BERLIN—The ancient flying reptiles called pterosaurs include the largest flying animals ever discovered, with estimated wingspans as wide as 11 meters, the width of a doubles tennis court. Exactly how such gargantuan creatures could have taken off, stayed aloft, and landed safely has long puzzled biomechanics experts. New calculations presented here last week at the Society of Vertebrate Paleontology’s annual meeting suggest that flying and landing weren’t problems even for the biggest specimens, but takeoff probably limited how large the animals could grow.

Pterosaurs existed from the late Triassic until the end of the Cretaceous period—about 200 million to 66 million years ago. Although they lived at the same time, pterosaurs are not dinosaurs; they form a distinct branch of the evolutionary tree. The most famous member of the group is the first named species, Pterodactylus antiquus, commonly known as a pterodactyl. They were some of the smaller pterosaurs, with an estimated adult wingspan of about a meter, about the size a peregrine falcon. The largest known pterosaurs, Hatzegopteryx, unearthed in Romania, and Quetzalcoatlus, found in Texas, are thought to have had wingspans of 10 or 11 meters—more than three times the wingspans of today’s largest birds.

Some researchers have argued that those giants were simply too large to fly. But given their large wings—a skin-and-muscle membrane that extended between an extended fourth finger and the animals’ hind legs—most researchers think they did spend time in the air. Many previous models and estimates were based on scaling up the physiology of birds, but pterosaurs had such different body plans that those models are potentially misleading, says Colin Palmer of the University of Bristol in the United Kingdom. He and Michael Habib of the University of Southern California in Los Angeles attempted to devise a more accurate model of the forces on the animals as they launched, flew, and landed. They used computed tomography scans of pterosaur fossils and wind tunnel tests of model pterosaur wings to develop a computer model of a pterosaur with a 6-meter wingspan. They then scaled up their model to have 9-meter and 12-meter wingspans and calculated the forces on the animals’ bones, wings, and muscles as they took off, flew, and landed.

Staying airborne was no problem for their model pterosaurs, Palmer told the meeting. Even animals with wingspans of 15 meters would have had enough muscle power to counteract the drag that exists when the animal is in the air. Landing is a more complicated process, he says, and those modeling experiments were less definitive. The calculations didn’t place a clear limit on the ability of bone to absorb the stress of landing, but even up to 12 meters, Palmer says, their model animals could land safely.

Taking off was the biggest challenge for the model pterosaurs. The animals probably launched using all four limbs (scientists think they walked on all fours) and so had more muscle power available than today’s birds do. Model animals with wingspans of 9 or 10 meters had no problem taking off. But according to the model, animals with wingspans greater than 11 meters had trouble jumping high enough to start flapping their wings fully before they fell back to the ground. Thus, the larger pterosaurs couldn’t launch very effectively. In theory, animals even bigger than that could get airborne under ideal conditions, with a hard surface under them and no headwind. “But without ideal conditions, you get eaten,” Palmer says. Habib agrees. An animal with a 12-meter wingspan “could leap in a computer,” he says, “but the real world had Tyrannosaurus in it.”

All such computer models have limitations, says Alexander Kellner of the Brazilian National Museum at the Federal University of Rio de Janeiro. But the new calculations do help researchers better understand the physiological limits of the flying giants. “They were very different from anything living today,” he says, so basing models on fossil data is important. Additional fossil scans could help refine the models even further, he says.