Doing the math on plying from a center pull ball

I’ve seen some discussion about the changes in twist to a singles when plying from a center pull ball. I thought it’d be fun to crunch the numbers.

WARNING: Really long post ahead!!

TL:DR- Center pull ball plying makes one ply consistently different from the other ply. The effect is small, but it is more noticeable on low twist yarns. Center pull plying consistently makes one ply ever slightly looser and one ply slightly tighter.

Pictures coming soon.
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Effects of plying from a center pull ball on finished 2 ply yarn:

My ball winder has a center core circumference of 6″. A 100g skein ends up with the outer strand (measured as wrapped for one rotation) that is 14″ long.

Assumption: The length of the strand created by each rotation smoothly increases from 6″ to 14″.

WORKING INFO: The inner end of the ball when pulled vertically will gain a twist for each rotation made by the ball winder.

When pulled vertically, the outer end will twist in the opposite direction of the inner yarn, so the outer ply will lose a twist for each rotation of the ball winder.

THOUGHTS:

The most extreme effect will happen when the inner yarn was wound directly on the core and the outer ply is farthest from the core. As the two ends are plied and the plies approach a point in the center of the ball, the effect decreases.

If I have a hypothetical ball of yarn with a 6″ strand for one wrap at the center and 14″ per one wrap at the outside point, the 1/2 way point will be 1/2 way long the layer when the yarn takes 10″ to wrap around the ball forming on my winder.

So here’s my math:

The formula to get the variance:
Divide 1 tpi (the twist created by the rotation of the ball winder) by the length of yarn for the wrap.

Each time I turn the ball winder, I add 1 twist per 6 inches of yarn to the innermost yarn. So in plying that end, the difference in twist in the inner ply will be +0.167 tpi.

Simultaneously, at the outermost piece of yarn, I’ll be losing one twist for every 14″. Or -0.07 tpi for each rotation.
Assuming I don’t turn the ball when plying, I will have a net change of 0.24 tpi when I start of plying.

When I finish plying, which will be when the yarn is 10″ long per rotation, I’ll be gaining 0.1 on the inner ply and losing 0.1 tpi on the outer ply. The difference in twist will be 0.2 twists per inch.

This means that over the yarn plied, the twist variation will slowly drop from 0.24 tpi to 0.2 tpi as the yarn is plied.

(**Note: this is true for my ball winder and this hypothetical ball of yarn. Different core sizes or making larger balls will change these numbers. Using a nostepinne would *really* change these numbers. )

It’s up to the spinner if that change in important in your finished yarn. A quarter of a twist per inch or less isn’t a big deal in a high twist yarn, but it would have more of an impact on a low twist yarn.

If your singles are 6 tpi, then the variance when you start plying is 4%. If your singles are 20 tpi, then variance is just over 1%

To me, the important thing is that the change in twist is happening to the singles not the 2 ply yarn- so one strand will be consistently off from the other. Unlike a yarn with variation along it’s length, center pull plying creates consistent variation between the plies. If there is already a lot of twist variation along the plies, center pull plying would emphasize that

THINKING ABOUT:
The variance is in the singles, so it would be interesting to see how that changes with the ply. A balanced yarn has 2/3 the twist of the singles. With two different twists, the yarn will be less balanced. It would also encourage blooming of the looser ply around the tighter ply. This could be advantageous when spinning halo lace yarns.

Plying off a center pull ball made on a 1″ nostepinne would make for greater variance because the initial variance would be almost doubled.

The variance in the twist won’t change with different yarn diameter. What does change is the quantity of yardage produced.

Thwacking won’t “balance out” the variance well because the change in twist is being made to the singles, but the snapping, thwacking, skeining from a distance acts primarily on plied yarn.

In general, plying from a center pull ball tends to emphasize uneven twist in singles because there isn’t the distance of the drop from the plying point to the bobbin. The 3′ or more stretch out of the singles allows uneven twist within the singles to balance out a bit. This is in addition to the change in twist from pulling the yarn from the ball.