The Spaceman Helmet
Above are several views of the collar that I wanted for the spaceman helmet. For the helmet itself I had the toy helmet to tape and pull a pattern from, but how do I come up with a pattern for the collar?
The illustrations above show the theory of attaching two flat pieces of leather together to form a three dimensional object. The silver objects are tubes which represent the helmet (or the crown of a hat). The gold objects represent the collar (or brim of a hat).
If we cut the collar in a donut shape with the inside hole having the same diameter as the tube, when attached the collar will be horizontal. If we cut the collar in a rectangle, when attached the collar will be vertical, ie. continue the lines of the tube.
Since the shape we want is somewhere in between these two extremes, we need to cut the collar in a large curve, as illustrated in the bottom drawing.
However, we don't want a collar that is uniformly angled down. Looking back at the first set of drawings we see that over the shoulders the angle needs to be closer to horizontal than vertical, whereas over the chest and back the angle needs to be closer to vertical than horizontal.
This final drawing shows the compromise made. Since the seams fall at the front and the back of the helmet wearer, the center of the pattern will be over the shoulders. And so, the middle is quite rounded (to make it more horizontal), while the two pattern ends are almost straight (to make them more vertical).