Purpose of bridge pins?

[Seth Ellis]

Hey all. This is a very interesting discussion.

I was wondering if anyone strings their guitars from the underside of the soundboard. I put a sound port in the side of my guitars and it would be easy to string from inside. Just a very small hole and the ball end would fit snug against the bridge plate.

Would you drill the holes straight through, angled so the ball ends are under the saddle, or angled away toward the back side of the bridge. Have you seen this done before?

Best,
Seth

[Jeff Highland]

David, since the question that set this all off was whether the glue joint is subject to less stress on a pinned bridge than a pinless, can you model for a pinless and put it side by side?

Seth, I have done this on a couple of ukuleles. just drilled straight though at the location you would normally put pins.

[Seth Ellis]

Thanks Jeff,

How well do you think it worked for sound and longevity? I think that a small hardwood "inlay" in the bridge plate where the ball ends would stop might be good on a steel string. Then I could make a little string well for each ball end.

I think drilling at an angle either away from or towards the saddle could have an effect on sound and/or how the bridge pulls up/twists. I suppose that bridge pin holes could be drilled at an angle also, but I've never seen this done before.

Cheers,
Seth

[Mario Proulx]

I suppose that bridge pin holes could be drilled at an angle also, but I've never seen this done before.


I've been doing that for years....

[Peter Wilcox]

I was wondering if anyone strings their guitars from the underside of the soundboard. I put a sound port in the side of my guitars and it would be easy to string from inside. Just a very small hole and the ball end would fit snug against the bridge plate.

That's how I'm making the bridge for my bass now. And it won't be glued down.

But then, what do I know?

[Rodger Knox]

Might I presume that you're angleing the pins to the rear at about 10°?

[Trevor Gore]

I was wondering if anyone strings their guitars from the underside of the soundboard. I put a sound port in the side of my guitars and it would be easy to string from inside. Just a very small hole and the ball end would fit snug against the bridge plate.

That's how I'm making the bridge for my bass now. And it won't be glued down.

But then, what do I know?

...that the string won't act like a big cheese cutter?

[Peter Wilcox]

...that the string won't act like a big cheese cutter?

What? You mean I can't make the bridge out of cheese?
Damn, I guess I'll have to rethink this.



Actually, my strings are made of weedeater line, so I should be OK unless I start up the weedeater.

[Trevor Gore]

Actually, my strings are made of weedeater line, so I should be OK unless I start up the weedeater.

Interesting! Especially the star section stuff.

I was just thinking that if you don't glue the bridge, the shear transfers to the front of the hole that goes through the top and bridge plate. The top won't resist the inline shear from the string, which means your bridge plate would have to be big enough and tough enough to take it all.

[Peter Wilcox]

The bridge plate is maple, and 1/4" thick, so should be substantial enough to withstand the shear, especially from plastic strings whose tension (I'm assuming) is less than steel, and whose total diameter for the 4 strings is >0.5".

If not, I have an alternative method for dealing with it before I throw in the towel and glue the bridge. The reason for not gluing, at least initially, is that I can try different bridge configurations simply by loosening the strings and replacing the bridge.

[Mario Proulx]

And you don't think that a 1/4" thick bridge plate is a bit too heavy???????????

Don't bother trying different "bridge configurations", because you've already killed any potential to be gained or lost via different bridges.

Sheesh! I knew I should have stayed out of this absurd thread. An absolute waste of time. Y'all continue on your own...

[Michael Lewis]

One purpose of a pin type bridge I enjoy is the fact the strings can be removed and reinstalled in short order to facilitate set up work or other repair access.

A firmly glued bridge sounds better than one that is partially glued (starting to lift). I don't imagine a non glued bridge would sound better.

I have to agree with Mario regarding bridge plate thickness, many old Martins that sound so good have plates about .100" (2.5mm). Now if you can get a thick bridge plate to sound good and loud then good for you, we can learn something from your design, but until you can show an improvement I think you are chasing a prospect of diminishing returns.

[David Malicky]

Steve, Barry, and Mario, glad you like the analysis. Barry, impedance mismatch is a vibrations issue (masses), but one could say there is a rough analog in how stresses have to negotiate the mismatch of areas at the tail.

Mario, I do plan to try smaller and larger bridges and plates, but I'm not sure I can go down to 1.0" without a new bridge model (parameters often run into other things). I changed the load to 28 lbs, which is conveniently about the average of the A, D, G, B strings for lights.

Jeff, great suggestion, thanks -- I've got it on the list.

