The weather was colder, and the "slot" breezier (gusts to 55). The Blue Monday sailed like an old Clorox bottle, blown and tossed by the wind across a meadow of sheep. Monday, night as we sat on the hook at Paradise Cove, we were in the mood for too much beer.

The skipper was math major at Columbia, and after he had talked of the beauty of the math related spheres, we moved on to DRS. A math major from Columbia admitted that the math was "interesting". He suggested that I restate the math. The mark of a great mathematician is that they can make excellent suggestions, even after several beers.

Core to the idea of DRS, we need a mathamatical model of yarn that allows us to plan our yarn in terms of type of construction, fiber, grist, and twist. Set any 3 of those and you have defined the 4th. And, twist can control grist, and grist can control twist. The grist:twist relationship can only be changed by changing construction and/or fiber, or by great effort by the spinner. This is taking Judith MacKensie's intentional spinner and make it quantitative. As Ed Deming would tell us, "You get what you measure!"

If you are spinning wool at a particular twist, then the grist will tend to be very uniform. If you are spinning wool at a particular grist, then the twist will tend to be very uniform. If you want to spin finer, increase the twist. If you want more twist, then increase the grist. These are both easy. If you want a finer yarn at the same twist, then you are going to have to put more work into drafting. Oh, yes, 95% of my spinning skill is on page 383 of Alden's big blue book.

Let us look at the model in more detail;

Let us begin with a flyer/bobbin spinning wheel with drive wheel diameter of "Wd". The bobbin has a effective diameter for winding up yarn of "Bc". The Bobbin has a whorl circumference of "Bwc". Flyer is driven by a whorl with circumference "Fwc".

Thus, the differential rotation speed;

DRS = Bwc/Fwc.

This is the ratio that I go on and on about.

The DRS is important because it controls the inserted twist, and inserted twist controls grist (G). In fact we can calculate/estimate grist from twist (T) and twist from grist.

G=(TPI*TF*FF*CF)^2,; where "TPI" is twist per inch, "TF" is twist factor, "FF" is fiber factor, "CF" is construction factor for woolen or worsted. FF are typically in the 5-10% range and can be ignored for hand spinning, and the construction factor is in the range 1,04 to 1.2 and become large enough to be of interest to hand spinners, but I often lump it in with twist factor leaving me with:

G=(TPI*TF)^2; and TPI= square root (G) / (TF) .

In yards per pound, it is easy, in metric, it is hard. This set of relationships makes working in yards per pound worthwhile.

Now given a particular bobbin whorl, or bobbin effective diameter or flyer whorl, we can calculate the other two components to produce a particular twist or grist, making spinning a particular grist or twist very easy.

Looking at tpi for 10s; we know that 10 hanks per pound is 5,600 yards per pound, and the square root of 5,600 is ~75. Looking at AA pg 383 we see the TF is 0.11. Using TPI= square root (G) / (TF) we get 75 * 0.11= 9 tpi. If I am going to spin worsted "10s", I need to insert 9 tpi. Any other tpi is more work.

Last spring, I put some effort into making a bobbin with a 3" effective diameter (Bc) and a whorl of 1.986" (Bwc). My wheel diameter is 22".

In making 10s with 27 twists in every wrap of the bobbin, the bobbin must rotate 27 times while 3" of yarn are wound on. As the bobbin rotates to insert twist, the flyer must rotate with the bobbin plus or minus 1/27th of a rotation relative to the bobbin. This tiny difference in the relative rotation speeds of the bobbin and the flyer allows twist accumulation; and take-up to occur continuously, and uniformly.

Thus, if (DRS) is = Bwc/Fwc=1.03 the flyer will wind one wrap around the bobbin as the bobbin inserts 27 twists into the yarn. If the effective diameter of the bobbin is 3" then twist will be 9 tpi, and effort by the spinner in drafting will be small. In this case, Bwc is 1.986" and Fwc is 1.912" and the difference is 0.07" (a little more than 1/16"). With DRS, very small differences between the diameter of the flyer whorl and the diameter of the bobbin whorl make very large differences in the grist that the wheel wants to spin. A hank per hour is a reasonable pace to spin this grist. Spinning any other grist with these whorls takes significant effort from the spinner.

However, once the wheel is set to spin a particular grist, spinning that grist is very easy, and much of what I would call spinning effort just goes away. In particular, most single drive wheels have much more slippage than is recognized. Rules of thumb for slippage in the published spinning cannon are for low speed, and drive band slippage increases dramatically as faster spinning is attempted. With double drive/DRS there is much less slippage, and hence much less spinning effort.

If DRS is = Bwc/Fwc=1.02; now the flyer will wind one one wrap of yarn in 50 rotations, so that twist is ~17 tpi, which is just right for 22,000 ypp which is 40 hanks per pound or 150 wpi. With a DRS of 1.02, one can easily spin Romney or Cotswold at its spin count. All of that magic ritual and hocus-pocus of spinning fine goes away, and one can just sit down and spin at the spin count. (That said, I freely admit that a whorl groove that should be producing 40s wants to do 56s. (It is 1/32" too small!) It is not the end of the world, it is ~ +3 tpi. That whorl will get relabeled, put away, and taken out for use for when I want to spin 32,000 ypp. ) At twice the twist, these 40s get spun at half the pace as 10s.

