The following code needs fiona and shapely installed, using either pip or conda, and expects a shapefile containing a single polyline.
It works by creating two shapely LineStrings and then using their length attribute to calculate sinuosity.
If you are using a geographic coordinate system, you will need to calculate great circle distances. To do this I usually use pyproj's geod.inv method.
Run the script with a shapefile filename as follows:
python sinuosity.py myline.shp
This will calculate the sinuosity of the line stored in myline.shp and output the result to the screen.
This code used shapely and fiona which can both be pip installed using:
pip install -r requirements.txt
This code is MIT Licensed, see LICENCE.txt for details.
If you would like to cite this script, you can grab the bibtex file here.