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  #61  
Old 12-24-2017, 04:19 PM
Wozer Wozer is offline
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Originally Posted by LouieAtienza View Post
1: The tension of the string at both sides of the saddle are the same, barring any excessive friction causing the string to bind at the saddle. But because any "stretch" between saddle and pin hole is insignificant in relation to the length o the string, we can think of said length as a solid, rigid piece of the bridge, therefore the center of rotation of the bridge, relative to the plane of the top, would be at that point at the front bottom of the bridge, and the "force" of the string is acting on the top of the bridge. But the "lever arm" is actually tilted since the saddle is set behind the front of the bridge (i.e. the angle is not 90 degrees but greater), so the torque is not force times distance. IT would be force times lever arm distance times the sine of the angle from the lever arm to the string. Whether the nut is below the saddle makes a tiny difference since it's only a couple extra degrees. Of course if the saddle coincided exactly perpendicular to the "fulcrum point" the formula is still force times distance times the sine of the angle, but sine of 90 degrees is 1 so it is not included in the equation. But the sin cannot be greater than 1, it is always less so the bridge "sees" less torque than what the string tension would imply.

2: Covered in the response to #1, above.

While there is mathematics involved, this is actually a physics problem in the area of mechanics, not mathematics.
my error was speed reading the post by David Malicky as MIMF and not understanding the T in the diagram on page two of the thread stood for Tension not τorque...well duh.

that being said, of course my statement of where the nut lies relative to where the strings ride the top of the saddle is irrelevant...and of course tension is the same on either side of the fulcrum (again, I was relating to τorque as defined by angles not to tension...again, well duh)

thank you for slapping me up the side of my head an making me realize the errors of my thought process...
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  #62  
Old 12-24-2017, 07:35 PM
runamuck runamuck is offline
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Originally Posted by Rodger Knox View Post
Where the string exits the top of the bridge up to the saddle is part of the bridge, that is, a rigid bridge/top/plate structure.
Yeah, I understand that now. Thanks, Roger.
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  #63  
Old 12-24-2017, 10:21 PM
Alan Carruth Alan Carruth is offline
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Just to muddy the waters a bit...

I did some experiments a few years back looking at the relative contributions of string height off the top and break angle to sound. I modified a Classical guitar bridge by drilling more holes in the tie block to make it an 18-hole bridge. This allowed me to tie the strings in two different ways to produce different break angles over the same saddle. By passing the string through the center hole ('normal' tie) I got a 25* break with the strings 11mm off the top. By passing the string over the top of the tieblock before going through the center hole ('high' tie) I got a 6* break over the same saddle. By then putting in a tall saddle, which put the strings 18mm off the top, I got back to the 25* break over the saddle. To give away the punch line on the original question; changing the string height off the top made it sound diifferent, but changing the break angle without changing the string height sounded the same. But, for purposes of this discussion...

One of the things I measured was the displacement of the bridge, both the rotation and the vertical displacment, as the strings went from no tension to full tension. What I found was interesting.

When I tightened up the strings the top was pushed downward, and the bridge rotated forward, with the back edge coming up. There is a point somewhere behind the saddle I'm calling a 'centroid', which was pushed down by the 'average' amount. This vertical displacement was the same (+/-) for the two cases where the string height was the same, and greater when the strings were higher off the top, as you'd expect. However, the 'centroid' location was different, depending on the break angle: with the low 6* angle it was 20mm back from saddle, while with the 25* angle it was 17mm back for both string heights. Of course, with the higher saddle there was both more rotation and greater vertical displacment.

Here's the model I came up with.

Suppose the bridge was glued to a top that was not strechy, but was perfectly flexible; something like a thin, strong piece of paper. As you put tension on the string it will try to form a straight line through five points: the nut, the top of the saddle, the tie block where the string goes in and comes out (to the extent that's possible), and the top of the tail block. Ultimately the string tension is being carried between the nut and the top of the tailblock, assuming those are 'fixed' points. The saddle is pushed down and the tieblock is pulled up. The stiffness of the real top prevents the line of pull from becoming straight, but that's where it looks like it wants to go.

So, it seems that the strings do pull the back of the bridge up as they push the saddle down. Overall the bridge on this guitar was pushed downward by the same distance (more or less, given measurement uncertainty) when the string height was the same and low, and more when the strings were higher off the top, and there was more rotation with the higher strings.

