Purpose of bridge pins?

[Chuck Tweedy]

Great mockup!
String height at the nut is going to change the overall up (or down) force on the top.
Looks like you have it pulling mostly down there.

[Peter Wilcox]

I assumed that the string's downward force would be approximately inversely proportional to the angle of the string at the saddle (90 degrees = 0 force) - negligible in this case -, but I will have to test that. I'll make a high nut to make the angle 90 degrees (without tension), and see if there is a discernible difference in the bow.

[Chuck Tweedy]

The force will be:

F = T * cos(angle)

Where T is the total string tension.
angle is the angle from vertical. As you say, cos() has a slope of 1 at (pi/2) radians (90 degrees), so that force will be approximately proportional to the angle, but IN RADIANS.

[Mark Swanson]

You rock Chuck!

[Peter Wilcox]

I made the nut the same height as the saddle above the rigid board (1 1/8", vs 3/4" before), and tuned the strings to the same pitch (tension.) The bow in the "top" decreased from 6/32" to 5/32", measured from the plane of the "top" when flat. That's a much greater amount than I would have expected for an angle change of less than 1 degree, but there are probably many non-linear factors at work here.

[Mark Tierney]

Why would a pin bridge peel off the top from the back? On several examples brought to me for repair the ball ends had chewed through the (usually soft or thin, or both) bridgeplate, then through the soft topwood, and were bearing directly on the bottom of the bridge itself.

Mark

[Chuck Tweedy]

Why would a pin bridge peel off the top from the back?

Mark, we have discussed this in great detail above. I think if you go back though this thread, looking carefully at the diagrams and pictures you can see the answer to your question.
Bottom line, since the strings are pulling on a lever (the saddle) above the bridge, there is a torque (rotational force) on the bridge which pushes the front edge down agains the topwood, and lifts the back edge up away from the topwood.
These forces exist with or without pins, so a pinbridge peels up the same way a pinless or tie-block bridge will.

[Mark Tierney]

Why would a pin bridge peel off the top from the back?

Mark, we have discussed this in great detail above. I think if you go back though this thread, looking carefully at the diagrams and pictures you can see the answer to your question.
Bottom line, since the strings are pulling on a lever (the saddle) above the bridge, there is a torque (rotational force) on the bridge which pushes the front edge down agains the topwood, and lifts the back edge up away from the topwood.
These forces exist with or without pins, so a pinbridge peels up the same way a pinless or tie-block bridge will.

If the ballends bear against the bridge plate, the rotational force acts on the bridge, the top, and the bridge plate as a unit, and does not pull the bridge away from the top. But if the ballends come to bear directly against the underside of the bridge,the bridge/top glue joint is stressed. My apologies if I did not express this clearly.

[Mark Swanson]

It's clear, but Chuck is still right. The lever action of the saddle and bridge lifts the back. I have seen a thousand guitars with good bridge plates but the bridge has lifted. Sure, if the ball ends are bearing on the bridge itself that will hasten the issue, but even with a good bridge plate it happens.

[Chuck Tweedy]

Yes, I understand you also Mark (T).
It may be counter-intuitive to you now, but analysis and reality (lifted bridges) agree here so there's really not much to argue.
I would only suggest that you consider all wood to be both flexible and plastic. When stressed - it bends. When stressed over long time, it plastic-ly deforms.

You say "...the rotational force acts on the bridge, the top, and the bridge plate as a unit...", true.
But that does not mean that internally they are trying to peel apart. Which they are.

[David Malicky]

Below are two more FBDs of a pinned bridge, not including the string itself in the free-body. These show the effect of the string's break angle over the saddle, as Alan mentioned. The 1st FBD shows the string tension itself in 4 places. The 2nd shows how the tensions resolve into forces A and B, at the saddle and string ramp. The relative sizes and directions of A and B depend on the break angle. As Alan said earlier, the force A could be further broken down into Ax and Ay, the tipping force and downward force on the saddle (hopefully those can be visualized. Similarly, B has a Bx and By.) Only because the forces are simpler, I assumed the pin holes are slotted while the pins are not and basically inactive.





These FBDs also show my guess of the pressure reactions on the bottom of the bridge (instead of the linear distribution earlier). I didn't try to guess the shear, though (in pink). Alan, I'm thinking that downward force at the saddle (Ay) would be transmitted through the stiff saddle, through the thin wood below the saddle, and reacted from the top/bridgeplate via a 'camel hump' in the pressure distribution, as shown. The R force originates from the compression at the ball-end, which is transmitted through the bridgeplate/top back to the bridge, giving a peaky pressure distribution just in front of the hole. Your experiments on break angle and rotation centroids sound interesting -- I'd like to see your results.

Roger, Trevor Gore analyzes bridge rotation, torque, and top stiffness in his book. I'm not sure how he dealt with the angled X-braces.

Peter, nice revision to the model. I'd agree the bracing would play a role in the rear hump. Another subtlety is the relative stiffnesses of the front and rear anchors for the 'top', both rotational and axial. Axially, as Rodger said, the string tension causes top tension behind the bridge, and top compression in front of it. That's called a "statically indeterminate system", where there are two paths a load can take, when it only really needs one. There's a simple rule to understand which path is dominant: the load will mostly follow the stiffer path, in proportion to its higher stiffness. So in a guitar, the compression path from bridge-to-neck is quite stiff, while the tail path is not, as it is anchored by the flexibly-oriented sides. In your model, the tail path is probably only a little less stiff than the neck path, increasing the tension (vs a guitar), which would help straighten it and keep the hump in check.

[Chuck Tweedy]

Nice diagrams David.
I would say that you have all the right "features" in you diagrams. Not sure the magnitudes are correct but hey!

