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Does changing the position of the bridge pin holes from a location very close to the saddle (a steep string break angle) to a distance further away from the saddle ( a lesser string break angle) change the amount of rotational forces acting on the bridge as a whole - and by extension less deformation of the soundboard? My intuition is telling me yes, but I know things are often not what they seem...at least to me.
Gerard

No. The amount of torque on the bridge is dependent only on saddle height and string tension.

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I don't agree. Imagine an extreme situation where say the bridge pins were mounted (for whatever hair-brained reason) in the tailblock. You would have all down force and little rotational. I think that the distance between the pins and the saddle makes a difference.

Hmmmmm. Maybe I should patent that idea....

The torque can be figured by plotting the position of the ball ends to the point of the top of the saddle. The answer is that torquing is effected and it isn't height alone. This is a typical resultant force equation

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John Hall
blues creek guitars
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I knew this would happen.

That's a totally different mechanical system than the OP's scenario. If we assume a perfectly rigid bridge, for a given sized bridge and a fixed saddle location, only the saddle height and string tension will determine the torque between the bridge and the top. Doing the vector diagram as John recommends will prove this. e.g.:

Let's say you take an 'L" shaped piece of steel with 1' long legs with a pivot point at the corner. Using a wire, hang a one pound weight off of the lower leg and you'll get 1 ft-lb of torque at the pivot point. Now attach the wire to the top leg but with the wire hanging over the bottom leg. Still 1 ft-lb or torque. Anchor the wire half way down the upper leg and you still get 1 ft-lb.

That said, bridges aren't perfectly rigid so there would be some minor effects from relocating the holes. The less rigid and bigger the difference in hole location, the more pronounced the effect would be.

Edit: To clarify, I'm talking about the interaction of the bridge with the top and the torque on the bridge. Changing pin holes locations will affect the down force on the saddle and I think that's what John's talking about. Neglecting flex issues, the torque is only dependent on the string tension and saddle height.

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I agree that if you keep the bridge pins on the bridge...and the bridge is something that is pretty stiff...then it really does not effect the stresses in the rest of the top to any noticeable amount.

As John mentions though, if you anchor the strings further back on the body (and off of the bridge) you do change the load on the top substantially.

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Excellent clarification - my statement only holds true if you keep the pins on the bridge and that's what I meant but failed to express.



Also totally agree with this statement.

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The torque that can be created will be influenced by 1 string tension , 2 angle of anchor . The resultant forces will then be turned into pull and push force. The only way you will have full string tension turned to torque loading , is if you attached the strings to the saddle. It isn't all as easy as it appears on first look. With the example of the loaded L beam , this is a good an analogy as can be .
Physics is physics and we cannot change that. Force will react in 2 directions when there is this type of displacement. The string tension will convert to pulling against the saddle and pushing down against the saddle. The 2 forces will couple to the creation of torque. The total torque available will be determined by where the string is anchored in relation to the saddle height. The wider the spacing, the larger the stressed foot print , the less rotational force applied to a given point.
Some may think the break angle is key here , but the reality is not the break angle but the true point where the force is applied. The ball end of the string will affix against the plate. that is the point of anchor . Then you have other engineering factors to figure in but you can now understand the pushing up against the ball end of the strings with the pushing down of the saddle . It can get cornfusin. The farther away those 2 points the less torque per sq inch. It had been a while since I did engineering math so I am sure someone out there has the equation and can punch in the numbers.
If you had an arch top and the strings were attached to a tail piece the amount of torque would be over a larger foot print. Thus the same torque energy is displaced over a larger foot print. If the total energy was the same the smaller foot print will have more torque per sq inch .
ahhh I knew I should have stayed awake in class more.

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John Hall
blues creek guitars
Authorized CF Martin Repair
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John, I really think you're mistaken here but, I could be wrong. Here's the thing though: I did stay awake in statics class because I found the topic fascinating and thus was one that I absolutely aced and knew cold. Now, it's been years since I've done any real engineering and I've been wrong before but this time, I'm pretty sure I'm not.



I think you're either confusing the diagram in your head or your definition of torque is wrong. It seems like you're mixing torque and linear forces or something like that. An arch top has zero torque on the bridge. In fact, as soon as you move the anchor points from the bridge, the bridge has zero torque* - now something else is torqued. Torque is a twist force and has nothing to do with energy and there's no such term as torque per square inch.

In my original example, the "L" section is the bridge. Again, consider the bridge & saddle perfectly rigid. If you attach the strings to the saddle, you get the same torque on the bridge as before but, you have zero downforce on the saddle.

