Am I using the correct formula for downward force?

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Dennis Duross
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Am I using the correct formula for downward force?

Post by Dennis Duross »

I decided to deflection-test one of my test mules, just to be sure I understand what's happening to the soundboard when downward force is applied to it.

The top is braced and glued to the rims (prior to attaching the back).

I tested the deflection under 10, 20, 30, and 40 lb of weight, applied directly over the bridge.

Then I strung it up and rechecked the deflection.

My 11 gauge strings pull at @ 142 lb, and my break angle is 12 degrees.

If the formula I'm using is correct:
  • string_tension x 2 x sin((break_angle x (3.14/180))/2)
the strung-up downward force should be @ 30 lb.

But the top is deflecting as if there were only @ 20 lbs of downward force being applied.

Is my formula off somehow? It's been so long now that I forget where I got it from.

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Barry Daniels
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Re: Am I using the correct formula for downward force?

Post by Barry Daniels »

Your understanding of downward force is incorrect. There is no overall downward force from the strings. Yes, there is some local downward force from string break angle but this is balanced by the upward force of the string ball ends pulling up on the bridge plate. And this creates a rotational force at the bridge. But the strings alone do not push the top of the guitar downward.
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Dennis Duross
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Re: Am I using the correct formula for downward force?

Post by Dennis Duross »

Barry:

This is a floating bridge design with a tailpiece.

I should have clarified that.

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Barry Daniels
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Re: Am I using the correct formula for downward force?

Post by Barry Daniels »

Never mind :)
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Matt Cushman
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Re: Am I using the correct formula for downward force?

Post by Matt Cushman »

Your formula is correct. More than likely your angle is measured correctly and the string tension is also likely to be close to correct. It is possible that the back not being attached may have had some effect on top deflection when you did your testing.

Rodger Knox
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Re: Am I using the correct formula for downward force?

Post by Rodger Knox »

I suspect you break angle is a little off. 12° sounds a little high for an archtop, and one degree of error causes about 15% difference in the final number.
A man hears what he wants to hear, and disreguards the rest. Paul Simon

Dennis Duross
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Re: Am I using the correct formula for downward force?

Post by Dennis Duross »

Thanks for the replies.

I will chase down both suggestions and see what I see.

However if the equation is correct, my measurement of the break angle would have to be 4 degrees lower in order to replicate the deflection I'm seeing.

And I would think that any rim deformation unaccounted for would be the same whether the soundboard was seeing 30 lbs of "live" downward force or 30 lbs of weight in the jig.

That said, I will definitely check out both suggestions---as soon as I can clear the current project off of my workbench.

Thanks again.

Dennis Duross
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Re: Am I using the correct formula for downward force?

Post by Dennis Duross »

Matt:

Having slept on it, I think you may be right. My apologies for being so dense.

In the jig, it's all just downward force, and the rims are likely deforming slightly under the weight.

But when strung up, the string tension helps the top resist the downward force and the deformation of the ribs---at least in the longitudinal (neck-to-tail) direction.

D'oh!

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Randolph Rhett
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Re: Am I using the correct formula for downward force?

Post by Randolph Rhett »

Was there a particular amount of deflection you were looking for? I have seen Alan Carruth's tuning of a plate with a signal generator and tea leaves, and of course old fashioned tapping and listening, but don't know the relevance to tuning a top of measuring the deflection.

Alan Carruth
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Re: Am I using the correct formula for downward force?

Post by Alan Carruth »

Dennis Duross wrote:
"the strung-up downward force should be @ 30 lb. But the top is deflecting as if there were only @ 20 lbs of downward force being applied."
and, in a later post:
"But when strung up, the string tension helps the top resist the downward force and the deformation of the ribs---at least in the longitudinal (neck-to-tail) direction."

That's a conjecture I've had for a while, but have not had a chance to check out.

Roger Knox wrote:
"I suspect you break angle is a little off. 12° sounds a little high for an archtop, "

Assuming you're measuring it right, I agree with Roger: 12 degrees seems a bit much. Benedetto shows a 6 degree break angle in his book, and experiments I've done confirm that that's enough, although only just enough.

The inward force of the strings pushing the top up is, of course, a function of the tension and the arch, while the downbearing depends on the tension and the break angle. I sometimes wonder if the 'correct' downbearing angle is the one that balances those two forces, leaving no net download on the top at the bridge. I know from experiment that too much downbearing will kill the tone, contrary to popular opinion.

Matt Cushman
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Re: Am I using the correct formula for downward force?

Post by Matt Cushman »

In my copy of the Benedetto book on page 178 Bob says "The optimum string angle from the bridge to the tailpiece is 13 or 14 degrees." I have a set of plans for a Benedetto guitar and it shows 13 or 14 degrees. So 12 degrees seems about right to me. I am not sure where Bob shows 6 degrees in his book?

Dennis Duross
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Re: Am I using the correct formula for downward force?

Post by Dennis Duross »

Randolph:

Sorry it's taken me so long to reply to your question.

The short answer is "no."

The "archtops" I've been building for the last several years (I'm just doing this for my own amusement) are actually "dometops." Not carved out of thick pieces of wood, but thin slats bent and glued together to form a section of a sphere (or dome) that ends up roughly equivalent in height to a carved top.

The radius of that dome is just over 6.5 feet.

It's not a question of whether building this way is better or worse than carving plates (I have no basis upon which to make that kind of claim anyway), I just don't have the temperament for carving (or for discarding 3/4 of every plate).

Anyway, I'm trying to understand the impact that downward force has on this dome.

And I was seeing one kind of impact under a "dead" load (in the jig) and another under "live" load (strung up), which caused me to wonder if the formula I was using was correct.

I had thought I stiffened the rims enough that they would not deform under load, but (like a dope) failed to take before/after measurements of the rims that might confirm or deny that assumption.

Naturally.

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