The Long Arch

[GerardM]

Hello everyone when shaping the long arch both back and front is there a particular measurement for the point at which it starts to curve downward towards the neck and tail? 

[uncle duke]

Not that these are particular but here are a few of mine taken from half templates derived from Otto and traced off of the p.c. screen over the years.

An old Bagatella plan has 16.7 mm high 27 mm in front of the bridge line.  16.5 mm at the bridge along with 16.5 mm 43 mm out in front of bridge.  20 mm behind the bridge is 16.1 mm high along with 16.1 reading also at 51 mm in front of the bridge.

1709 Strad has a height of 14.8 mm just in front of proposed stop line along with 14.6 mm high 51 mm in front of the stop line even though these are heights for a back plate, not a belly.  22 -23 mm behind the stop line also reads 14.6 high.

So just draw a horizontal line on paper and use the above figures on that line to get an idea.  The 1733 d.g. template I have has similar height placement but uses different heights.   

[Brad Dorsey]

Do you mean the point's location or its height?

[GerardM]

I’ve looked at pictures on line some arching appears to have a flat area before starting the gradual curve downward, and this point appears to be in line with the corners. I have purchased an old violin to help visualise the arching, and it’s arching has no flat area. A very slight arch in between the corner area then running downwards. If the total arching height was say 15mm at what point would you start the curve downward?  I hope I’m explaining question coherently. 

[Don Noon]

There are varying opinions about what the long arch should be, especially regarding the top.  I know that on many old violins, the island area under the bridge has sagged into concave by a mm or so... but I can't believe it started out that way.  Still, I'm of the opinion that it started out relatively flatter in the island, rather than a continuous arc.

To my eye, typical good arches become most convex above the upper corners, and straighten out going into the upper block.  In the lower bout, the convexity is farther away from the lower corners, to keep the island and the F-hole area relatively flat.

On the back, I have never seen the variation in curvature so extreme.

The Kreisler GdG is a nice example...

[Ken_N]

I do mine from the inside. The long arch on the inside is started with diagonal catenary arches that are closer at the top than the bottom. The corners are defined by lines through the upper eye. Cross arches through the diagonal arches raise the central long arch so it rises much faster than a catenary arch. Since the diagonals cross the centerline above center, the high point of the arch ends up around the bridge area. And the arch is fairly flat for a long distance.

It sounds far more complicated than it is.

For the back I just use a radius on the outside 800-1200mm or so; with a recurve at the ends. The inside is 2 catenary arches, but you could maybe use one on very low arches. The arches go from the block to the opposite bout, or corners. This gives you a thick area. Where the arches go to places the thick area high, mid, or low. 

The thick area can be smoothed out, or kept thick. On my cello back it only has a 26mm or so arch, but it is 8.5 thick. Violins could get almost that thick if you went to the corners. I don't think that you want a back that doesn't move.

You can figure out what to use from the poster, or you can just make things up as you go along. That's what I do when I make something from a photo online.

Once the main arching in the middle is done, it's just a matter of making the rest right.

Yes, this in not the usual method. But it works.

 

 

 

 

[David Beard]

Opinions do vary.

Some believe deformation is the primary cause of the characteristic long flattish stretch of classical tops.

I do not.  My opinion is that the classic top arched were deliberately made basically as you see them.

 

Some points of observation:

Through arch top v flattish demends much more on school of making than date.

In many cases, you can see that age deformation has expressed itself, but in unstructured assymetric depression very local to the bridge area.    Yet, all the classical Cremona examples show well structured flattish tops.

 

 

[Don Noon]

55 minutes ago, David Beard said:

My opinion is that the classic top arched were deliberately made basically as you see them.

It depends how you define "basically".  Distortion certainly is responsible for pushing down the island and bubbling up in the upper and lower bouts, my guess is it can be 1 or 2 mm, although before (new) and after un-re-arched Cremonese measurements are hard to come by.  But still, I believe as well that the general shape of the top as-manufactured, was flat-ish across the island and up to the upper corners.  There are variations, though.

