Sleeve Caps, Armscyes and Conic Sections

by Susan Partlan on January 28, 2013

I haven’t been able to stop thinking about sleeve caps and armscyes since I read Kathleen Fasanella’s fascinating p0st Sleeve cap ease is bogus on Friday.

Most of my RTW (ready to wear) pieces fit poorly at this interface, which is why I hate RTW!

At church Sunday, daydreaming during communion, I saw approximately 150 RTW sleeve cap/armscye interfaces go by and estimated that 9 out of 10 of them fit poorly.

Why?

I asked Martin to explain why Kathleen’s modified sleeve cap pattern is more anatomically correct and he reminded about conic sections.

Conic sections. Click for source.

If you pretend your arms are the cones and the bisecting planes are the sides of your body where your arms attach, it’s easy to visualize how rotating the cones (keeping the planes in the same position) to approximate the way our arms move will change the shape of the armholes.

It’s hard to see in the above diagram because the planes are moving, not the cones, but you can see that any change in the angle of intersection, of either the cone or the plane, or of both, changes the shape of the intersection.

This animation (viewable using Windows Media Player — I didn’t test other players) illustrates the idea in motion.

In the case of our bodies, our core trunk is fixed. It’s our arms that move, dynamically changing the shape of intersection.

As Kathleen Fasanella points out, since our arms don’t hang at our our sides but are hanging slightly forward on our bodies, the shape of the sleeve cap/armscye intersection needs to approximate that positioning.

Let’s see how this looks in three dimensions, assuming an xyz axis (z is the depth, or near/far axis).

Relating Kathleen’s post back to conic sections, I see two discrete position changes, from the standard sleeve pattern, affecting shape: 1) a depth (near/far) translation of the hanging arm slightly forward along the z axis towards the front of the body (think of rolling clothes in on a clothes line), and 2) a slight x, z arm rotation forward and outward reflecting the fact that our arm pits face forward, not sideways, when our arms are raised over our heads.

To visualize these position changes in 3-D I made two 3-D paper sleeves following Kathleen’s instructions.

First, I hand sketched a copy of Kathleen’s drawing of the typical sleeve pattern and added a dotted line approximating her suggested changes to make the pattern more anatomically correct.

sleeve

The dotted lines show the more anatomically correct shape.

Second, I made two paper sleeves based on the original and modified patterns.

cones

Note that the seam line also moves. It is no longer directly in line with the shoulder seam.

Obviously, in real life, the bottom of our sleeves don’t make a perfect horizontal intersection with a plane, as pictured here, but let’s pretend they do so we can stand them up (any angle at all would make them fall right over).

Can you see that the sleeve opening on the right intersects an invisible plane at a completely different angle than the more anatomically correct one on the left?

Can you see that the way the sleeve opening on the left intersects an invisible plane is a better approximation of how our arms actually hang on our bodies? You kind of have to imagine yourself doing a one-arm hand stand, on your side, with the arm ending not in your hand but in a flat surface, as pictured, to get the idea.

Since it’s not possible to design a sleeve cap/armscye for every shape our arms create as we move, pattern makers like (hopefully) us need to settle on approximating one shape, usually the shape created as our arms hang at our sides, at rest, then add some ease so our arms can move freely in the garment.

{ 26 comments… read them below or add one }

Sarah W January 28, 2013 at 7:12 pm

Hey, my geometry teacher was right—parabolas ARE cool!

BTW, is it the sleeve opening on the right or the left that is anatomically correct? Right is mentioned twice . . .
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Susan Partlan January 28, 2013 at 7:16 pm

Hi Sarah, you’ve got a fast eye! It is the sleeve on the left that is anatomically correct.

It’s so frustrating to me how many times my eyes can go over a post looking for typos before posting and not see any, until I post! I caught that one and updated immediately, probably while you were in the middle of commenting.

Thank you for catching it!

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deja pseu January 28, 2013 at 7:19 pm

Wow, color me impressed. I always find the science behind these things fascinating.
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Susan Partlan January 28, 2013 at 7:31 pm

Susan, I know, I couldn’t put it down!

It was such an eye opener seeing all of that ill-fitting RTW go by on Sunday.

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Pat: SSB January 28, 2013 at 8:27 pm

The only way I figured out the left side was the correct one is the dimple in it — which suggested it moves which you say is good thing. Other wise -let me be frank – the whole thing went miles over my head (think I missed all the geometry classes when that kind of stuff was discussed).

Although I do agree fitting armholes was always a big toughie. Looks like we will be getting a good education here on pattern fitting…
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Susan Partlan January 28, 2013 at 8:48 pm

Nope. The dimple isn’t the difference.

