As far as dragon types go, Tolkien had a variety.
Smaug was (as far as I can remember) always described as that type, with the forearms attached to the wings. Glaurung was 4 legged and didn't have wings. Ancalagon the Black was pretty much the Deathwing of Middle-earth, gigantor as all fuck, 4 legs, and 2 seperated wings. Scatha was another, and was more of a long wurm without wings (longer than Glaurung, like Asian dragon style).
Attaching this fan-made image of Earendil vs. Ancalagon just for a size representation. That little glimmer on the left there is Earendil in his ship on the attack. Yeah - pretty much Deathwing-sized.