Here's one, before arching correction:

[Davide Sora]

Yes, but what does flattish mean? Also for me the top is flatter than the back in the central area, but always slightly curved and not really flat, otherwise the sinking would be almost immediate.

Just my opinion.

[David Beard]

42 minutes ago, Davide Sora said:

Yes, but what does flattish mean? Also for me the top is flatter than the back in the central area, but always slightly curved and not really flat, otherwise the sinking would be almost immediate.

Just my opinion.

Absolutely!

[Dennis J]

The latest top long arch template I've made has the highest point at the narrowest cross-arch location in the Cs. The height of the arch at the bridge position is .1 mm lower.

Using that approach the overall long arch is asymmetrical. That means that the fall in the upper bout has to be more pronounced than in the lower.

I think the back arch might follow different rules. There I think the high point logically should be at the sound post position. And that extra mass there should be added to the outside curve of the arch, rather than having a flattened floor on the inside surface. That approach will lead to a visible peaking of the back at that point.

 

[Don Noon]

5 hours ago, Davide Sora said:

Yes, but what does flattish mean? Also for me the top is flatter than the back in the central area, but always slightly curved and not really flat, otherwise the sinking would be almost immediate.

Just my opinion.

Flattish = convex, but much less so than elsewhere.  Probably in the range of 2000 mm radius.

Sinking will be immediate when the strings are tensioned (elastic deformation), and then over time there would be added plastic deformation.

This got me thinking...  How much does the longitudinal curvature help prevent the sinking?

One possible source is the longidudinal string compression of the long arch counteracting vertical bridge pressure.  To do some calculations, the longitudinal curvature can be treated similar to a pressure vessel, with the longitudinal string force acting like "pressure", and the bridge as a localized force trying to dent it inward.  Short answer: this is a negligible source of support across the island, although considerable when looking at overall arch sinking and the "bubbling up" of the upper and lower bouts.

That leaves structural stiffness as the primary source for resisting deformation in the island area.  It's complicated by the bass bar and soundpost, making calculations difficult... but I measured deflection at the foot position on my most recent violin, supported at the endblocks.  For normal bridge vertical pressure (19 pounds), there would be .50 mm deflection at the bass foot, and .28 mm at the treble foot (soundpost in place).  These are the immediate elastic deflections, and I have no way to guess what the creep deflection might be (but it would almost certainly be less with torrefied wood )

I didn't make a research project out of this, so I have no idea how the deflection vairies across the long arch, and how the curvature amount and location contribute to stiffness.  However, in my engineering judgement, the amount of convexity across the island (within normal bounds) is at best a minimal contributor to local stiffness, with beam/bending stiffness being the main contributor.  The reason to make it convex is so it won't go concave when it deflects.  But that happens anyway on a lot of old violins anyway, and even new violins appear to have a tiny dip right around the bridge foot.

[Don Noon]

3 hours ago, Dennis J said:

I think the back arch might follow different rules.

There are no "rules". 

[Dennis J]

4 hours ago, Don Noon said:

There are no "rules". 

If that's the case any speculation about arching stands or falls on how logical it is. 

 

[David Beard]

There are no rules for free ahistorical creation today. Do what you will.

But, there are observable rules to what was and wasn't don't in historical old Cremona making.  Indeed, with diligence, many such 'rules' can be seen at play.

For instance, they didn't not extend long flattish regions comparable to the tops woth the backs.   And, they did not skip the flat an just bulid through arches for tops.   So, the 'rules' for top and back long arches were different.

And, the absolute peaks in tops and backs were not exactly at the bridge line or sitting on the post.  Rather, they were a bit in front of the bridge.  Maybe half a bridge height generally for violins and violas.

And, with most backs you can observe a very short flattish bit for the back, but only running about as far as a bridge height, just under and infront of the brodge line.

So, if you want to take you lead historical Cremona example, it is not anything goes road at all.

 

But, it's a free choice.

[Dennis J]

Yes, basically that confirms what I think. And I think there are logical reasons for that.

However, because the back varies so much in thickness other aspects of arching come into play. That is why the longitudinal arching is so different to the top arching.

In the long run it comes down to what might be practical and functional.

