Calculations:Changing Cloth Weight and Weave Pattern While Keeping the Same Structure

Changing Cloth Weight and Weave Pattern While Keeping the Same Structure

This post deals with a slightly more advanced fabric-construction problem. Earlier, the rules helped us answer this question:

How do we make the same cloth heavier or lighter while keeping the same pattern?

Now the question is broader:

How do we make a cloth of a different pattern and different weight, but still keep the same structural character?

So, two changes are happening at the same time: the weight of the cloth is changing, and the weave pattern of the cloth is also changing. This makes the calculation more complex.

Meaning of “Equal in Structure”

“Equal in structure” does not mean that the cloth will look exactly the same. Since the pattern is changing, the appearance will also change. It means that the new cloth should preserve a similar structural balance in terms of yarn thickness, thread spacing, firmness, cover, and general fabric character.

In other words, the new fabric should not become too loose, too crowded, too light, or too heavy merely because the weave pattern has changed.

Why Pattern Change Matters

A woven fabric is not determined only by yarn count and ends or picks per inch. It is also affected by the number of intersections between warp and weft.

An intersection happens where warp and weft cross each other. A plain weave has many intersections. A twill weave has fewer intersections. A satin weave has still fewer intersections.

The number of intersections affects the closeness, firmness, flexibility, cover, and weight of the cloth. If there are fewer intersections, the yarns float more freely. Because of this, more threads may be needed to produce a cloth of similar firmness and structure.

So, when the weave pattern changes, the ends and picks per inch must also be adjusted.

Why the Earlier Method Is Not Enough

One simple method would be to first calculate the new yarn count and threads per inch for the changed weight, assuming that the pattern remains the same. Then, we could adjust the ends and picks for the new pattern using the earlier pattern rule.

But this creates a problem. When the pattern is changed, the weight changes again. For example, changing from a four-end twill to a six-end twill changes the number of intersections and the length of floats. This may require more or fewer threads. That new change in threads then changes the weight again.

So, if we first adjust for weight and then adjust for pattern separately, the second step may disturb the weight obtained in the first step. This means another correction would be needed, and the calculation becomes unnecessarily long.

Therefore, the better method is to combine both changes — weight change and pattern change — in one calculation. This is why the we introduce compound proportion.

Given Example

A cloth is made with the following construction:

Item	Given Cloth
Weave	Four-end twill
Warp	60 ends per inch of 20s yarn
Weft	60 picks per inch of 20s yarn

The fabric is to be changed to:

Item	Required Cloth
Weave	Six-end twill
Weight	One-eighth heavier

We need to find the required yarn count, required ends per inch, and required picks per inch. Since the warp and weft are the same in the given cloth, the same calculation applies to both.

Understanding the Weight Ratio

The required cloth is to be one-eighth heavier. This means the original cloth weight may be treated as 8 parts.

An increase of one-eighth adds 1 more part.

\[ \text{Given weight} = 8 \] \[ \text{Increase} = 1 \] \[ \text{Required weight} = 9 \]

Therefore:

\[ \text{Required weight} : \text{Given weight} = 9 : 8 \]

This is why the calculation uses the numbers 9 and 8.

Understanding the Pattern Factor

Lets  compare the two twill structures by considering:

Pattern factor = number of ends in the repeat + number of intersections

For the given four-end twill, the repeat has 4 ends, and the weft passes over and under two ends. The number of intersections is taken as 2.

\[ \text{Given pattern factor} = 4 + 2 = 6 \]

For the required six-end twill, the repeat has 6 ends, and the weft passes over and under three ends. The number of intersections is again taken as 2.

\[ \text{Required pattern factor} = 6 + 2 = 8 \]

So the pattern factor is:

\[ \text{Given pattern factor} : \text{Required pattern factor} = 6 : 8 \]

This means the required six-end twill has a larger pattern factor than the four-end twill. Because of the longer float structure, the construction must be adjusted to keep the cloth structurally comparable.

Rule:Finding the Required Yarn Count

As the required weight squared is to the given weight squared, and as the ends plus intersections in the given pattern is to the ends plus intersections in the required pattern, so is the given count to the required count.

