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Exactly, been doing it that way for as long as I can remember. (But then when you are my age it might only be a matter of weeks.)

It is no big deal with a jig like this. Want to incline the Saddle? Just raise the jig some.

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Joe Beaver
Maker of Sawdust

I do experiments because my math and trig skills are relatively poor. I'm always finding out stuff that I didn't expect to see, and having somebody tell me later that it's right; backed up with equations that I sure can't set up.

The string is trying to make a straight line from it's anchor point, over the top of the saddle, to the nut. The stiffness of the top won't allow the string to straighten out, distorting until the forces are equal each way. The ultimate anchor point on the top is the tail block. If the strings are anchored at the tail and then run over the saddle the only forces on the top are the one pushing it down due to the break angle, and the one pulling up on the tail block, and the centroid is somewhere in between, but very close to the tail since that's pretty stiff. The higher the strings are off the top the greater the forces, but the centroid will be in the same place (assuming linearity). If you make the bridge wide enough to that the strings are anchored a little ways in front of the tail both of those forces are larger, and the centroid is closer to the saddle, with the force magnitudes again depending on the string height off the top. Having a very low break angle is like moving the anchor point back in terms of where the centroid ends up, but doesn't change the up and down forces on the top. Does that make sense?

My thought is a tilted saddle either way isn't really a good thing. It can cause bridges to crack. But I do understand where you are coming from with the self compensation. Either way a bellying top will still make an instrument difficult to play even if intonation isn't affected.

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Shaw wrote:
"My thought is a tilted saddle either way isn't really a good thing. It can cause bridges to crack."

I guess that depends on which way the saddle tilts, and whether it was made that way.

We often see old bridges where the saddle is tipping forward owing to distortion of the front wall of the slot. The slot becomes somewhat 'D' shaped, and the saddle tips forward in the center. This is certainly a disaster in the making. The saddle wants to tip because of the fact that it's not on the bisector of the break angle, so there's a net force on the top pushing it forward. If the slot is tight, and the saddle reasonably rigid, it helps to resist this, but a plastic saddle can bend enough to concentrate the force in the center, and off we go. The forward tip is certainly not a design intention.

Tipping the saddle back by making the slot at the proper angle minimizes the tipping force, and greatly reduces (at least) the chance that it will split out the front of the bridge. In theory it would even work with a soft plastic saddle, so long as the back angle is really on the bisector.

Can you explain why you feel that way? I can't see why tilting a saddle would have any negative effect on the cracking of a bridge.

Thank you Alan Carruth for picking up the torch on this thread.

I just want to reiterate the initial idea purely from a longevity standpoint.
Long before you reach the optimum of bisecting the break angle, almost all bridge slot failures have been eliminated. That's a lot of money, heartbreak, and usually a bit of rain forest.
Anybody who has messed with a tent pole and a rope knows the forces trying to lay it down go up at a very steep rate as angle changes.
Regardless of what is optimum for sound, I will never understand why makers, especially factories, don't tip the dang thing back a bit.

I have just seen numerous times where leaning saddles over the years have caused the bridge to crack at the saddle slot area while doing repairs. The pressure isn't being applied straight up or down it's on an angle and now the pressure pulling forwards or backwards depending on the angle. These are just my opinions. Maybe I'm wrong and some of the more scientific can chime in.

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I think we might be talking about two different things here. What I "think" you are talking about is when the saddle is tipping in a slot that is too big for said saddle. So, yes, uneven force can cause all sorts of problems.
What I'm talking about is when the saddle slot is cut at a back tilted angle. Then the saddle is fit PROPERLY (strange concept for many guitar manufacturers) so the force is still even along the front edge of the saddle slot. There is no reason the bridge would crack before a straight saddle. In fact, I'd go as far as argue that it might prevent cracks because the slot is cut across multiple grain lines, not allowing a micro crack to "run".

All else equal, a well fitted vertical saddle experiences more rotational force from the strings than a well fitted back-tilted saddle and therefore applies more force to the front side of the saddle slot than a back-tilted saddle does. The lower force that the back-tilted saddle applies to the front of the saddle slot is the rationale for it being less likely to cause a failure.

As Pwoolson points out, for bridges with vertical grain, a tilted saddle would distribute the load across more grain lines and reduce the chances of a split, at least in theory.

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Once in a while you get shown the light in the strangest of places if you look at it right - Robert Hunter

Your thoughts on the force and the saddle being spread further across the grain is a good one. It's something I will have to look into more

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