Sinuosity

The distance between both ends can also be evaluated by a plurality of segments according to a broken line passing through the successive inflection points (sinuosity of order 2).

The classification of a sinuosity (e.g. strong / weak) often depends on the cartographic scale of the curve (see the coastline paradox for further details) and of the object velocity which flowing therethrough (river, avalanche, car, bicycle, bobsleigh, skier, high speed train, etc.

): the sinuosity of the same curved line could be considered very strong for a high speed train but low for a river.

The sinuosity S of: With similar opposite arcs joints in the same plane, continuously differentiable: In studies of rivers, the sinuosity index is similar but not identical to the general form given above, being given by: The difference from the general form happens because the downvalley path is not perfectly straight.

For rivers, the conventional classes of sinuosity, SI, are: It has been claimed that river shapes are governed by a self-organizing system that causes their average sinuosity (measured in terms of the source-to-mouth distance, not channel length) to be π,[3] but this has not been borne out by later studies, which found an average value less than 2.