Just to clarify, I believe Beth is asking about steel string slotted headstocks as opposed to classical. Is that corect Beth? I think that is what you were trying to get at with your last post.

Josh

If the results I got on looking at bridge break angle hold for the nut (and I don't see why they would not) even ten degrees of break is probably more than you 'need'. Here's one way to think about it...

If you are trying to get the most possible sound out of a string, the way to do it is to push the string down as far as you can and release it so that it's traveling exactly 'vertically' with respect to the soundboard plane. This is because the 'transverse' string force is the most powerful signal the string makes, and driving the top 'vertically', so that it acts like a loudspeaker cone, is the most efficient way for it to produce sound. Naturally, there is a limit to how far you can push the string down; once it touches the fingerboard you're done.

If you look at the string in the 'time domain', that is, track the shape of the string over time, you'll find that the 'kink' you made at the spot where you pushed it down runs out toward the ends of the string at a certain speed, which is the bending wave velocity of that string. After a certain time had had been a triangle shape just before you released it is truncated: the point is chopped off and there's a flat there. The string goes from having two straight sections joined at the kink to three straight sections, joined at two kinks. The initial angles at the ends remain unchanged: no information about the bending of the string can travel up it faster than the speed of the bending wave, so the ends of the string take a little while to find out that you've let it go.

When the kink reaches the nut it reflects back down the string. The small 'down' angle of the string at the nut (remember, you pushed it down) is replaced by an 'up' angle. If there has been no loss of energy from the string, the 'up' angle at the nut will be the same as the original 'down' angle the string made at the bridge. So long as that angle does not exceed the break angle, the string will remain in contact at the nut

So how much of a 'down' angle can you put on the string? Well, that depends on how far you push it down, and how close to the bridge you are. If your action is 1/8" at the 12th fret, then you will bottom out on the frets if you push the string down by 1/4" at the bridge. As you move out away from the bridge it gets easier to push the string down by any given amount, and you bottom out with a smaller deflection. I found that, for me, deflecting the string downward by more than about five degrees when I pluck it is a lot of work, and unlikely to happen in real life. YMMV

That being the case, a five degree break angle at either end ought to suffice. In my bridge break angle experiments I used a minimum of six degrees, and that seemed to be just enough: it's possible that the string did hop off the saddle top at the initial pluck, but it was hard to see of hear any evidence of that.

I hope this makes sense: there are animations on line showing the way a string moves, and you can look it up in a number of texts, such as Fletcher and Rossing's 'Physics of Musical Instrumets', or (of course) the Gore/Gilet books. This says nothing about the need for slots in the nut to keep the string from moving sideways under pushes from the left hand, of course. It's interesting to note that Benedetto, in his book on archtop making, uses a six degree break over the bridge top, iirc.

...I'd like to see a guitar with a 6 degree, because I wonder if it would look unusual, being so much straighter than what I'm accustomed to seeing on a steel string...