I suppose now we can throw a few bricks at each other about how to modify this for a steel string pin bridge, or a pinless one. Somebody ought to repeat this experiment just to show me where I screwed up. I'm going to bed. Merry Christmas everybody!
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  #64  
Old 12-25-2017, 10:33 AM
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Rodger Knox Rodger Knox is offline
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Quote:
Originally Posted by Alan Carruth View Post
One of the things I measured was the displacement of the bridge, both the rotation and the vertical displacment, as the strings went from no tension to full tension. What I found was interesting.

When I tightened up the strings the top was pushed downward, and the bridge rotated forward, with the back edge coming up. There is a point somewhere behind the saddle I'm calling a 'centroid', which was pushed down by the 'average' amount. This vertical displacement was the same (+/-) for the two cases where the string height was the same, and greater when the strings were higher off the top, as you'd expect. However, the 'centroid' location was different, depending on the break angle: with the low 6* angle it was 20mm back from saddle, while with the 25* angle it was 17mm back for both string heights. Of course, with the higher saddle there was both more rotation and greater vertical displacment.

Here's the model I came up with.

Suppose the bridge was glued to a top that was not strechy, but was perfectly flexible; something like a thin, strong piece of paper. As you put tension on the string it will try to form a straight line through five points: the nut, the top of the saddle, the tie block where the string goes in and comes out (to the extent that's possible), and the top of the tail block. Ultimately the string tension is being carried between the nut and the top of the tailblock, assuming those are 'fixed' points. The saddle is pushed down and the tieblock is pulled up. The stiffness of the real top prevents the line of pull from becoming straight, but that's where it looks like it wants to go.

So, it seems that the strings do pull the back of the bridge up as they push the saddle down. Overall the bridge on this guitar was pushed downward by the same distance (more or less, given measurement uncertainty) when the string height was the same and low, and more when the strings were higher off the top, and there was more rotation with the higher strings.

I suppose now we can throw a few bricks at each other about how to modify this for a steel string pin bridge, or a pinless one. Somebody ought to repeat this experiment just to show me where I screwed up. I'm going to bed. Merry Christmas everybody!
Thanks for that, I don't think I've seen those results before, although I've seen the break angle many times. I believe that there's no need to repeat the experiment, it looks to me to be completely consistant with the rigid brige/top/plate model and the more detailed FEA analysis, so it would be empirical data in agreement with a mathematical model. On the other hand, duplication of an experiment is never a bad idea. I think a test mule would be required, with a bridge that has the pin holes differing distances from the saddle. I'd use three pairs, with three saddle heights. The rest would replicate Mr. Carruth's procedure as closely as possible.
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  #65  
Old 12-25-2017, 01:32 PM
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Bruce Sexauer Bruce Sexauer is offline
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Originally Posted by runamuck View Post
In 2D, isn't there a fulcrum at each change of angle?
There is at least 1 change as the string exits the bridge and then another at the saddle.
Again, the entire bridge must be viewed as a unit, functionally. It does not matter what the string does before it exits the bridge unit. . . unless it exits it again AND has tension on it at the other exit. Which situation I have not seen.
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  #66  
Old 12-26-2017, 05:40 AM
Otterhound Otterhound is offline
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Soon enough , I am going to put together a test mule that should put the proof in the pudding .
I am curious about the results and will share them regardless of outcome .
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  #67  
Old 12-26-2017, 08:53 AM
printer2 printer2 is offline
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Pictures would be nice.
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  #68  
Old 12-26-2017, 10:52 AM
LouieAtienza LouieAtienza is offline
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Quote:
Originally Posted by Alan Carruth View Post
Just to muddy the waters a bit...

I did some experiments a few years back looking at the relative contributions of string height off the top and break angle to sound. I modified a Classical guitar bridge by drilling more holes in the tie block to make it an 18-hole bridge. This allowed me to tie the strings in two different ways to produce different break angles over the same saddle. By passing the string through the center hole ('normal' tie) I got a 25* break with the strings 11mm off the top. By passing the string over the top of the tieblock before going through the center hole ('high' tie) I got a 6* break over the same saddle. By then putting in a tall saddle, which put the strings 18mm off the top, I got back to the 25* break over the saddle. To give away the punch line on the original question; changing the string height off the top made it sound diifferent, but changing the break angle without changing the string height sounded the same. But, for purposes of this discussion...

One of the things I measured was the displacement of the bridge, both the rotation and the vertical displacment, as the strings went from no tension to full tension. What I found was interesting.

