# Violin bow hair

November 15, 2017, 10:21 PM · What is Mongolian hair look like under a strong microscope? I am not planning to buy one. I am told that they have no barbs as some think.

## Replies (8)

November 16, 2017, 12:06 AM · Um, I wasn't aware any type of horse hair has barbs...!
November 16, 2017, 1:10 AM · You can get a complete study on bow hair, including microscope images of different types, here: https://iwk.mdw.ac.at/?page_id=96
November 16, 2017, 6:41 AM ·
November 16, 2017, 6:42 AM · Thank you Carlos
Edited: November 16, 2017, 8:33 AM · Very good, Carlos. I have seen this information previously, but this link is a very concise and most valuable contribution for this violinist.com forum.

At the turn of the century I was almost obsessive in my testing of bows to try to better understand what is going on and I developed the following (here quoted from my "bow calculator" spreadsheet):

"My measurements give elastic properties of a single hair as 0.79% per Newton = 0.0079m/meter of hair/N/hair = 0.0774 m/m/kg. Or, this could be given as 126.6 N/meter deformation/meter of hair/hair Or 12.9 kg/m/m = 0.0198kg/mm/ bow hair length = 0.194 N/mm. The optimum hair strain for best sound seems to be 0.5 mm, so a force of about 2.5 grams /hair will cause this. A normal force of 0.15 gram will move the hair 1 mm closer to the bow stick. The moments of the forces on the bow (1) bow weight, (2) resolved finger force on bow, and (3) string force on bow hair are resolved about the right thumb as a pivot. So for an optimally tightened bow the required finger force about 60 mm from the right thumb can be estimated from the normal hair deformation.

Anders Askenfelt (Google his name) has reported a Young's modulus for bow hair in the range 4.9 Gpa (GN/m^2), or about 0.2 N/mm for a single hair, with hair elastic up to about 4 N. His measured hairs averaged 0.20 mm ± 0.05 diameter, with a mass (0.65 m long) of 0.03 g/hair and density between 1200 and 1400 kg/m^3. THUS Askenfelt's value of 0.2 N/mm is within 3% of mine (0.194N/mm)."

The last day I worked on this project (that resulted in a "bow calculator" that I had on line for the next 12 years) was 9/10/2001. All my subsequent "bow work" has been devoted to playing music with them.

It is clear that there must be an algorithm relationship between stiffness of a bow stick and the number of hairs in a bow for optimum performance and bow technician should follow this for rehairs (many don't). The origin of the hairs and their thickness distribution will have influence. I believe that not only the "stiffness of the whole stick" as one might measure it, but also the the differential flexibility along the stick affect it's efficacy as a musician's tool in major ways - in other words, where it bends and how much.

I think it is possible to spend a lifetime playing without knowing this - but I have found it helpful these past 16 years.

November 16, 2017, 11:14 PM · I have a question. The data you give is related to the hair flexibility and from that to calculate the number of hairs to give the string the best sound but in the calculation nothing is mentioned regarding the stick flexibility/stiffness apart from a "normally tightened bow". Does that mean that normally tightened bows would have the same properties in the transmission of the force to the hair and to the string? That would be counter to what seems to be the regular practice of looking for almost mystical sticks and pay a lot less attention to the hair...
November 17, 2017, 10:52 AM · I have often wondered about how much of bow evaluation is really about the hair. And I have had a very hard time getting good and consistent rehairs.

People often talk about bow stiffness as if that's a single property. But the overall "stiffness" is a combination of springiness and damping. And stick vibration frequency is affected by how tight the hair is set. And then there is stiffness variation along the length of the bow which is a function of the bow cross section.

Maybe the complexity is why people just look for a magic stick.

November 17, 2017, 5:11 PM · That is some pretty deep bow physics you have experimented with and explained for us Andrew. Thank you even though I did not understand very much of it, especially the numbers part.

Sometimes I am not happy with my rehairs when they try to use a bit too much hair for the stick but since I get a rehair every six months I just live with it till the next one comes along.

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