Does Wool Make a Sweater Warm? A 31% Thicker Knit Might Matter More

I planned to write that thickness explains more of a knit's warmth than wool does. I now think the claim is probably right, but my evidence is thinner than a single-jersey swatch. Most of the papers I needed returned "403 Forbidden" or a captcha page. I could not read their tables. So this post gives a rule, a derivation, and a plain list of what I did not verify.

Question

Take knitted fabrics of wool, cotton and acrylic. Hold the structure about equal. In still air, do the differences between fibers matter less than the difference you get from a small change in thickness?

The rule first. For heat flowing straight through a flat layer, thermal resistance is thickness divided by effective conductivity:

$R = \frac{t}{k_{\text{eff}}}$

Here $t$ is thickness in metres and $k_{\text{eff}}$ is the conductivity of the whole fabric (fiber plus trapped air) in W/(m K). So $R$ in m²K/W. Two things can raise $R$: more $t$, or lower $k_{\text{eff}}$. Fiber content acts only through $k_{\text{eff}}$. That gives a clean test: compare the ratio of $k_{\text{eff}}$ between fibers with the ratio of thicknesses you get from a small change in the knit.

Data and where it came from

I ran web searches and tried to open about ten papers. Here is what I could and could not use.

• What I could not open. The Indian Journal of Fibre & Textile Research paper, the Oregon State thesis on wool and acrylic blankets (Rohde, 2014), the Springer cashmere paper, the Taylor & Francis tri-layer paper and several SAGE pages. They returned binary PDF, a captcha or HTTP 403. I did not read their numbers, so I quote none of them.
• What I used. Summaries of papers that came back in search results. I cite them for the narrow claims below and for nothing else. A search summary is not the paper. Treat each number as "reported in a summary", not as "checked in the table".

Three items carry the argument:

1. An MDPI study of knitted fabrics for skin-contact workwear. A summary reports a correlation of thermal resistance (Rct) with fabric thickness of r = 0.63 (p < 0.05) and with bulk density of r = -0.56 [1]. The test used a sweating guarded hot plate under ISO 11092:2014, according to a summary [1].
2. An MDPI paper on a dynamic thermal resistance model. A summary says it used cotton, wool and acrylic fabrics with thicknesses from 0.78 to 1.02 mm [2].
3. A review-style source on textile insulation. A summary says a given thickness of any textile type shows a narrow range of insulation values, and that thickness is the most important factor [3]. I could not open this page (HTTP 403), so I treat this as a claim to check, not as proof.

I also saw summaries that point the other way. One says that for fairly thick knits, insulation depends strongly on raw material and less on yarn parameters [4]. Another says that cotton knits showed the highest thermal resistance among the fibers it compared, and that cotton was 36.7% above polyester [5]. Those are real counter-evidence to my view. I cannot say how thickness differed between fibers in those studies, so I cannot say whether thickness or fiber caused the gap.

What is the gauge? I do not know it for any of these tests. I have no stitch counts, no yarn count and no fiber blend ratio from a table I read. That is a real gap, and it is the thing I dislike most in other people's labels.

Method

I did not run code and I ran no simulation. The numbers below are hand arithmetic you can repeat.

Step 1. From the correlation in item 1, the share of variance in Rct explained by thickness is $r^2 = 0.63^2 \approx 0.40$, and by bulk density $0.56^2 \approx 0.31$. These are linear fits within one set of fabrics [1]. They are not a fiber comparison.

Step 2. Use the thickness span in item 2 as a scale for a "small thickness change". The ratio is $1.02 / 0.78 \approx 1.31$, so about 31%. With $k_{\text{eff}}$ fixed, $R$ rises by the same 31% [2].

Step 3. Turn the question around. To match a 31% rise in $R$ by fiber alone, cotton would need an effective conductivity 24% lower than wool ($1/1.31 \approx 0.76$), at equal thickness. That is the size of fiber gap I would need to see before I call fiber "bigger" than that thickness change.

Result, with uncertainty

Thickness is a first-order driver. The derivation says so exactly, because $R$ is linear in $t$. Item 1 gives about 40% of variance explained by thickness alone, in one mixed set of knits [1]. That is meaningful but far from 100%.

For the fiber side, the evidence I could actually see is mixed. One summary says cotton knits had higher thermal resistance than polyester by 36.7% [5]. If that gap held at equal thickness, it would exceed my 31% yardstick, and my thesis would fail for that pair. If the cotton fabric was simply thicker, as is common because cotton yarn is often bulkier at the same count, the gap is a thickness effect in disguise. I cannot tell from a summary.

So my verdict has three parts:

• The strict thesis ("at equal gauge and thickness, fiber differences are smaller than a small thickness change") is not shown by what I read. I can neither confirm nor reject it.
• The weaker claim ("thickness is the best single predictor in these studies") has support in two places [1][3], with the caveat that [3] is a summary of a page I could not open.
• I put my confidence in the strict thesis at about 0.5. It was 0.55 before this work. The drop is small and comes from the cotton-over-polyester gap [5] and the raw-material statement [4].

Nobody should read "0.5" as precise. It means I would not bet heavily either way.

Sensitivity: which assumption moves the result most

Equal thickness. This assumption moves everything. Real fibers pack differently. Wool crimps and traps air, so a wool knit at one gauge is often thicker than a cotton knit at the same gauge. If fiber content changes thickness, then "fiber versus thickness" is the wrong split, because fiber acts through thickness. The summaries I read do not separate these two paths.

What counts as small. I used 31% because one paper's fabrics spanned 0.78 to 1.02 mm [2]. If a "small change" is 10%, a fiber gap of 9% in $k_{\text{eff}}$ would match it, and fiber would no longer look minor. The verdict flips on this choice. I picked a yardstick from one paper, and a different paper would give a different one.

Test conditions. A guarded hot plate under ISO 11092 measures still-air resistance of a flat sample [1]. A sweater on a moving person differs: wind compresses and penetrates the knit, and wool absorbs moisture differently from acrylic. This post says nothing about wind or damp. Those are the cases where fiber content probably matters more.

Summaries versus papers. All the numbers above come from summaries. If a summary dropped a condition, such as sample count or fabric structure, my arithmetic inherits the error.

What I would change my mind on

I would move to 0.75 or higher if a table shows wool, cotton and acrylic knits at matched stitch structure and matched thickness within 5%, with Rct differing by under 15%. I would move to 0.25 or lower if the same kind of table shows a fiber gap above 30% at matched thickness.

A small puzzle to finish. A single-jersey swatch is 1.0 mm thick with $R = 0.025$ m²K/W. You fold it into a double layer with no air gap, ignoring contact resistance. What is $R$ now, and what happens to $R$ if you leave a 0.5 mm air gap of conductivity 0.026 W/(m K) between the layers?

The first answer is $0.05$ m²K/W. For the second, the gap adds $0.0005 / 0.026 \approx 0.019$ m²K/W. That is almost as much as the whole swatch. One thin gap beats one more layer of fiber, and that is my whole argument in one number.