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New books for me

 
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wm_crash
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Joined: 24 Feb 2013
Posts: 140
Location: Wilmington, DE - USA

PostPosted: Thu Jan 01, 2015 1:51 am    Post subject: New books for me Reply with quote

Looks like I am starting the new year on a good note, or closing the old one on a good note. Either way, today I got 3 bow making books:

- yet another copy of Henderson (this would make it my 3rd copy)
- Bolander - the actual book
- The Bow Drawings of Scott Zumberge

This last one was the one I was very interested in. I was hoping for detailed measurements of bows from reputable makers. It's that and a lot more. There are extremely detailed frog measurements, button and screw measurements, even ferrule measurements.

It covers mostly violin bows, a few viola bows, and just a few cello bows. Sadly, no double bass bows. I happen to have a pernambuco board thick enough to yield 3-4 bass bow blanks. I think there was a book treating of bass bows only, but I forget the name right now.

Alright, that's all the bragging I had in schedule Wink

cheers,
Cosmin

PS - I guess I was too tired to notice, there are 2 bass bows in the Zumberge book.
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whatwasithinking
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Joined: 26 Jan 2013
Posts: 227
Location: Washington State

PostPosted: Thu Jan 01, 2015 4:12 pm    Post subject: Reply with quote

Hi Cosmin,

I've found the Zumberge book to be helpful. I have an original. I do wish there were complete profiles of the sticks, to reveal the camber and the dimensions of the entire stick. Also, the widths of a stick can be interesting. But three copies of Henderson? I'm thinking maybe one was too many. Wink You have to give him credit for being inventive, though.

When are you going to start making your bass bow?

Bob
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wm_crash
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Joined: 24 Feb 2013
Posts: 140
Location: Wilmington, DE - USA

PostPosted: Thu Jan 01, 2015 5:05 pm    Post subject: Reply with quote

Howdy Bob,

I can totally explain those 3 Hendersons . . . . first one well, it was the first one which also happened to be autographed by Henderson and Siegl. I felt bad carrying it around and potentially abusing it. I found a second copy on eBay a little later which was not as "collectable" (some pencil writing and some highlighting) so I got that as a user. The third one came in an auction bundle of three books as listed in the first post here. I promised myself I'd sell it, but haven't quite gotten there.

Bass bow . . . . it will most probably come before violin bows because the nature of it being bigger - I would figure - makes it easier to handle with respect to shaping. The cambering will be a totally different beast. Everything taken into account, I'd like to have it finished before the end of February. But I've had plans before that didn't go the way I was planning, so don't hold your breath Smile

cheers,
Cosmin
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wm_crash
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Joined: 24 Feb 2013
Posts: 140
Location: Wilmington, DE - USA

PostPosted: Fri Jan 02, 2015 9:56 pm    Post subject: Reply with quote

So about Zumberge and his missing numbers, I downloaded Graphmatica from http://graphmatica.com and tried some logarithmic curve fitting on the Vigneron bass bow model. I ignored the first 3" of measurements for the fitting just because they didn't make sense (i.e., the thinnest point on the stick was 3" away from the head). So I used about 5" worth of stick measurements.

Formula it spits at me is:

y=0.3232+0.0381ln(x)

where x is in inches measured from the the head, x=0 being just below the head (and of course, log doesn't like x=0)

Here are numbers:

0 Error
0.5 0.2968
1.0 0.3232
1.5 0.3386
2.0 0.3496
2.5 0.3581
3.0 0.3651
3.5 0.3709
4.0 0.376
4.5 0.3805
5.0 0.3845
5.5 0.3882
6.0 0.3915
6.5 0.3945
7.0 0.3973
7.5 0.4
8.0 0.4024
8.5 0.4047
9.0 0.4069
9.5 0.409
10.0 0.4109
10.5 0.4128
11.0 0.4146
11.5 0.4163
12.0 0.4179
12.5 0.4194
13.0 0.4209
13.5 0.4224
14.0 0.4237
14.5 0.4251
15.0 0.4264
15.5 0.4276
16.0 0.4288
16.5 0.43
17.0 0.4311
17.5 0.4322
18.0 0.4333
18.5 0.4344
19.0 0.4354
19.5 0.4364
20.0 0.4373
20.5 0.4383
21.0 0.4392
21.5 0.4401
22.0 0.441
22.5 0.4418
23.0 0.4427
23.5 0.4435
24.0 0.4443
24.5 0.4451
25.0 0.4458
25.5 0.4466
26.0 0.4473
26.5 0.4481
27.0 0.4488
27.5 0.4495
28.0 0.4502
28.5 0.4508
29.0 0.4515
29.5 0.4521
30.0 0.4528

Now looking at the butt end of the stick, the actual measurement is 0.478 compared to a predicted 0.45 (give or take depending on unpublished stick length).

I could just use the butt end of the stick in the linear regression to better the model, but I wanted to use it as a sanity check to the function generated by the points at the tip.

