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  #31  
Old 12-22-2017, 12:55 PM
Alan Carruth Alan Carruth is offline
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I always find vector diagrams confusing....

Think of the static load of the string on the bridge as being of two sorts. One is the shear load; what the glue line between the bridge and the top would have to withstand if the strings came off the bridge at the level of the top surface. The other is a torque load, imposed by the fact that the strings can't be on the top, but have to be above it. These loads are going to be distributed differently depending on the geometry of the bridge.

As I understand it, the stress of the shear load in the glue line is not the same everywhere. I've seen this illustrated by the example of two sticks that have been glued together, and are being pulled along the axis. Imagine that one of the sticks is perfectly rigid, so that it can't stretch, while the other one can. The load on the joint at the end toward the stretchy stick will be high, since it's trying to pull away. However, the joint takes up some of that load, so as you go along the length of the joint the stress becomes lower and lower, reaching zero at the back end. Now look at it the other way: make the stretchy stick rigid and the rigid one stretchy: the diagram will look the same, but flipped. Of course, on a real glue line both parts are stretchy, so what you're actually going to see is a sum of both. That is, the shear stress will be high at the front an back ends of the joint, and lower in the middle. The low stress will be determined in part by the nature of the glue line. The total area under the curve will be the total shear load. Note that extending the glue line; making it longer along the line of the pull, reduces the amount of stress at the leading and trailing edges disproportionally. This is why 'belly' bridges work better than 'bar' bridges, at least in terms of staying down.

The torque load is a bit simpler, at least in the ideal. You've got the total tension of the strings acting at the top of the saddle, trying to rotate the bridge forward. The upward stress in the glue line is low at the foot of the saddle, and higher as you go further back, reaching a peak at the back edge. If the bridge were not glued down, but screwed down along the back edge only, the withdrawal force on the screw would be easy to calculate. If you have, say, 150# of string tension acting 1/2" off the top, and the screw is 1" behind the saddle, the upward load on the screw would be 75#, if I've done the math right. Since the glue acts over the whole surface you divide that up into however many microscopic screws you want, with each one taking part of the load, and the sum of all their contributions has to equal 75 inch pounds. Once again, extending the bridge in the back helps reduce the maximum load.

It's the maximum load along the back edge that determines whether the thing will lift or not. Most glues are not very good at resisting peeling loads, and that's what you have along the back edge of the bridge. Once the back edge starts to come up the stress increases, and the failure accelerates.

Bridges are not rigid, of course, nor are tops, and distortion in either can serve to alter the stress in the joint, usually in a way that increases it along the back edge. The closer things are to 'rigid' the more they will approximate the textbook ideals. So that's one reason you might want to make a bridge with some thickness; to keep it from flexing too much and peeling loose to soon. Ditto the top, by use of a well designed bridge plate.

The primary function of the bridge is to tell the string how long it is, so it will 'know' what note to make. It does this by being massive and stiff enough to make the top of the saddle look 'fixed', so that a wave traveling down the string will bounce off it. If it was too massive and stiff al the energy would stay in the string, and the guitar wouldn't produce any sound. If it's not massive and/or stiff enough the energy 'leaks' out too fast, and you get a note with lots of volume but no sustain. Somewhere in there is a 'sweet spot' that produces a good sound, and that's where most bridges are in practice.

The bridge is also the heaviest, and one of the stiffest, braces on the top, and that affects the way the top vibrates. Once again, there's a balance to be struck there, and the 'standard' bridge comes close to that.

Ultimately, the point is that there are a lot of considerations in play here. There are a lot of different ways to do a bridge, depending on how the top is put together, what sound you want, how much string tension you need to carry, and so on. As in any craft, tradition has acted to home in on things that work pretty well, so that it's hard to improve on the standard designs by much. On the other hand, a good craftsman, who knows why things are done the way they are, will know ways to 'tweak' things to optimize them. For the most part in such complex systems we don't use calculations but rely on rules of thumb and intuition. Again much of this is embodied in tradition, so we end up doing things that work without necessarily knowing why in any rational sense.
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  #32  
Old 12-22-2017, 08:04 PM
Trevor Gore Trevor Gore is offline
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Quote:
Why is a bridge as thick as it is generally accepted to be ?
Because that's how it's generally accepted to be. That doesn't make it right (or wrong). If you have the engineering chops, you can make it pretty much what you like. For example, keeping a fairly traditional bridge shape and footprint area, you can take the back side of the bridge down to something like this:



