## The Making of Rukario (part 2)

The cones:

These are the cones that stick out from Rukario’s chest and the back of his hands. (I tried to determine whether they were closer to his wrists, but it appears they are closer to the back of his hands.) I assume these are bits of protruding bone.

I was initially going to use polystyrene cones from a craft shop. However, they are way too steep for my liking. If Rukario’s cones were that steep, (a height-to-base ratio of about 2.33) then a backhand slap would have pierced Ash’s throat. Not that the Twerp doesn’t deserve it. It would also have left me with a nine-inch spike sticking out of my chest! However, a rather unscientific measurement of various pictures would suggest a height-to-base ratio closer to 1.5. This simplifies calculations greatly, as can be seen below.

I need to cover only the exposed part of each cone, ie. the lateral surface, in white felt. Now, the net of the lateral surface of a cone is given by the section of a circle with a radius of the cone’s slant height, ie. (r²+h²)½ (where r is the radius of the base of the cone, and h is its height), subtended by an angle of θ = (2πr)/(r²+h²)½.

For a height-to-base ratio of 1.5, ie. h/2r = 1.5, so h = 3r. This gives θ = (2πr)/(r²+(3r)²)½ = (2πr)/(10r²)½ = (2πr)/(r(10)½) = (2π)/(10)½ ≈ 0.632π.

As this is just under (2π)/3, I can make three cones out of one circle, with a π/30 overlap for the seam. And, I just happen to need three cones. How very convenient!

Taking a nine-inch bit of felt, this gives a maximum radius of the circle of 114, ie (r²+h²)½. As (r²+h²)½ = r×10½ and h = 3r, this gives r = 36 and h = 108. This is fine for the chest cone, but for the wrist ones, I want something a bit smaller; one about 45 diameter seems a good size for my hand. This will give r = 22.5 and h = 67.5, requiring a circle of diameter 143.

To actually create the cones, instead of polystyrene pre-fab cones, I decided to laminate a piece of 160 g m-2 card with 2×125 µm film. This gave me the opportunity to print out the nets to cut out.

The cones actually turned out better than I had expected, though probably a bit fragile.  I actually made the cones slightly larger, to give them a “flange” around the base to be attached to the other bit of fabric.