In an effort to have at least one hat that fits comfortably, I searched for directions for sewn hats or caps. A beret or Tudor hat wasn't quite what I had in mind. Directions for other styles are hard to find.
Following this link I did find this tutorial from which I got the math to figure out band to top piece ratio. I must keep this link; math is not my strong suit, I could never figure out the formula on my own.
Unfortunately, I didn't take during pictures. This is partly because I was figuring things out as I went and didn't feel like stopping the flow of ideas for photo shoots. It is also because I finished the hat before work instead of doing something practical like eating breakfast or packing my lunch.
I used the waistband of an old jacket for the "headband" area and cut the top piece out of the jacket's back. The "headband" part is two inches tall; the minimum for the top of the hat to sit on the top of my head. In the future, I might make this 2.5 inches so that the top of that hat isn't sitting directly on my head.
For the lining, I took all the flexible soft pieces of fabric from my scrap stash and rubbed them on my head, looking for the fabric that produced the least static. They all caused my hair to fly out, so I used the animal print because it called to me more than the grey sheets and I didn't like the look of the bright blue sheets with the sage green hat fabric.
For the bill, I traced the bill of my store-bought black hat, but forgot to add in seam allowance, so my green hat bill is smaller than expected. I think the hat would look more proportional to my head if the bill was a bit larger.
I interfaced the bill piece and the bill lining, but not the rest of the hat.
I cut the top lining approximately one inch larger than the top hat piece, but the "headband" parts are the same size.
I sewed the bill pieces together. The hat and lining pieces I sewed separately (essentially making two hats).
I gathered the top piece to fit it into the "headband." In the tutorial, it says to pleat the lining so that it will fit into the hat. I simply gathered the top lining piece as I had the top hat piece.
I put the lining and hat right sides together (inside each other) and pinned the bill between the layers. I sewed around the open edge of the hat and lining headband, leaving open enough space to turn the hat (pull it through itself so that wrong sides are together). Once turned, all seams are enclosed.
It wasn't my intent, but the hat is reversible.
Somehow, the photos I took of the hat make it look far more flattering than the way it looks in real life. Anyway, at least now I have the formulas and the techniques so I can experiment with sewing hats that fit and flatter.