Yet another math question

[ken cierp]

Forget the weight for a minute, you are looking for the deflection "measurement" under x conditions -how can you disregard the conditions and jump to an answer?

Plus the arch top has totally different dynamics -- the movable bridge is like and arrow in a bow -- nothing is pulling on it or the top all the force is going downward.

That's all I got. Maybe do an experiment?

[Dave Bagwill]

Yep, I've been thinking that maybe I'll look around for some cheap top materials and brace up a couple of tops for experimental purposes.

[Dave Bagwill]

Herman - does your math guy still stick with the vector formula, in light of Ken's contentions above?

[John Link]

One way to do the experiment without going to the trouble of making special guinea pig tops would be to take an already made guitar, loosen the strings, and place a more reasonable weight that 34 pounds (!) on it, say 5 pounds. Then maybe 10. Sort of sneak up on 34 pounds, as much as you dare. I believe, but it remains to be proven, that the deflection you get in the unstrung instrument will quickly make it obvious that 34 pounds is too much.

As Ken points out, once a dome is formed and/or its radius is decreased, the top triangulates and becomes much more stiff, in addition to the the effect of tension from the horizontal pull of the strings.

Intuitively, just the thought of plopping down 34 pounds on the top of an unstrung guitar sends shivers up my spine. Wouldn't really want to do it to even a beat up old plywood guitar, though plywood comes to mind as the most likely top material for surviving the insult.

[Dave Bagwill]

I'm dense, I reckon, but I do know that the string tension is 131 lbs or up to 185 lbs, in that range. So we are dealing with significant forces here.
I've got the question into Roger Siminoff, I'm hoping he has the time and inclination to respond.

edit: no doubt I'm wrong about this, but I'd like to know why, and would like to know the calculations, if different that the one that yields the 34 <gasp> lbs. :-)

Siminoff regularly applies 58 lbs of TORQUE in his tests. What does that mean?

[John Parchem]

one point to keep in mind is that when a guitar is strung up it is being pulled up as well as pushed down within the short span of the bridge saddle to hole distance. So at no time is the top carrying 34 pounds of vertical weight. It is balanced. That is why torque is the important consideration. When playing the instrument the top balanced in tension is responding to a pluck of the string that is nowhere near 34 lbs force. The diagram back in the posts has a force vector at the saddle, but there is another one at the termination of the strings. So for the top those forces balance out. But given that they are separated a bit there is a rotational force.

[Dave Bagwill]

What I've been asking since the beginning of this thread is: how to calculate the amount of downward force at the bridge. It must be a factor of the torque in some manner.
Of course 34 pounds is too much - though for archtop instruments the downward force is in fact calculated much like Herman's formula, and does come in at 30 lbs or so depending. See that calculator on Mattola's page.