Depending what you choose for materials (the one above is Bloodwood) you can make very low mass bridges. For example, a bridge like the above made of American black walnut will weigh about 14 grams. That's pretty light for a bridge, where some people consider 60 grams to be in the normal range. BTW, that dark line you see in the bridge wing is carbon fibre.

And, of course, it changes the sound of the guitar. First up, a low mass bridge is easier to accelerate under the meager vibration forces produced by the strings, and as sound radiation is proportional to the acceleration of the guitar top, the guitar gets louder. It can also get brighter and maybe somewhat raucous, (think flamenco) which is fine if that's what you (or your customer) wants, but it is a long way from sounding like a banjo (which works on different principles). Having made guitars with some very low mass bridges and some with more normal mass bridges, I would say that it is pretty hard to make a bridge too light whilst still maintaining fairly traditional outline shapes, materials and foot print area. Much easier to make it too heavy.

With regard to the stresses on the glue line, traditional simple analysis (rigid body diagrams etc.) whilst very useful in engineering in general, doesn't serve us well here, because the bodies under consideration are too far from being rigid for the usual assumptions to apply. The actual forces are very dependent on the local physical geometry and the variation in flexural rigidity as one transitions the bridge/top/bridge plate sandwich, to the top and bridge plate to just the top. At a section change (say bridge+top to just bridge) there is always a stress concentration and in a normal bridge failure mode (a peel failure from the back edge) it is the degree of that stress concentration that determines whether or not the glue line fails. The stress concentration can be seen on this finite element analysis of the bridge/top interface that was done by the late David Malicky (who also originated some of the other diagrams posted in this thread):



We can see in this diagram that the stress concentration factor is 10 or more at the back side of the bridge and is exacerbated by thick back edge of the bridge. By tapering the back edge of the bridge and by suitable design of the bridge plate that stress concentration factor can be reduced considerably, to the extent that the actual local stress on a well designed steel string bridge can be less than found on a typical classical guitar bridge where there is a large step-down from the tie block to a thinner, more flexible top, often with no bridge plate.

Quote:
The material used to anchor the pins or support the string ends becomes purposeless mass . Because of this the bridge can be trimmed to eliminate this now unnecessary mass or am I wrong about this ?
If you slot the bridge pin holes, you should be able to remove the bridge pins with no ill effect. Therefore not only is the mass at the back of the bridge "purposeless", so are the pins.

So you're not wrong, but you do need to understand what's going on to guide your design decisions.
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  #33  
Old 12-23-2017, 08:34 AM
LouieAtienza LouieAtienza is offline
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...was done by the late David Malicky...
Trevor, didn't realize or heard word of this. He was a great contributor to the CNC Zone, and wondered about his absence there.

----------------------------------------------------------------------------

In my last bridge iteration, I had tapered the wings more, and reduced the height of the bridge at the bridge pins. I do this in conjunction with a shift of my bridge plate a little further back.

[IMG]KIMG0069 by Louie Atienza, on Flickr[/IMG]

ediot: This is what happens when I tried to link an image from flickr from a cell phone; missed the whole image size thingie. Of course this was deserving of a lambasting by the elders...

Last edited by LouieAtienza; 12-23-2017 at 02:10 PM.
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  #34  
Old 12-23-2017, 10:39 AM
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Bruce Sexauer Bruce Sexauer is offline
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That oversized image makes this thread untenable on my iPad.
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  #35  
Old 12-23-2017, 11:06 AM
charles Tauber charles Tauber is offline
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Originally Posted by Bruce Sexauer View Post
That oversized image makes this thread untenable on my iPad.
It's not so great on a desktop computer either.

