Continuation of arching discussion

[Johnmasters]

Something occurs to me that would help the outline determine the arching. What might be desired is a simple construction technique.

This has to do about where one wants to place the recurve. The rest of the rough arching would follow in a simple way.

The line of recurve may be one of the easiest things to lay out on a plate that is being carved. But it is very difficult to see with the eye once it has been carved. There is a simple way this could have been done quickly. We are back to inside-first vs outside-first. I suggest that roughing and finishing are two different opperations, and the roughing could have been done inside-first.

The suggestion is to draw an hourglass on the flat side. Rough this with a longitudinal shape and use a chain for the transverse roughing.

Note that three points determine a unique catenary for a given width and depth.

The line drawn would not be exactly the position of the recurve, but it would be close. At least if it were done in a consistent way from one instrument to the next, a worker could very quickly decide the desired hourglass shape and size. A close external arch could be taken from a rough thicknessing. For me, it is easier to carve a concave surface. Also it is easier for me to feel irregular bumps inside.

After this, fine finishing could have been done externally by eye, except at the edges. But if the inside of the plate (with catenaies) were rounded to the edge, that would very closely approximate the cc shape one actually sees.

For the portion outside the recurve line, that would have largely been done after the body was assembled. This too could have been done with a "nice" continuous depression.

I know that the pinpricks of Strad's thicknessing tool can be seen inside his plates at times. This could have been the result of finishing the inside after the external arch was refined. But still, in the roughing stage, One COULD start from the inside with a very simple system.

This seems to be a more natural way to work than simply mapping out some complicated parametric equation. Also, it seems that an internal roughing to catenaries would give a good approximation to an arch. The internal shape would roughly determined by the line of recurve.

At the risk of being too repetitive, I will reprint the curves I plotted to show just how close the inner part of a cc can be to a catenary.

Evidence? If the graduations near the edges of typical Master plates were slightly more irregular than in the center, that could suggest that a method such as this was actually used.

[Roger Hill]

Hi John:

This method is essentially what I suggested in the thread I started on Cremonese arching and the inhomogeneous catenary.

The method of construction generally follows that laid out by Torbjörn. The arch shape is decided using the appropriate chain and a horizontal line on the wall the length of the distance between the end blocks. The high point is decided upon and that point marked on the chain (for most cases, this isn’t necessary for the back curve). The high point is located on the plate and drilled to a depth equal to the desired (exterior) height of the arch minus the maximum thickness of the finished (graduated) plate. The longitudinal arch is carved using the appropriate chain between the end-blocks as template. The interior cross arching is then carved using the plain chain as a template. The depth of the longitudinal arch at any point defines the cross arch catenary. Once the interior is carved, the arching is transferred to the exterior using the graduation punch set to the maximum desired thickness of the plate. The punch is set up with a support post having a rounded top. After the top shape has been carved and scraped down to the punch marks the plate will be of uniform thickness. The support post on the graduation punch is next replaced with one having a hollowed center to allow the convex top surface to fit securely and rigidly into the hollow as the punch forces the wood onto the post. The interior is then punched and scraped to the final graduation pattern.

A couple of observations: the marks on the top of the cello in the picture given by MD are totally consistent with the above procedure, as are the inside punch marks on the Strad violin. The punch is used twice, first on the outside, then on the inside. Secondly, there is no need to use a drill with a special end-point to begin the carving of a plate. Guarneri may have used one simply to save time. Thirdly, it is much quicker to make a few chains than to make templates for every desired arching shape.

The principal difference is, of course, I suggest that the longitudinal arch be defined with a catenary of an inhomogeneous chain to set the depths of the cross arches. At this point, I would suggest drilling holes of the appropriate depth just in front of the end block locations and using those two points to plus the high point hole to define the longitudinal catenary. Note also that if the heavier sections of the inhomogeneous chain end near the widest points of the upper and lower bouts, the catenary along the length will be virtually identical to the cross catenary, and the "bellows" effect naturally results along two perpendicular axes.

One observation I have made in the cat scans of the various violins is that the plates always join the ribs with a horizontal section of the plate perpendicular to the ribs. Rounding the edge between your hourglass edge of the catenary and the horizontal section will necessarily produce the underside of a curve that approximates that which would result from a CC on top transferred to the bottom of the plate with the thicknessing punch. In my opinion, based soley on study, not experience with building violins, the inside first roughing is more consistent with evidence than anything else I have seen.

edit: one of the most instructive things I have seen regarding edges and recurve is the CT animation at Terry Borman's site of a 1735 del Gesu (maybe the Plowden?) http://www.bormanviolins.com/CTResearch.asp

[Johnmasters]

Hi John:

This method is essentially what I suggested in the thread I started on Cremonese arching and the inhomogeneous catenary.

