Big Question+Myth

My question is what does the Greek myth of Icarus and the sun look like through the eyes of science? The myth of Icarus and the sun goes that Icarus and his father Daedulus were trapped on a high point ( Tower/Cliff ) and that they made a set of wings out of a leather frame, moulted eagle feathers and beeswax to hold it together. Before they flew Daedulus warned that Icarus should not fly too low or the sea would dampen the feathers to the point of them being too heavy to fly with nor too high or the sun would melt the wax and he would fall. But during flight, Icarus was too engrossed in the joy of flying and soared high, high in the sky despite his father's warnings and the wax melted and he plummeted into the sea and drowned.

Sub-Questions 

My sub-questions are: 1) could a man feasibly fly with a set of wings like the ones in the myth? 2) At what temperature or height would the wax melt? 3) Can feathers absorb a sufficient amount of water to result in a crash?

My first question is could a man fly? 

To fly you need sufficient lift and thrust to overcome weight and drag. While birds can produce sufficient thrust using their muscles, humans' muscles are not strong enough.  

To create enough lift birds use their wings which are in the shape of aerofoils which means air has to blow over both sides of the wing. But as the wings are in a teardrop shape the air molecules have more area to travel over on top and they get spread out which reduces air pressure on top of the wing. But the pressure below remains the same which pushes it up to create lift. Humans can replicate this lift by making wings in the same aerofoil shape - think hang glider.

Icarus could have glided but would have lacked the muscles to fly.

According to the myth Icarus used beeswax, leather and molted eagle flight feathers. Leather and tanneries were important parts of the Minoan economy  (The kingdom that was found in Crete). Raising and farming honey bees was also a big part of the Minoan culture. Eagles did, and still do, live on Crete, so all three would have been available.

So in theory there should have been sufficient quantities of wax and leather. However, eagle feathers may have been available in smaller quantities. While the average eagle has 7,000 feathers, only 56 of those are the flight feathers necessary to fly. 

To ascertain the amount of feathers necessary I needed to figure out how large the wings would have to be. For flight, lift is calculated using wing loading which is how much weight can a given surface area carry in flight. ( Weight in kilograms divided by metres squared of wing surface ),

First, I figured out the weight of Icarus. The average weight of a man in ancient Greece was 68 kg. I decided that a modern hang glider was a good frame of reference. The average hang glider has a maximum wing loading of 6.3 kg/m² . So I calculated the size of the wing by dividing the weight of Icarus ( 68 kg ) by 6.3 kg which equals 10.8. Then I multiplied 10.8 by 1 which is 10.8. Thus the wing size would have to be 10.8 m².

Next, I  calculated the number of eagle feathers necessary.   The average eagle feather is 12-18 inches long and 3.5-5 inches wide. I needed to use the same unit of measurement as I used for the wing loading ratio above. 18 inches in metres is 0.46m And 5 inches is 0.13m. So one large eagle feather has a surface area of .46m times .13m which is .06 m². So to calculate the number of feathers I divided the required wing size of 10.8 m² by the feather surface area which is  .06 m². This equals 180 feathers required. As you might recall one eagle has 56 flight feathers that they molt every year. Thus, you could get the required 180 feathers from one eagle over 3.5 years or one year of moulted flight feathers from 3.5 eagles.

My second question is would the beeswax melt leading to a crash?

The myth says Daedalus warned Icarus that he shouldn't fly too close to the sun or the wax on his wings would melt.

I researched the melting point of beeswax (62 to 64^o C). I then researched the hottest temperature recorded on Crete (44.5^oC).  I also discovered that the temperature decreases with height. This is known as the atmospheric lapse rate which is -6.5^oC per thousand metres of altitude.

In conclusion, the melting point is higher than the hottest recorded temperature on Crete thus the wax would not have melted resulting in the destruction of the wings. 

However, I also discovered that beeswax below 18^oC gets brittle. Average monthly temperatures in Crete are below 18^oC half of the year. For the other half of the year, the temperature typically gets no higher than 27^oC. As a result, if the atmospheric lapse rate is -6.5^oC per thousand metres of altitude, above 1500 metres the wax would have become brittle and broken the wings.

My third question is could the feathers have absorbed enough water to lead to a crash?

Daedalus warned Icarus that he shouldn't fly too close to the waves or the feathers would absorb water, become heavy and he would crash. 

My research suggests that feathers are hydrophobic which means they can not absorb water.               

Answer One

Yes. He could have made wings from the available natural resources. However he would have lacked the muscles to actually fly but, he could have glided with the wings.

Answer Two

No. The melting of beeswax would not lead to the crash. Temperature and altitude could have affected the wings, but not because of an increase in temperature as the myth suggests, but rather through a decrease in temperature. If the wax got too cold it would have become brittle and snapped resulting in Icarus crashing.

Answer Three

No. The feathers would not have absorbed enough water to result in a crash as they are hydrophobic.

Conclusion

In conclusion, Icarus would have crashed as a result of gravity and nothing else as everything else would either take altitude or a long, long amount of time that would surpass when he was at the bottom of the sea. 

Areas of future study

I would really enjoy studying other Greek myths, maybe an engineering project about the labyrinth. As I have learned from this project, Greek myths have a lot to dive into scientifically.  

References

• Men and Gods: Myths and Legends of the Ancient Greeks‎, Rex Warner
• The Penguin Book of Classical Myths, Jenny March
• The Greek and Roman Myths: A Guide to the Classical Stories, Philip Matyszak
• Usbourne Complete Greek Myths, Henry Brook and Anna Milbourne) 
• “Did the Ancient Greeks Have Leather,” quora.com
• What is Aerodynamics? (Grade 5-8), nasa.gov
• All About Feathers,  https://www.allaboutbirds.org/
• Beeswax, Wikipedia
• How People Practiced Beekeeping in Ancient Greece, livebeekeeping.com
• Golden Eagles, Wikipedia
• Golden Eagles, San Diego Zoo https://animals.sandiegozoo.org/
• Minoan Civilization, Wikipedia
• Principles of Flight, https://selectaviation.com/
• All About Bald Eagle Feathers, Loudoun Wildlife Conservancy 
• How much does a Spartan soldier weigh?, Quora.com
• Wing Loading, Science Learning Hub
• Crete Weather, Met Office, https://www.metoffice.gov.uk/
• List of Extreme Temperatures in Greece, Wikipedia
• Hang Gliders, Wikipedia
• Hang Gliding (hanggliding.co.uk)
• Avian Adaptation, https://www.montananaturalist.org/