Calculate Sleeve Cap Height Given Top Arm Circumference and Armscye Perimeter

I previously explained why I think the Sleeve Cap can be described by an oval. Basically, a sleeve can be thought of as a cone which intersects the “plane” of the sweater/cardigan.

This produces an ellipse.

The perimeter of the ellipse is at least the same as the perimeter of the matching armscye on the body of the garment. If the perimeter of the ellipse is smaller than the armscye, it won’t “fit” – used in cap sleeves only. If the perimeter of the ellipse is larger than the armscye, you can ease the excess all around, or into the top to produce a gather. In any event, the armscye perimeter can be calculated from the garment body measurements.

You also will have a measurement for top arm circumference. The top arm circumference for a woman of average height is around

Bust 32 36 40 44 48
Top Arm Circumf. 10.5 11.5 13 14 15.5

Don’t forget to add ease! This is an unclothed measurement.

You can see from the diagram below, that the top arm circumference, i.e. the widest part of the sleeve, is equivalent to the width of two ellipses (0.5 + 1 + 0.5 ellipse widths). Hence, the horizontal radius of the sleeve cap ellipse is a quarter of the top arm circumference.

The sleeve cap height is twice the vertical radius of the ellipse, i.e. the same as the height of one ellipse.

If you plug the values for perimeter and horizontal radius into Ramanujan’s Approximation for the perimeter of an ellipse, you can get a good-enough value for the sleeve cap height.

The sleeve cap height is twice the value for c, the vertical radius of the ellipse, approximated by

Where p is the armscye perimeter / pi

And w is the top arm circumference / 4

The approximation above is essentially Ramanujan’s Approximation expressed in terms of one of the radii.

Where did Elanor keep her Armies?

Up her sleevies!

Still working on armholes and armscyes and caps and ellipse perimeters. Was very happy to discover Ramanujan’s approximation for the perimeter of an ellipse:

perimeter formula

from mathsisfun.com

And this great page from My Measuring Tape on drafting different styles of sleeves is easily adaptable to knitted wares.

I have been slowly working my way down through Knitty’s Knitted Sleeve editorial from ’05, and I’m now around about the point where I realise I really have to get the armscye sorted before going ahead with designing the sleeve cap :)

I have the bodice armscye mostly sorted now, but I’ve been looking for some kind of indication as to what slope to use for the curve of the cast off (working up) at the armhole. If it’s too slow to decrease, the armscye will be triangular, and if it’s too quick, it’ll be square. What’s the happy, curvy, medium? I found a physical armscye curve online, having read this article on pattern drafting on Your Wardrobe Unlocked.

So, if the physical object exists, there must be a software equivalent, right? (my design’s totally digital) Or even just an equation… but can I find one? Nay, I say unto thee, my google searching skillz extends not to such a hit.

Still workin’ on it.

Boy is design hard.

But I absolutely looooove it!!!!!

Ooh, update! I’ve discovered from this UTube video by munnikusum, that a good place for the curve to end (just before the vertical rise to the shoulder) is halfway up that shoulder line.