Then he caught sight of the feathers on the waves, and cursed his inventions. He laid the body to rest, in a tomb, and the island was named Icaria after his buried child. —Metamorphoses Book VIII
In a mythology beset by monsters created by malice (and sometimes bestiality) shines one crafted out of hope and ultimately hubris—the ill-fated Icarus. Though his fatal flight was mentioned only in passing over 2,000 years ago, Icarus remains an enduring symbol of human folly. The fate of Icarus—flying too close to the Sun—proliferated into Western culture as a warning against excessive ambition and a tale of its consequences. But in reality, Icarus should have flown as close to the Sun as he could.
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Despite how much the myth of Icarus is cited in pop culture and classical literature, his entire tale spans barely four paragraphs in Metamorphoses—the magnum opus from Roman poet Ovid in the first century. As the story goes, Daedalus, Icarus’ father, was a master craftsman hired to build the Labyrinth for King Minos of Crete. Of course, the King betrays Daedalus (as these stories usually go), and Daedalus soon finds himself trapped in his own maze. Seeking to escape, the engineer in Daedalus gets the idea to build he and his son wings of feather and wax.
Daedalus was the first to try his creation. As he hovers in a fast-moving breeze, he instructs Icarus to fly in between two extremes—fly too low and the ocean will swallow you, fly too high and the Sun will scorch you. With a “never to be repeated kiss,” the master engineer takes off and waits for his son to do the same. Icarus hesitates, unsure of his fitted wings. Soon after take-off, Icarus loses all fear. “The boy began to delight in his daring flight, and abandoning his guide, drawn by desire for the heavens, soared higher,” says Ovid in Metamorphoses. His aerial acrobatics bring him too close to the Sun, which melts the wax wings. With arms flailing, Icarus plunges into the sea, never to fly again.
Icarus’ demise is the classical example of what happens when you get too cocky, too greedy, or too full of yourself. But would such ambition really have brought him down? Physics says no. Icarus could have flown as close to the Sun as he wanted to; the distance from the Sun is not what brought him crashing into the sea.
Like any good physics problem, the first thing you establish when looking at a scenario like this are the initial conditions. For example, we know that the wings Icarus used were made of wax. This allows us to look up the energy required to melt wax, which will be important later on.
The next step is to make a bunch of assumptions (some will be better than others), which is exactly what an endearingly nerdy student paper on the subject has done. Jonathan Cogle, Jake Cox, and Jimmy Pierce from The Centre for Interdisciplinary Science at the University of Leicester first estimated the size of Icarus’ wax wings. To do this, they scaled up the wingspan of a golden eagle as if the eagle was human height. The bigger the wings, the more sun they will soak up. Like all back-of-the-envelope calculations physicists do, they assume that the wings are basically rectangles. This gives us the surface area.
[Personally, I think this estimation is off, because weight is more crucial to flight than height. No really, it makes Cupid look really weird. But since all the numbers in the paper are based on the height scaling, I’ll continue to use them here.]
The last step is to insert the conditions of the myth and make the final assumptions. In the paper, the authors assumed that the day of Icarus’ flight would be a clear one with little cloud cover. Since Icarus was flying from the Labyrinth of Crete, his location would have been near the equator. Both of these assumptions determine how much of the Sun’s energy would make it to the wings. When the authors also combine this assumed power from the Sun with the square footage of the assumed eagle wings, they calculated the final power—830 watts, or about half the power of an electric kettle—that would radiate over Daedalus’ waxy construction.
Once the authors had the solar power imparted to the wings, they had to figure out how it would spread into the wax. Modeling the wings as a white, smooth surface, they determined that the wings would absorb only 40 percent of the energy hitting them every second (the rest would be reflected).
Finally, the wax. If the wax Daedalus used was spread very thin over both wing surfaces, Icarus would still be carrying almost six kilograms of wax on his back. That’s an assumption, but at least we know exactly how much energy it would take to melt that wax. Using the latent heat of fusion as the figure—the energy required to melt a substance—the authors ultimately calculated that the Sun would have melted Icarus’ wings in between 42 and 67 minutes.
Notice how Icarus’ proximity to the Sun was never mentioned? If he stayed within breathable atmosphere and didn’t fly into any significant weather systems, the amount of sun hitting the wings would be almost constant. In the grand scheme of things, changing the distance between Icarus and the Sun makes no difference (within the zone he wouldn’t asphyxiate or freeze in). Flying 10 meters off the ground or 10,000 still puts you 150,000,000,000 meters from that big ball of gas.
So, Icarus could fly as close to the Sun as he wanted to, it wouldn’t have made a practical difference for melting his wings. But the height-independence for sun exposure of Icarus’ flight means something else too—he should have flown as close to the Sun as he possibly could.
Sun exposure hardly changes in the altitudes that you could feasibly fly wax wings at, but temperature changes a great deal. In the first 10 kilometers above the Earth’s surface, the temperature can decrease from 20 degrees to -60 degrees Celsius. The higher you go, the colder it gets.
Like most solids, wax first needs to reach a certain temperature before melting. And unlike water, which amazingly boils faster when it is cold, the colder the wax starts off, the more energy required to get it up to the melting temperature. So, a piece of wax at the ground will melt faster from Sun exposure than some wax way up in the frigid atmosphere, “too close” to the Sun. Taking all of the physics into consideration—the size of the wings, the melting energy of the wax, how temperature changes as you get higher in the atmosphere—the conclusion is clear: Not only could Icarus fly as close to the Sun as he wanted, he should have flown “too close” in order to prolong his flight.
If the classical allusion of Icarus is scientifically inaccurate, maybe it’s time to change the cultural significance. Think of how many times in history someone told an inventor or scientist or thinker not to dream too big. Now think of all the cautions that were thrown to the wind and paid off. Think of all the rule-breakers and explorers and experimenters who flew as close to the Sun as they could get and continued to soar unscathed. A few names come to mind: Rosa Parks, Buzz Aldrin, Edward Jenner (and certainly many, many more). If, in reality, Icarus could have embraced the miracle of his flight, maybe we can allow more interpretations of it.
Be courageous, be curious, and fly as close to the Sun as you can get. You might be surprised how high you fly.
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Paper Source: Chargrilled Icarus’ Wings
Cogle, J., Cox, J., & Pierce, J. (2013, March 18). Chargrilled Icarus’ Wings. Journal of Interdisicplinary Science Topics.