I wanted to see what various sinuosity values actually looked like, so I wrote a small mma script using filtered random walks to visualize it. In the attached image a path is shown in each grid and in the top-left corner of each is the percent you have to add to the straight-line distance to get the path distance. eg: +20% is a 1.2 times multiplier, ie: add 20% of the straight-line length to get the path length
Sinuosity is the length of a path divided by the shortest distance between the endpoints. Its how much you have to multiply the straight-line distance between two points to get the real distance. Very useful for estimating distances
I also discovered that you can estimate the sinuosity using the width of the path (the maximum straight-line-orthogonal distance between points on the path). Roughly, you take the width of the path, multiply it by 1.6 and add 0.9. The attached image is the fit for that line
