Biology would leave the Game of Thrones dragons grounded

As part of the Game of Thrones blog carnival, Dave Hone takes a look at whether Daenerys Targaryen's dragons could fly if they were real

The dragons from the Game of Thrones books and TV series are, sadly, a fiction but that does not mean they are not worthy of some serious (OK, semi-serious) scientific thought and musings. Certainly they are not the most unlikely animals that scientists have seriously suggested could fly as made famous by the proposition in 1920 that Stegosaurus could take to the air (yes, that Stegosaurus, the one with the plates).

Fictional creations in science fiction and fantasy can certainly be instructive and a great launch point for discussion and thoughts about what might be possible or plausible in reality. Many ideas and concepts have appeared in fiction before serious scientists looked at them, and some have been provided a real inspiration for later research and technological developments. With that in mind, just how plausible are these animals, in particular given their huge size?