In simpler formula form:

\[ \text{Required count} = \text{Given count} \times \frac{(\text{Given weight})^2}{(\text{Required weight})^2} \times \frac{\text{Required pattern factor}}{\text{Given pattern factor}} \]

For this example:

Given count = \(20s\)

Given weight = \(8\)

Required weight = \(9\)

Given pattern factor = \(6\)

Required pattern factor = \(8\)

Therefore:

\[ \text{Required count} = 20 \times \frac{8^2}{9^2} \times \frac{8}{6} \] \[ = 20 \times \frac{64}{81} \times \frac{8}{6} \] \[ = 20 \times \frac{512}{486} \] \[ = 21.07s \]

So the required yarn count is about:

21s

This means that although the cloth is becoming heavier, the pattern change also affects the calculation. The new yarn count does not simply become coarser. Because the six-end twill requires a structural adjustment, the final count becomes slightly finer than 20s.

The pattern change can neutralize or even reverse the effect of the weight change.

Rule Finding the Required Ends and Picks Per Inch

As the required weight is to the given weight, and as the ends plus intersections in the given pattern is to the ends plus intersections in the required pattern, so is the ends per inch in the given cloth to the ends per inch in the required cloth.

In formula form:

\[ \text{Required sett} = \text{Given sett} \times \frac{\text{Given weight}}{\text{Required weight}} \times \frac{\text{Required pattern factor}}{\text{Given pattern factor}} \]

For the example:

Given sett = \(60\) ends per inch

Given weight = \(8\)

Required weight = \(9\)

Given pattern factor = \(6\)

Required pattern factor = \(8\)

Therefore:

\[ \text{Required ends} = 60 \times \frac{8}{9} \times \frac{8}{6} \] \[ = 60 \times \frac{64}{54} \] \[ = 71.11 \]

So the required ends per inch are approximately:

71 ends per inch

Since the weft also originally has 60 picks per inch of 20s yarn, the same calculation gives:

\[ \text{Required picks per inch} = 60 \times \frac{8}{9} \times \frac{8}{6} = 71.11 \]

So the required picks per inch are also approximately:

71 picks per inch

Final New Cloth Construction

The original cloth was:

Item	Original Cloth
Weave	Four-end twill
Yarn count	20s
Ends per inch	60
Picks per inch	60

The required cloth is:

Item	Required Cloth
Weave	Six-end twill
Yarn count	Approximately 21s
Ends per inch	Approximately 71
Picks per inch	Approximately 71

Why the Ends Increase Instead of Decrease

This may seem surprising. In earlier examples, when the cloth became heavier, we used coarser yarn and fewer ends. But here, the fabric is not only becoming heavier; it is also changing from a four-end twill to a six-end twill.

The six-end twill has longer floats and fewer binding points per unit of repeat. To maintain the same structural firmness and cover, the fabric needs more threads per inch.

So the pattern change demands more threads. At the same time, the weight increase demands a change in yarn count. When both effects are combined, the final result becomes:

\[ \text{Yarn count: } 20s \rightarrow 21s \] \[ \text{Ends per inch: } 60 \rightarrow 71 \] \[ \text{Picks per inch: } 60 \rightarrow 71 \]

The fabric becomes heavier mainly because there are more threads per inch, even though the yarn itself becomes slightly finer.

Why Compound Proportion Is Better

Compound proportion is useful because it considers two influences at the same time:

Weight change

Pattern change

Instead of adjusting for weight first and then pattern later, it combines both factors into one calculation. This avoids repeated corrections.

If we first calculated for the same pattern and then changed the pattern, the pattern change would alter the weight again. So a further calculation would be required. Compound proportion prevents this.

Applying the Rule to Warp and Weft

The same rule applies to both warp and weft.

For Warp	For Weft
Use warp count	Use weft count
Use ends per inch	Use picks per inch

If warp and weft are different, calculate them separately. If warp and weft are the same, as in this example, the same result applies to both.

General Nature of the Rule

It is again emphasized that the rule is based on proportion. Therefore, it is not limited to one fibre, one yarn type, or one count system.

It can be applied to cotton, wool, silk, linen, or any other yarn, provided the same type of yarn and the same counting system are used consistently.

The same applies to sett systems. Whether the fabric closeness is expressed as ends per inch, picks per inch, or another equivalent sett system, the proportional logic remains the same.

In Simple Terms

This rule is used when both the weight and the weave pattern of a cloth are changed.

If only the weight changes, the earlier rules are enough. But if the pattern also changes, the pattern affects the number of intersections and therefore affects the required number of threads.

