These look like reasonable rib loads. I decided to have some fun this weekend and did an experiment that you may or may not find interesting. I made several spring scales and placed them under each rib location of the long bridge. Then i placed gram weights on top that simulates the load distribution of the strings on the bridge and the reaction was not what I expected on the spring scales.
The numbers came out like this.
This is just the long bridge. But what was interesting, was that due to the curvature of the bridge the load went heavy(added weight in the treble) and had a lifting effect on the low end (the weight on top of the low end was 32). I believe the lifting was because the Heintzman bridge is strongly an S shape bridge( as seen in the photo).
Next experiment of course will be to add the bass bridge and see how that effects the long bridge.
Chernobieff Piano and Harpsichord Mfg.
Original Message:
Sent: 10-29-2016 23:36
From: Chris Chernobieff
Subject: A Refinement of Equilibrium for Maximum Soundboard Flexibility
David,
Here is a little chart I did of the downward forces on the Heintzman, and the sections they are located along the bridge. Now I know you were only going by my previous numbers, which were based on point loading. But your response of trying to even up the forces
1
|
64 lbs
|
2
|
65
|
3
|
66
|
4
|
67
|
5
|
68
|
6
|
69
|
7
|
70
|
8
|
71
|
9
|
72
|
10
|
73
|
11
|
74
|
was intriguing. But that it too could be counter-intuitive to the original design.
Notice that most of the load is at the ends 400+ plus lbs on the treble end and 220+ on the bass end with a mere 96 lbs in the center.
I'm curious on how you would find the centroid of the long bridge? And how you would compensate for any lateral forces due to the curvature of the bridge? Or maybe what formula you use to calculate the load distribution.
Ron N. Are you using a predetermined load curve of some kind?
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ChrisChernobieff
Chernobieff Piano and Harpsichord Mfg.
Lenoir City TN
865-986-7720
chrisppff@gmail.com
www.facebook.com/ChernobieffPianoandHarpsichordMFG
Original Message:
Sent: 10-28-2016 20:50
From: Paul Klaus
Subject: A Refinement of Equilibrium for Maximum Soundboard Flexibility
Z= .73^2 x .82/ 6 = .07282 (by the way .73 is .43 + .30)
Chris: Thank you for your help. Okay .43 + .30 = .73 but why square this and divide by 6. I understood another post to explain you treat components separately but here the board adds significantly to the rib height and seems combined with it. How does this equate?
Original Message:
Sent: 10-25-2016 19:15
From: Chris Chernobieff
Subject: A Refinement of Equilibrium for Maximum Soundboard Flexibility
Well gosh Paul, that was awhile ago. But..........after searching through 200 old posts, I found what you were referring to.
The problem was to find the length of the rib using the following details. Which as you mentioned, nobody solved it.
Here was the details
Heighth- .43
Width- .82
Stress- 1.854 lbf
Force in Center- 60lbs
soundboard thickness- .30
So to solve it you use the Stress formula M/Z=S in reverse. Z x S = M
Lets solve for Z
Z= .73^2 x .82/ 6 = .07282 (by the way .73 is .43 + .30)
So now Z x S =M is .07282 x 1,854 = 135 in-pounds (Moment)
So half the Moment(bearing) is 30Lbs
so 135 / 30 = 4.5 inches( half the lever length)
so 4.5 x 2 = 9
The rib length is 9"
Hope that makes us friends again Paul
-chris
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ChrisChernobieff
Chernobieff Piano and Harpsichord Mfg.
Lenoir City TN
865-986-7720
chrisppff@gmail.com
www.facebook.com/ChernobieffPianoandHarpsichordMFG
Original Message:
Sent: 10-25-2016 18:31
From: Paul Klaus
Subject: A Refinement of Equilibrium for Maximum Soundboard Flexibility
Chris: Awhile back you challenged us to find a ribs length by giving other variables. I do not recall seeing the details of your solution or if any sent the right answer. Mine was wrong but I would have liked to see how you did it. But that’s ok. Thanks anyways. Paul
Original Message:
Sent: 10-25-2016 12:23
From: Chris Chernobieff
Subject: A Refinement of Equilibrium for Maximum Soundboard Flexibility
Hi Paul,
The #s mean what?
The blue line is the moment in inch pounds (Force). The red line is the size and strength of the rib(Resistance).
On graph #2 is the red line usually just under the blue line showing the bridge effect mentioned by David?
No. Since each line is expressing different values (force, mass), above, below or on top doesn't matter. I just look at the contours, and try to get them to have a similar shape.
Why the big exception for rib #11?
Because there is no moment.
I missed your solution for the previous rib length riddle of 9” when I found 27”. Share math details please. Maybe I cubed what you squared. Paul
Not sure what you mean. Did I forget something?
Thanks Paul
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ChrisChernobieff
Chernobieff Piano and Harpsichord Mfg.
Lenoir City TN
865-986-7720
chrisppff@gmail.com
www.facebook.com/ChernobieffPianoandHarpsichordMFG
Original Message:
Sent: 10-24-2016 23:48
From: Paul Klaus
Subject: A Refinement of Equilibrium for Maximum Soundboard Flexibility
Chris: Rib graphs are interesting. Why 2 Ys (axes)? Axes are unlabeled. The #s mean what? On graph #2 is the red line usually just under the blue line showing the bridge effect mentioned by David? Why the big exception for rib #11? I missed your solution for the previous rib length riddle of 9” when I found 27”. Share math details please. Maybe I cubed what you squared. Paul
Original Message:
Sent: 10-23-2016 23:10
From: Chris Chernobieff
Subject: A Refinement of Equilibrium for Maximum Soundboard Flexibility
For optimum resonance the string scale and rib scale must be in equilibrium. If the string scale is altered, then so must the rib scale also be altered. Of course, this also assumes that the original designer put it in equilibrium in the first place. If not, then that too must be fixed. Afterall, you wouldn’t want the new board to go flat like the original did.
Due to the-
- Strings changing lengths, angles, and fanning.
- The curvature of the bridge.
- The angles and spacing of the ribs
These combined factors create a downward force that is uneven across the soundboard. In fact, each soundboard has its own “signature”.
Below is an example from a Heintzman Grand.
The blue line is the downward force across the soundboard. The red line is the rib structure that is suppose to support it.
Notice that they are not synchronized. They should be so that each rib can be efficient in its job. Not too weak, nor too stiff. The true state of equilibrium.
Below is the corrected rib structure for the Heintzman that now correctly supports the downbearing force. This was achieved by changing the dimensions of the ribs accordingly. As shown by the parallel contours of the lines.
This refinement allowed the soundboards flexibility to increase by another 3% in the Heintzman beyond the 20% that I had obtained from the earlier modification. Thus reaching the maximum flexibility that the Heintzman board would allow.
Maximum flexibility equals maximum resonance.
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ChrisChernobieff
Chernobieff Piano and Harpsichord Mfg.
Lenoir City TN
865-986-7720
chrisppff@gmail.com
www.facebook.com/ChernobieffPianoandHarpsichordMFG
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