Forget Icarus, Fly As Close To The Sun As You Want!

By Kyle Hill | April 22, 2014 10:30 am

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

Draper_Herbert_James_Mourning_for_Icarus

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.

 

More Geeky Science:

Squirtle, I (Should) Choose You! Settling a Great Pokémon Debate with Science

Why Rudolph Should Have Never Joined Santa’s Reindeer

You Can’t Take a Bullet for Someone Hollywood-Style, Because Physics

The Walking Dead Shuffles Into Science Education With Bolts, Brains, and a Physics Quiz

What The Nerdiest Chart of Sci-Fi Ships Says About Our Dreams of Space

Image Credit: Lament for Icarus by Herbert James Draper (1863–1920)

Paper Source: Chargrilled Icarus’ Wings

Reference:

Cogle, J., Cox, J., & Pierce, J. (2013, March 18). Chargrilled Icarus’ Wings. Journal of Interdisicplinary Science Topics.

CATEGORIZED UNDER: Space & Physics, top posts
  • http://www.mazepath.com/uncleal/qz4.htm Uncle Al

    Icarus would do much better with a parasail, an updraft, and a human powered propeller to cover contingencies. How is it that the all-knowing, all-powerful gods never brought forth nylon?

  • disqus_atlq8Zmtsd

    Wait… does this calculation assume 100% heat retention? You have to account for conduction of heat away from the wings by the air. Certainly the massive surface area will increase conduction by the same factor as radiant heat absorption.

    • Marion Meads

      it was indirectly mentioned that the air temperature is colder higher up and could keep the wax solid. It implies sensible heat transfer from the solar heat absorbed by the wings to the colder air around it.

      • disqus_atlq8Zmtsd

        Ah, I stopped reading after the calculated time that was given about midway through. I assumed the rest of the article was a discussion of the implications.

        You know what they say about assuming….

  • stevedodge833

    Of course all this distance-to-the-Sun discussion is based on the modern world as we know it. That doesn’t apply to this fable, as the rules have changed.

    The story of Icarus took place in the ancient world, where Gods controlled everything, the Earth was the center of the universe, and the Sun was “just up there” almost within stone-throwing distance if you stood on the tallest mountain to chuck it. In THEIR world, flying closer to the sun would be like moving your hand closer and closer to a campfire.

    > DO agree about the flaw of comparing height of an Eagle vs a Man as a reference. Flight-capable birds in general have a much lighter body construction per foot of height if stood upright next to an adult human. Truly, Cupid would have required an even larger span than this article dictates to lift his weight. Prior studies and articles I have read on the topic say someone of Icarus’s HEIGHT AND WEIGHT would need wings of a 40-45 foot span AND a breastbone/chest projecting 5 feet forward to support the massive muscles necessary to flap them sufficiently.

    .

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It has been said that you should try to make a problem as simple as possible, but not simpler. Here, that problem is finding the real science behind pop culture. But Not Simpler is a place where you can ask the questions you thought were too nerdy for real answers. The physics of video games? Sure! The chemistry of dragon breath? Why not? When you can find the realities behind your favorite fiction, and seriously nerd-out in the process, everyone wins. Simple.

About Kyle Hill

Kyle Hill is a science writer and communicator who specializes in finding the secret science in your favorite fandom. His work has appeared in Wired, The Boston Globe, Scientific American, Popular Science, Slate, and more. He is a TV correspondent for Al Jazeera America's science and technology show TechKnow and a columnist for Skeptical Inquirer magazine. Find his stream of nerdery on Twitter: @Sci_Phile Email him at sciencebasedlife [at] gmail [dot] com.

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