Wednesday, February 20, 2008

Zig Zag uphill.....

This is relevant for all of us hillwalkers......

zig-zagging is more efficient than a straight line

We know this already of course, intuitively and also with support from the wonderful stalkers paths scattered round the Highlands (my favourite being on Gleouriach).

Well, scientists have now looked into this with a mathematical model, showing that a zigzag course provides the most efficient way for humans to go up or down steep slopes.

"There is a point, or critical slope, where it becomes metabolically too costly to go straight ahead, so people move at an angle, cutting into the slope. Eventually they need to go back toward the direction they were originally headed and this creates zigzags. The steeper the slope, the more important it is that you tackle it at the right angle.”
The abstract is available here

Human and animal trails on steep hillsides often exhibit dramatic switchbacks and shortcuts. Helbing et al. have recently examined the emergence of human trail systems on flat terrains while Minetti and Margaria established the effect of gradients on human metabolic efficiency. In this paper we use these ideas to develop a semi-quantitative theoretical model of the behaviour of humans moving on a terrain with relief. The model determines the direction of movement by minimising metabolic cost per unit of distance in a desired direction. The structure of the theory resembles the Landau Theory of Phase Transitions, much used in theoretical physics. We find that both hairpin bends (switchbacks) and shortcuts appear as efficient strategies for downhill walkers, while uphill walkers retain switchbacks. For weakly inclined slopes, the best strategy involves walking directly uphill or downhill. For sufficiently steep slopes, however, we find that the best strategy should undergo a transition to a broken symmetry solution corresponding to the switchback trail patterns typical of rugged environments. The critical slope at which this transition takes place should be less steep for uphill and downhill walkers. The theory should be amenable to empirical investigation. Amongst other applications, this model will enable us to generalize the work of previous authors to real landscapes, eventually permitting the reconstruction of ancient patterns of movement in archaeological landscapes.

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