Why angled saddle (and where is energy transferred)?

[methodinsane]

Hi guys,

I've never posted in this forum but I have some questions regarding saddle on an acoustic guitar (my own in particular). The very crude image below shows that the saddle fits into the bridge at an angle.

1. Why is the saddle angled?
2. Where does the energy get transferred into the bridge? (a) Directly below where the strings sit or (b) at the bottom of the saddle.

I am asking this as I'm fitting some an SBT (Dazzo in this case) and I know with certain SBTs (like the K&K, Dazzo, FRAP, Trance audio) the saddle line can be important for placement.
I am drawing a saddle line inside on the bridge plate but because of the angle of the saddle I don't know if it should lie directly under the top of the saddle (where the strings sit) or under where the saddle touches the bottom of the bridge (I'm guesstimating roughly 1mm away from "directly under the top of the saddle".

Is there a way I can accurately find this line?

I hope I'm making sense.
Thanks in advance,
John Paul

[John Arnold]

I would go with the bottom of the slot. Most of the pressure of the strings is on the bottom.
The back angle on the saddle is to counteract the tendency for the saddle to tilt forward, because the strings bend at an angle across the top of the saddle.

[Ned Milburn]

John's advice won't steer you wrong. I'll add, though, that you don't need to be ultra accurate and dogmatic with pickup installation on the underside of the bridge plate. Two millimeters or so will have little, if not completely zero, effect on the tone. The bridge, top, and bridge plate when glued together are so stiff that there will be insignificant and inconsequential differences in vibration for bridge plate pickups.

[Alan Carruth]

The back angle helps reduce the tipping force on the saddle top that breaks out the front edge of the bridge. If you set up a vector diagram the actual string pressure on the top of the saddle runs along a line that bisects the break angle. If the strings dip down behind the saddle at, say 30 degrees, the force on the saddle top is directed 15 degrees forward of the vertical. This gives some tipping force on the saddle top. If the saddle is angled back in that example by 15 degrees, then there is no net tipping force on the saddle top, and the down force at the bottom of the slot is greater.

You can see this sort of thing on violins, where the central plane of the bridge approximately bisects the break angle, minimizing the tipping force. That's how they can get away with such a tall, narrow bridge. If the bridge angle is even a little off it might still stand up, but the tipping force causes the bridge to bend over time and ruins the sound. The same might happen on a guitar saddle, of course, but they're relatively thicker and much shorter, so it's probably not an issue. It would take a lot of work to find out if it has any measurable effect on the sound.

One maker, whose name escapes me at the moment, claims that a back angle of 9 degrees has the benefit of automatically correcting the intonation as the saddle is raised or lowered. When you make the action higher by putting in a taller saddle you need to increase the compensation a bit, and this supposedly does that automatically.

I'm not sure if there's anything to be gained by discussing where the energy gets transferred. Ultimately the only thing the string 'sees' is the saddle top, and that's where the force is exerted by the string. You can split that up into a fairly large static force from the string tension, and smaller 'signal' forces. The two main signals are the 'transverse' force, which can be either 'vertical' or 'horizontal' with respect to the plane of the top, or (usually) some combination of the two. There's also a much smaller 'tension change' signal that's tugging the top of the saddle toward the nut twice per vibration cycle of the string and causing the bridge to 'rock' forward and back. A third signal is the 'longitudinal' wave, at a much lower level yet, which is a very high frequency vibration that also acts to tip the bridge. How much of which of these signals you get in the sound of the guitar depends on all the usual variables: the height of the strings off the top, the structure, stiffness, mass and resonances of the top, some of the other resonant modes of the guitar, the phase of the moon, the state of the stock market, and the wholesale price of coffee: the usual stuff.