Explanations for the long arch cause more heat than light - take four experts and you will get five opinions.
What you can say is this. Despite there being lengthy descriptions of it is many anatomical texts, there is rarely if ever an explicit explantion of its function. Explicitly what it does do is to reduce bending stresses during gait, but that is a bit of a cop-out. To understand it more fully, one has, as always, to think fourth dimensionally and go back to the phylogeny and the embryology. Here you willl see the long arch as being not one structure, but a unit of several sub-structures.
I published a fair bit on this perhaps 25 years ago; if anyone is interested, email me privately and I will send them the references. Rob