The basic facts that you need to consider on this are that:
1) softwoods have a Young's modulus from 5 to 12 times higher along the grain than across, and,
2) glues usually have very low peel resistance. Once you start the edge of a glue joint lifting it's usually real easy to peel the part off if there's some flexibility and you're willing to take some time.
Think about a brace about .250" tall glued crosswise on a top that is, say, .125" thick. If that brace just cuts off abrubtly somewhere out in the middle of the top it makes a huge stress concentration. The stiffness of the brace is proportional to the Young's modulus of the material and the cube of the height. The brace is twice at tall as the top is thick, and the Young's modulus along the grain of the brace is (say) eight times as high as that of the top. Thus the brace at it's end is (2x2x2)x8= 64 times as stiff as the top. If there's some load on the top right at the end of the brace (your fat cousin sits on your guitar) the top is far more likely to bend than the brace, and that puts all of the stress on the glue line, which tends to peel apart.
If you shave the end of the brace down to about 1/2 as thick as the top at that point then the brace end is (1/2 x 1/2 x 1/2) x 8 = 1 times as stiff as the top at that point, and can bend along with it to some extent. So long as the brace end comes smoothly down to that height at the end and the taper is reasonably long you've avoided a stress concentration, and reduced the liklihood of the brace peeling loose.
There's a problem with this when there is normally a large static load down on the brace, such as you have with the shoulder brace from the neck, or the upper ends of the X that take up the bridge torque. If the brace is shaved down to nothing then all of that down load will have to be dissipated by the top itself, distributed over a more or less wide area depending on how fast you taper your brace ends. You'd be likely to end up with a pretty good dimple in the top if you did that, so you have to leave some brace ends tall enough to take up that stress. Those braces must, therefore, be inletted into something to support them and keep them from peeling loose.
The bridge patch serves, as far as I can figure out, two structural purposes:
1) it provides a bearing surface for the ball ends of the strings, and
2) it 'balances' the construction of the top at the bridge location, helping to avoid stress from the cross grain of the bridge on the top surface. Bridge +top+plate=plywood.
In addition it adds some stiffness and mass, which has an acoustic effect.
If the bridge patch extends beyond the front edge of the bridge then the deformation of the top due to staic torque will tend to peel it loose if it's stiffer than the top. You are, of course, dealing with the long grain direction of the top in this case, so it's pretty stiff, but hardwoods don't lose as much by being in cross grain bending as softwoods do, and they're still pretty stiff. Thus I like to taper the front edge of the bridge patch down to avoid a stress concentration there, too. I don't see any real need to inlet the bridge patch into the braces, though, as it's not being subjected to a peeling load. As always, you want to either have things fit tightly or else not touch at all, to avoid buzzing.
|