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Tourte Bow Dimensions

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Hello everyone, 

I am trying to determine the precise design of the Tourte bow.  I read in Fetis’ account of Vuillaume’s discoveries of Tourte’s bows and want to know if this account is precise and accurate.  When you decrease the lengthwise intervals a cm at a time starting with the 11 cm cylindrical(length of which the diameter does not change) portion starting at the button, when you arrive at and complete the final distance of 1 cm, you reach a total of 66cm in length from button end toward the head of the stick.  Fetis’ account depicts one more lengthwise decreasing interval beyond where we end up (at 1 cm being the last interval), as there is needed to be one more interval to reduce the diameter the 10th and final time from 5.3mm to 5mm likewise.  I need to know the length of this last interval as depicted in the diagram to be the perpendicular y,z , how do we arrive at this final decreasing length, and there are a total of 4 cm unaccounted for which we need to reach the 70cm the account states is the length of the stick minus the bow head; how do we finally account for the total length of the last 4 cm.  Fetis gives an additional perpendicular length B, D at 22mm as depicted on the chart, and could this be the length of the head?  If so, the length of the head added to the length of the button, approximately 1.5 cm would equal 3.7 and add this to the 70 cm the account gives for the length of the stick minus the head and we reach 73.7 cm for the entire bow length.  If I am erring please let me know; and could you please let me know how I am mistaken too.  Thanks a lot in advance everyone.

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Have you read this? http://knutsacoustics.com/files/gough-taper,-jasa-camber-and-flexibility.pdf

from page 6 in the pdf: (ignore some of the maths in the last two lines as its garbled when i copied and pasted it)

" the base line, a point was first marked off along the base line equal to the height of the first perpendicular representing the initial 110 constant diameter section of the stick. At the end of this section, a new vertical line was raised to intersect the sloping line. Using a compass, this length was added to the first section. The process was then repeated until the remaining sections exactly fitted into the length of the bow stick.The height of the 22 mm upright at the end was chosen so that the fractional decrease in length b = 1-(A-B)/700=0.874 between successive sections had the correct value to allow this perfect fit. Apart from the initial, constant-diameter, section, each subsequent section marked the lengths over which the diameter decreased by 0.3 mm (3.3 mm in total). Vuillaume presumably determined the length B by trial and error. Mathematically, this requires the sum of the lengthsAP11obn¼700 mm;with a ratio of lengths B/A¼b12¼22/110¼1/5. This gives the above value forbwithAP11obn¼700:5mm"

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For what it's worth...both tracts are rabbit holes I fell into and wasted way too much time with.


It's wood. You don't need to be that technical. It won't do anything for the quality of your bows.

 

Most sticks can be adequately defined by grads at six evenly spaced  points connected by long smooth planing.

 

 

 

 

 

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9 hours ago, bengreen said:

For what it's worth...both tracts are rabbit holes I fell into and wasted way too much time with.


It's wood. You don't need to be that technical. It won't do anything for the quality of your bows.

 

Most sticks can be adequately defined by grads at six evenly spaced  points connected by long smooth planing.

 

 

 

 

 

I agree:)

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For those of us who are largely ignorant of details of bow making, could some walk through the main points of making in French style?  Maybe compared to a different process like German making.

Perhaps even the framing of my question is ignorant?

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On 6/15/2019 at 4:28 AM, fiddlecollector said:

Have you read this?

I read and misunderstood much of this a while back.  After looking at it now, I see that I falsely assumed the progression of the length increments.  After comparing this with the Woolhouse account pasted below and referred to in the afore article, it appears much simpler.  All you need to do is draw the Vuillaume diagram in actual life size, starting from the frog end, the cylindrical portion measures out to 110cm, then mark all the mm increments all the way to Vuillaume's 22 mm perpendicular, which will totally add up to, not including the 22mm, 700mm.  With this explanatory millimeter rule, all you need to do to arrive at the 0.3 mm diameter decreasing increments’ positions, is to calculate and mark them below the drawn millimeter rule  at each decreasing perpendicular on Vuillaume’s chart, calculating their diameter in mm starting with 8mm at the cylindrical portion, subtracting 0.3 mm at each perpendicular until you reach 5mm.  With this length real life scale with the corresponding diameter incremental readings below the mm depicted rule, you will be able to size up and accurately carve any bow stick to the chart’s model, which is the model Vuillaume and his students employed, and this enumerated chart will likely prove to be a worthwhile life size reference for checking any Tourte model’s  bow’s accuracy of craftsmanship.   

56 minutes ago, David Beard said:

could some walk through the main points of making in French style Maybe compared to a different process like German making

I’ve noticed two different bow models: the Tourte model, and countless bows with a model that decreases in diameter from the button/frog end to the thumb position and then increases in diameter toward the middle of the stick and progressively decreases toward the head.  I don’t know where the second model I’ve seen originated.   

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9 minutes ago, martin swan said:

I would think the most  fundamental difference is between sticks planed entirely by hand and sticks with their handles turned on a lathe.

Would this account for a handle narrowing from the button to the thumb position?  What difference do you see between hand planed sticks and sticks with their handles turned on a lathe?

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Voirin started making bows   i believe that  increase in diameter from button to a bit past the lapping then gradually decrease towards the head. (if thats what you mean?)

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2 hours ago, fiddlecollector said:

increase in diameter from button to a bit past the lapping then gradually decrease towards the head

Here is a picture of a bow that reduces diameter from the button to the thumb position from 8.5mm to 8.25mm and remains at 8.25mm till about 12cm when it increases to 8.7mm at 14cm from the button and the diameter begins to decrease toward the head at 19cm.  I have commonly seen this, not on just this bow.

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2 hours ago, fiddlecollector said:

Voirin started making

Thanks for letting me know this; I’ll look at pictures of his and others’ bows and try to identify this if I ever see it.

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I believe the Tourte dimensions reflect a linear change in the area moment of inertia as one travels from nut to tip.

The camber represents the way the stick would deflect if it started straight and was subject to a pure bending at one end.

Both of these principals can be used to predict the diameter and camber of the bow. And when the predictions are compared with typical Tourte bows,  they match very well.

However, I doubt the early makers were thinking of such things when they made their bows. It is pure speculation on my part, but the geometry might have been the result of some esoteric ideas they had, and the methods they used to bend the bow.

If you are interested in a mathematical derivation, send me a private message. 

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1 hour ago, ctanzio said:

I believe the Tourte dimensions reflect a linear change in the area moment of inertia as one travels from nut to tip.

The camber represents the way the stick would deflect if it started straight and was subject to a pure bending at one end.

Both of these principals can be used to predict the diameter and camber of the bow. And when the predictions are compared with typical Tourte bows,  they match very well.

However, I doubt the early makers were thinking of such things when they made their bows. It is pure speculation on my part, but the geometry might have been the result of some esoteric ideas they had, and the methods they used to bend the bow.

If you are interested in a mathematical derivation, send me a private message. 

Besides working with Viotti in developing his bow, perhaps Tourte also worked with Fourier?

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At the time Tourte was working out the details of his bow design with Viotti, Fourier was in his late teens to early twenties. But who knows? Fourier appears to have been well connected politically starting in his 20s, but I think the mathematical advances credited to him came much later.

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