Calling all Scientists and Engineers for a Brush Experiment

There has been a lot of talk here about knot density, how one brush may have a better packed knot than another and one knot may be more dense than another. Well as it has been mentioned before much of this is subjective to feel and appearance. I was going through some threads here and some people mentioned that no one has ever come up with an objective way to measure knot density so I say lets do it. Maybe hairs per square inch, or hairs per square centimeter is the answer but how can one quickly figure this out without counting every hair on a brush. Do we do the measure pre or post break in (although it should not really change. What are we actually trying to measure and how are we going to do it. I think that with the collective power here we can come up with good results. If everyone runs the test on their brush or brushes and then we post the data to a common source we may be able to come up with some interesting results. This may also make it easier for new people to choose brushes and veterans to compare brushes more accurately.

Post your thoughts on how you think we should do this and when we get something coherent I will start a new thread with directions.

Regards
Dave

If we can get the average diameter for each grade of hair we could calculate approx how many hairs per circular area. Anyone have access to a SEM?

Here is a very crude comparison of two 30mm knots, each with a different thickness border. The knot diameter is measured from the outside edges so the thicker the binder material, the less inside diameter remaining for hairs. In the picture below, the top knot has a 2mm thick border, leaving an inside diameter of 26mm. The bottom knot has a 1mm border, leaving an inside diameter of 28mm. Just 2mm of additional diameter translates to roughly 85 SQ mm of additional area available for hairs to be packed in. Assuming a badger hair has a thickness of 0.05mm (human hair has a thickness of 0.0025mm), this means you can fit roughly 11,000 more hairs in just 85mm SQ of area. And I'm only assuming badger hair is twice the thickness of human hair. If badger hair is not that thick, then you could get more hairs per sq mm. Of course, this assumes all other variables are held constant such as packing technique, etc.

I think I am too lazy for that approach.

Traditional brush makers weigh out the hair for each knot. Hair weight should be a good proxy for density.

Of course the problem is that we do not know exactly how much the handle weighs, and the epoxy and the knot glue also contribute. The knot makers no doubt have a target weight for each knot, so it would be ideal if we could get them to publish their specifications.

Also keep in mind that more is not always better - or not for everyone anyway. I have owned a couple of brushes that were a little too dense for my taste.

It's been a long time since I've had any math courses, statistics etc., so I'm sure someone with better knowledge can use this: Would there be a way to get some knots from various sources of the same diameter, determine the average width of a badger hair (if it's not already known) and then measure the circumference of the knot when all the hairs are squeezed as tightly as possible by a string etc.? If you knew the average width of hair and could take that number and divide the total circumference by it, wouldn't that give the approximate number of total hairs per knot? Then, you could measure the knot when fully opened to determine how many hairs per square inch there were, which "should" vary according to the loft, i.e. "floppy brushes" etc. Just thinking "out loud" here. I may be way off in my thinking.

WVUfanMG said:

It's been a long time since I've had any math courses, statistics etc., so I'm sure someone with better knowledge can use this: Would there be a way to get some knots from various sources of the same diameter, determine the average width of a badger hair (if it's not already known) and then measure the circumference of the knot when all the hairs are squeezed as tightly as possible by a string etc.? If you knew the average width of hair and could take that number and divide the total circumference by it, wouldn't that give the approximate number of total hairs per knot? Then, you could measure the knot when fully opened to determine how many hairs per square inch there were, which "should" vary according to the loft, i.e. "floppy brushes" etc. Just thinking "out loud" here. I may be way off in my thinking.

Click to expand...

Sort of like reverse engineering my approach. You could do the string method but how "tight" you pull the string will have to be kept constant and I'm not sure how you do that.

[FONT=&quot]I think that if you couldroughly map the silhouette of the brush knot above the handle while wet, youwill be able to put those numbers into a 3d mapping program to get the hair volume.Once you know the volume of the knot above the handle, you know how much thedisplacement would measure at 100% density. In other words, if you know thevolume of the knot as it sticks out above the handle, you can just dunk it intoa water dish with measurement markings on the side to see how close the brushgets to displacing 100% of its volume. [/FONT]
[FONT=&quot] [/FONT]
[FONT=&quot]At a guess[/FONT]

To add:

[FONT=&amp]Personally, I think that once you start to tie the knot together or put bands around it to try measure the knot width when compressed, the whole density measurement becomes pointless. If tightly wrapped, the know is 100% dense. We are interested in how dense the brush is at rest or in use… right? [/FONT]

[FONT=&amp]We want a knot set at 49mm loftto measure more dense than the same knot set at 55mm loft… right? Or are welooking for knot density regardless of loft? [/FONT]

inspiringK said:

To add:

[FONT=&amp]Personally, I think that once you start to tie the knot together or put bands around it to try measure the knot width when compressed, the whole density measurement becomes pointless. If tightly wrapped, the know is 100% dense. We are interested in how dense the brush is at rest or in use… right? [/FONT]

[FONT=&amp]We want a knot set at 49mm loftto measure more dense than the same knot set at 55mm loft… right? Or are welooking for knot density regardless of loft? [/FONT]

Click to expand...

I was assuming knot density at the base, not at the average or at the middle. Just my assumption.

However, after reading through the whole thread I think that someone else (who is not a wet shaver) may think we're all nuts!