When I tightened up the strings the top was pushed downward, and the bridge rotated forward, with the back edge coming up. There is a point somewhere behind the saddle I'm calling a 'centroid', which was pushed down by the 'average' amount. This vertical displacement was the same (+/-) for the two cases where the string height was the same, and greater when the strings were higher off the top, as you'd expect. However, the 'centroid' location was different, depending on the break angle: with the low 6* angle it was 20mm back from saddle, while with the 25* angle it was 17mm back for both string heights. Of course, with the higher saddle there was both more rotation and greater vertical displacment.

Here's the model I came up with.

Suppose the bridge was glued to a top that was not strechy, but was perfectly flexible; something like a thin, strong piece of paper. As you put tension on the string it will try to form a straight line through five points: the nut, the top of the saddle, the tie block where the string goes in and comes out (to the extent that's possible), and the top of the tail block. Ultimately the string tension is being carried between the nut and the top of the tailblock, assuming those are 'fixed' points. The saddle is pushed down and the tieblock is pulled up. The stiffness of the real top prevents the line of pull from becoming straight, but that's where it looks like it wants to go.

So, it seems that the strings do pull the back of the bridge up as they push the saddle down. Overall the bridge on this guitar was pushed downward by the same distance (more or less, given measurement uncertainty) when the string height was the same and low, and more when the strings were higher off the top, and there was more rotation with the higher strings.

I suppose now we can throw a few bricks at each other about how to modify this for a steel string pin bridge, or a pinless one. Somebody ought to repeat this experiment just to show me where I screwed up. I'm going to bed. Merry Christmas everybody!
This is pretty much results I'd expect. I believe the similar results in "dip" with different "centroid" locations is just a matter that even with a 4 degree change in angle between lever arm and string, it only accounts for about a 6% change in torque.

I think a good visualization would be to imagine a plain string, under tension, which would represent the top. A thin piece of bar stock is silver-soldered onto the string at the approximate location of the bridge. Now if you took a small clamp and tightened it in the middle of the bar stock and pull the top of the clamp toward where the neck heel would be, you'd probably see the string "dip" more on the side toward the nut, because it is less "stiff" in relation to its length, even though it is at the same tension as the other side.

In the analysis of an actual guitar top, that part of the top from bridge to neck heel is made stiffer by design, so it will dip less than what it would if that area was braced the same as the area behind the bridge to give it the same stiffness. Also, while the bridge is rotating, it's taking the back area of the top along with it. But that back area of the top is also restricting how far the bridge can rotate. I've seen a couple plywood topped guitars that had the top deform so much that there was almost zero break angle at the saddle, almost to the point where the strings didn't even touch the saddle anymore!
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  #69  
Old 12-26-2017, 09:31 PM
Otterhound Otterhound is offline
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Pictures would be nice.
Of course .
In order to test purely for bridge factors , I will be using a Tele style body . No flex in the top wood on that to muddy the waters .
Even better is that it is a string through body , so testing can be done as a string through and with strings anchored to the bridge .
Using a shorty bridge with the saddles fully forward should do . No need to set intonation for this test .
And maybe 1 or 2 things that I am not going to divulge until the test is complete .
This way , no one loses face for making a wrong prediction of the results because I am keeping a select few very important factors undisclosed .
May you all have a wonderful 2018 .
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  #70  
Old 12-27-2017, 09:17 AM
printer2 printer2 is offline
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Quote:
Originally Posted by Otterhound View Post
Of course .
In order to test purely for bridge factors , I will be using a Tele style body . No flex in the top wood on that to muddy the waters .
Even better is that it is a string through body , so testing can be done as a string through and with strings anchored to the bridge .
Using a shorty bridge with the saddles fully forward should do . No need to set intonation for this test .
And maybe 1 or 2 things that I am not going to divulge until the test is complete .
This way , no one loses face for making a wrong prediction of the results because I am keeping a select few very important factors undisclosed .
May you all have a wonderful 2018 .
I look at being wrong about something for all to see as not a loss of face but as having humility in saying you are not all knowing (military clearances, budget cuts). I was once escorted out the door of a place of employment with no warning. At a later date when I was back with the company the engineer that picked up my work asked about a circuit I had designed in the simulation software I used.

I felt a bit embarrassed as it should have been obvious it was completely wrong, actually it was the only thing I would have liked to delete on my previous exit. I explained it was a brain fart moment and after drawing it up I realized my error but I kept the file as a template as the page was formatted how I wanted it. He was ok with the explanation, he nodded yeah he had moments like like that, and I went back up in his assessment of my work.

