# Tortuosity - alternative method

## Description

Tortuosity is a property of curve being tortuous (twisted; having many turns). There have been several attempts to quantify this property.

Tortuosity is commonly used to describe diffusion in porous media, such as soils and snow.

Subjective estimation (sometimes aided by optometric grading scales) is often used.

The alternative method to estimate tortuosity in 2D is shown here.

In 2002 several Italian scientists proposed this alternative method. At first, the curve is divided into several (N) parts with constant sign of curvature (using hysteresis to decrease sensitivity to noise). Then the arc-chord ratio for each part is found and the tortuosity is estimated as shown here.

In this case tortuosity of both straight line and circle is estimated to be 0.

Related formulas## Variables

τ | tortuosity (dimensionless) |

N | number of parts parts with constant sign of curvature (using hysteresis to decrease sensitivity to noise) (dimensionless) |

L | length of the curve (dimensionless) |

n | index of summation (dimensionless) |

L_{n} | length of the incremental part (dimensionless) |

S_{n} | sampling (dimensionless) |