Physicists Say Cinderella's Glass Heels Would Have Shattered

Science has cautionary advice for fairy godmothers, vampires, and Superman: Ignore the laws of nature at your own peril.

We all know the story: The clock strikes midnight and Cinderella, facing an imminent wardrobe malfunction, flees the royal ball, leaving behind a single glass slipper. The prince travels the kingdom until he finds the woman who fits the shoe, and the two are married.

But, Cinderella’s chance to live happily ever after could just as easily have been shattered, say physics students who used stress calculations to assess the durability of her glass footwear

“When standing, the force acting downward is assumed to be evenly shared between her feet,” they explain. But, if she’s walking or running, that downward force is pushing entirely on one foot at a time. 

The result? Cinderella’s glass slippers would have broken (as would her heart) unless her heels were less than half-an-inch high—thus proving that aspiring princesses should always opt for flats over pumps.

This and other cautionary tales for imaginary characters can be found in the Journal of Physics Special Topics. Published by the University of Leicester, the online journal publishes the work of students who apply real physics skills to creative problems, then "peer review" one another.

Some of their papers tackle real-world calculations—such as why doors slam when you leave windows open in your house—but most are rooted in fantasy and fiction, including fairy tales, Greek mythology, comic books, films, and video games. 

“There’s only one real world,” says physics professor Mervyn Roy, who oversees the course. “Students can run out of relatively simple problems because other groups have done them in the past. But once you start to look at fiction, there’s a huge realm of things to explore.”

In doing so, the students are in good company. Over the decades, prominent scientists have written their fair share of fanciful papers. The esteemed oceanographer Karl Banse published a journal article, "Mermaids: Their Biology, Culture, and Demise." Thomas Woolley, at Oxford University's Mathematical Institute, showed how diffusion equations could be used to predict zombie migration patterns. 

Scientists love problem solving, says Roy, and curiosity-driven research can yield unexpected insights. He cites as an example some papers written on the physics of coffee-ring stains in the 1990s. “I imagine when scientists were doing that, a lot of people we saying, what's the point?” he says. “But now, the models that they worked out are used for things like techniques to self-assemble nanoparticles.”

And, of course, there’s the simple fact that scientists, like everyone else, just wanna have fun. 

“In my career, I have seen both scientists and the public criticize scientists for having 'fun,'” declares oceanographer Craig McClain, the founder and chief editor of the blog Deep-Sea News. “I for one went into science to have fun, and if my Ph.D. gives me the skills to calculate the urine production of Godzilla then I will wear that nerd badge with glee."

In that spirit, here’s a sampling of some of the other research papers just published in the Journal of Physics Special Topics:

Superman’s Super Error

In the 1978 film, Superman, the Man of Steel, grief-stricken by the death of Lois Lane, travels backwards in time by flying at speeds that cause the Earth to spin backwards.

Of course, time travel using this method is nonsense, but could the Last Son of Krypton reverse the rotation of an entire planet?

It’s possible. According to Einstein’s General Theory of Relativity, a moving object increases in mass as it approaches the speed of light. If Superman were to fly fast enough, his relativistic mass would be 13.7 million times his normal mass. Doing so would generate a gravitational field sufficient to change the polarity of the Earth’s spin.

Unfortunately, that gravitational field would also attract nearby asteroids that would pummel Superman’s adopted planet into extinction. “So spread the word: Do not try this at home,” the students caution.

The Santa Paradox

Einstein’s theory also stipulates that time moves slower for an object in motion relative to one standing still (the “Twin Paradox”).

So, what does that mean for Santa Claus? In order to deliver all his presents in one night (12 hours) he would need to be traveling at 0.76% of the speed of light during the entire time. 

As such, the principle of time dilation stipulates that, after spending 194 years transporting gifts on Christmas Eve, Santa is 242 seconds younger than the rest of us.

The Vampire’s Drinking Problem

Vampires who wish to optimize their feeding habits should drink no more than 15% of a human being’s blood. Beyond that point, the human heart rate begins to change, increasing and allowing more blood to be lost through the puncture holes in the external carotid artery (where the vampire drinks). It would be like turning a drinking straw into a firehose. 

Using fluid dynamics, students calculated that it would only take 6.4 minutes for a vampire to drain this much blood and make a swift getaway.

Flashy Footwear

On the TV show The Flash, the lighting-quick superhero runs so fast that, in one scene, his shoes catch fire. 

Assuming that he’s wearing rubber soles, he would have to reach a speed of 15,459 miles per hour (6,911 meters per second) to generate enough frictional heat to, literally, burn rubber.  However, in “real life,” the Flash’s shoes would have completely worn out upon hitting 881 miles per hour (394 meters per second).

The Best Laid Evil Plans

In the James Bond film, Die Another Day, evil genius Gustav Graves threatens the world with his Icarus satellite, which harnesses sunlight to generate a deadly laser beam. How big would the satellite’s solar panel have to be? 

Taking into account the initial energy of the laser—plus the additional energy required to counteract atmospheric effects as it rains destruction down on the Earth’s surface—the panel would need to be 52,420 square feet (4,870 square meters) about half the size of a city block.

“The satellite could possibly be built in stages,” the students conclude, “however, funding this would be very difficult as it would take several launches to complete.” Perhaps evil villains should crowdsource?

Follow Mark Strauss on Twitter.

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