If DRS is = Bwc/Fwc=1.016. Now I can sit down and spin combed 56 count wool at its spin count of 32,000 ypp by using 20 tpi resulting in a spinning pace ~240 yards per hour. I oil the fiber and divide it into slivers of pencil thickness, but that is all very quick, the wool very cheap, and the result is singles that are much thinner than most of the Orenburg lace singles we see today. These singles ares about 60 meter/gram making them finer than any of the wool/Alpaca/goat singles yarns that Lacis sells. (Of course, my fine worsted singles do not have the soft halo that gives Orenburg its lovely softness. My singles do not have enough visual bulk for the Orenburg patterns.)

If DRS is = Bwc/Fwc=1.014, then I am up into 25 tpi, and able to spin Rambouillet and other very fine wools into 80s (45,000 ypp or 91 m/g). I know they are 80s because the staples are finer than 19 microns and there are between 18 and 22 fibers in the cross section of the single. The actual spinning is slow at a couple of hundred yards per hour -- even when working with freshly oiled and combed fiber. Fiber combed with English (5-pitch) combs works very well. The little lice combs work, but are not necessary, and are so slow as to be considered an academic exercise at best. Lice combs are not suited to spinning a useful amount of yarn in a reasonable time frame. I spoil about a third of the flyer whorls in this range that I try to make. If I made more of them, I would get better at making these whorls.

Note well, that small changes in DRS can result in very large changes in grist. Between DRS of 1.016 and 1.014 grist changes by 15,000 ypp. With my current bobbin whorls, 0.1 mm makes a large difference in grist. This process takes a craftsman's attention to detail, but it works.

This is very different from single drive systems or DD with slip, where there is either twist accumulation (during yarn lock) or take-up. For one thing, with less slip, it is faster. For a second, twist, and hence grist is predictable. For 3d, fine yarns can be spun without a tendency for them to drift apart before they accumulate enough twist. For a 4th, the fiber can retain its orientation, so there is no need for inch-worm drafting to produce true worsted lace weight singles. Without the need for inch-worm drafting, worsted can be produced as fast as long draw. (Since worsted requires a lower twist factor, production of worsted can actually be faster than long draw producing the same grist.)

The skipper was math major at Columbia, and after he had talked of the beauty of the math related spheres, we moved on to DRS. A math major from Columbia admitted that the math was "interesting". He suggested that I restate the math. The mark of a great mathematician is that they can make excellent suggestions, even after several beers.

Core to the idea of DRS, we need a mathamatical model of yarn that allows us to plan our yarn in terms of type of construction, fiber, grist, and twist. Set any 3 of those and you have defined the 4th. And, twist can control grist, and grist can control twist. The grist:twist relationship can only be changed by changing construction and/or fiber, or by great effort by the spinner. This is taking Judith MacKensie's intentional spinner and make it quantitative. As Ed Deming would tell us, "You get what you measure!"

If you are spinning wool at a particular twist, then the grist will tend to be very uniform. If you are spinning wool at a particular grist, then the twist will tend to be very uniform. If you want to spin finer, increase the twist. If you want more twist, then increase the grist. These are both easy. If you want a finer yarn at the same twist, then you are going to have to put more work into drafting. Oh, yes, 95% of my spinning skill is on page 383 of Alden's big blue book.

Let us look at the model in more detail;

Let us begin with a flyer/bobbin spinning wheel with drive wheel diameter of "Wd". The bobbin has a effective diameter for winding up yarn of "Bc". The Bobbin has a whorl circumference of "Bwc". Flyer is driven by a whorl with circumference "Fwc".

Thus, the differential rotation speed;

DRS = Bwc/Fwc.

This is the ratio that I go on and on about.

The DRS is important because it controls the inserted twist, and inserted twist controls grist (G). In fact we can calculate/estimate grist from twist (T) and twist from grist.

G=(TPI*TF*FF*CF)^2,; where "TPI" is twist per inch, "TF" is twist factor, "FF" is fiber factor, "CF" is construction factor for woolen or worsted. FF are typically in the 5-10% range and can be ignored for hand spinning, and the construction factor is in the range 1,04 to 1.2 and become large enough to be of interest to hand spinners, but I often lump it in with twist factor leaving me with:

G=(TPI*TF)^2; and TPI= square root (G) / (TF) .

In yards per pound, it is easy, in metric, it is hard. This set of relationships makes working in yards per pound worthwhile.

Now given a particular bobbin whorl, or bobbin effective diameter or flyer whorl, we can calculate the other two components to produce a particular twist or grist, making spinning a particular grist or twist very easy.