In the example:

\[ \text{Original cloth: Four-end twill, 20s yarn, 60 ends per inch, 60 picks per inch} \] \[ \text{Required cloth: Six-end twill, one-eighth heavier} \]

Final result:

Yarn count = about 21s

Ends per inch = about 71

Picks per inch = about 71

So, the new cloth becomes one-eighth heavier and changes to a six-end twill, while still remaining structurally comparable to the original cloth.

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Warp and Weft Calculations: How to Make a Fabric Heavier Without Changing Its Character

Applying Cloth Weight Rules to Both Warp and Weft

The earlier calculations and rules were explained mainly with reference to warp yarns. However, the same rules are equally applicable to weft yarns.

The only change is in terminology. For warp, we speak of ends per inch. For weft, we speak of picks per inch. The principle of calculation remains exactly the same.

Therefore, when a whole cloth is to be made heavier or lighter while keeping the same character, both the warp and the weft must be adjusted proportionately.

Earlier, the rules were used to find the new warp count and the new ends per inch. But a real woven cloth usually contains both warp and weft.

Warp means the lengthwise yarns in the fabric.

Weft means the crosswise yarns inserted during weaving.

If the cloth weight is to be increased or decreased while preserving the same fabric character, then the following must be recalculated:

The warp count must be changed.

The weft count must be changed.

The ends per inch must be changed.

The picks per inch must be changed.

This keeps the cloth balanced. Otherwise, the fabric may become too dense, too loose, too stiff, or quite different in handle and appearance.

Given Example

The original cloth is made with:

Part of Cloth	Original Construction
Warp	56 ends per inch of \(2/30s\) yarn
Weft	60 picks per inch of single \(18s\) yarn

The requirement is:

Increase the weight by one-fifth.

So we need to find the new warp count, new weft count, new ends per inch, and new picks per inch.

Step 1: Convert the Folded Warp Yarn to Equivalent Single Count

The warp yarn is given as:

\(2/30s\)

This means that two yarns of \(30s\) count are folded or twisted together.

In an indirect count system, when two equal yarns are folded together, the equivalent count becomes half.

\(2/30s = 15s\)

Therefore, the warp behaves like a single yarn of approximately:

\(15s\)

So:

Given warp count \(= 15s\)

Given weft count \(= 18s\)

Step 2: Understand “Increase the Weight by One-Fifth”

If the cloth is to be made one-fifth heavier, the original cloth weight may be treated as 5 parts.

An increase of one-fifth adds 1 more part.

\[ \text{Original weight} = 5 \]

\[ \text{Increase} = 1 \]

\[ \text{Required weight} = 6 \]

Therefore, the required cloth weight and given cloth weight are in the ratio:

\[ \text{Required weight} : \text{Given weight} = 6 : 5 \]

Step 3: Find the New Warp Count

The rule for finding the required yarn count is:

\[ \text{Required count} = \text{Given count} \times \frac{(\text{Given weight})^2}{(\text{Required weight})^2} \]

For warp:

\[ \text{Given warp count} = 15s \]

\[ \text{Given weight} = 5 \]

\[ \text{Required weight} = 6 \]

Therefore:

\[ x = 15 \times \frac{5^2}{6^2} \]

\[ x = 15 \times \frac{25}{36} \]

\[ x = \frac{375}{36} \]

\[ x = 10.42 \]

So the required warp count is approximately:

\[ 10.4s \]

In the old notation, this may be written as about:

\[ 10 \frac{5}{12}s \]

So the warp changes from:

\[ 15s \rightarrow 10.4s \]

Since the fabric is becoming heavier, the yarn count becomes lower, meaning the yarn becomes coarser.

Step 4: Find the New Weft Count

The original weft count is:

\[ 18s \]

Using the same rule:

\[ x = 18 \times \frac{5^2}{6^2} \]

\[ x = 18 \times \frac{25}{36} \]

\[ x = \frac{450}{36} \]

\[ x = 12.5 \]

So the required weft count is:

\[ 12.5s \]

The weft changes from:

\[ 18s \rightarrow 12.5s \]

Again, because the cloth is becoming heavier, the weft yarn also becomes coarser.

