Sinuosity

Calculation of sinuosity for an oscillating curve.
Switchbacks on mountain road with high sinuosity at Luz Ardiden
The meandering Rio Cauto at Guamo Embarcadero, Cuba, is not taking the shortest path downslope. Therefore, its sinuosity index is > 1.
Two ski tracks with different degrees of sinuosity on the same slope

Sinuosity, sinuosity index, or sinuosity coefficient of a continuously differentiable curve having at least one inflection point is the ratio of the curvilinear length (along the curve) and the Euclidean distance (straight line) between the end points of the curve. This dimensionless quantity can also be rephrased as the "actual path length" divided by the "shortest path length" of a curve. The value ranges from 1 (case of straight line) to infinity (case of a closed loop, where the shortest path length is zero for an infinitely-long actual path[1]).

  1. ^ Leopold, Luna B., Wolman, M.G., and Miller, J.P., 1964, Fluvial Processes in Geomorphology, San Francisco, W.H. Freeman and Co., 522p.