Alright, end of ramblings from this occasional math geek Smile

cheers,
Cosmin
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whatwasithinking
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Joined: 26 Jan 2013
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Location: Washington State

PostPosted: Fri Jan 02, 2015 10:28 pm    Post subject: Reply with quote

Very clever! There are some drawings where the stick diameter seems to be still increasing with an increase in distance from the butt, so it might be difficult to guess at the maximum diameter. One could hope that Mr. Zumberge indicated the maximum diameter. And any additional increase might be slight. The camber probably takes only very slight detours from the trend suggested by the drawing of the forward end of the bow. So with your math exercise, we should have a more complete picture.

Bob
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whatwasithinking
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Location: Washington State

PostPosted: Sun Jan 04, 2015 3:37 pm    Post subject: Reply with quote

Cosmin,

Here's one more thing to try, if you're interested. This would probably be a breeze for you as a math geek.

Bow maker Anthony Baylis has suggested that the use of a fourth power equation might be more useful in tapering a bow.

The formula is (db4- da4) ∝ Iab where da and db are the diameters at any two points a and b on the stick, and Iab is the distance between them. The number 4 is the exponent. The advantage of using this formula seems to be that you can start at either end of the stick, and correctly calculate the taper from that point—from the small end just behind the head, or from the fat point just past the wrapping. Might your math utility easily handle that for various bows?

I'll have to admit that I quickly put this into a spreadsheet, and the output didn't look right, to me. I probably did something wrong.

Bob
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wm_crash
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PostPosted: Sun Jan 04, 2015 6:23 pm    Post subject: Reply with quote

Hey Bob,

I assume ∝ means proportional, so you need to massage the factor involved. A growth inversely proportional to a fourth power difference has a different growth pattern than a log function. Funny enough, with power of 8, the output is closer to a log. Going to power of 20, stuff gets funny.

It was easy to compare to a log function. I'll see how numbers stack up against an actual bow once I finish some work emergencies (being oncall is fun, I tell ya!)

You (or anyone else for that matter) can email me at wm_crash@hotmail.com for a copy of the excel I have. I don't do dropbox Sad

cheers,
Cosmin
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whatwasithinking
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PostPosted: Sun Jan 04, 2015 7:03 pm    Post subject: Reply with quote

Well, here's how it's supposed to look, comparing the two methods:
(the site deletes spaces, so you have to imagine neat columns)

Diameter Distance along bow

4th power Fetis
5.3 0 0
6.0 64 64
7.0 203 203
8.0 417 410
8.6 590 590
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wm_crash
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Location: Wilmington, DE - USA

PostPosted: Sun Jan 04, 2015 8:09 pm    Post subject: Reply with quote

Here is what I have that produces numbers in inches:

=SQRT(SQRT(refdiameter^4 + factor*(targetpoint - refpoint)))

refpoint = point along stick where diameter was measured
refdiameter = value of measured diameter
targetpoint = point where you try to compute diameter
factor = fudge factor to bring some sanity

in my case

refpoint = 1
refdiameter = 0.3232
targetpoint = vary this from 0 to 30 in an excel row
factor = 0.002

For 8th power:

=(refdiameter^8 + factor*(targetpoint - refpoint))^(1/Cool

factor = 0.0001, rest of numbers same as above

Now, here are produced numbers at 28":

ln from previous post: 0.45016
4th power: 0.50475
8th power: 0.4800
20th power: 0.4185 (this had fudge factor of 0.000000001)
actual bow: ~0.478

And numbers produced for 8" from the head:

ln from previous post: 0.4024
4th power: 0.3973
8th power: 0.4113
20th power: 0.3915
actual bow: 0.403

I should mention that I adjusted the factor in order to minimize overall deviations from the y=0.3232+0.0381ln(x) produced numbers. Not a great choice, but an easy choice.

cheers,
Cosmin

Edit: is there an emoticon in that formula? It actually is one divided by eight close paren.

Edit 2: not sure I made it clear, the formulas compute expected diameter at the targetpoint.
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whatwasithinking
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PostPosted: Mon Jan 05, 2015 2:38 pm    Post subject: Reply with quote

Cosmin,

You kind of lost me, but it's interesting how these different approaches produce similar results. The fourth power method is common as a way of calculating beam strength in structural engineering.

If you haven't already read this article by Colin Gough, it might be worth a look.

Bob
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wm_crash
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Location: Wilmington, DE - USA

PostPosted: Mon Jan 05, 2015 10:23 pm    Post subject: Reply with quote

Hi Bob,

Managed to upload the file I have to MS' OneDrive:

https://onedrive.live.com/redir?resid=A70453CEB3AFDC4C!156&authkey=!ADsZ8vz3rkmOnzI&ithint=file%2cxlsx

(need to copy paste the whole line since the forum engine misinterprets the url)

You will see the Excel file online, or you can hit the Download on the top left and play with the file locally.

I just had to reformat the equation a little since I like to specify position on a stick and obtain desired diameter, as opposed to specifying diameter and finding the position where it occurs.

cheers,
Cosmin
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