It’s the shape of the armhole, centered in one view and slightly askew in the other, more correct one.

I know people hate thinking about this stuff!

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Kathy Peck Leeds January 29, 2013 at 4:53 am

Math was not a class I excelled in, more like barely slipped by. And even now, I go into a brain haze when faced with a geometrical explanation in space (particularly at 4:30am) ~ however, I will say this, being a very visual person. I have never understood the attraction of cap sleeves on a woman’s body. The most universally unflattering sleeve to my eye. If a woman is going sleeveless, I think it’s much nicer to see her shoulder as well. A cap sleeve cuts everyone’s arm off visually, at exactly the wrong place. OK, officially an idiot – just read the link and this has absolutely nothing to do with cap sleeves! But, I’m going to post it anyway as I still dislike cap sleeves. Susan, your brain continues to amaze me.

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Susan Partlan January 29, 2013 at 8:32 am

Hi Kathy,

I don’t like sleeve caps in women’s wear either.

The sleeve cap I’m talking about in this post is specific to pattern making, not sleeve design. All sleeve patterns have a cap which is the part of the sleeve that attaches to the armhole. This part of the sleeve pattern typically looks like a cap, but that’s not anatomically correct. It should look more like an S shape turned sideways.

Back to sleeve cap designs. I know exactly what you mean about it visually looking like the shoulder is being cut off in exactly the wrong place!

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Vix January 29, 2013 at 7:29 am

Goodness me, Susan, you are such an interesting woman, I’m going to looking at sleeve construction from now on in. You’re dead right, so many women wear ill-fitting tops with badly constructed sleeves. x
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Susan Partlan January 29, 2013 at 8:35 am

Hi Vix! All of my RTW fits badly in the sleeves. I dream of arm freedom!

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stacy January 29, 2013 at 9:17 am

Daydreaming about sleeves during Church? You’ve definitely caught the design bug! Love it!

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Susan Partlan January 29, 2013 at 9:25 am

Ha ha! I know. I’m busted!

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RoseAG January 29, 2013 at 10:44 am

Set-in sleeves were a sewing bug-a-boo for me. I always ended up with a pucker someplace.
The picture with the dashed lines showing the improved design was illustrated the point better for me. I found myself thinking about someone whose shoulders are stooped over, wondering if their tailor would add to the back of their sleeve and substract more from the front?
If you’re a woman with a large chest and a lot of underarm tissue would that fitted sleeve make the blouse too small?

The linked article was interesting. I never thought about the pattern maker doing a seperate pattern for each different fabric. Probably that’s one of the little details that distinguishes items you buy at Forever 21 from more upscale retailers.

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Susan Partlan January 29, 2013 at 11:04 am

Yes, I think that’s correct, the more the shoulders sit forward the more you add to the back and subtract from the front to adjust.

You might want a bigger sleeve and armhole to accommodate a larger bust, but I believe there are better adjustments for that case. The deep learning we’re doing is about tailoring menswear. The chest shape is more predictable. I’m also reading about pattern drafting in general, which is geared to women’s wear, so I am coming across discussions of bust fit, but am still a novice. My impression is that the better way to solve the breast/side tissue problem is to get a properly fitting full-cup bra, and then adjust the bust of the garment to fit the bust with bra. A good full-cup bra should take care of the side tissue. This should result in a more flattering look than the baggy look you get widening the sleeve/armhole.

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K-Line January 29, 2013 at 12:02 pm

As a person who’s in the process of doing just this, I concur. Unless there’s a special scenario that I can’t think of (and I’m sure there is) one should not aim to alter armscye depth or sleeve position to accommodate the bust. A good bra and a properly fitted bodice should fix that challenge.

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Susan Partlan January 29, 2013 at 12:16 pm

Kristen, I am so glad you chimed in as you are the one I’ve gleaned most of my bust-fitting knowledge from :).

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K-Line January 29, 2013 at 3:44 pm

I’m earning my keep :-)
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Susan Partlan January 29, 2013 at 4:59 pm

Definitely! And on many levels. xoxo

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coffeeaddict January 30, 2013 at 7:30 am

I’ve already read this article a few months ago and I’m still undecided about the whole sleeve ease dilemma. I still use the sleeve ease in my sewing when I do tops and dresses and I’ve found the sleeve ease provides a great motion range and comfort when wearing clothes that are made of slightly strechy fabric, as for stiff fabric I’ve found the sleeve ease to be a nightmare, mostly becase of the whole pinning and basting but the comfort and range of motion are severely restricted. I’ve been dying to get into a good fitting class but such classes are hard to find here.
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Susan Partlan January 30, 2013 at 9:25 am

To be clear, what I mean by sleeve cap ease is a slight lengthening of the sleeve cap such that fitting it to the shorter armscye seam involves some easing.

