変分原理にもとづく富士山登山道の分析

概要

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The variation principle is a concept for investigating the spatial pattern of any path on a given curved surface. From this point of view, properties of the Mt. Fuji climbing route are discussed, based on morphometric data. The route goes straight towards the summit on the gentle slope at the foot of the mountain, and shows a zigzag pattern on the steep slope near the summit.The variation principle maintains that the route can be a stationary one which minimizes some quantity. The straight portion of the route near the foot is the geodesic on a conical mountain, which gives the shortest distance to the summit. In order to explain the zigzag pattern near the summit, however, the amount of energy required to climb the mountain has to be taken into account. From this point of view, two types of models, namely, the excess energy model and the total energy model are possible, among which the latter seems better.If the latter model is employed, it is reasonable to assume that the energy required is proportional to the reciprocal of the power function of cosine of the slope. The exponent of the power function here is approximately 12. The zigzag route in this case has been designed so that the route needs 1.6 times as much energy as on a flat surface. The portion of the climbing route higher than 3200m in elevation is less steep, and this may correspond to the lower oxygen content above this level.
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