I read that thread when it came out. The most important issue is: Where does the inflection occur? How do you handle this in your method ?

In other words, how do you determine the width of a catenary for a particular transverse section?

My interest is not in the shape of a catenary per se.

[Roger Hill]

I read that thread when it came out. The most important issue is: Where does the inflection occur? How do you handle this in your methoc?

In other words, how do you determine the width of a catenary for a particular transverse section?

My interest is not in the shape of a catenary per se.

I agree, John, where the inflection is placed is a big deal. How you lay out the hourglass is the "art" for the maker to decide. My guess is that the old masters simply did it by "TLAR", ie "that looks about right" for whatever they wanted to try with that particular violin. Perhaps they did use an actual CC to set the inset of the hourglass from the ribs. The inset of the hourglass in the center bouts would certainly be different from that in the upper and lower bouts. I checked four of my posters for the distance (in mm) from the plate edge to the minimum point for the lower, center and upper bouts. The results are interesting:

del Gesu:

Kochanski 1741 14,10,10

Lord Wilton 1742 7,6,6

Stradivari:

Viotti 1709 7,4,6

Kruse 1721 7,5,8

I think what we draw from such arching/inflection differences is that the old guys were experimenting, just as we are. I have to wonder if del Gesu was going back to a Strad arching when he carved the Lord Wilton.

[Torbjörn Zethelius]

In my experience, the 'flattening' stretches between 6-8 mm outside the layout of the catenary. From this, you may lay out the catenary as you please, as long as it is at least 6 mm inside the linings.

I recommend a catenary distance 7 - 13 mm inside the lining, or 13-19 mm from the edge. The lower measurement corresponds to a 'full' outside arch (late Strad/del Gesù), and the higher to a more cc type arch.

Edit: I am rather practical in my approach, as Roger Hill suggested. In the C-bout I let the catenary almost touch the lining as illustrated in the article.

[Johnmasters]

I agree, John, where the inflection is placed is a big deal. How you lay out the hourglass is the "art" for the maker to decide. My guess is that the old masters simply did it by "TLAR", ie "that looks about right" for whatever they wanted to try with that particular violin. Perhaps they did use an actual CC to set the inset of the hourglass from the ribs.

Actually, I am also agreeing to TLAR. I don't believe they forced the inflection with any equations. However there is ONE important thing that could have determined the curve marked on the inside of the top in particular. Can you guess? I will bet Stradofear can.

[Roger Hill]

Actually, I am also agreeing to TLAR. I don't believe they forced the inflection with any equations. However there is ONE important thing that could have determined the curve marked on the inside of the top in particular. Can you guess? I will bet Stradofear can.

Well, you certainly don't want the minimum to go through the lower eyes of the F holes, or even too close to them. Maybe those dope-smoking hippies had some other "insights" that I wouldn't think of at my advanced age.

[Oded Kishony]

Hi John,

I hope this isn't too far off topic here but I was very intrigued by your FEA finding that a curve will settle (distort?) into a curtate cycloid shape. Your model was a dome shape with force applied at the center (IIRC). Since the violin is a somewhat different shape what would need to be done to verify that a real violin arch will change to a cc shape over time?

(should this be a new topic?)

ONE important thing that could have determined the curve marked on the inside of the top in particular.

I would think the F hole area and how the F hole profile looks is very dependent on the concave portion of the top.

Oded

[Johnmasters]

Hi John,

I hope this isn't too far off topic here but I was very intrigued by your FEA finding that a curve will settle (distort?) [ move immediately for elastic materials, creep for wood] into a curtate cycloid shape. Your model was a dome shape with force applied at the center (IIRC). Since the violin is a somewhat different shape what would need to be done to verify that a real violin arch will change to a cc shape over time?

(should this be a new topic?) No, it was the perfect question. As for the actual violin arch, even if it is not rigorously a cc, the difference is very hard to see. If you locate the inflection in the right place, I think that the detailed curvature away from that would be very difficult to differentiate from a cc. That is, make it a nice slowly changing curvature, and you are in..... especially if the center is a catenary. You would need a micrometer to measure a difference.

I would think the F hole area and how the F hole profile looks is very dependent on the concave portion of the top.

Oded

The upper and lower bouts are close to half circles, and they are constrained by what is in between. I have no problem with these parts. In general, minimal potential energy for a perfectly elastic material would be a stable configuration. It would still have an inflection, but perhaps not precisely a cc. My FEA program does not provide enough points to make a very good model for a complicated violin shape.

In one dimension, you can clamp down the ends of a bowed metal strap and see something rather familiar, but closer to a cosine curve.

To elaborate, the inflection might move some, but it would not run off the edge of the plate. Try pushing down the center of your clamped strap and you will see what I mean.

