From: Textile Conservation and Research. A Documentation of the Textile Department on the 20th Anniversary of the Abegg Foundation.
Bern, Schriften der Abbeg-stiftung, 1988
These hats are similar to those found in the excavation of the Mary Rose. They are knit, and are almost the same red color as those I remember from the MR book, "Before the Mast".
The first hat is a part of an overall set of clothing from the Berne Historical Museum. *see full clothing detail here: PANTS
* The clothing was originally attributed to Andreas Wild von Wynigen, who fought in at least one battle in 1499 (Dornach). However, the clothing has since been reexamined and it has been determined that this is more likely a reproduction by other members of the von Wyningen family - specifically a grandson who was a tailor and who may have made the set as a 'historical costume' for himself.
So, if you make the same set of clothing, you at least will be copying a reenactor from the 16th C! *grin*( I really do need to learn how to knit... )