I'll reject for inclusion in posts internet images that are too large, for that reason. If posting my own images, I'll resize them for the purpose: the added labor is one of the reasons I don't often post my own images.
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  #36  
Old 12-23-2017, 02:13 PM
LouieAtienza LouieAtienza is offline
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Originally Posted by charles Tauber View Post
It's not so great on a desktop computer either.

I'll reject for inclusion in posts internet images that are too large, for that reason. If posting my own images, I'll resize them for the purpose: the added labor is one of the reasons I don't often post my own images.
It's one mouse click on a pop up menu with flickr. Maybe occasionally missed on my 42" desktop screen, but microscopic on a 4.5" smart phone in desktop mode.
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  #37  
Old 12-23-2017, 02:48 PM
Otterhound Otterhound is offline
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Quote:
Originally Posted by Bruce Sexauer View Post
Otterhound: You appear to be confusing shear with torsion (twisting). Shear forces will remain the same as they are dependent on string tension, which does not change. Torsion is a function of leverage and can be loosely defined, in terms of the bridge, by the length of the base in relation to the height of the saddle off the top. I.e.: 1 3/8" x 1/2", which is typical in my work. Perhaps counter-intuitively, it doesn't make a lot of difference whether the bridge is pins or non-pins. The conventional bridge nearly everybody uses is rigid enough that it is best thought of as a solid unit including the saddle and the bridge pins AND the strings from the saddle to the ball end. By extension, the top and bridge plate directly under the footprint of the bridge are part of the mass equation, but perhaps less so of the torsional equation, and not at all of the shear equation.

The important point here is to think of the bridge (from the side) as a solid triangular geometric form with a specific variable footprint, depending on design.

The problem with lowering the height is that since the shear does not change, the footprint cannot be diminished, and the top structure must be able to hold the tension, while at the same time the torsion has been reduced below the level required to drive the top. The up shot is that the guitar may act overbuilt, sound thin, and lack volume. . . or so I'd expect.

I have written of this concept before and taken some criticism, but it is how I think of it and it has served me well.

Also, your suggested bridge plate is a bit thick IMO. I believe few go over .1", and I find .075" very adequate.

This thread has proven more interesting that I first expected.
I picked random numbers that were very easy to work with but what I considered to be somewhat realistic .
I do agree that .125 is overkill for bridge plate thickness .
The point was to illustrate the difference .
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  #38  
Old 12-23-2017, 02:54 PM
Otterhound Otterhound is offline
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Originally Posted by runamuck View Post
I think you're wrong. For a thought experiment, imagine a bridge an inch thick compared to a bridge a foot thick . The distance the string travels vertically is irrelevant until it leaves at X angle.
The point of angle X , as you refer to it , makes a difference when you consider the length and how much leverage it creates at X .
1 pound at the end of a 1/2" lever will not create the force of 1 pound at the end of a 1" lever .
Please consider this .
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  #39  
Old 12-23-2017, 04:07 PM
runamuck runamuck is offline
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Quote:
Originally Posted by Otterhound View Post
The point of angle X , as you refer to it , makes a difference when you consider the length and how much leverage it creates at X .
1 pound at the end of a 1/2" lever will not create the force of 1 pound at the end of a 1" lever .
Please consider this .
But doesn't the lever start at angle X (the bridge) rather than under the bridge plate?
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  #40  
Old 12-23-2017, 04:46 PM
Otterhound Otterhound is offline
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Originally Posted by runamuck View Post
But doesn't the lever start at angle X (the bridge) rather than under the bridge plate?
Tension is present along the entire string path , is it not ?
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  #41  
Old 12-23-2017, 05:46 PM
runamuck runamuck is offline
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Originally Posted by Otterhound View Post
Tension is present along the entire string path , is it not ?
Yeah, but the tension is the same from the bridgeplate to wherever the string angles on the bridge regardless of how long that distance is - whether it's an inch or a foot. I think!
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  #42  
Old 12-23-2017, 07:14 PM
charles Tauber charles Tauber is offline
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Quote:
Originally Posted by Otterhound View Post
1 pound at the end of a 1/2" lever will not create the force of 1 pound at the end of a 1" lever .
Please consider this .
That is exactly what it will do. The magnitude of the force is the same.

