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  #46  
Old 12-23-2017, 09:09 PM
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Bruce Sexauer Bruce Sexauer is offline
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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 .
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 .
IMO: The mistake here is that the string in/under/emerging from the bridge has nothing to do with the geometry I described earlier. ALL that matters is the length of the base and the height of the triangle, and that is all about torque, not tension. The bridge is best viewed as a rigid mass. Yes, it is actually a little short of absolutely rigid, but that is a mere technicality in this case. Again, IMO.
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  #47  
Old 12-24-2017, 07:07 AM
Otterhound Otterhound is offline
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Originally Posted by Bruce Sexauer View Post
IMO: The mistake here is that the string in/under/emerging from the bridge has nothing to do with the geometry I described earlier. ALL that matters is the length of the base and the height of the triangle, and that is all about torque, not tension. The bridge is best viewed as a rigid mass. Yes, it is actually a little short of absolutely rigid, but that is a mere technicality in this case. Again, IMO.
What creates the torque ?
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  #48  
Old 12-24-2017, 08:31 AM
Wozer Wozer is offline
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What creates the torque ?
the string tension...what else?
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  #49  
Old 12-24-2017, 09:23 AM
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What creates the torque ?
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  #50  
Old 12-24-2017, 09:47 AM
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Originally Posted by Bruce Sexauer View Post
IMO: The mistake here is that the string in/under/emerging from the bridge has nothing to do with the geometry I described earlier. ALL that matters is the length of the base and the height of the triangle, and that is all about torque, not tension. The bridge is best viewed as a rigid mass. Yes, it is actually a little short of absolutely rigid, but that is a mere technicality in this case. Again, IMO.
Mr. Sexauer is not one of the "math & physics" guys, but they/we are in agreement with him. The bold part of the text was the subject of some discussion during the development of the FEA model, because the accuracy of the estimation of those physical properties has a direct effect on the results of the analysis, and the reliability of the model. Mr. Malicky's analysis took the math about as far as it would go, considering the variability of the physical properties of wood. There is one more iteration of the model back in the original thread, I believe it was on MIMF, which is well worth a read if you're interested in mathematical modeling. I'll find a link and post it.
edit:http://www.mimf.com/phpbb/viewtopic....=1126&start=20
It is a long thread, with a lot of the math guys contributing after page 3 or so.
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Last edited by Rodger Knox; 12-24-2017 at 10:07 AM.
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  #51  
Old 12-24-2017, 10:05 AM
charles Tauber charles Tauber is offline
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Originally Posted by Otterhound View Post
What creates the torque ?

Let's turn the question around.

If you remove the strings from the instrument, other than gravity, what forces are applied to the bridge/saddle unit?

If you reattach and tension the strings, other than gravity, what forces are applied to the bridge/saddle unit?



What is torque and what is the relationship between force and torque?

https://www.physics.uoguelph.ca/tuto...que.intro.html


Refer back to the static force diagrams I posted previously: you'll see, diagrammatically, the applied forces and the torque they produce.
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  #52  
Old 12-24-2017, 10:42 AM
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Tension is the straight pulling force. Torque is the rotational force developed when tension is applied as leverage, in this case to the saddle's upper edge which causes the bridge structure to try to rotate around its base.

Let's agree to avoid bringing enertia into the mix.

I AM relieved to hear that science bears me out.

Merry Christmas, pilgrims.
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  #53  
Old 12-24-2017, 11:46 AM
Otterhound Otterhound is offline
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Originally Posted by Bruce Sexauer View Post
Tension is the straight pulling force. Torque is the rotational force developed when tension is applied as leverage, in this case to the saddle's upper edge which causes the bridge structure to try to rotate around its base.

Let's agree to avoid bringing enertia into the mix.

I AM relieved to hear that science bears me out.