Pictures are not necessary, I just like seeing how others tackle a problem to see if I can learn something from them.
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  #71  
Old 12-27-2017, 09:52 AM
Mr Fingers Mr Fingers is offline
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I don't think this observation was made in the thread thus far: Where do bridges break? In my experience, lots of them crack at the saddle slot, for obvious reasons. The strings do not just press down (straight) on the saddle, but exert some forward pressure as well, and the saddle acts like a short level (like using a screwdriver blade) pushing the bridge top/front forward while also pressing back at the bottom of the slot. This happens in an area where there actually is not a whole lot of bridge material at all. So while the sonic considerations mentioned above are, or should be, primarily, one factor affecting the overall mass of conventional bridges is simply the durability factor. We do see a lot of forward-leaning saddles and deformed/cracked bridge fronts, at least with conventional slotted designs. Make it less massive, and we would see more.
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  #72  
Old 12-27-2017, 11:17 AM
Alan Carruth Alan Carruth is offline
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There are two simple ways to address the break-out of the slot. One is to make the slot further back from the front edge of the bridge, so there's more material there to resist splitting. I'm not sure why the tradition of putting the saddle so far forward has persisted for so long. The other is to angle the slot back, as seen from the side. If the saddle axis bisects the break angle over the top there is no net tipping force on it, and it will never break out the front of the slot. This is how violins get away with that tall, skinny bridge. Even a little bit of back angle helps. That and, of course, not using too much break angle.... As far as I can tell 15 degrees or so of break should be 'enough'. Rick Turner espouses the idea of tipping the saddle back by 9*. Not only does this reduce the tipping force, it also (slightly) increases the down force on a UST, and automatically adjusts the compensation when you raise or lower the saddle.
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  #73  
Old 12-27-2017, 06:54 PM
LouieAtienza LouieAtienza is offline
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Originally Posted by Alan Carruth View Post
There are two simple ways to address the break-out of the slot. One is to make the slot further back from the front edge of the bridge, so there's more material there to resist splitting. I'm not sure why the tradition of putting the saddle so far forward has persisted for so long. The other is to angle the slot back, as seen from the side. If the saddle axis bisects the break angle over the top there is no net tipping force on it, and it will never break out the front of the slot. This is how violins get away with that tall, skinny bridge. Even a little bit of back angle helps. That and, of course, not using too much break angle.... As far as I can tell 15 degrees or so of break should be 'enough'. Rick Turner espouses the idea of tipping the saddle back by 9*. Not only does this reduce the tipping force, it also (slightly) increases the down force on a UST, and automatically adjusts the compensation when you raise or lower the saddle.
I had a long discussion with Ken Parker around 2013/2014, and he strongly believes in not having more break angle than necessary.

I believe the reason the saddle is as far forward is because that's what allows the strings to "apply" the most "torque" on the bridge for the given string height off the top. You could move the saddle back, which does increase the "lever arm" of the edge of the front of the bridge to the top of the saddle, but that also "slants" that lever arm, which reduces the strings' ability to "torque" the bridge.
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  #74  
Old 12-28-2017, 03:29 PM
Alan Carruth Alan Carruth is offline
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Louie Atienza wrote:
"I believe the reason the saddle is as far forward is because that's what allows the strings to "apply" the most "torque" on the bridge for the given string height off the top."

Ummm....

I think you could say that the further the back edge of the bridge is from the centroid of rotation the lower the maximum stress is on the back edge of the glue line holding the bridge to the top. The centroid is not at the saddle location, so far as I can tell, but some way behind it, depending on the break angle. The actual torque of the bridge is a function of the string height above the top and the total tension, assuming the strings are attached to the bridge and not to some sort of tailpiece. At least, that's what my measurements said.

Torque on the top is mostly detrimental so far as I can tell. It does allow the tension change and longitudinal wave signals in the string to drive the top, but these hardly add any power (none that I could measure) and only change the timbre a bit.

I'll note that Flamenco guitars can be quite loud, even though they generally have the string much lower to the top than Classical guitars. In fact, I'd say that having the strings lower is what allows them to be so loud. The top can be built more lightly, since it doesn't have to resist as much torque load, and that makes it easier to move. This shows that torque doesn't produce sound, but can actually hurt sound production.

At any rate, if the goal is the reduce the peeling stress at the back edge of the bridge why can't you just make the bridge wider? It worked for Martin. If you're making it narrow to keep the weight down, why not use a lower density wood? With lower stress along the front of the slot from moving it back and/or slanting it you don't need the strength of rosewood or ebony to keep it from splitting out or peeling up.
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  #75  
Old 01-01-2018, 11:22 PM
Mr Fingers Mr Fingers is offline
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I don't know why that back-angled slot idea never occurred to me. It really makes sense. Thanks.
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