Actually, I think Kathleen’s post didn’t address the purpose of sleeve cap ease as much as it explained why the shape of a sleeve cap on a typical sleeve pattern is not anatomically correct.

After reading further, including this post at The Sewing Corner, I think there’s a case for sleeve cap ease being necessary to accommodate the curved shape of the shoulder.

However, I still agree with Kathleen’s main point that the shape of the sleeve cap should be shaped more like a ‘~’ than a bell shape to accommodate the natural position of our arms at rest, even though this means our other arm positions will be somewhat restricted. For example, suppose you wanted to optimize for the position of your arms lifted so that they’re perpendicular to your body. Assuming no sleeve tapering to the wrist (to make the example easier to visualize), the correct shape of the sleeve to accommodate this arm position would be a perfect rectangle. Sewing along the seam would create a perfect cylinder. Why would a perfect circle armscye/sleeve cap shape be correct for this position? Well, looking at the conic sections above, you can see that when the cone intersects the plane at a right angle the shape of the intersection is a perfect circle. And in fact this perfect circle shape is the ideal shape for maximizing full 360 degree range of motion of the arms. Sounds good, but it doesn’t work, because holding our arms out perpendicular to our bodies is exhausting! In order to optimize for the natural position of our arms at rest, we have to give up a little bit of range of motion.

I’m not convinced increasing sleeve cap ease increases range of motion. I get that it accommodates the shoulder curve but don’t get that it increases range of motion, at least not very much. I need to study this further but think the 2 main ways to increase range of motion are to 1) lengthen both the armscye and sleeve cap (by the same amount), and 2) change the shape of the sleeve cap.

Update: studying these three diagrams tells me that you do get a little bit of increased range of motion with added sleeve cap ease, but not that much.

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coffeeaddict January 31, 2013 at 2:56 pm

phew, you’ve totally got me here! Looks like your research into this is far more indepth as well as your understanding on this whole circle, cones, planes… as mine I had to re read what you wrote twice and whilte the theory makes sense, I have no idea how I’d change a pattern to fit my body better
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Susan Partlan January 31, 2013 at 3:22 pm

What I would do and plan to try to do myself is to figure out a good technique for capturing the shape of my armscye/sleeve cap intersection. I’m not sure yet how to capture this shape but one thought I had, similar to the method described in Kathleen Fasanella’s post on saran wrap wrapping to get the bodice shape, is to have Martin wrap multiple layers saran wrap around my arm all the way up to and including the shoulder, mark a dotted line around and under my arm at the armscye/sleeve cap intersection, then cut the wrap off of my arm. I think I should be able to trim to the dotted line for a perfect sleeve cap shape. It would still need to be graded up a size to add the ease. I haven’t tried this yet but will soon.

Update: I realized I didn’t finish this. You need to carefully mark the shoulder seam, and mark points along the dotted line indicating, front, back, sleeve seam, etc. so that you can line it up correctly with the armscye hole in the bodice. I still have no idea whether this is going to work but I can’t wait to try it!

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Ms. M February 3, 2013 at 7:51 am

I used to be very much into flat pattern drafting, and read a lot of Kathleen Fasanella’s posts as well as her book.

I agree with what she says about the shape and position of the sleeve, but I’m not convinced that sleeve cap ease is bogus. I like a little bit of ease in my sleeve caps, and the fact that it’s still used in couture garments and fine tailoring suggests to me that there is a purpose for it. I do, however, tend to use less ease than most commercial patterns allow for.

Kathy in her comment brings up some interesting thoughts about cap sleeves. I love cap sleeves, because they cover up just enough of the flabby part of my inner arms, without cutting off my arms visually at the halfway point, where a regular short sleeve would. Maybe it has to do with the shape of one’s arms. Mine are not big, but just have that little spot of fat that I prefer to cover up.

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Susan Partlan February 3, 2013 at 1:48 pm

Hi Ms. M! I’m not convinced either, but don’t see that ease gives you much in terms of increased range of motion. As for cap sleeves, I’m sure you’re right that whether you like them has to do with the shape of your arms. I find them terribly unflattering on me because the upper part of my arms have grown heavier with age (and weight gain).

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WendyB February 3, 2013 at 4:38 pm

I saw stuff that looked like geometry and blacked out from fear…
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Susan Partlan February 3, 2013 at 6:38 pm

A sharpie like you can learn anything you want to learn.

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