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Neck Binding: a mathematical analysis

21 Jun

I mentioned earlier how I had problems with the neck binding, and I found this video which was very helpful to me.

The video gives some logic behind how to measure for a proper binding length, but it’s more based on feel.  You just “stretch it more” and “it depends on your fabric.”  Now might be  the easiest way to get a good result, but how about some math anyway?

So a neckline is basically a circle that you’ve cut out of your  fabric.  I’m reminded of the scene in Sleeping Beauty where the fairies try to make Aurora (aka Rose) a dress and so they cut a hole in the bottom “for the feet to go”.  Do you remember that?  Classic.

But anyway.. a neckline is a circle.  Not a perfect circle, mind you, it’s more of a lopsided ellipsoid kind of thing, but bear with me.

So let’s measure the circumference ( or the length of the neckline, which we will call neckline_length ) from the pattern.

measure the neckline

For now, we’re going to assume that it’s a perfect circle, so we follow the formula

neckline_length = 2πR

So, say you want your binding to stick out ½”, we will call this binding_width, that means that the radius should also decrease by ½”

binding circumference

binding_length = 2π(R-binding_width)

to find out the proper length of your binding, you do some algebra and come up with this

neckline_length/2π = R
binding_length = 2π(neckline_length/2π - binding_width)

binding_length = neckline_length - binding_width*2π

So, say your neck length is 15″, and you want a binding width of ½”

binding_length = 15 - 1/2*2π
binding_length = 15-π
binding_length = ~11.85 =~11 7/8

So you will need to cut a piece of binding that is 11 7/8″ long.

Yay!  A formula for figuring it out instead of relying on something as intrinsic as feel!

In a perfect world, this would work swimmingly and it should, in theory, be close enough to work well.  But we all know that isn’t the whole story.  Where the curvature of a circle stays the same throughout its circumference, the curvature of your neckline does not.

curvature of necline changes

So what happens then?  Luckily for us, curvature is defined by the radius of a circle that would make it, and radius is already in our formula so we just have to plug it in and see what happens.

say R = 2

binding_length = 2π(R-binding_width)
binding_length = 2π(2-.5)
binding_length = 9.42

now say R = 3

binding_length = 2π(R-binding_width)
binding_length = 2π(3-.5)
binding_length = 15.7

Greater curvature = smaller radius = less binding length = “stretch it more

But there’s something else, you have to take into account the stretch of your fabric.  Why?  Because it’s possible that the correct length for your binding will be so short that you will be unable to set it into your neckline without the neckline gathering.  Why does this happen?  The most probable reason is that your binding fabric is simply not stretchy enough.  So yeah, it “depends on your fabric.” But there must be something you can do!

  • You can iron the gathers out.  Think of it as stretching out the bottom of your binding to be a larger length than it would be naturally.
  • You can decrease the width of the binding.

larger binding width = more easing, shorter binding width = less easing

  • You can try to compensate by sewing the binding together at an angle.  What I mean is that instead of sewing a perpendicular line from top to bottom, you angle your stitches so they go in toward the fold, and out toward the edge.  Thus, you have added extra fabric to the bottom of the binding (where you will be sewing) letting you have more length to ease, which should remove some of the gathering.  This only works up to a point though, otherwise you’ve created a “V” and not a curve.

So tell me, do you feel smart now?  Do you ever use math to figure out this whole sewing thing?

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