Posteado por: cikatriz | noviembre 26, 2010

Route Choice in Hilly Terrain

Se llega a un extremo donde las matemáticas llegan a dar respuesta a todo…hasta a la orientación.

“The sport of orienteering requires participants to determine the fastest route along a leg between two given points in terrain which is often hilly or even mountainous. This is an example of a minimum cost path problem: nd the path in 2-dimensional space whichminimises the integraltAB =Z(integral) BAp ds (1)where A and B are given points, p is a cost eld (Miller & Bridwell, 2009) and s is distance. In our application, p is pace, the reciprocal of running speed (Scarf, 2007).More precisely, p is de ned as the time per unit horizontal distance, as shown on the map (as opposed to distance over the sloping ground). A runner’s pace is likely to be afunction of three factors (Arnet, 2009):-

 The gradient at which the runner is climbing or descending, henceforth called routegradient and denoted m, with m positive uphill;

The gradient of the terrain, denoted m? hereafter;

 The runnability of the terrain, which is the e ect of vegetation or uneven groundin reducing the runner’s speed relative to that on a smooth path.Route gradient is related to terrain gradient by

m = m? sin   ; where   is the angle between the route and the contours. The route gradient isanisotropic (dependent on the direction of travel), while the other two factors areisotropic….”

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