The Hudud al-'Alam describes how the Rus "wear woolen bonnets with tails let down behind their necks". See here: http://www.kroraina.com/hudud/index.html and click on item 44. Or see here: http://www.kroraina.com/hudud/hud_44_c.html.
Also, finds from two Birka graves show the presence of 'conical silver terminal mounts' (Arbman 1940-3; Geijer 1938; Roesdahl & Wilson 1992). One of these hats, in grave Bj644, had a 'passement' band fastened from brow to peak (Hägg 1986).
So, there: my short research on the famous Rusvik hat which is so popular amongst Vikings.
I've started on the band which will go from tip to head, and you won't be surprised this is again a bird. Hey, I can't help it, I love birds... I used to be a volunteer bird doctor.
This is what the bird looks like so far, the burgundy outline and the dark yellow stitches make a good body on the green linen. I'll finish the head of the bird first before I decide on the wing colours.
The silver hat-end which is normally used (also known as the Birka end) was too big for Einarr's fancy so we found a smaller one, which is originally from a silver necklace but no doubt it'll make a nice tip on Einarr's new hat.
We have yet to find fabric for the hat itself, but together with the embroidered bird and the fox fur we bought in May this won't be a challenge.
I will keep you posted on further developments.