Strad poster Titian arching heights

[jowl]

Can someone please explain to me why there are 4 separate readings each for the belly and back arching heights in the Titian Strad poster (see attached)? I can understand the measurements with and without the edge, but why are the readings different when measured across vs lengthwise? Which reading do you use when building the instrument? 

Titian.pdf

[Don Noon]

If the plate/rib gluing surface was a perfect plane, cross and longitudinal arch measurements would be the same.  It's warped/bent, so you'll get different measurements depending on what part of the edge you measure to.

[jowl]

OK thanks. I understand that. So which reading does one use?

[jowl]

The readings were made from CT scans of the instrument. Given that the upper bout ribs are narrower than the other two bouts, and that the belly angulates ever so slightly from the upper corner blocks to the top block, one would expect the lengthwise reading in the belly to be greater than the cross arch reading in the (unwarped) instrument. Interestingly the reverse is the case.

[Don Noon]

I would expect the longitudinal belly arch to be lower, as the body will bend that way under string forces.  If you want an unbent measurement, I'd expect the crosswise arch height to be closer to original.

[jowl]

Hi Don

Attached is how I am conceptualizing an unwarped Strad on a side view, with the reduction in height of the upper bout rib greatly exaggerated. If the arching height is measured from the highest point to a line drawn from one end of the arch to another, then b > a. String tension may reduce b somewhat, but the belly will have to become concave upwards before b < a. Where have I gone wrong? 

Titian_0001.pdf

[MaestronetLurker]

Jowl, the rib structure may have started out that way, but string tension may pull the rib structure so that the back joint is not straight anymore.  In this case it seems as though the arch is 1.5mm shorter as measured from upper and lower blocks, which suggests that the top/rib joint is bowed upward at the upper and lower blocks, which is I think what Don was saying.

[jowl]

Thank you to you both. Amazing to think that wood can creep like this, but I suppose it has happened over several hundred years.

[Don Noon]

I don't follow the diagram.

 

Perhaps if you think of the violin body as a solid flat plank, then load up one side with string tension... it will bend (even more over time).  The arch will be zero if you measure across, but less than zero if you measure longitudinally.