* In real life there would be a little bit of torque due to friction between the strings and the saddle

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What were are talking about is rotational forces. The rotation on a bridge with the sting attached is more pronounced. The example on the archtop will have the linear force in string tension and rotaional force off the bridge totally and on to the tail block. I think we may be talking the same thing but the application of the force would be off the top. The tension off the bridge and on the tail block changes the force .
So lets keep the force on the bridge and that makes it easier. I think the point I want to make , not being a math wiz is that the forces must be figured from the strings end to the point of the saddle.

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John Hall
blues creek guitars
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Maybe we are. I don't know if you're an engineer or not but there's often confusion when engineers (or lawyers or doctors or MBAs) discuss engineering topics with laypersons because engineering terms have precise meanings.

In engineering, the components of force diagrams can be broken down into elements e.g. the bridge is an element, the top is an element etc and each element has specific forces working against it which can be described.

In the case of a guitar with a tailpiece, there are no rotational forces acting on the bridge and no rotational forces on the top. There are rotational forces acting on the tail-block though but not on the tailpiece. Again, for the bridge element of this system, there is zero rotational force acting on the bridge.

In the case of a pinned (or tied) bridge, there is a rotational force on the bridge. This rotational force can also be resolved as a pulling up force at the back of the bridge and a pushing down force at the front of the bridge. The rotational force does not depend on where the strings are anchored on the bridge (which is I think the OP's question) but simply the height of the saddle and the tension of the strings. Raising the saddle will increase the rotational force. Lowering it decreases it. That's it. There is also a rotational force on the top because the bridge is glued to the top. There is no rotational force at the tailpiece.

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Maybe what you're both trying to say is....

Torque stays the same as the bridge pins move. What changes is the ratio of downward force at the front edge of the bridge to upward force at the back edge.

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thanks . that is what I think I am trying to say. Please if I am wrong educate me

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John Hall
blues creek guitars
Authorized CF Martin Repair
Co President of ASIA
You Don't know what you don't know until you know it

I'm working at present on a project to look at the effects of break angle and saddle height on a classical guitar. It's a bit different system, but should be the same overall; e.g., if changing the break angle has a certain effect on a classical, it should have the same sort of effect on a steel string. At the moment, I'm in the middle of this, and I don't want to say too much about what I've seen so far because I haven't got it all worked out yet.

What I'd like to suggest is that some of you guys DO THE EXPERIMENT! It's not all that difficult, and mostly just takes time. We keep arguing about this sort of thing and throwing vector diagrams around but nobody DOES THE DARNED EXPERIMENT!

Alan
I have done a number of experiments on this . . On the steel strings I used typical martin style bridges. I have found that the break angle has less than one would think . The overall string height is more important . There seems to be a sweet spot where overall height is concerned. Too low and you loose too much energy transfer and too high of a height the over torque seems to be detrimental . The same of break angle. There seems to be a point where once you exceed the angle you loose tonal quality. I was surprised at how low the break angle could actually be .
The best analogy I can say is the break angle is more of a tone control and string height volume . That is an over simplification but what I seem to hear. I would love to hear what your findings are.
I haven't done anything on classical.

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John Hall
blues creek guitars
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Hi John,

String height above what? soundboard to strings? top of bridge to strings?

Thanks,

Dennis

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Dennis Leahy
Duluth, MN, USA
7th Sense Multimedia

If you look, you'll see I haven't mentioned anything about tone! From an engineering perspective, you don't need to do an experiment to know that so long as the strings attach to the bridge, the break angle won't affect the torque on the bridge. You do need to do an experiment to see if changing the downforce on the saddle changes tone though.

I have done some experiments as well, just on bandura bridges, not guitar bridges. Banduras have a tailpiece type design and the string passes over the bridge and through a hole out the back to the anchor point. What I'm finding is that so long as I have enough break on the string and saddle to keep the string from bouncing off the saddle (a 1/16" steel wire in my case) when plucked,I don't need much downforce at all (if any) to get a good tone. I get my break angle by drilling an angled hole in the bridge for the string.

I've been eliminating downforce by raising the anchor point of the strings, raising it more and more with each instrument and so far so good. I should also note that I glue my bridges down to the top and I don't think you'd get the same results with a floating bridge. I think that a floating bridge would need enough downforce to "pre load" the top and bridge to avoid buzzing.

As to this statement:

[quote] What changes is the ratio of downward force at the front edge of the bridge to upward force at the back edge. [/bold]

I'm not sure that's true, but I'm also not sure it's not. I'm leaning toward the "it's not true" but hedging because real wood does flex some so there may be some effects there. I'll see if my statics book is here at the house (I think it is) and see if I can find an answer.

