how does one put a brim on a cap.
the basic idea is that of constructing a cone. but the simple answer is to construct it mostly like a collar. trace the curve on the flat and then extend or shorten the outer edge by cutting and spreading.
one tool that I’ve found invaluable for making hats is a profile copier, (or ‘contour gauge’ if you want to google it.) if you get the lightweight plastic variety, they don’t hurt as much as you press them against your head. (the wire ones can be a bit ‘sharp’…)
anyway, once you get a perfect profile of your head at the level you wish your hat to sit, you can trace it out onto cardboard and cut it out. providing the cutout fits your head perfectly, you’re golden. if not, adjust until perfect. then gild that template, you can use it for everything. secondarily, measure over the top of your head from front to back and side to side. notate the measurements on the gilded cutout disk that you now have for your head pattern and you pretty much have everything that you need for making pieced hats in the future. (by pieced, that is stitched material, leather, twill etc., rather than shaped felt…)
anyway, if you trace that profile onto a material and cut it out, you will end up with a hat with a flat brim. most hats have a bit of an arced brim. the arc is defined by whether the hole is made narrower (left to right) or shorter (front to back) than the original hole. classically, if you are looking at things like western hats, you have those two choices. if you want the front of the hat to come down to a point in front of your face, you make the hat a little wider but shorter than the head profile. that way you have to pull the front and back of the hat out to fit the head. causes the front and back to dip and the sides to rise. but the folds tend towards the front and back. if the hat is constructed to be longer but narrower. causing the fold of the front brim to fold down crosswise across the eyes. the former is far more common than the latter. best to work out the curve you want with some thick paper or thin cardboard before you commit to actual hat samples.
so, in this case, the brim is made a bit wider but shorter.
another way to think about it is that for a flat brim, you use the precise head profile, and for a vertical brim you use a straight line for the back edge of the brim. what you probably want is somewhere in between. actually you can probably mix and match a bit. this might require some experimentation… I may have to get back to you on that. diagrams to follow at a later date…