Running Shoe Shanks

How do plastic shanks in running shoes help with propulsion? I know shanks are often used for foot support (if you overpronate) … but some brands such as Asics and Adidas advertise Propulsion Trussic systems and Sprint Frames (respectively). Reviewers generally say that the Adidas Sprint Frame (a full length thermoplastic shank) actually works - as in it provides a noticeable amount of propulsion … but what are the mathematics behind such structures? What are the geometric concepts? The biological concepts? Etc. I’m not interested in the advertising - just the math and science.

I assume they add some spring to your step. The arch of the shank bends back into place when the weight comes off it. Sounds iffy whether it would add much propulsion.

I just switched to minimalist shoes; those shoes with five toes. I find I get more spring from them because my foot bends at the toes, and my toes splay out. Because of that extra surface area, I can push more with each step. It is hard on my calves and shins though, but it is getting easier.

I think I would run barefoot at the indoor track if they let me.

I think the science would be that it absorbs some energy and returns it more directly to help propel, rather than directing it in some other non-helpful direction. Imagine punching a punching bag and it goes sideways and vibrates sideways until stopping. Having the energy go in the wrong direction is not helping with the back ‘n’ forth you would prefer. In shoes, this happens, but if you target the rebound, it can be used with some purpose.