Having faced off the Green Goblin and Mysterio, Spider-Man has been defeated by his greatest enemy; maths. According to a team of scientists from Cambridge University, for the webslinger to stick to a wall, he'd need hands and feet equal to 40 percent of his entire body surface area. Though this may dismay web head's fans, it may provide insights into how to improve gecko-like adhesives.

Outside of comic books, the largest creature that can climb smooth vertical walls is the gecko, which it manages using large, sticky footpads. The problem is that the larger the animal, the larger the pad needed, with the pad requirements growing much faster than the animal.

"If a human, for example, wanted to climb up a wall the way a gecko does, we'd need impractically large sticky feet – and shoes in European size 145 or US size 114," says Walter Federle of the Cambridge Department of Zoology.

In all, the Cambridge team studied 225 climbing animals with a seven-magnitude range of weights, which included insects, frogs, spiders, lizards, and a mammal. They found that the feet were very similar, with the main difference being that the pads increase in size at a greater rate than the animals.

Climbing animals range in size from mites to geckos, but a mite's footpads are only one half of one per cent of their body area, while they look like snowshoes on a gecko. The reason for this is the Square Cube Law, which states that for every increase in the size of an object squares the surface area and cubes the volume. In other words, an animal ten times larger than normal has a hundred times the surface area and a thousand times the volume.

What this means in practical terms is that you can't have a mouse the size of an elephant or vice versa. A mouse of an elephant scale would collapse under its own weight as its legs bones shattered, and an elephant the size of a mouse would rip itself to shreds with its disproportionate muscles.

The same applies to sticky pads. A small increase in size means a larger increase in surface area and a much greater increase in volume and, therefore, mass. The upshot is that as climbing animals get bigger, their sticky pads grow dramatically in surface area to support the extra weight, but it's a losing race.

Calculations show that a gecko is the largest an animal using sticky footpads can be. Beyond that, making the pads bigger is impractical, but there are minor workarounds to push the envelope. According to the team, many species independently developed sticky pads that are very similar to one another and that a common solution to the problem of size was to make the pads stickier

"We noticed that within some groups of closely related species pad size was not increasing fast enough to match body size yet these animals could still stick to walls," says team member Christofer Clemente. "We found that tree frogs have switched to this second option of making pads stickier rather than bigger. It's remarkable that we see two different evolutionary solutions to the problem of getting big and sticking to walls."

Since gecko-like adhesives are of major interest these days, the Cambridge team sees their research as providing answer to the question of how to scale up the technology

"Our study emphasises the importance of scaling for animal adhesion, and scaling is also essential for improving the performance of adhesives over much larger areas," says Dr David Labonte of the Department of Zoology. "There is a lot of interesting work still to be done looking into the strategies that animals use to make their footpads stickier – these would likely have very useful applications in the development of large-scale, powerful yet controllable adhesives."

The team's study is published in the Proceedings of the National Academy of Sciences.

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