 

 

[Davide Sora]

3 hours ago, David Beard said:

There are no rules for free ahistorical creation today. Do what you will.

But, there are observable rules to what was and wasn't don't in historical old Cremona making.  Indeed, with diligence, many such 'rules' can be seen at play.

For instance, they didn't not extend long flattish regions comparable to the tops woth the backs.   And, they did not skip the flat an just bulid through arches for tops.   So, the 'rules' for top and back long arches were different.

And, the absolute peaks in tops and backs were not exactly at the bridge line or sitting on the post.  Rather, they were a bit in front of the bridge.  Maybe half a bridge height generally for violins and violas.

And, with most backs you can observe a very short flattish bit for the back, but only running about as far as a bridge height, just under and infront of the brodge line.

So, if you want to take you lead historical Cremona example, it is not anything goes road at all.

 

But, it's a free choice.

Even then someone was apparently going against the tide, just to break the rules.

Late GdG (photo posted by Bruce Carlson some time ago).

[David Burgess]

5 hours ago, David Beard said:

For instance, they didn't not extend long flattish regions comparable to the tops woth the backs.   And, they did not skip the flat an just bulid through arches for tops.   So, the 'rules' for top and back long arches were different.

Since no living person has seen any of these instruments when they were first finished, and we don't have any examples of these instruments which have never been under string tension, we simply don't know.

However, we can sort of "reverse-engineer" distortions which careful observers have tracked over many years, and reliably conclude that the archings we see on old instruments today are not as originally made, unless some restorer happened to guestimate correctly when re-arching a plate.

[David Beard]

2 hours ago, Davide Sora said:

Even then someone was apparently going against the tide, just to break the rules.

Late GdG (photo posted by Bruce Carlson some time ago).

How so? Somewhat short flattish stretch on top, but still extending 'toward or past the corners'.   And a nearly through long arch on the back.

How is this any sort of exception?

[David Burgess]

2 hours ago, Davide Sora said:

Even then someone was apparently going against the tide, just to break the rules.

Late GdG (photo posted by Bruce Carlson some time ago).

The archings on the later Guarneris suggest that having come along late enough in the game to have had a chance to observe the shapes of instruments which had already been in use for a couple of hundred years, Del Gesu applied some pre-emptive top-distortion-reduction strategies. And that these may have been quite successful.

[scordatura]

I have noticed that Strads have a longer flat region than DG. This is a broad stroke generalization and prone to exception. This makes me consider if a longer flat region makes the arch higher in the bouts and therefore stronger or is a more curved long arch stronger than a flat one. Another consideration is when the end grain comes into play at the ends of the arch. Sooner by a more curved long arch and later by a longer flattish region.

[David Beard]

Structures correlate much more by maker rather than by time.

[David Burgess]

45 minutes ago, scordatura said:

This makes me consider if a longer flat region makes the arch higher in the bouts and therefore stronger or is a more curved long arch stronger than a flat one.

The strongest, in terms of resistance to longitudinal compression and distortion, would probably be straight lines going from both the upper and lower blocks to the bridge.

On the Guarneri photo, there is an unusually long straight section under the fingerboard, a region where many old violins have become quite bulged.

[Don Noon]

I would be very interested to find out how that late Guarneri actually sounds, and get some kind of response plot from it.  These outliers can be very informative about how things work, and saves the effort of having to build one to find out.

[Michael Darnton]

David, There's a quirk in the Ole Bull that would please you, and I wish I had shot this view when I was making the B&F pix, because in the normal side view shot with the lens positioned in the middle of the ribs this feature is "over the hill" and not visible: that violin's top has a pointed peak in the center, as if two half-long-arch templates intended for a lower back arch were used, but raised slightly higher than normal (the Ole Bull does have a slightly higher top arch than normal). From that point it's a relatively straighter line down to each end. 

Don, that's not an outlier for late del Gesus. Most of them don't have very much of a flat spot in the center, if any. I've always thought of those as being the first "modern" violins, in that they don't have much in common with what happened before in other respects as well, not made with a classical Italian eye. You've heard me say it before, but I blame Katarina for these.