Hi Scot
OK for No 2 morse taper:- the taper per foot is 0.5986" or taper per inch is 0.0498" this equates to a included angle of 2.85 deg.
The best way to turn a morse taper is to do it between centres and off set the tail stop.
I don't know if you are familiar with this process, but breifly,
1:- Centre drill each end of your bar stock.
2:- Remove your chuck and replace it with a fixed centre and a driving dog, and a carrier on your bar stock, put a running centre in your tail stock.
3:- To set the taper you can do it by trial and error until you get a good fitting taper in a No 2 sleeve, turning between centres you can remove the job without losing your setting. Or you can put a clock in the tool post and run it along your bar stock until it reads the correct taper per inch.
The tail stop should have two bolts one ether side low down, you slaken one and tighten the other this gives the off set.
When you've got it right just turn it to size.
What ever you fixing on the taper the best way to get it running tru is to but the blank taper you've just turned in your head stock, and turn it to fit your chuck, end mil or what ever your going to do with the buisness end.
Turning a taper is a good maching exercise but the easy way is to buy a blank taper they have soft ends so you can machine it to your requirements.
Hope this makes sense
Cheers
Stew