User blog comment:WitchKingofMorgul/Black Arrow theory/@comment-3981209-20130203210119

Bear in mind Bard didn't usually get into such conflicts as the one with Smaug, his regular battles were probably against bandits and small packs of wargs, from which it would be fairly easy to find. I figured it was called a Black Arrow because of the wood or the fletchings used, not because of the arrowhead itself (which is the smallest part of the arrow). Using a heavy longbow, fully drawn, has the power to punch through the soft underbelly of a dragon's hide. It seems highly unlikely that the arrow was forged from a broken sword, particularly one that had a reputation/tradition of killing its owners.

Regarding Gurthang/Anglachel: "There is malice in this sword. The dark heart of the smith still dwells in it. It will not love the hand it serves, neither will it abide with you long." This was spoken in a prophecy-type deal, and came true for its previous owners. Therefore, it is unlikely that any part of this sword would be so loyal/useful/effective in its future.

In addition, Tolkien hadn't even thought of Gurthang/Anglachel when he wrote the Hobbit.