The Physics of Fabric -- or the Fabric of Physics August 19 2014



As I wrote the description for a hat recently, it seemed like a good opportunity to point out the physics of fabric, or the fabric of physics.

Sewing a length of satin fabric to the same length of knitted mohair fabric for the first time requires -- ummm -- it never works the first time. (That's why it is almost impossible to mass produce hats from small lots of fabric, because it takes too much time to perfect the seam and changeover equipment, such as lower and upper needle tension, presser foot pressure, feed-dog height, adjustment to differential feed-dogs, etc., etc., etc.)

So here's the physics: sewing these two fabrics together AND having the seam end at the same place without buckling or stretching is really a problem of solving a series of quadratic equations of the form Ax^2 + Bx + C = 0, where the variables account for the physical properties of the fabric. 

Now, when I was in high school or college, it would have been really helpful if the professors brought to class swatches of fabric to demonstrate mathematical concepts (instead of just writing a bunch of numbers on the board, drawing car engines, and waving their hands about). I would have GOT IT a whole lot sooner.

Well, at least my mom taught me to sew and Home Ec was a required subject. 

Likewise polynomial expressions are easily explained by showing a ball of sock yarn which, when knit up, would have a fascinating pattern -- the result of dying the sock yarn at intervals expressed by the polynomial, and accounting for the variables of needle size, foot size, yarn weight, and the color patterns. Hah!

And it's no wonder physicists use the notion of stretchy fabric to describe Einstein's Special Theory of Relativity and 'space-time.'