I live in Yuma, AZ. I set the taper by..... I may misunderstand what exactly you're asking for so I'll try to be thorough. Maybe it's best to briefly describe what i do. I take the straight stock...(preferably long enough to avoid using tongs in the beginning) and I work the socket first.
I hammer a bit at the end to start flattening it into the beginning of a fish tail. I then uses my cross pien to spread it side to side. (this is very necessary when i use the 1/4" stock as there is little to go around....pun intended.) (If it's rebar i will likely have to cut excess off with a simple chisel). Anyhow I spend a substantial amount of time flattening the socket material starting from the inside and working my way out to the edges..... this takes me quite a few heats. After I have the basic fish tail shape I use a dull chisel (on occasion... not sure if it matters honestly) to put a dent in the junction between the fish tail and the rest of the square stock. Long wise of course.... Then I take the fish tail to my vise where i use a small gap in the jaws to initiate the socket. Starting at the very apex of the fish tail I hammer the crap out of it while turning making sure that symmetry is followed. I basically work from the top of the taper on the socket on down to the bottom very slowly with kind of like a bit of some sweeping-like strikes all the while rotating the piece. Kind of like drawing it out but gently as not to crush the socket. As I'm doing this the junction or apex is right at the edge of the anvil and my hammer is usually at an angle. With the rest of the stock hanging off the anvil it does not get struck and therefore remains quite thick. The neck continues to be drawn out making a natural tapered socket to bulbous point. So to sum it up it's just hammer work.... hard at first..... gentle at the end.....giggety. I usually finish the socket with a quick use of my ghetto lil' mandril (it's a piece of the same stock the i filed down and stuck it out of a log). Just to insure the inside of the socket is aligned and trued up. (also this is the point (while on the mandril) you can align the rest of the stock behind the socket.... basically make sure that the stock and mandril line up like they are one piece or in the end you'll have a point that has a gangster lean and is not lined up behind the arrow. (don't know if any of that makes sense). Then the rest is cutting it from the stock and finishing out the point which is quick vigorous work. A lot of the time the hammering of the actual point can bend things out of alignment so i always finish the point by truing it up and putting it on the mandrel one last time to make sure its' all lined up. I use three hammers (big and small ball pein and a crosspien), long needle nose for tongs, and a file to finish the points.... that's it really. If I wanted a sharper transition between head and socket there are many ways to do so, one being a spring fuller, but alas i am a simple smith.
Hope somewhere in there you got your answer, let me know if it didn't.
-Cbert-