I made a few refinements to the model:
- The slice is now .45" thick (in the lateral direction), which corresponds to a 2.25" spring spacing (last model was 0.5").
- The bridge pin hole is now a 5 degree tapered cone.
- The string load is 28 lbs (it's a linear system, so any other string tension can be inferred by ratios).
- The materials are now orthotropic. Here are the orthotropic properties I used (data from the Wood Handbook and Trevor's book, all moduli in ksi):
Conventions
1=Long, 2=Radial, 3=Tangential
Poissons Ratio, NuPQ: P=Applied stress direction, Q=Lateral deformation direction
Rosewood
E1 = 2045, E2 = 284, E3 = 126, G12 = 252, G13=154, G23 = 52
Nu12 = 0.37, N13 = 0.60, Nu23 = 0.64
Spruce
E1 = 1579, E2 = 163, E3 = 80.5, G12 = 148, G13 = 143, G23 = 10.3
Nu12 = 0.40, N13 = 0.47, Nu23 = 0.48

Material Orientations
Bridge: Riftsawn at 45 deg, ring lines as viewed by player: \\\\
Top: Quartersawn
Plate: Riftsawn at 45 deg, same as bridge.

The deflection plot for orthotropic materials is similar to the isotropic case.

Here are the corresponding stress plots:
Stresses in the vertical direction (Syy), sliced through centerline. The "stress column" from the ball-end force is more spread out compared to isotropic, probably because the QS spruce top gives a "cushion" in the vertical direction (E3 is very low), and is a nice "bridge" in the long direction (E1 is very high). The stress concentration at the rear extends only a shallow distance into the top, probably for similar reasons.

Stresses in the vertical direction applied to the top surface. The R distribution is similarly more spread out.

[David Malicky]

Here are the Von-Mises stresses on the centerline and top surface. I changed the stress scale compared to the isotropic plots, as the VM stresses peaked about twice as high. Compared to iso, the longitudinal stresses in the top propagate a long way under the bridge, probably because the top's E1 is so high compared to E2 and E3 of the bridge and plate.

I'll post some line plots that more clearly compare stresses due to different materials, hopefully tomorrow.

[Steve Senseney]

I have stayed out of this as I don't feel I have much to offer.

First question--Would our bridge design work better if we tapered all of the edges to a much thinner edge? This would eliminate the "stress riser" effect.

Second question--All of the stress analysis is pretty impressive. Is it relevant without including the bracing effect?

I agree about the "mass" of the bridge (and bridge plate) being an important aspect of what controls the sound of a guitar.

[Trevor Gore]

I can't do reality checks in my head in psi. I only put psi in my car tyres, everything else is Pa. (or MPa or GPa).

However, if I've done the conversions right, there's a lot of wood failure going on in this model!

[Rodger Knox]

As David and I have pointed out in previous posts, the relevance of this analysis is dependant on the simplifing assumptions, and how completely they are satisfied. While neglecting the bracing does reduce the relevance of the analysis, this type of modeling can provide some insight into the internal stresses at work. Each level of detail that's added to the model may increase it's accuracy and relevance, but it may also add another level of assumptions that are not completely satisfied and therefore degrade the accuracy of the model. This type of modeling usually reaches a point of diminishing returns after two or three iterations.
David, do you have numbers for the displacement? I'm interested in the translation and rotation, within an order of magnitude.
I'd like to see a separate saddle added to the model, if that's not too difficult. It would also be useful for the back of the bridge to be beveled at 60° and 45° to see the effect on the stress risers at the back of the bridge.
I don't believe this analysis can produce any real_answers(after all, we already know the real answer is 42), but it is worthwile for the insight that can be gleaned from the results.

[Seth Ellis]

Wow! This thread is hopping.

Mario, I think I misscommunicated above, but maybe not. With bridge pins, angling the holes makes sense. I was talking about stringing the guitar from inside with holes just large enough for the diameter of the strings. No pins. Are you saying you do this already? I'd be curious to see a picture and know how you angle the holes and if the angle matters.

Peter, how well does it work to string from inside. What do you think the advantages are of having no pins and having a specific break angle of the stings through the bridge?

Best,
Seth

[Peter Wilcox]

Peter, how well does it work to string from inside. What do you think the advantages are of having no pins and having a specific break angle of the stings through the bridge?

Seth, the holes in the bass I'm building are vertical from the bridge plate up through the top and out of the bridge. I did round them a bit toward the saddle at the exit from the bridge due to the thickness and material (plastic) of the strings. They're easy enough to string as the sound hole is large and on the bass side of the top on the upper bout. Each hole is just enough larger in diameter than the string to allow the string to pass through without having to force it, but otherwise having a fairly snug fit.

I doubt that there's any advantage to doing this, over a pinned bridge.

