Ëarendil and Ancalagon

[Pitchwife]

Intriguing question, assuming that Vingilot carried neither phasers nor photon torpedoes... Catapults, maybe?

But seriously, if I had to kill a flying dragon in mid-air, I'd go for the wings. A couple of burning arrows should do the trick.
On the other hand, the more heroic thing would probably be for Earendil to stand on the prow with a spear in hand and wait for Ancalagon to present the soft spot on his belly that every decent dragon's supposed to have.

Great picture, by the way, but incorrect in the way the ship is represented, as we are told by Bilbo in Rivendell that

...no shaven oar
nor sail she bore on silver mast

but was propelled by 'wings immortal' made by Elbereth herself.

PS. Formendacil, you posted while I was still writing. Actually, I like your idea better than mine!