veteran runners find ascent relatively more difficult, and therefore should they be more inclined to go around? If the over and around routes between points on opposites sides of a simply shaped hill are equivalent, is there a quicker route in between? What is the shape of an isochronic hill? Is the rule applicable to cycling?
Kind Regards,
Dr Steffen Unkel (Department of Mathematics and Statistics, The Open University)
http://statistics.open.ac.uk
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