Adjusting Ends Per Inch When Yarn Count Is Changed
This post continues from the earlier rule where we first found the new yarn count needed to make a cloth heavier or lighter while keeping the same character.
In the earlier example, the original cloth used 20s warp, and we wanted the new cloth to be one-sixth heavier. By that rule, we found that the new warp count should be approximately 15s. Since 15s is coarser than 20s, it will help increase the weight of the cloth.
But after finding the new yarn count, one more adjustment is necessary: we must also find the correct ends per inch, also called the sett.
Why Ends Per Inch Must Be Changed
If we simply replace 20s yarn with 15s yarn but keep the same number of ends per inch, the cloth will not remain of the same character.
There are two reasons for this.
First, the diameter of the yarn changes. A 15s yarn is thicker than a 20s yarn. Therefore, the spacing between yarns must also change. If we put the same number of thicker yarns into one inch, the fabric may become too crowded, stiff, dense, and different in feel.
Second, the weight change will not remain in the required proportion. The target was to make the cloth one-sixth heavier, meaning the weight ratio should be:
6 : 7
But if the same number of ends is used after changing from 20s to about 15s, the weight increase will be too much. The passage says the increase would be roughly in the ratio:
15 : 20
or approximately:
3 : 4
This means the cloth would become about one-third heavier instead of one-sixth heavier. So, to keep the fabric character balanced, the number of ends per inch must be reduced.
Rule: Finding the New Ends Per Inch
As the square root of the count of yarn in the given cloth is to the square root of the count of yarn required for the new cloth, so is the ends per inch of the given cloth to the ends per inch of the required cloth.
In formula form:
√Given count : √Required count :: Given ends : Required ends
This rule is based on the idea that yarn diameter changes according to the square root relationship of yarn count.
In indirect count systems, such as cotton count:
Lower count = coarser yarn
Higher count = finer yarn
So, when we move from 20s to about 15s, the yarn becomes thicker. Therefore, fewer ends per inch are needed.
Example
Suppose the original cloth has:
60 ends per inch
The original count is:
20s
The required count is approximately:
14.69s
or nearly:
15s
Using Rule 48:
√20 : √14.69 :: 60 : x
Now:
√20 ≈ 4.47
√14.69 ≈ 3.83
So:
4.47 : 3.83 :: 60 : x
Therefore:
x = (60 × 3.83) / 4.47
x ≈ 51.4
So the required sett is approximately:
51 to 52 ends per inch
or roughly
51.4 ends per inch
Therefore, the new cloth should use about 51 to 52 ends per inch, instead of 60 ends per inch.
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Rule: Same Rule Using Squares
As the count of yarn in the given cloth is to the count of yarn in the required cloth, so is the square of the ends per inch of the given cloth to the square of the ends per inch of the required cloth.
In formula form:
Given count : Required count :: Given ends2 : Required ends2
Using the same example:
20 : 14.69 :: 602 : x2
This becomes:
20 : 14.69 :: 3600 : x2
Therefore:
x2 = (14.69 × 3600) / 20
x2 = 2644.2
x = √2644.2
x ≈ 51.4
So again, the required sett is about:
51.4 ends per inch
This rule avoids using square roots at the beginning, but eventually the square root has to be taken at the end.
Meaning of “Ends Per Inch” or “Sett”
The words ends per inch and sett are used together.
Ends per inch means the number of warp threads in one inch of fabric.
Sett means the closeness of the threads in the fabric. In some systems, sett may be expressed differently, but the principle remains the same. The rule is based on proportion, so it can be applied to any sett system, not only ends per inch.
This is similar to the earlier rule about yarn count. The exact count system does not matter, as long as the same system is used consistently.
Rule: The Shortcut Rule
After explaining the two rules, there is a much simpler practical rule.
As the required weight is to the given weight, so is the ends per inch of the given cloth to the ends per inch of the required cloth.
In formula form:
Required weight : Given weight :: Given ends : Required ends
In our example, the cloth is one-sixth heavier.
So:
Given weight = 6
Required weight = 7
Therefore:
7 : 6 :: 60 : x
So:
x = (60 × 6) / 7
x = 360 / 7
x = 51.43
So the required ends per inch are:
51.43
Again, this gives the same answer. So the new sett should be about:
51 to 52 ends per inch
Why the Shortcut Works
The shortcut works because the yarn count was already adjusted using the square of the weight ratio.
In the earlier example:
20s → 14.69s
This count change already follows the relationship needed for the new cloth weight. Therefore, when finding the new sett, the relationship between the old and new yarn diameters corresponds directly with the weight ratio.
That is why:
√20 : √14.69
becomes equivalent to:
7 : 6
So instead of doing a longer square-root calculation, we can directly use:
7 : 6 :: 60 : x
This gives the same answer much faster.
Practical Interpretation
The full process is this:
First, to make the cloth one-sixth heavier, change the yarn count from:
20s → 15s approximately
Second, because the new yarn is thicker, reduce the ends per inch from:
60 → 51.4 approximately
So the new cloth construction becomes approximately:
15s warp with 51 to 52 ends per inch
This should produce a cloth that is heavier, but still of the same general character as the original cloth.
In Simple Terms
When yarn count is changed to alter cloth weight, the sett must also be changed.
If we make the cloth heavier, we use coarser yarn. But because coarser yarn is thicker, we must reduce the number of ends per inch.
In this example:
20s, 60 ends per inch
becomes approximately:
15s, 51.4 ends per inch
This gives a cloth that is one-sixth heavier but still similar in character to the original fabric.
