Look at the birds outside your window: little feathery things that beg for crumbs and make cute chirpy noises. What if they were nine metres across and could fold up their wings and walk on all fours? Not so cute. Long ago, just such hulking creatures ruled the skies.

Pterosaurs were Earth's first flying vertebrates. Although birds and bats have taken wing in the 66m years since their extinction, we don't have any flying creatures that approach the size of the biggest pterosaurs. The largest known specimen, Quetzalcoatlus, had a 10-metre wingspan. An immense vertebra recently found in Romania suggests that pterosaurs may have grown even bigger than that. The largest flying animals today, such as the wandering albatross and the Andean condor, average a wingspan of around three metres.

Where have all the giant flyers gone?

Flying animals need three traits to get truly large, according to Michael Habib, who studies the biomechanics of flight at the University of Southern California: launch, lift and sturdy limbs.

It's no accident that hang gliders run off the edge of cliffs: takeoff is the hardest part of flying. Gathering enough force to launch is a major barrier for a flying creature that wants to grow big. "Animal takeoff is mostly ballistic," says Habib, "either a runup into a leap or just a leap. The animal has to rely on the limbs it has touching the ground." Pterosaurs had an enormous launch advantage over birds: they were quadrupedal, which helped them generate twice the power – possibly even more – of a similarly sized bird leaping into flight.

The pterosaur's ability to walk on all fours has an interesting evolutionary and historical background. Under x-ray, a bird wing looks pretty much as you'd expect: a crooked bone set inside a wing that extends well beyond the bone on all sides. A pterosaur's wing, though, is essentially a four-fingered hand with a very long fourth finger. In fact, it appears that the wing began as a hand: the fourth finger got progressively longer over generations, dragging a webbing along with it, forming the wing. The remaining fingers stayed put, allowing the pterosaur to fold up its wings and stand on all fours.

While this fact is now widely acknowledged, experts fought about it for decades. In 1957, when the palaeontologist WL Stokes identified pterosaur tracks that proved the animal walked on all fours, his colleagues dismissed the find. They argued that the tracks belonged to a crocodile-like creature, not a pterosaur. Stokes went to his grave with his greatest accomplishment in serious dispute. It wasn't until the late 1990s that he was vindicated.

Part of the exhibition Pterosaurs: Flight in the Age of Dinosaurs at the American Museum of Natural History in New York. Photograph: Don Emmert/Getty

Back to the pterosaurs, though, and their second trait: tremendous lift. Pterosaur wings appear to have been more elastic than the wings of a modern bird. The changing shape of the wing maximised its lift, enabling the animal to keep more weight airborne than a bird with similarly sized wings could. (Quetzalcoatlus probably weighed more than 68kg.) "A modern bird's coefficient of lift [a measurement of the upward forces the wing can produce] is around 0.4 at cruising speeds, and maxes out at 1.6," Habib says. "Pterosaur wings could probably break 2. Those numbers are small, but a 25% advantage is very significant."

The structure of the bones was also a major factor in the massive size of some pterosaurs. Flying involves a balancing of weight and stiffness, two competing attributes. Pterosaurs, like modern birds, had hollow bones, which maximised their strength-to-weight ratio. Heavy bones are the greatest limitation to bats' increasing their size: although they can take off using four limbs, they have solid bones rather than hollow bird bones.

There's a final factor that prevents birds and bats from getting much larger. It has nothing to do with anatomy or physics. "There has to be an ecological opportunity," Habib says. "If there's no advantage to getting bigger, you stay small."

If you take a walk through the forest, you're likely to see a lot of birds – probably more than in other environments. But the birds are all pretty small. That's because the forest is a terrible place for a massive flying animal. The spaces are too tight for long-winged creatures to soar and corner. The crook of a branch is also a poor place for a gigantic creature to raise a family. It's no coincidence that most of today's larger birds inhabit grasslands and coastal areas. Many of the larger pterosaur fossils have also been found in areas that were once coastal. The areas that a giant flyer like Quetzalcoatlus could inhabit are limited and are now dominated by humans.

Who knows? Maybe, given a few more millions of years and the right environmental conditions, birds or bats will find a way to get big. Mark Norrell, chair of the division of palaeontology at the American Museum of Natural History, which just unveiled a major pterosaur exhibit, cautions against viewing modern birds as the only kinds that can exist.

"There have been some pretty big birds," he says. "Argentavis [a condor-like bird that lived in the Andes about 6m years ago] may have had a 8.2-metre wingspan. There were many larger animals in the past, and we now have just a sampling of that diversity. Large birds evolved before, and they could evolve again."

This article appeared in Guardian Weekly, which incorporates material from the Washington Post