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Member Since 15 Aug 2005
Offline Last Active Today, 08:20 PM

Topics I've Started

CONFORMAL mappings

09 October 2015 - 11:57 AM

These are interesting.  I think that "Raguz" or Mr. Robert Zuger actually is intending to do something like this.  If he used the word "conformal map"  he could write the whole thing in 100 words or less.


I think he makes a transverse line at the post and either side is intended to be what we would call a conformal map of the opposite side.  (flipped over as in a mirror)   Doing this would map points of one end of the violin into the other end.  At corresponding points,  the thicknesses and arch height would be the same.  But did he really arrive at a true conformal map ??   I don't know,  I am asking HIM.


I arrived at this in a period of waking up from my sleep.  I often get insights this way.  I recalled that on his website, Mr. Zuger drew a rectangle and drew in it a violin with top and bottom the same size and shape.   Then he moved (continuously) the rectangle sides outward to make a trapezoid.  The drawing went along for the ride.  I thought it was a complete fudge and I threw out the idea completely.  Jim Woodhouse had asked me to take a look at Zuger and I wondered why Jim was not alarmed at this strange pseudo-science.  I now see something of interest.  If only Mr. Zuger had the word "conformal map" in his model,  he could have boiled down his website to a single page.


If y'all find this interesting,  I can post more about the special properties of conformal maps.  In the meantime,  here is a page with many illustrations of conformal maps.   Notice that they preserve angles and shapes at CORRESPONDING POINTS but not "all over the map'  as one could say.  That is to say,  they preserve shapes and angles LOCALLY.  A transformation exists,  but it varies as one moves through one of the areas.  (If you choose the other area,  you use the inverse of the transformation.)



For the math geeks

24 September 2015 - 12:23 PM

I corresponded with ABAQUS student addition manager about a problem with installation and he took an interest in my usage. Here is a site if anyone wants to see how FEA is being used by someone involved with guitars.

He is just revising his site, so perhaps it will eventually be interesting.


Smashed cello top

10 September 2015 - 05:47 PM

I am finishing a smashed cello top for a school. It was a more than a bssic cello, but I offered to fix it cheap as an experiment.

Cleats went under a new bassbar and a shoe inserted for the soundpost which had passed through the top. This was a tiny bassbar-like thingy about 2.5" long with a conical hole in the center. I will make a post with a point to fit in that.

I have done this before for that school, and such a soundpost-hole repair delighted the teacher. The cello was actually better in sound, perhaps because the old post was not fitting.

But that is not what I wanted to say ......... This newer repair had me revarnishing the entire top. So far so good. But now that I am gluing it on, I see that the top has extra perimeter all around.

That must because the arching has flattened out. I won't try to work this out, but it seems to me that a couple of props would push up the arching and allow regluing in the old position, the outline being shown by the remaining varnish on the underside of the top (next to the ribs)

I again wonder if the ventral pin could not have been what is left after such a prop is cut away. Pushing a top to fit tapered ribs in the upper part causes a very noticeable flattening of an arch. It is easily visible to the eye.

I think that if I had put such a prop up between the upper corners (glued into a conical hole) and one between the lower corners (this time not glued in, just put in with soundpost setter.) the arch could remain proud.

I have mentioned this before. Now, I see that the idea of the conical hole being made by the end of an auger bit is also appealing. But what about this other business of a prop ?

Longitudinal Arching

03 September 2015 - 03:02 PM

Uncle Duke has asked me to suggest a good longitudinal arching.

I was able to fit my function to a photograph posted by Mr. Hargrave (I think it was)

Anyway, the shape from the middle of the top to each end was given as cosine to a power of something in the range of 1.3 to 1.7

Of course, calculating all these and plotting by hand is tedious. Just to see the shapes, anyone can go to


and download this software for free. I can then send files for experimental graphs I have made.

They look very close to what I like in an long arch that looks like the old-timers.