What is different is the leverage/mechanical advantage/moment/torque.

Those are two different things.
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  #43  
Old 12-23-2017, 08:38 PM
LouieAtienza LouieAtienza is offline
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Quote:
Originally Posted by Otterhound View Post
The point of angle X , as you refer to it , makes a difference when you consider the length and how much leverage it creates at X .
1 pound at the end of a 1/2" lever will not create the force of 1 pound at the end of a 1" lever .
Please consider this .
Torque is directly proportional to the radius of the lever arm since it is a product of said radius and the force. But in my view that "lever arm" runs from the base of the front of bridge, to the top of the saddle. Since the saddle is always set in from the front of the bridge, the resultant lever arm is actually "tilted" away from the neck a few degrees. The torque would be greatest if the force were at exactly 90 degrees to the lever arm but it actually greater than 90 (relative to the direction of the lever arm). Thus the torque is a product of the length of the lever arm, force, and sine of the angle between lever arm and force.

Consider two extremes. To simplify explanation I'll pretend the strings are attached to the top of the bridge. If I had a bridge of zero thickness, and a saddle of zero thickness, and the string pull was in the direction of the saddle pulling toward the butt of the guitar, there would be zero torque on the bridge. You can do the opposite, have the string pull toward the nut flat against the body, and the torque would also be zero.

So, given a same string height, you can reduce the torque at the bridge about its leading edge by simply moving the saddle back. However I believe this would have a similar effect to having a lower string height above the top - the strings would play stiffer, you'd probably lose some bass...
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  #44  
Old 12-23-2017, 08:40 PM
Otterhound Otterhound is offline
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Originally Posted by charles Tauber View Post
That is exactly what it will do. The magnitude of the force is the same.

What is different is the leverage/mechanical advantage/moment/torque.

Those are two different things.
Forgive my formal training .
Communication is the ultimate goal .
There are 2 points where torque is applied to a bridge as we are discussing it .
Where the string emerges from the bridge and where the string breaks over the saddle/s .
By lowering the point at which the string emerges from the bridge , you lessen the leverage applied and torque at that point .
There is another idea that I want to pitch here but I don't know how to relate it verbally . It has to do with the line from the point where the string emerges from the bridge to where the applied loading by the string bisects the top and how that moves rearward as the emergence point lowers . Oh well , it probably is meaningless anyway .
I do have a tendency to overthink things and then verbalize them .
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  #45  
Old 12-23-2017, 08:41 PM
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Rodger Knox Rodger Knox is offline
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Quote:
Originally Posted by Otterhound View Post
The point of angle X , as you refer to it , makes a difference when you consider the length and how much leverage it creates at X .
1 pound at the end of a 1/2" lever will not create the force of 1 pound at the end of a 1" lever .
Please consider this .
The only angle that makes any difference is the break angle, which is the deflection the string makes as it passes over the saddle. See the FEA plot in post #32, it was developed and refined by people who understand the math and physics, and it's a decent model.
Quote:
Originally Posted by runamuck View Post
But doesn't the lever start at angle X (the bridge) rather than under the bridge plate?
I agree.
Quote:
Originally Posted by Otterhound View Post
Tension is present along the entire string path , is it not ?
Yes, what's your point? It exerts a compressive force on the bridge plate, and a compressive force on the top of the saddle. After it passes the saddle, the string is a rigid part of the bridge.
Quote:
Originally Posted by runamuck View Post
Yeah, but the tension is the same from the bridgeplate to wherever the string angles on the bridge regardless of how long that distance is - whether it's an inch or a foot. I think!
The tension in that section has no effect other than the compression on the bridgeplate and top of saddle.
Quote:
Originally Posted by Otterhound View Post
Forgive my formal training .
Communication is the ultimate goal .
There are 2 points where torque is applied to a bridge as we are discussing it .
No, there's only one.
All these forces have been discussed at length, and the experts are all in general agreement about what they are. This is a relatively simple statics problem, dynamic response is where it gets more difficult.
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Last edited by Rodger Knox; 12-23-2017 at 08:48 PM.
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