The curve must be continuous between the two ends. The sinuosity value is really significant when the line is continuously differentiable. 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. The calculation of the sinuosity is valid in a 3-dimensional space, although it is often performed in a plane. The classification of a sinuosity often depends on the cartographic scale of the curve and of the object velocity which flowing therethrough : the sinuosity of the same curved line could be considered very strong for a high speed train but low for a river. Nevertheless, it is possible to see a very strong sinuosity in the succession of few river bends, or of laces on some mountain roads.
Notable values
The sinuosity S of:
2 inverted continuous semicircles located in the same plane is. It is independent of the circle radius;
With similar opposite arcs joints in the same plane, continuously differentiable:
Rivers
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. The sinuosity index can be explained, then, as the deviations from a path defined by the direction of maximum downslope. For this reason, bedrock streams that flow directly downslope have a sinuosity index of 1, and meandering streams have a sinuosity index that is greater than 1. It is also possible to distinguish the case where the stream flowing on the line could not physically travel the distance between the ends: in some hydraulic studies, this leads to assign a sinuosity value of 1 for a torrent flowing over rocky bedrock along a horizontal rectilinear projection, even if the slope angle varies. For rivers, the conventional classes of sinuosity, SI, are:
SI <1.05: almost straight
1.05 ≤ SI <1.25: winding
1.25 ≤ SI <1.50: twisty
1.50 ≤ SI: meandering
It has been claimed that river shapes are governed by a self-organizing system that causes their average sinuosity to be, but this has not been borne out by later studies, which found an average value less than 2.