Step 5: Find the New Ends Per Inch

Once the warp count is changed, the sett must also be adjusted. For this, we use the shortcut rule:

\[ \text{Required weight} : \text{Given weight} :: \text{Given ends} : \text{Required ends} \]

Here:

\[ \text{Required weight} = 6 \]

\[ \text{Given weight} = 5 \]

\[ \text{Given ends} = 56 \]

Therefore:

\[ 6 : 5 :: 56 : x \]

\[ x = \frac{56 \times 5}{6} \]

\[ x = \frac{280}{6} \]

\[ x = 46.67 \]

So the new ends per inch should be approximately:

\[ 46.7 \]

In practical terms, this may be taken as:

47 ends per inch

The number of warp threads per inch is reduced because the new warp yarn is coarser.

Step 6: Find the New Picks Per Inch

The same rule is applied to weft, but instead of ends per inch, we use picks per inch.

\[ \text{Required weight} : \text{Given weight} :: \text{Given picks} : \text{Required picks} \]

Here:

\[ \text{Required weight} = 6 \]

\[ \text{Given weight} = 5 \]

\[ \text{Given picks} = 60 \]

Therefore:

\[ 6 : 5 :: 60 : x \]

\[ x = \frac{60 \times 5}{6} \]

\[ x = 50 \]

So the required picks per inch are:

\[ 50 \]

The weft sett changes from:

\[ 60 \text{ picks per inch} \rightarrow 50 \text{ picks per inch} \]

Final New Cloth Construction

The original cloth was:

Part	Original Construction
Warp	\(56\) ends per inch of \(2/30s\) yarn
Weft	\(60\) picks per inch of \(18s\) yarn

The new cloth, one-fifth heavier, should be approximately:

Part	New Construction
Warp	\(46.7\) ends per inch of \(10.4s\) equivalent warp
Weft	\(50\) picks per inch of \(12.5s\) weft

Since the original warp was a folded yarn, we should remember that the new warp count is the equivalent single count. If it is again to be made as a two-fold yarn, then the folded yarn must be chosen so that its resultant count is about \(10.4s\).

For example, a two-fold yarn close to that might be:

\[ 2/21s \]

because:

\[ 2/21s = 10.5s \]

So, in practical mill terms, the new warp could be approximately:

\(2/21s\) warp and \(12.5s\) weft

Why Ends and Picks Are Reduced

This is the most important point.

To make the cloth heavier, we are using coarser yarns.

\[ \text{Warp: } 15s \rightarrow 10.4s \]

\[ \text{Weft: } 18s \rightarrow 12.5s \]

Because the yarns are thicker, we cannot keep the same number of ends and picks per inch. If we did, the fabric would become too heavy and too crowded.

So the sett is reduced:

\[ \text{Ends per inch: } 56 \rightarrow 46.7 \]

\[ \text{Picks per inch: } 60 \rightarrow 50 \]

This keeps the fabric in the same general character while increasing the total weight by one-fifth.

Why the Rules Apply to Any Yarn Count System

There is a very important general point: these rules are not restricted to cotton counts.

They apply to any yarn-counting system because the calculation is based on proportion.

The author avoids referring to a particular yarn class or count system because the principle is general. It can apply to cotton, worsted, linen, silk, or any other yarn system, provided that the same system is used consistently.

However, one condition is important: the new cloth must be made from the same class of yarn as the original cloth.

That means if the given cloth is made from cotton yarn, the required cloth should also be calculated as cotton yarn. If it is worsted, it should remain worsted. If it is linen, it should remain linen.

Changing from one class of yarn to another is a different problem because different fibres and yarn systems behave differently. That is why separate rules are needed for changing from one class of yarn to another.

In Simple Terms

The earlier rules for changing yarn count and sett are not only for warp. They also apply to weft.

For a whole cloth, both warp and weft must be recalculated.

In the example, the original cloth was:

\[ 56 \text{ ends per inch of } 2/30s \text{ warp} \]

\[ 60 \text{ picks per inch of } 18s \text{ weft} \]

The required cloth is one-fifth heavier. The final result is:

\[ \text{Warp count: } 15s \rightarrow 10.4s \]

\[ \text{Weft count: } 18s \rightarrow 12.5s \]

\[ \text{Ends per inch: } 56 \rightarrow 46.7 \]

\[ \text{Picks per inch: } 60 \rightarrow 50 \]

So, the whole cloth becomes heavier, but because both yarn count and sett are adjusted proportionately, it remains of the same general character.

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Yarn Count and Cloth Weight: How to Make the Same Fabric Heavier or Lighter- Continued

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.

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.

