The Many Dimensions of Fiber
Published Alpacas Magazine Spring 2012
We measure our luscious 3D fiber in one dimensional diameters. We can begin to visualize the impact of that fact, with a short refresher in geometry.
First, let’s define density. Many of us check for density on our huacayas by evaluating the resistance we feel when parting the fleece, grabbing a handful, or pushing on the alpaca’s topline and sides. Isn’t that density? Not exactly. That’s assessing fleece weight, mass and volume. True follicular density is the number of fibers per area of skin, which we are taught to assess by feeling for the compactness or solidity of locks of fiber between your fingers.
The best method for obtaining the true follicular density is a skin biopsy, though there are caveats, such as the significant variations in results from different laboratories. But, the expense of biopsies is prohibitive when attempting to evaluate an entire herd, and we all hope to be able to assess density somewhat accurately on an alpaca at any given time.
In this article we’ll explore using fleece weight and volume to aid in assessing true follicular density, when properly factoring in additional information such as average fiber diameter (AFD) and length.
We began by discussing the impact of AFD on our attempts to compare the follicular densities of our alpacas. I mentioned that if two alpacas had equal follicular density and length, and if alpaca #1 was 15 microns, and alpaca #2 was 30 microns, then #2 should have twice as much fleece on him, right?
That seemed pretty significant to me.
“Nope”, Math Guy (AKA Rus) says - “That’s 1 dimensional thinking. You’re trying to assess 3 dimensions: volume. If alpaca #2 is equally dense and long, with twice the AFD he would have 4 times as much fleece on him.”
“No way! How do you figure?”
“Simple, It’s pi - r - squared (π r 2). It’s how you figure the area of a circle, or in the case of 3 dimensions, the volume of a cylinder, and fibers are cylinders. Just ask any guy that’s had to ship pipe. Double the diameter and it takes up 4 times the space.”
To really ‘get’ the concept of ‘π r 2’ - Math Guy had me draw a cross section of four 15 micron fibers. Then in the same sized space - draw a single 30 micron diameter fiber. The picture said “volumes” to me. (see diagram 1). OK! So one 30 micron fiber really does look like it could have the same volume as four 15 micron fibers.
Then we created a chart so I could compare the relative space taken up by fibers of microns from 10 to 30. Using the formula 3.1416 (π) multiplied by the radius (1/2 the diameter) squared, we calculated the area of each fiber. For example, the area taken up by a 15 micron fiber would be: 3.1416 X 7.5 squared (56.25) = 176.7
The area of a 30 micron fiber would be: 3.1416 X 15 squared (225) = 706.9
To include the variable of length, you can multiply the resulting area by the length, to get the total volume of a single fiber. But for now, we assumed identical length and identical true follicular density. Because with those givens, we could calculate the expected effect of different microns on the total fiber volume.
(see chart 2)
And, with few caveats, we can apply those results to fleece weight. We started with a hypothetical example alpaca, which produced 10 pounds of 20 micron fleece. We then used the figures from the Area and Volume chart to extrapolate the expected fleece weights of alpacas that had different microns, but with an equal follicular density and length to our example alpaca.
(see chart 3)
Now how do we use this information?
We examined a number of alpacas in our herd with known microns, and similar fleece length. We compared their approximate current fleece volumes, using tactile resistance and mass checks (pushes and grabs). For example, if one alpaca is 17 micron, and the other is 24 microns, by checking the chart you’ll see that the 24 micron alpaca should feel like it has twice as much fleece as the 17 micron alpaca, if they had equal follicular density and length. Does that seem to be the case? If not, which alpaca likely has superior follicular density?
When making breeding selections, we must be able to select specifically and therefore successfully for the singular trait of follicular density, apart from volume and weight. In our herd, this information explained why several females had failed to breed up as well as expected. I had previously classified one as extremely dense, though she matured at 27 microns. She had been bred to what I had classified as a somewhat less dense, but very fine male. She produced crias less dense than the male, and less fine too. Why didn’t she pass along some of her density? When I used our charts for assessing how much more fleece volume, and more precisely, shorn fleece weight, she should be carrying at 27 microns, I realized she wasn't an extremely dense female after all. Yes, her fleece could hold up a brick. But no, she was not densely packed with follicles. In hindsight, the sire we were breeding her to had a higher follicular density than she did. So the density of the crias was indeed between that of the dam and sire, as was the fineness, resulting in an average cria in both categories. My errors in judgement, which did not properly factor in the impact of AFD, resulted in valuing individuals as superior in the trait of follicular density, when in fact they were not.
