Sizes
This hat has two sizes: adult medium (6.5 in or 16.5 cm laid flat, fits 20-22 in or 51-56 cm) and large (8 in or 20 cm laid flat, fits 22-24 or 56-61 cm). It is difficult to adjust the length of this pattern other than the length of the ribbing. You could omit rounds 24-27 to make it a bit shorter. My finished hat is about 11 inches (28 cm) deep, unfolded.

Materials
Yarn: approximately 180/240 yds (165/220 m) of worsted weight yarn for sizes Medium/Large. I used Malabrigo Rios. This is a lighter worsted weight yarn (210 yd/200 m per 100 g). If your yarn is heavier, you might run out of yarn and/or have a larger hat. If you are worried about running short of yarn, you can opt for a single brim.

Needles: Size US 6 (4 mm) needles, or whatever size is needed to make gauge, 16-inch (40 cm) circulars, and double-pointed needles (or your preferred method of medium- and small- circumference knitting in the round).
Size US 4 (3.5 mm) needles, or 1-2 sizes smaller than your main needles, 16-inch circulars for knitting the brim ribbing.

Gauge
20 stitches and 27 rows in 4 in x 4 in (10 cm x 10 cm) of stockinette, using the larger needles.