chain length & rings and cogs
 

So here's the situation:
Bike is an old Cannondale road bike with the derailleur hanger completely broken off. So I can't use a chain tensioner. I also don't want to pay a few hundred dollars to have someone build me a wheel with one of those White Industry hubs. And, I've read some weird stuff online about half-links and get the feeling that if I use one, I'll end up going up a hill somewhere and have my chain snap on me.

So after playing with different combinations of rings and cogs on the weekend, and not being able to get a nice chain tension, I'm wondering if there is any sort of measurement you can use - for example the distance from the middle of the bottom bracket to the middle of your freewheel - to determine what combinations of chain rings and cogs you could use to have an adequate chain tension.

Anyone have a measurement system like this? Or a "rule of thumb" they go by?

Thanks!

half links are fine, if properly installed - just like any other piece of chain.
master links are what have a bad reputation, but even those are fine in my book if installed and maintained correctly.

a calculator it'll work but can be quite a hassle.