Don't extrapolate from what I'm doing to a steel string guitar. It is completely experimental and everything is different - twice the surface area, four times the air volume, completely different bracing arrangement, thicker bridge plate, different woods; the strings are lower tension, larger diameter, different material. My next plan is to bring the strings out of the top just at the rear of the bridge and over the top toward the saddle, with no holes in the bridge - maybe just some shallow grooves.

Don't ask me why - it's all pretty nebulous.

[David Malicky]

Steve, Trevor, and Rodger, thanks for the good points, questions, and suggestions. Comments like this are very helpful because they'll either improve the model, make its limitations more clear, or both.

Steve and Rodger, yes, after I made the first Iso model I tried some thinner and tapered edges on the bridge rear corner. But I was getting ahead of myself as the basic model first needed the kind of refining and vetting that is going on now. Those initial runs showed a 1/16" thick ledge reduced the stresses near the corner by about 1/2. I'll be running geometry mods more methodically in the future.

All, yes, the 2.5D nature of the model and lack of bracing is a major simplification. At least some string torque is off-loaded laterally/torsionally to the bracing. So this 2.5D model's stresses are probably over-estimates, and should mainly be used for relative comparision within model variations. For that, I think the model is appropriate, but a 3D model is planned for future. I'd like to stay in 2.5D-land until those effects are better understood, also because the meshing and solution only take about 6 minutes, whereas 3D will need hours or more. (Model development usually takes many dozens of runs to fine-tune the mesh, validate, and catch errors.)

On units, I realized that I gave the material properties in ksi (kpsi) but I didn't state that the plots were in psi -- sorry! My brain is calibrated in pounds and inches, but in the future I'll try to post plots with both psi and MPa scales. So on the prior plots, the Syy ones ranged from -450 psi to 450 psi (-3.1 MPa to 3.1 MPa), and the Svm ones ranged from 0 to 2000 psi or 4000 psi (13.8 or 27.6 MPa).

My aim for this model is to understand the interface stresses, but reality checks on wood failure like Trevor suggested are important. First, though, some general issues on stresses, plots, and failure criteria:
1. For orthotropic mats, von Mises stress has some problems. It does conveniently lump all stresses into 1 number, but von Mises (and principal) stresses are generally NOT the same across an interface of orthotropic mats (e.g., in the last plots, the high top stress migrated under the quiet bridge). Also, it isn't a good failure predictor for wood.
2. To describe the stresses across an interface, especially for orthotropic mats, the shear stress (Sxy) and normal stress (pressure, Syy) are probably best. They have to be equal and opposite across any interface (Newton's 3rd).
3. If the wood is in more than uniaxial stress, failure prediction needs a complex orthotropic criterion like Tsai-Wu (ugh). But we can at least look at ~uniaxial regions like the top surface behind the bridge--see below.
4. To predict glue failure, it depends on the type of glue. Regular PVA is probably ductile isotropic, so Tresca or Von Mises (calculated from Syy and Sxy) are good choices. I understand hide glue is extremely brittle (?), so max principal stress may be more appropriate. I don't know enough about Aliphatic PVA (Titebond). Does it have any ductility, like, even 2%?

So, back to the reality check on wood failure. The last plots for the top showed a large red region of high stress; querying that region showed a typical maximum principal stress of about 4600 psi, or 32 MPa (tension and compression on opposite surfs). At the very corner it goes to ~infinity, of course. The Wood Handbook says the compression strength parallel to grain of Engelmann and Sitka is 31-39 MPa. (One validation I ran was cantilever bending of an ortho spruce beam -- stresses and deflections were within 2% of textbook, so the solution of the 2.5D ortho model should be working normally... not that it simulates the braces, of course.) So the model stresses are similar to the compression strength of wood over a wide area (and higher near the corner) suggesting a good fraction of the actual string torque is indeed off-loaded to the braces.

Rodger, earlier I did a few runs with a very narrow slot behind the integrated "saddle". That allowed the bridge to hinge there, and made a "camel hump" in the pressure distribution, but didn't seem to affect the corner stresses. To do a downtown saddle, I'd need a contact condition between it and the bridge--doable but would slow the solution 10x. I can compare them to see if the simple slot is good enough. Or, it might work to replace the contact condition with some soft foam-like material with very low shear modulus. That would be speedy to solve, but behave similar to reality.

On displacements, the bridge rotates 0.73 deg (0.001" down at front, 0.018" up at rear), but the length of spruce fore/aft is rather arbitrarily set at 1" from the bridge (long enough for St. Venant to smooth end effects). I just ran some other validation runs and it looks like that length is having a small effect on the rear corner peak stresses. So I'm now doing a bunch of runs to find a length that is long enough to not affect the interface stresses. Will post updated results after that.