Theoretically, I think if you could somehow calculate the density at the base of the knot you could then derive a ratio of # of hairs:air at any height along the knot

btw...we are all nuts!

m139 said:

Sort of like reverse engineering my approach. You could do the string method but how "tight" you pull the string will have to be kept constant and I'm not sure how you do that.

Click to expand...

IF you could pull the string so it wouldn't tighten anymore, thereby getting as much free space out as possible, you might be able to obtain a pretty decent guess of the numbers of hairs. If each knot was squeezed completely in this manner it wouldn't need to be constant to get a number of hairs. In fact, it shouldn't be constant if different knot manufacturers stuff their brushes differently. You'd have to get a pretty finely tuned measuring device if the difference is only a few hairs though.

I am from the World of Synths, where there are two primary factors that determine knot density.

Because synthetic fibers are solid (not hollow like natural hairs), the number of fibers that can be placed into a given knot size is a function of their diameters. Thinner fibers make denser brushes, and fiber diameter is a measure of absolute density. The Muhle V2 series, the new Frank Shaving PUR-Tech series and the H.I.S. brushes all have Generation 4 fibers, the thinnest in current use for shaving brushes. So fiber diameter is directly related to knot density.

Another factor is the apparent density of knots, which is a factor related to loft, tapering, crimping, flagging and other treatments to the fibers themselves that determine the feel of brushes in actual use.

Manufacturers do have methods to measure the number of fibers per given knot size, but I an not familiar with measures used to determine relative density other than through subjective product testing.

"Arf, arf..."

maxzoran said:

btw...we are all nuts!

Click to expand...

Estimate about 1000 hairs in one gramm of weight for the hair. The hair that goes into the knot is always weighed before the knot is made. The shaving brush makers have a guide that tells them how much hair to weigh for a certain knot size - one reason the effective knots size may vary a bit. I think there are some videos out that shows how the hair is weighed.

Codfish said:

I am from the World of Synths, where there are two primary factors that determine knot density.

Because synthetic fibers are solid (not hollow like natural hairs), the number of fibers that can be placed into a given knot size is a function of their diameters. Thinner fibers make denser brushes, and fiber diameter is a measure of absolute density. The Muhle V2 series, the new Frank Shaving PUR-Tech series and the H.I.S. brushes all have Generation 4 fibers, the thinnest in current use for shaving brushes. So fiber diameter is directly related to knot density.

Another factor is the apparent density of knots, which is a factor related to loft, tapering, crimping, flagging and other treatments to the fibers themselves that determine the feel of brushes in actual use.

Manufacturers do have methods to measure the number of fibers per given knot size, but I an not familiar with measures used to determine relative density other than through subjective product testing.

Click to expand...

To add to the brief synthetic discussion, thinner fibers are one of two major reasons why Generation 4 brushes are different from earlier synthetics in feel and backbone ability. You can pack more fibers into the same space making a stouter knot. The other is the composition of the fibers are closer to higher grade cosmetic brush fibers so the tips are softer.

Rudy Vey said:

Estimate about 1000 hairs in one gramm of weight for the hair. The hair that goes into the knot is always weighed before the knot is made. The shaving brush makers have a guide that tells them how much hair to weigh for a certain knot size - one reason the effective knots size may vary a bit. I think there are some videos out that shows how the hair is weighed.

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Very interesting photo, got any more?

What we really want to know is what you reference; how much hair does each manufacturer specify for each size knot? Since that is presumably proprietary information, we're trying to back into it.

Rudy Vey said:

Estimate about 1000 hairs in one gramm of weight for the hair. The hair that goes into the knot is always weighed before the knot is made. The shaving brush makers have a guide that tells them how much hair to weigh for a certain knot size - one reason the effective knots size may vary a bit. I think there are some videos out that shows how the hair is weighed.

Click to expand...

Well, that's the most mesmerizing picture I've seen this year

Rudy Vey said:

Estimate about 1000 hairs in one gramm of weight for the hair. The hair that goes into the knot is always weighed before the knot is made. The shaving brush makers have a guide that tells them how much hair to weigh for a certain knot size - one reason the effective knots size may vary a bit. I think there are some videos out that shows how the hair is weighed.

Click to expand...

My late-2012 TGN 22-mm finest XH fan knot weighed in at... wait moment, I know I weighed it before I set it. Where did I put that piece of paper? Ah, here it is... 19-g.

That includes the glue at the base of the knot, though. And does the set loft make a difference? I tend to think so.

mblakele said:

My late-2012 TGN 22-mm finest XH fan knot weighed in at... wait moment, I know I weighed it before I set it. Where did I put that piece of paper? Ah, here it is... 19-g.

That includes the glue at the base of the knot, though. And does the set loft make a difference? I tend to think so.

Click to expand...

Even the shape will make a difference weight wise and in terms of density at the tips.

This may be crude, but it might be effective. And I think the OP was looking for simple.

You take the number of hairs in the knot. Let's say it's 60,000. Take the knot size, lets say a 22mm knot. Add two zeros on the end of it. So it becomes 2200.

60,000 / 2200 = 27.27, round to the tenth place, so 27.3 is the knot density.

If the brush was a 22mm knot with 50,000 hairs it would be:
50,000 / 2200 = 22.7

25mm knot, 68000 hairs:
knot density = 27.2
68,000 / 2500 = 27.2