madison bob
I have a thought myself from a lot of research with shaft sizes and taper,s but i,am sure everyone won,t agree. i,ve noticed that if you cut a taper that comes up slowly 2 to 3 thousands a inch from the ferulle back toward the joint about 15 inch,s and cut the dia of the tip about 12.9 mm the shaft seem,s to have very little deflection at all if you put on a nice ferulle such as millimine threaded with a base to the ferulle in other words drill the ferulle all the way thru and from the bottom of the ferulle open up the hole about a 1/4 of a inch up toward the top to a larger size and this area will not be taped just open like a open hole ferulle then when you install the ferulle on the shaft the larger hole at the base gives the tenon extra support so it has almost no deflection in the ferulle area . it,s a little more work but when you machine the ferulle you can see there is little flex because the ferulle cut,s perfectly striaght all the way thru when you measure it it will measure the same at the bottom closer to the chuck and at the top closer to the tip end if you don,t do it this way you will see 2 to 3 thousands different,s no matter how sharp your tool,s are because of the flex of the tenon.i,ve been useing this shaft taper for years now after trying many other,s before and have found set up in this fashion will have very little deflection almost non. and i,am running this with a .850 joint size . one thing with this taper it feels at 12.9mm more like a 13mm because of the rapid increase in the rise of the taper but it sure hold,s your stroke in line on power stroke,s . also this taper allow,s only the first 5 are 6 inch,s of the shaft to work releasing the cueball at a faster rate with less deflection and this doe,s away with all that center shaft movement that the so called pro taper,s have cutting down on deflection . madison bob