Merry Christmas, pilgrims.
Is there any other fulcrum on the bridge where string tension applies leverage ?
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  #54  
Old 12-24-2017, 11:58 AM
runamuck runamuck is offline
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Is there any other fulcrum on the bridge where string tension applies leverage ?
On a pinned bridge design, there are at least 2 fulcrums: the point at which the strings exit the pin hole and the saddle.
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  #55  
Old 12-24-2017, 12:33 PM
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Is there any other fulcrum on the bridge where string tension applies leverage ?
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Originally Posted by runamuck View Post
On a pinned bridge design, there are at least 2 fulcrums: the point at which the strings exit the pin hole and the saddle.
If you mean a point where a torque is applied by string tension, then in 2d there's only one, the centroid of the cross section of the top and braces where it intersectects the plane of the saddle. I 3d it's more complex. In either case, the string tension beyond the saddle contribute to the internal stresses of a rigid bridge/top/plate structure, and not to the torque on that structure.
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  #56  
Old 12-24-2017, 01:26 PM
Wozer Wozer is offline
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look...this is all mathematics, and therefor follows the terms of math.

"there can be only one" fulcrum in this model of torque and how it is applied to an acoustic guitar top with a pinned/unpinned bridge.

the lever(S) are the paths of the string (I note there are 2 paths...one to the nut and the other to the balls of the strings).

now, it has been decades since I've delved into anything more complex than trigonometry so I'll do my best to make any "arguments".

from reading through the supplied links and images, I see 2 things I don't think have been fully discussed:

1: as I noted, I see 2 paths from the fulcrum and the applied torque would seem to be the differential between the 2 (if they are equal, then there would be no torque (?))

2: I see H as being defined as the height above the top...I feel this is incorrect as the nut is going to be below that elevation, and to me the elevation differential of the top of the saddle and the location of the nut is what H should be defined as

everything else follows directly from the numbers and is defined by the math of it all, and as such is incontestable...1 fulcrum.
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  #57  
Old 12-24-2017, 02:16 PM
LouieAtienza LouieAtienza is offline
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Originally Posted by Wozer View Post
look...this is all mathematics, and therefor follows the terms of math.

"there can be only one" fulcrum in this model of torque and how it is applied to an acoustic guitar top with a pinned/unpinned bridge.

the lever(S) are the paths of the string (I note there are 2 paths...one to the nut and the other to the balls of the strings).

now, it has been decades since I've delved into anything more complex than trigonometry so I'll do my best to make any "arguments".

from reading through the supplied links and images, I see 2 things I don't think have been fully discussed:

1: as I noted, I see 2 paths from the fulcrum and the applied torque would seem to be the differential between the 2 (if they are equal, then there would be no torque (?))

2: I see H as being defined as the height above the top...I feel this is incorrect as the nut is going to be below that elevation, and to me the elevation differential of the top of the saddle and the location of the nut is what H should be defined as

everything else follows directly from the numbers and is defined by the math of it all, and as such is incontestable...1 fulcrum.
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.
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  #58  
Old 12-24-2017, 02:50 PM
runamuck runamuck is offline
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Originally Posted by Rodger Knox View Post
If you mean a point where a torque is applied by string tension, then in 2d there's only one, the centroid of the cross section of the top and braces where it intersectects the plane of the saddle. I 3d it's more complex. In either case, the string tension beyond the saddle contribute to the internal stresses of a rigid bridge/top/plate structure, and not to the torque on that structure.
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.
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  #59  
Old 12-24-2017, 03:05 PM
LouieAtienza LouieAtienza is offline
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Originally Posted by runamuck View Post
There is at least 1 change as the string exits the bridge
You could apply all the torque you want to the saddle relative to the bridge or vise versa, but the saddle cannot move relative to the bridge anyway.
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  #60  
Old 12-24-2017, 04:13 PM
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In either case, the string tension beyond the saddle contribute to the internal stresses of a rigid bridge/top/plate structure, and not to the torque on that structure.
Quote:
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.
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.
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