Looking at tpi for 10s; we know that 10 hanks per pound is 5,600 yards per pound, and the square root of 5,600 is ~75. Looking at AA pg 383 we see the TF is 0.11. Using TPI= square root (G) / (TF) we get 75 * 0.11= 9 tpi. If I am going to spin worsted "10s", I need to insert 9 tpi. Any other tpi is more work.

Last spring, I put some effort into making a bobbin with a 3" effective diameter (Bc) and a whorl of 1.986" (Bwc). My wheel diameter is 22".

In making 10s with 27 twists in every wrap of the bobbin, the bobbin must rotate 27 times while 3" of yarn are wound on. As the bobbin rotates to insert twist, the flyer must rotate with the bobbin plus or minus 1/27th of a rotation relative to the bobbin. This tiny difference in the relative rotation speeds of the bobbin and the flyer allows twist accumulation; and take-up to occur continuously, and uniformly.

Thus, if (DRS) is = Bwc/Fwc=1.03 the flyer will wind one wrap around the bobbin as the bobbin inserts 27 twists into the yarn. If the effective diameter of the bobbin is 3" then twist will be 9 tpi, and effort by the spinner in drafting will be small. In this case, Bwc is 1.986" and Fwc is 1.912" and the difference is 0.07" (a little more than 1/16"). With DRS, very small differences between the diameter of the flyer whorl and the diameter of the bobbin whorl make very large differences in the grist that the wheel wants to spin. A hank per hour is a reasonable pace to spin this grist. Spinning any other grist with these whorls takes significant effort from the spinner.

However, once the wheel is set to spin a particular grist, spinning that grist is very easy, and much of what I would call spinning effort just goes away. In particular, most single drive wheels have much more slippage than is recognized. Rules of thumb for slippage in the published spinning cannon are for low speed, and drive band slippage increases dramatically as faster spinning is attempted. With double drive/DRS there is much less slippage, and hence much less spinning effort.

If DRS is = Bwc/Fwc=1.02; now the flyer will wind one one wrap of yarn in 50 rotations, so that twist is ~17 tpi, which is just right for 22,000 ypp which is 40 hanks per pound or 150 wpi. With a DRS of 1.02, one can easily spin Romney or Cotswold at its spin count. All of that magic ritual and hocus-pocus of spinning fine goes away, and one can just sit down and spin at the spin count. (That said, I freely admit that a whorl groove that should be producing 40s wants to do 56s. (It is 1/32" too small!) It is not the end of the world, it is ~ +3 tpi. That whorl will get relabeled, put away, and taken out for use for when I want to spin 32,000 ypp. ) At twice the twist, these 40s get spun at half the pace as 10s.

If DRS is = Bwc/Fwc=1.016. Now I can sit down and spin combed 56 count wool at its spin count of 32,000 ypp by using 20 tpi resulting in a spinning pace ~240 yards per hour. I oil the fiber and divide it into slivers of pencil thickness, but that is all very quick, the wool very cheap, and the result is singles that are much thinner than most of the Orenburg lace singles we see today. These singles ares about 60 meter/gram making them finer than any of the wool/Alpaca/goat singles yarns that Lacis sells. (Of course, my fine worsted singles do not have the soft halo that gives Orenburg its lovely softness. My singles do not have enough visual bulk for the Orenburg patterns.)

If DRS is = Bwc/Fwc=1.014, then I am up into 25 tpi, and able to spin Rambouillet and other very fine wools into 80s (45,000 ypp or 91 m/g). I know they are 80s because the staples are finer than 19 microns and there are between 18 and 22 fibers in the cross section of the single. The actual spinning is slow at a couple of hundred yards per hour -- even when working with freshly oiled and combed fiber. Fiber combed with English (5-pitch) combs works very well. The little lice combs work, but are not necessary, and are so slow as to be considered an academic exercise at best. Lice combs are not suited to spinning a useful amount of yarn in a reasonable time frame. I spoil about a third of the flyer whorls in this range that I try to make. If I made more of them, I would get better at making these whorls.

Note well, that small changes in DRS can result in very large changes in grist. Between DRS of 1.016 and 1.014 grist changes by 15,000 ypp. With my current bobbin whorls, 0.1 mm makes a large difference in grist. This process takes a craftsman's attention to detail, but it works.

This is very different from single drive systems or DD with slip, where there is either twist accumulation (during yarn lock) or take-up. For one thing, with less slip, it is faster. For a second, twist, and hence grist is predictable. For 3d, fine yarns can be spun without a tendency for them to drift apart before they accumulate enough twist. For a 4th, the fiber can retain its orientation, so there is no need for inch-worm drafting to produce true worsted lace weight singles. Without the need for inch-worm drafting, worsted can be produced as fast as long draw. (Since worsted requires a lower twist factor, production of worsted can actually be faster than long draw producing the same grist.)

## 1 comment:

Thank you for this post. About half way through, the light came on- and mind you, I thought the light was already on. No, I really got it this time.

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