When Clark Kent's alter-ego first made his comic debut, he owed his dramatic superpowers to the different conditions prevailing on his home planet, Krypton. Coming from a world with greater gravity, DC Comics claimed, would have magnified Superman's physical prowess on Earth, as his muscles would have grown to cope with the stronger forces of his home.
Initially, Superman was not able to fly, but he could comfortably leap over a 30-storey building. Kakalios has used this to calculate exactly how much greater the gravity on Krypton must have been. "For a native of Krypton to have arrived on Earth with such prodigious leaping abilities, the gravity there would have had to be at least eight times greater than here," he says. "We figured out how much force he'd need to jump 30 storeys in the lesser gravity of Earth, and worked it out from there."
Such gravity, however, presents something of a scientific problem: there is no way that Krypton could possibly have sustained life. It would have had to be eight times larger than Earth - making it a gas giant like Jupiter - or eight times denser, which would have made it highly unstable. "At least all this explains why Superman had to get out when Krypton exploded," Kakalios says.
The Flash, renowned for his blazing speed, relied heavily on an ability to avoid any wind resistance or friction. Just as well, because he would have burnt up otherwise in the heat generated as he ran, on occasion, at close to the speed of light.
He would also have been blessed with a voracious appetite. "To run at 200mph, which is nothing like his top speed, he would have had to eat every recipe in The Joy of Cooking 26 times over, just to get enough calories for a single sprint," Kakalios says.
ANT MANGIANT MAN
Ant Man, who had a second incarnation as Giant Man, could shrink to the size of an ant or grow to a stature of 100 feet. Shrinking would have been fine as far as it goes, but he would have been deaf and dumb in this state: his vocal cords would have been so small as to make sounds at frequencies too high for humans to hear, and the bones of his inner ear would have been similarly tuned. His enemies would have found it easy to immobilise him, too, with a drop of water: it would double his weight, making it impossible for him to move. Air currents would also have blown him around the room.
These problems are nothing, however, compared to those that face Giant Man. Once growing beyond a height of about 60 feet, his bones would have collapsed under the massive weight of the rest of his body, Kakalios has calculated.
Cyclops, who appeared in the recent X-Men movie, could fire powerful force beams from his eye, to knock out villains and burn through chains. "This was not his only mutant superpower, though," Kakalios says. "Every action has an equal and opposite reaction, yet we never see his head spring back from the recoil. He must also have been blessed with mutant super-strong neck muscles."
THE INVISIBLE WOMAN
Invisible because no light stops in her body, she would also have been blind: if that were true, Kakalios says, no light would have stopped in her eyes, either.
Mark Henderson is science correspondent of The Times