Start top-shape over again

03 September 2015 - 01:56 PM

I was asked by Dan-S to start over as what I said was confusing. So I will do that. I am sorry that this has run into a long posting, but maybe the extra wording will keep things clear and make it quick reading if you follow along.

First of all, let me use an example that is not a surface. Forget a violin, and use a simple one-dimensional springsteel strap that is deflected somewhat by being clamped flat at the ends and has a bump in the middle. After a few exchanges with Ctanzio, I finally think I made a point and have not yet heard a response.

First, look at this picture. An article on the net

discusses the bending of a strap (or column of zero cross section). Look down to figure 7.5.5 and see "mode n=2 shape. The end conditions of this strap is "fixed-free" which means one end is not allowed to bend (the free end). This end slides on a frictionless plane. In any case, look at the left-side 2/3. I could spot weld the strap here to the x-axis. That would be the shape of a fixed-fixed strap under end forces. I said it was sinusoidal; Ctanzio said "No" and I think because he thought I was trying to say something else. I assume he is right, he just was not following me, hence my re-delivery.

So, clamp up such a strap. Its shape is sinusoidal (say I) and does not depend at all on how much end forces, at least for small displacements (movements). So if I ADD a little force the bump will be pushed up a little but it will STILL be sinusoidal. Or lets place x,y=0 at the center and call it a cosine. The extra distortion from the extra end forces wil NOT CHANGE the shape.; that is, the extra displacement will be at all points in proportion to the original (bent) shape. (and still a cosine)

This kind of curve I call "optimal." The distorted shape is the original shape just magnified (vertically) by a constant. As such, the potential energy stored in the spring is an absolute minimum. (for all possible shapes at fixed height.)

My experiment will be to see if a pre-bent piece of metal will do the same thing. In other words, if I initially shape a piece of springsteel to be a cosine and put under end forces, it should distort to a magnified cosine. NOW for the real experiment. If I carve the initial piece of metal in a shape that deviates from a cosine, will end forces distort it in a shape CLOSER to a cosine than the original model"?

If the starting bent shape is very shallow, a large force will make nearly a cosine. This is obvious, since if the original shape is at least continuous and of very small amplitude, it will be almost a straight line. (use the typical calculus arguement to shrink the shape to an arbitrarily small magnification in the vertical direction.)

I intend to take a strap with an initial non-cosine shape and a given bump-height which is what I want. Then put end forces on it. The distorted shape should be closer to a cosine than the initial strap. Now I take this shape and magnify it so that the bump is the height is as before. Redo all this. Then take THAT result and repeat. (Or take an average of the first and last shape, or do whatever turns out to be convenient) Do this several times.... or just keep doing it.

The QUESTION IS .......... will this method of reiteration eventually converge to a cosine shape ????

The same situation could be done with a violin top which is now a 2-D SURFACE. I would expect curtate cycloids to work perfectly on a circular dome. The CC is a cosine curve with a distorted x-axis unit spacing. For a violin, in the upper and lower bouts, CC may be close because their shape is roughly circular.

Finally, for a violin top, CC transverse archings may be very close to optimal, but not precisely. (because of the odd outline, the odd boundary conditions) But can the arching-shape be modified slightly by doing an FEA experiment? To do this, I would hold the longitudinal arch, bassbar, f-holes, and sounpost constant. Then put string loads on in FEA and make the bridge force proportional to the string loads. [Some will ask about the constraining of the long-arch,,, I will reply later to keep this short.] At each step of the testing, a new distortion will be taken and put back into an FEA. (bridge forces will be proportional to applied string loads)

IFFFFFF ......... if this process converges to a situation where all distortions from loads in the n-th iteration are in proportion to the last distortion (n-1 th iteration) then I have arrived at the OPTIMAL shape for a violin top... It distorts in a way that distributes stress in an optimum way.

This is a calculation. A similar thing could be done by making a very thin violin and look at the warping. The long-arching is very rigid compared to the warping because of the inflection WHICH CAN MOVE. (Clamp a strap into a cosine and see how easy it is to move the bump back and forth... you are shifting potential energy from one side to the other)

But enough already.