[David Malicky]

Thanks, Chuck. Good point on the magnitudes -- the break angle is on the shallow side, so A is relatively small as shown. The R peak is probably much taller right in front of the pin hole, and much shorter between the pin holes. And the "camel hump" peak under the saddle could be tall or short, depending on the bridge stiffness around the slot.

Mark T, your questions are good ones. In addition to the posts by Chuck and Mark S, see my first post on page 2, in particular the issue of the non-rigid bridgeplate/top, which does 2 things: 1) that nice clamping at the pin holes is not carried around to the tail of the bridge like it would be if the parts were rigid, and 2) instead, the clamping gives rise to the "R" force. R mostly cancels the benefit of the string tension at the pin holes. Also see Peter's last picture on page 2: after the bridge has tipped enough to create an air gap in the pin area, "R" goes to zero, so the string tension through the holes can now be effective at preventing further rotation. But with a glued joint, R and T mostly cancel each other.

I just thought of another way to get the R force to go away, or more accurately, move it to where it's more useful: cut out a hollow in the middle of the bridge's footprint, as below. The ballend force on the plate is now reacted around to form compressive (clamping) stresses at the front and tail sides of the bridge. At the tail side, that compression will serve to reduce the tensile reaction stresses caused by torque. So, while there's less total glue area, the glue that experiences the highest tensile stress (the tail edge) should have less of it. Shear stresses would be higher, though. Hollows like that are used in other clamping situations, where you want the clamped object (like the bridge) to have a more stable footprint. Food for thought.

[Jeff Highland]

I'm with Mark here.
The fact that in his last experiment without glue, the bridge just sits there with a small separation shows there is no net rotational torque on the pinned bridge. If there was, it would continue to rotate.
Do the same with a pinless bridge.........
Pinned bridges do peel up from the back, but it is just the deformation of the soundboard which is causing this.
Its too long since I did much analysis, but I think there is some confusion between action and reaction happening with some of those diagrams.

[Chuck Tweedy]

Jeff, you say: "there is no net rotational torque on the pinned bridge"
That is true, any object that is not moving has no net forces on it.
Glue the bridge down and the same statement is true for the pinless bridge.

What seems to be the confusion is this: Once the pin/piness bridges are glued down, the two assemblies becomes much more the same (forces, stresses, strains, etc.)

The stresses inside the material/assembly cause the peeling, this is what needs to be understood. Mechanics of materials is the subject at hand here http://en.wikipedia.org/wiki/Strength_of_materials

[Barry Daniels]

I think the role of the strings being anchored at the bridge plate is being over-rated in preventing bridge delimitation. The ball ends do provide an anchor to the bridge, but it is not a rigid anchor since it is transmitted through stretchable strings. This element of downward force affects the bridge movement but not so much for the bridge's glue joint. A tiny bit of movement there will negatively affect the integrity of the bond which may ultimately lead to the bridge peeling off at some point in the future.

[Jeff Highland]

Jeff, you say: "there is no net rotational torque on the pinned bridge"
That is true, any object that is not moving has no net forces on it.
Glue the bridge down and the same statement is true for the pinless bridge.

What seems to be the confusion is this: Once the pin/piness bridges are glued down, the two assemblies becomes much more the same (forces, stresses, strains, etc.)

The stresses inside the material/assembly cause the peeling, this is what needs to be understood. Mechanics of materials is the subject at hand here http://en.wikipedia.org/wiki/Strength_of_materials

Thanks Chuck, but I don't need a reference to wikipedia
You really can't use a free body diagram to analyse the stresses on a glued joint within that body.
If you want to do a Free body diagram of bridge, soundboard and bridgeplate you would have to separate it at the front and rear edges,
Separate it at the bridge/ soundboard junction if you want to analyse stresses on the glue joint.

[Chuck Tweedy]

I'm not sure I should respond, because I really don't want to offend, and it does not seem that I'm making any headway, however...

Jeff, if you had followed that link and searched for the term "free body" on the page - it does not exist there.
Because a free body diagram is not the analysis that is needed to see if there is peeling stress at the back-edge of the bridge glue joint. David Malickey already qualified his pictures with this statement, he's just paining broad-brush concepts of what is going on with the bridge. And he's pretty much right on the money. The strains from all of the stresses he has drawn have been observed by we who have repaired multiple bridge failures. It's all there, peeled back edge, creased front edge, puckered bridge plates from the ball-ends, split bridge at the saddle slot. Those are all from the stresses in the drawings above.

Anyway, on that evil Wikipedia page is a section named "Failure Theories". Those theories address exactly what we are talking about. The fact that the back edge of the bridge peels (fails) up due to internal stresses in the bridge/top/bridge-plate assembly.
I'm out.

[Jeff Highland]

I do not doubt all the things you have observed.
However I would not attribute them to the mechanism of the bridge itself rotating (assuming intact bridge plate), but rather that the uplift of the ball ends on the bridge plate is causing deformation of the bridgeplate/soundboard which induces the peeling at the gluejoint at the rear of the bridge.
This is a very different situation to a pinless bridge where the glue line takes all the load

[David Malicky]

Its too long since I did much analysis, but I think there is some confusion between action and reaction happening with some of those diagrams.

Jeff, Could you provide more detail? It's important to get the FBDs right so we can make sense of the mechanics. If there's an error, I would like to know about it specifically.

However I would not attribute them to the mechanism of the bridge itself rotating (assuming intact bridge plate), but rather that the uplift of the ball ends on the bridge plate is causing deformation of the bridgeplate/soundboard which induces the peeling at the gluejoint at the rear of the bridge.

That's an interesting alternative theory and is worth looking at. I don't have time to draw them now; I'd suggest starting by posting the corresponding FBDs of the Bridgeplate + portion of the Top between plate and bridge.