Curve on Bridge Bottom

[Ron Nossaman]

>I'm not sure that I want to sign up to pedigreed (it makes me sound like a 
>poodle) but I think I meet the other qualifications.  I'm a bit busy right 
>now, but if you'll allow me a little time, I'd be willing to give it a 
>try. 

Deal, no more poodles.


> I think I need a clearer picture of what you would like to see.  The 
>deflection of the bridge and board under load?  Stress levels in the 
>board?  The stiffening effect of the curved bridge (or in other words the 
>difference in deflection under load with and without the curved 
>bridge)?  The difference in stiffening effect between a curved bridge and a 
>straight one?
>
>Also, am I allowed to make some simplifying assumptions, at least for a 
>first cut?  A couple of things that would complicate the modeling would be 
>a curved outside shape and a crown.  So, I would probably like to make the 
>following assumptions for a first cut:
>
>1.  All outside edges are straight lines (such as in a upright soundboard).
>2.  No crown.
>3.  Soundboard same thickness everywhere.
>4.  Bridge same cross section everywhere.
>5.  Ribs same cross section along their length (no tapering or scooping at 
>ends).
>6.  All ribs same cross section.
>7.  Ribs equally spaced.
>8.  Rim has no flexibility (soundboard is fixed along its edge).
>
>Do you think any of these assumptions would void the results?
>
>Phil F

I'm after a couple of things. The first relating to crowned bridges
supporting soundboard crown, and the second relating to the killer octave
being the first place a soundboard goes flat. These are both related to the
curve in the bridge. The centerline of rib support along a bridge, I assume
to be along a line from just about the treble end of the bridge to a point
about 30% up the length from the low tenor. The centerline of load,
however, is going to be on a line from somewhere nearly an octave from the
treble end, to nearly half the bridges length from the low tenor. The
centerline of load is considerably forward of the centerline of support,
and I wanted to generate some data, charts, drawings, or whatever
illustrating how much effective load from the resulting leverage is
actually put on each part of the bridge, and how it differs from the
picture you get from looking at the string bearing loads. The two can't be
even close to the same except at the ends of the bridge, and by my eye, the
killer octave area has to be carrying considerably more load than we are
aware of. My original idea was/is, using measured rib dimensions, measured
load positions, and assumed uniform loads with a beam deflection formula,
to determine from derived deflection of each rib about where the centerline
of support is on the bridge. From there, I thought the string bearing loads
could be used with the leverage offsets from the support centerline to
determine effective loading. But it gets a tad complicated, and I haven't
had the time to devote to it when I'm really not sure what I'm doing. I
prefer answers to more elaborate misconceptions, when they are available.
For instance, a load on a point an octave from the treble end will be
putting more load on the curve further down the bridge because the board is
deflecting more at the load point than at the top end. Or will it? If so,
how much more? I'm looking at either a more complicated iterative process
than I'm probably capable of, or a SWAG based on logic and what information
I already have or can generate. And we know what that gets me in the long
run, so I'm looking to borrow a more specific education for a while.

As to the first cut:

A rim isn't really necessary for anything but supporting the ends of the
ribs. Rib dimensions and bridge position would tell me what I'm after.

The crown would only be to provide a starting elevation for deflection
under load comparisons. Orientation.

The panel would be all the same thickness (this time). In fact, it could
probably be eliminated altogether and produce a good enough illustration of
principal and an adequate approximation of actual vs apparent loading. 

Bridge same cross section throughout. I'm not concerned with how or whether
the bridge bends at this point.

Each rib can be the same cross section along it's length. In fact, the
deflection figures done that way with just the ribs aren't far off of what
you get with the ribs feathered and panel installed.

Each rib needs it's individual length and cross section, I think, if the
deflection figures and load distributions are to be reasonably accurate.

Equally spaced is OK.

Inflexible rim OK.

So what do you think? 
Ron N