Stovepipe hat

A stovepipe or stove-pipe hat was an unusually tall top hat favoured by the newly-regenerated second Doctor. He first donned the hat prior to exploring the planet Vulcan. (DW: The Power of the Daleks) However, he apparently became disenchanted with the hat rather quickly, as he rarely wore it following his adventures with Ben, Polly and Jamie in Atlantis. (DW: The Underwater Menace)

Abraham Lincoln also famously wore a stovepipe hat. Will Johnson once wrote Claire Bartlett a letter describing the president's post-war trip to Richmond, Virginia. He said that the "grand stovepipe" allowed the president to stand "two heads taller than any of those around him", making him easy to identify in a crowd. Peri, who was in that crowd with Erimem, later said that the hat was about the only thing they could see of the president. (TN: Blood and Hope)

Behind the scenes

 * Though the televised series never calls it a "stovepipe hat", at least a couple of works of prose fiction — PDA: The Murder Game and TN: Wonderland — do. Nevertheless, some fashion experts might disagree that it's actually a stovepipe, as it doesn't have a flat top.
 * Although Troughton lost the hat after only his third serial, the character was still depicted as wearing it in every one of the second Doctor annuals. Thus, stories were being published after Troughton had relinquished the role — like DWAN: The Mystery of the Marie Celeste — which depicted the second Doctor in his stovepipe.