How to make a pattern for an arm bracer- Part 2; Enter the nerdery

I do a lot of 3-D modeling, but I never was a clothing designer. I sewed a shirt once in home ec from a pattern, it was horrible. The breakthrough I had in my design was that a forearm could be approximated as a truncated cone (meaning a cone with the tip cut off- like a megaphone).

All I had to do was unroll it. As a quick image search on Google showed me, a truncated cone basically looks like a rainbow. The top and bottom arcs are concentric and the sides are lines that radiate from the center of the two arcs. The arc lengths (A) and (B) are equal to the diameter of the circles at the top and bottom of the truncated cone. The edges (L) are as long as the distance along the surface of the cone between the circles.

For the true geeks out there here is some trig and algebra -just in case you are transported back in time with only a string, steak and pencil and need to make some Farthings as an armorer, These are the formulae:

Given:

A= wrist circumference= cr₁α (some constant multiplied by the radius and angle); B= forearm circumference= cr₂α; L= external distance between A and B

c= constant= 2π; r= radius; α= angle; r₂= r₁+L

solve A for α, substitute in to equation B, substitute r₁+L for r₂, solve for r₁

substitute c into A solve for α

Be careful with these, they might mistake you for a witch

How it works in real life:

I took the following measurements on my arm:

1. Circumference around the wrist.
2. Circumference of the largest part of my forearm (near where the bicep tendon connects to the forearm when the elbow is at 90).
3. The distance between the two measurements along the top of the arm.
4. The tip of my elbow to my elbow to the location of my wrist measurement.

Measurements A and B are the arc lengths of the concentric arcs.
Measurement L is radial distance between the two arcs.
Using just these three measurements and the formulae, you create a fully constrained pattern for the truncated cone.

Spoiler alert – and I only put this in now because if you’re trying to follow these directions you might miss this bit. I found out later that it is very uncomfortable to have leather on the inside of your elbow reach all the way to your bicep tendon when your elbow is at 90°. It digs in when you try to bend your elbow any further. I suggest 2 inches of space between your bicep tendon and the beginning of the bracer when your elbow is at 90°. For people with other arm lengths than mine, measure from your wrist to your bicep tendon (measurement 3), cut it back about a quarter of the total length.

Don’t worry about measurement M yet, for now assume it stands for magic.