I think the f-hole areas could be finished last, as you in fact do anyway. I was thinking that one could easily get a central barrel arch this way, maybe the easiest way to see such a thing.

[~ Ben Conover]

Of the few Guarneri's with original thicknesses, the area around the f holes was not thinned out as much as makers often do today.

Just a thought.

[Ken_N]

I used a light box to find the width of a catenary curve that fits inside of the 5 cross arches of the different posters I have. The resulting shape is different for all of them. Some are very similar, but they may look like a butternut squash shape or a pear shape. That would be a starting point, just like John described in the first post. But, just as Stradofear says, that will account for about 1/2 of the outside shape (he says 33%). The point of inflection is easily figured out if you know where your low point is and how high the arch is. If using a perfect cc it will be somewhat further out from the center to the low point, farther out to the edge where the arching is higher. So what do you do for the recurve, besides using templates, or eyeballs?

[Torbjörn Zethelius]

Of the few Guarneri's with original thicknesses, the area around the f holes was not thinned out as much as makers often do today.

Just a thought.

I believe that's because the thicknessing tool almost doesn't reach into the recurve area of the c-bouts (because of tilting of the plate). You have to do it by feel more or less. But it's not a problem. It's a very natural and straightforward process to finish the outside once the inside is finished.

[Torbjörn Zethelius]

Before we delve much deeper into the problem of finding the perfect outside shape, I must say that in my opinion it's a totally backwards way of engineering. The way I look at it, once the inside is finished I don't worry about the resulting outside. I know that with my method the violin will end up with good classic archings, cc curves or not. The foremost reason for the arch is sound, not the shape.

[Oded Kishony]

once the inside is finished I don't worry about the resulting outside

Once the outside is finished I don't worry about the resulting inside

[Oded Kishony]

John M wrote:

If you locate the inflection in the right place, I think that the detailed curvature away from that would be very difficult to differentiate from a cc.

I'm thinking of the Brescian instruments with the very full arching, often with no concave section. It seems to me (without specifically having examined any recently) that they have not reverted to a cc arch. Is one of the requirements that the arch has to start with some recurve to end up a cc ?

Oded

[Wm. Johnston]

If you are insistant on using little wheels to generate your arching templates then you could use a plain old cycloid or prolate cycloids which can be generated in a similar fashion and won't have the recurve region. Or if you want to go really overboard to try to match an arch to a simple geometrical construction then you could use the same wheels that you do for cycloids but instead of using them on a flat surface roll them on a circular surface and generate epicycloids. If you throw enough variables into the mix you can fit functions to any arch.

[Ken_N]

Since there are no arching templates from the old masters, it is hard to believe they used them.

[Oded Kishony]

If you cast a shadow of a hanging chain with the same width and height over an identical arch, the shadow forms a straight line if your arch is also a catenary

These things are fun!

Oded

[Oded Kishony]

Since there are no arching templates from the old masters, it is hard to believe they used them.

Someone clever pointed out that no rulers were found either, do you find it hard to believe that they never used a ruler?

~OK

[stradofear]

Is Stradivari's chain in the museum in Cremona?

[Roger Hill]

one of them is, kept under lock and key. Cozio pawned the gold ones and used the money to buy dope..........

[Johnmasters]

I'm thinking of the Brescian instruments with the very full arching, often with no concave section. It seems to me (without specifically having examined any recently) that they have not reverted to a cc arch. Is one of the requirements that the arch has to start with some recurve to end up a cc ?

Oded

Yes, that is what I meant ...

What I found was that IF you have an inflection to start with, it might migrate but not clear to the edge. You are saying that the Brescians often don't have any inflection at all (except for a trivial case where the purfling is let in.)

[Johnmasters]

If you cast a shadow of a hanging chain with the same width and height over an identical arch, the shadow forms a straight line if your arch is also a catenary

These things are fun!

Oded

That is a very useful thing to keep in mind, I had not thought of it. Thanks. I plan to use the method to make new patterns for my carving machine.....

[Johnmasters]

Is Stradivari's chain in the museum in Cremona?

It was a previous poster who convinced me that archings were likely more crucial than graduations. I made it a point to try to understand why that might be......

I have seen drawings of a type of C-clamp with a leg, Strad apparently had at least 3. One could hold up a back and ribs........ That is not illustrated in Saconni's book at all.

[Oded Kishony]

JM writes:

.....archings were likely more crucial than graduations.

Some questions i would want to ask from an FEA point of view:

Are there areas that are more sensitive (crucial) ?

How can these areas be identified? Flatter areas, more curved areas?

What is the relationship between changing a larger area of the arch a little bit vs a smaller area more?

I know from my own analysis that these are more or less impossible questions to answer but I'm wondering what can be learned from the attempt.

Oded