A duckbill cap was the first item I ever purchased from CC Filson. A decade ago, you could buy a Filson duckbill cap in tin cloth, shelter cloth, cotton poplin or wool. Filson even offered a short billed model (my personal favorite). The original duckbill version was fitted and came with a leather sweatband. Filson has dropped the wool and poplin models and switched over to a one size fits all model with a cotton sweatband.
I have a small collection of caps that I rotate through the seasons: poplin for summer, tin cloth for fall, wool for winter and shelter cloth cloth for spring. The duckbill cap makes for an ideal cycling cap. The long bill keeps the sun and rain out of your eyes and the low profile, four panel crowd closely hugs the head (making it possible to tuck the hat under a bike helmet).
I’m unclear on the origin of the duckbill style but there may be a military connection. A gent at the Pacific Aviation Museum in Honolulu once mistook mine for a WWII military reissue.
A few sample duckbill caps from my archives: