Measuring Sinuosity of Walking Paths

I'm currently working on a project that examines the movement of consumers through different kinds of retail spaces in Central Asia – namely, bazaars versus supermarkets. I've equipped dozens of shoppers with GPS trackers that record their movements throughout these different retail spaces, and I'm now working on analyzing the resulting data.

I'm primarily interested in comparing overall walking distances and walking speeds – easy enough. But I've also noticed bazaar paths are highly irregular, with shoppers weaving this way and that through the crowded stalls, whereas the supermarket tracks are highly straight, efficient, and consistent between shoppers. So, I'd like to quantify the sinuosity or efficiency of these walking paths – i.e., how frequently the shoppers turn and/or backtrack.

I'm not sure how to approach this analysis – much less accomplish it in QGIS. Should I define this "spatial efficiency" index as the ratio of overall distance traveled to overall degrees of rotation, or something? Or should I use the simple river sinuosity calculation (direct distance vs. curvilinear length) – and if so, how should I determine the critical waypoints? Any advice is appreciated.