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"hair-brained"?

Now I know why my hair is gray: gray matter from my hair brain leaking out.

Dennis

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Dennis Leahy
Duluth, MN, USA
7th Sense Multimedia

John:
Thanks; that fits.

The problem is that so often somebody will say they changed the break angle and the tone changed, When you ask what they did, they will say they raised (or lowered) the saddle height, so really, they changed two things; the height of the strings off the top and the break angle. So what was it that made the difference, and why?

I've got an 18-hole tieblock on one of my 'test mules'. Tieing the string in the normal manner gives a 25 degree break angle with the strings 11mm off the top. Running the strings off the saddle and over the _back_ of the tieblock gives a 5 degree break angle with the same saddle. I then made a tall saddle that puts the strings 18mm off the top, and yields a 25 degree break angle with the 'back' tie. So I've got two sets of data points with the same break angle and two with the same string height.

So far I've measured the change in deflection of the top in each case as the strings go from full tension to zero, 2" in front of and 2" behind the saddle. I've looked at the Chladni patterns, and taken an 'impulse spectrum' for each case. I've also done six automated plucks for each open string in each case and recorded the sound for analysis, which is what I'm doing now, with a LOT of help from a student who's an expert in statistical analysis. I'm also hoping to compile a six string strum of each case, and play those back for people in random pairs through earphones to see if they can hear any difference.

There do seem to be some patterns in the data so far, and, as usual, there seems to be more going on than the simple models suggest, but maybe less than some like to think. Again, I don't want to say too much until we can clear up just what's happening and suggest why.

I've already had one IM from somebody who's interested in the same thing, and has been thinking of experiments. That's GREAT! We can speculate until the cows come home, or we can get some data and settle the whole thing. And there's no such thing as too much data, so, John, let's see YOUR data.

I think the downforce of the strings is more static and the more you move the anchor location the larger the footprint can disperse the energy. This makes the dynamic force less at one given point but more points are accepting the forces . In a nut shell the same amount over a larger area downplays the lbs per sq inch.
I want to see .500 in front of the bridge of string height. That seems to be about the average sweet spot for the standard steel string bridge.
A top on a steel string will have 3 distinct areas affected by the forces of the strings. From the pins to the neck we have 1st a compressive load , as the strings are pulling on the top , secondly we have a rotational force from both the bridge and the neck block . They are both being twisted and exerting some force. Thirdly is the top behind the bridge is under tension.
What is your opinion on what the influences of these forces with changes in the torque from the bridge? If we use a tail piece the tensional force is eliminated . This is where I think the force footprint is expanded and the energy is just dispersed over a larger area. Remember that energy cannot be created or destroyed , it can only be transformed . So the total energy is the same and that would fit the physics .

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John Hall
blues creek guitars
Authorized CF Martin Repair
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You Don't know what you don't know until you know it

So, I consulted with two structural engineers who are a lot closer to this sort of thing than I am and here's the results:

If the Bridge & Saddle were perfectly rigid, it would not matter where the bridge pin holes were located, the top would "see" the torque in the same way. i.e. the top wouldn't know where the string was anchored, it would only "know" the height of the saddle.

Because the bridge is not perfectly rigid, this complicates things and the "pivot point" of the torque may move depending on bridge pin location. The torque on the top doesn't change, just to location of the moment changes. This effect will be bigger or smaller depending on the rigidity of the bridge.

None of this says anything about how this could affect tone though as I mentioned, even if the torque doesn't change, the downforce on the saddle changes which could do things.

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I have a mechanical engineering degree. There is a resultant relationship of the forces . if there is tension on the strings on a fixed pin bridge they will push down on the saddle . The ball ends will be pulling up. The coupled forces are causing a torque !

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John Hall
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I wanted to add that I agree that the data shows the amount of force is constant to the amount of tension on the strings. the farther the anchor point to the saddle allows the force to disperse on a larger footprint , thus a lower psi over the footprint. I think we may be seeing the same thing only I may not be getting my point understood. For that I apologize.

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John Hall
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Just for the record, I too have an engineering degree - although I'm an electrical engineer, I think my true calling should have been mechanical. All engineers must take mechanical and electrical engineering classes - I tended to get better grades in my ME clasees. I always scored highest in my statics classes.

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I did Mech , EI and Industrial. Sometimes , I know what I want to say but just can't say it
john

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John Hall
blues creek guitars
Authorized CF Martin Repair
Co President of ASIA
You Don't know what you don't know until you know it