In Peter Jacksons Hobbit trilogy we see his depiction of the black arrow.
So what exactly is a black arrow and what do we know about it? If large iron arrows launched from seige devices are all that is needed to penetrate a dragons hide than what is the signifigance of a black arrow? Let's do a thorough analysis and come up with some rational, logical theories as to what exactly Jacksons black arrows are.
Balin: Girion, the lord of the city, rallied his bowmen to fire upon the beast. But a dragon's hide is tough, tougher than the strongest armor. Only a Black Arrow fired from a wind-lance could have pierced the dragon's hide. And few of those arrows were ever made. The store was running low when Girion made his last stand.
Dwarves are some of the finest forges throughout all middle earth and have continually been progressing in their weaponry technology as new materials were mined. Dwarves have devised weapons out of many materials of the finest grade and have a vast knowledge of the durability these materials possess. Dwarves have fashioned some of the finest iron, and steel grade weapons that middle earth has ever seen and have even advanced as far as making Mithril based armors and weapons in rare ocassions. Dwarves have a long history of confrontation with dragons due to their tendancies of hoarding treasure. Dwarves armor is naturally pretty resistant to dragon fire and Dwarves themselves are highly resistant to heat and cold. Due to their long history and experience with such matters they have knowledge of how to hold their own against dragons in some circumstances. In fact, the dwarves were one of the only races able to stand against Glaurung and make him retreat. Perhaps we can better understand some questions if we refer back to all the LOTR lore to fill in the gaps for more answers regarding visual depictions of certain matters in the movies. I think it is even speculated that Erebor had been attacked in the past by dragons before Smaug. Point being, is the Dwarves were prepared for this kind of thing and even in the movies treated it, like it was a common drill. The thing to take away from this is, perhaps the purpose and intent of Dwarven Wind lances and black arrows, in regards to why they were created and their designs in the first place.
So let's examine what we know. We know Smaug destroyed dale, than smashed right through the front entrance of Erebor rather easily, walked right through the legion of elite Dwarven infantry and shrugged off anything and everything they had to throw at the Dragon. Essentially, he basically decimated two armies of two different factions and convinced the Elves, aiding either of these two armies was useless without a means to kill the dragon.
"A dragons hide is tough, tougher than any armor".
So what would be needed to penetrate the armor? Mithril is said to be as hard as dragon scales and just a small chain mail shirt, much thinner than a dragons hide, made of comparable substance in durability, was sufficient in preventing a cave troll from stabbing through Frodo. Due to the durable nature of not only how hard a dragons scales are, but the thickness of them, we know that it would require some serious fire power and high grade weaponry to penetrate a beast that renders entire armies useless and sacks the greatest kingdom in Middle Earth at the time after destroying Dale, single handidly. Theoritically, you would need something that can cut through armor as strong as Mithril to get through dragon scales. Refering back to the lore of Tolkien, dragons scales gradually built up their strength over time as the case with Glaurung, when he was first vurnable to weapons fire when he was younger and less developed, so I also believe Smaug is a fully developed, old, Dragon.
It should also be noted that most iron and steel have distinctive colors, yet Black Arrows are black. Now given some of these observations, obviously I don't think Black arrows are made of normal material, or have normal properties to be able to punch through dragon scales, but obviously the fact that it is fired from such a device against a fast approaching dragon, 130 meters long, and probably weighing hundreds of tons will play a factor due to all the weight, coupled with the force of the weight, running into a fast moving projectile.
However another quote, perhaps, gives us more insight.
"ONLY a BLACK ARROW, fired from a wind lance could have pierced the dragons hide"
This obviously has to be a reference to the type of material it was made of, and since it is implied that wind-lances were designed to be weapons utilized at attacking dragons and set up in strategic postions inside the city, rather than the outside walls, and refering back to the lore that Dwarves fought dragons on many occcasions, we know that these weapons served the tactical purpose of killing invading dragons. These weapons were designed for this sole purpose in mind.
Disagree? Let's examine the next clue.
"and few of those arrows were ever made".
Once again, it is implied this is a extremely rare material, not easily found, harvested, or produced by convential means. If Black Arrows were nothing more than large iron arrows, they could have made as many as they needed, especially with the economy system Dale was ran on. Yet Smaug decimated two armies and convinced the Elves, that it was a pointless conflict to pertake in, without a means to kill the beast. Even after the Dragon had taken an unimaginable amount of wealth, and mighty kingdom, the dragon sat there undisputed for nearly two centuries. Both Dwarves and men, and even elves for that matter had every plausible motive to kill that dragon afterwards. The Dwarves were devided, and had everything to gain by regaining their kingdom and wealth. Nobody dared wake the beast, and the entrance was sealed. With all the advanced siege weapons the dwarves had, how easy would it have been to take giant Bastillas and await for the dragon to exit the front entrance? If wind lances with iron grade arrows were all that was needed, than why not make more? Why not create so many, that it would ensure a victory against the dragon the second time? Why up until Smaugs death was there only one remaining black arrow that remained?
Obviously, I think in Peter Jacksons films, any critical thinker can come to the conclusion that black arrows are made of a rare metal or material and given all the different things they found in the mountain who knows. Perhaps it is made from partial metoerite or bares similarities to the sword Gurthang in LOTR lore. I hope they explain the exact details in the future, but for now all we can do is speculate.