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Yarn Count and Cloth Weight: How to Make the Same Fabric Heavier or Lighter

Changing Yarn Count to Make Cloth Heavier or Lighter

This rule is used when we want to make a new cloth of the same character, but with a different weight, by changing the yarn count.

In simple words, it answers this question:

If I want the same type of fabric, but heavier or lighter, what yarn count should I use?

Here, “same character” means the cloth should remain similar in general construction, appearance, handle, and fabric type. The main change is only in the weight of the cloth.

Meaning of the Rule

The rule says:

The yarn count changes in inverse proportion to the square of the cloth weight.

In the old wording:

As the square of the weight of the required cloth is to the square of the weight of the given cloth, so is the yarn count of the given cloth to the yarn count of the required cloth.

In formula form:

Required yarn count / Given yarn count = (Given cloth weight)² / (Required cloth weight)²

Or:

Required yarn count = Given yarn count × (Given cloth weight)² / (Required cloth weight)²

The important point is this:

If the cloth becomes heavier, the yarn count becomes lower/coarser.

If the cloth becomes lighter, the yarn count becomes higher/finer.

This is because, in cotton count and many indirect count systems, a lower count means a thicker yarn, and a higher count means a finer yarn.

Example Given

A cloth is made with:

20s warp

Now we want to make a cloth of the same character, but:

One-sixth heavier

This means the original cloth had 6 parts of weight. If it becomes one-sixth heavier, its new weight becomes:

6 + 1 = 7 parts

So the weight relationship is:

Given cloth weight : Required cloth weight = 6 : 7

Or in the form used in the rule:

Required weight : Given weight = 7 : 6

Applying the Rule

The rule says:

7² : 6² :: 20 : x

That means:

49 : 36 :: 20 : x

So:

x = (36 × 20) / 49

x = 720 / 49

x = 14.69

So the required yarn count is approximately:

14.7s

In practical terms, this would be taken as nearly:

15s

Therefore, to make the cloth one-sixth heavier, the warp should be changed from 20s to about 15s.

Why Does the Count Become 15s?

At first, it may seem surprising that increasing the cloth weight by only one-sixth changes the yarn count from 20s to about 15s.

But the rule uses the square of the weight ratio, not the simple weight ratio.

The required cloth is heavier in the ratio:

7 : 6

So the yarn count changes in the ratio:

6² : 7²

That is:

36 : 49

Therefore:

20 × 36 / 49 = 14.69

Since the required cloth is heavier, the yarn must be coarser. In cotton count, coarser yarn has a lower count, so 20s becomes approximately 15s.

Understanding “One-Sixth Heavier”

This part is very important.

If a cloth is made one-sixth heavier, it does not mean the ratio is 6:5. It means the original cloth had 6 parts, and one more part is added.

Original weight = 6

Increase = 1

New weight = 7

Therefore, the proportion is:

7 : 6

That is why the calculation uses:

7² : 6²

If the cloth were made one-seventh lighter, then the reverse would apply. The required cloth would be lighter than the original, so the yarn count would need to become finer, meaning a higher count.

Why the Count System Does Not Matter

This means the rule is not limited to cotton count, worsted count, linen count, or any other specific yarn count system. The rule is based on proportion.

So whether the yarn is expressed as 20s cotton, 20s worsted, or any other count system, the proportional calculation remains the same, provided the same count system is used consistently throughout the calculation.

The rule is concerned with the relationship between:

Cloth weight and yarn fineness/coarseness

It is not primarily concerned with the material itself.

Simple Interpretation

If we want to make the same type of cloth heavier, we need a thicker yarn.

If we want to make the same type of cloth lighter, we need a finer yarn.

But the change is not calculated directly by simple proportion. It is calculated using the square of the weight ratio.

Heavier cloth ⇒ lower yarn count

Lighter cloth ⇒ higher yarn count

In Simple Terms

A cloth made with 20s yarn is to be made one-sixth heavier while keeping the same character. Since one-sixth heavier means the weight changes from 6 parts to 7 parts, we use the squared ratio:

7² : 6² :: 20 : x

This gives:

x = 14.69

So, the required yarn count is nearly 15s.

Therefore, to make the fabric one-sixth heavier, the yarn must be changed from 20s to about 15s, because 15s is coarser and will produce a heavier cloth.

Having found the counts required, it will be necessary now to find the ends per inch of that count which will produce a cloth of the same character as the given cloth. Please continue here to read more. 

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