If you stroll around eBay long enough looking for memorabilia related to the Brodhead family and make use of alternate spellings to increase your odds, you’ll eventually run into advertising posters for Broadhead Worsted Mill in Jamestown, New York.
No, as the spelling strongly suggests, a descendant of Captain Daniel Brodhead and Ann Tye (arrived on these shores in1664, and both from Royston, West Riding, Yorkshire) was not involved in the Mill’s founding. Nonetheless, at some point it seems likely that we, the descendants of the Captain and his wife, share a common ancestor given the Mill’s founder, William Broadhead (1819-1910), also hailed from Yorkshire (from a town called Thornton). Royston is a very tiny village located to the northeast of Barnesley, and Thornton is a bit to the west of Bradford. The two are just about 25 miles apart.
Per the Jamestown, New York, website, William had worked in Thornton as a blacksmith before emigrating to the US in 1843. He would have been about 24 years of age when he undertook that great adventure. It appears that initially he took up similar work in Jamestown, but eventually became interested in the textile industry.