There is a higher profit margin in producing finer fleece, even with lower yields.
As an example: One AUS buyer offers $10 per kg for 24 micron fleece, and $44 per kg for 17 micron fleece. If equally dense and long, an alpaca of 24 microns will produce twice as much fleece weight as a 17 micron alpaca. But the 24 micron alpaca will generate $40 for 4 KG of fleece, while the 17 micron alpaca would generate $88 for his 2 KG. Selecting for finer alpacas, over equally dense alpacas with higher fleece weights and micron, will insure a better future for our fiber industry.
Generally speaking, conventional theory implies that truly folliculary dense fleeces tend to be finer. Conventional theory also implies that finer fleeces tend to be shorter, and so fine fleeces are limited in yield. But there are significant exceptions to that theory. And since exceptions exist, those exceptional individuals can eventually create herds carrying the ultimate fleece, that which is dense, fine and long; producing both excellent yield and premium value.
We have used total fleece weights on individuals in our herd to evaluate the accuracy of the fleece weight chart. To remove the variable of true follicular density from the equation, you can use the same alpaca. We assume that an individual adult alpaca does not significantly changed in it's follicular density over time. Imagine this individual has increased by 2 microns a year for 3 years. We would expect his fleece weight to increase proportionally as represented on the weight chart. Using total fleece shearing weights, annualized, with consideration to staple lengths, compare your own alpacas with the charts and see if the weights increase as expected. We have found it to be consistent.
But just when I thought we might have a handle on assessing density -
let’s toss in a few more variables!
Fluffy versus Locky.
I had an interesting discovery when preparing huacaya fleeces for a spin off, weighing out 2 ounces of clean fleece for each alpaca.
I had noticed that some of the fleeces filled up the gallon sized bags more than others - but I hadn’t given it much thought - till I got to the last one. I grabbed a wad of crimpy locks - pulled out a few pieces of hay, and tossed it in the bag. Thinking, well I’m about half way there, I tossed the bag on the scale to see how much more I had to go.
Done. It was already 2 ounces.
Wait - why did 2 oz. of "Fluffy's" fleece fill the bag to overflowing, while "Locky's" just sits there in the bottom 1/2 of the bag? The significant difference? Lock structure.
Fluffy’s fleece was voluminous. She had received good comments on her combination of density and fineness. She was fine - at 18 microns - and had well organized crimp - but little lock structure. Locky's 16 micron, very compact locks hung down on her, and made her seem less voluminous than Fluffy, when we felt her sides and her more open top line. But after shearing, with benefit of fleece statistics such as her surprisingly heavy fleece weight, we found that Locky had a much higher true density than Fluffy. And in fact, one of the highest on the farm.
With suris, we assess fleece weight on the alpaca by feeling for compact locks, lifting the fleece, and visually looking for a lack of volume. We want to see fleece that drapes tightly and heavily along the body. Keep in mind, suris can often be every bit as follicularly dense as huacayas. With huacayas, however, high volume is thought of as correlating with an increase in density and weight. Any hint of the open topline seen on a dense, heavy fleeced suri is thought to be a sign of poor fleece weight on a huacaya.
With Fluffy and Locky’s help, I’m realizing fleece style has also effected my judgement. Some huacaya styles have compact locks of long, very well aligned fibers, which tend to weigh down the fleece. Those traits may result in a slightly suri-like impression, with some styles a bit closer to the suri spectrum than others. With these individuals, when feeling for resistance as is typically done with huacayas, those pushes and grabs can be deceptively unrewarding. Once shorn, however, if these individuals truly have a high follicular density, this may easily be confirmed with their high annualized fleece weight. And once those compact locks are carded, that very crimpy fiber will produce voluminous lightweight yarn.
Which brings us full circle.
We’ve discovered that we can approximate the mathematical impact of micron on volume and weight using π r 2. And while the style of fleece may mislead when assessing volume, annualized fleece weights can provide the information needed to compare the true density of alpacas of different microns.
Of course, no calculations can replace the expert hand in the assessment of alpaca fleece. Many of the fleece traits we prize cannot be measured. Handle. Scale structure. Luster. If your first impression is “ahhhhhhh” and a big smile . . . . don’t rationalize that away! But if you’ve discovered some “aha” tidbits by sharing my recent refreshers in geometry, perhaps you’ll consider adding a few new landmarks to your density map.
(article copyright Delphi Alpacas 12/08/2009 - graph; 2/4/2010)