Why Can't Humans Fly?

“The most beautiful dream that has haunted the heart of man since childhood is to have wings and fly high in sky like a bird……and breathe the same way as the angels do……..breathe up there in the clouds where air is very pure and fine, bracing and delicious…..”

Surely, humans have tried to make this work. It seems like it could work. Unfortunately, we are doomed to remain as ground-based animals. Well, that is unless you count powered flight or gliding. We can do both of those. Then why not? Perhaps the simplest answer is “we are too big.” Oh, too big you say? Well, surely we aren’t too big. Maybe if we just had bigger wings, it would work. Nope. It won’t work (well, probably won’t work). This falls into a category of things called “stuff that doesn’t scale like your intuition.” Or perhaps I should say “bigger things aren’t the same as smaller things.”

 DA VINCI'S WING 

Now for my super short calculation hopefully to be followed by some useful data. Let me represent the muscle of an animal as the following cylinder. So, the diameter is 2r with a height of h. Let further suppose that the strength of this muscle is proportional to the cross sectional area (not strictly true – but just hold on) and the weight is proportional to the volume of the cylinder. This would give a strength to weight ratio of: Here, C is just some constant. 

But what matters more is the result. If we make an animal twice as tall and scale the rest of the dimensions proportionately, r would double and so would h. But the strength to weight ratio would be half as much as the smaller animal. Ok, well we can fix that. Let us double the mass (volume) but keep the same strength to weight ratio. We would need the same height, and the radius would have to be sqrt(2) times larger. Here is what that would look like. 

ACTUAL BIRDS

This bird has a wingspan of 3.7 meters and a mass of about 12 kg. Here is the plan. Let us look at a whole bunch of birds and see if there is a correlation between mass and wingspan. Here we go. Almost all of this data has been scraped from Wikipedia. Not all birdWikipedia pages are alike. Some list wingspan, some don’t. And here is the data. 

Well, that turned out a little bit better than expected. But what next? It would be nice if We could fit

some function to this data. We could just start guessing functions to see what works, or We could see

what makes sense. The data actually look parabolic. This would suggest a function something like:

Where w is the wingspan, m is the mass and C is some constant. This is􀅶’t really what we would have expected, but we will go with it. In order to find the constant C, We have to plot w2 vs. the mass. This should be a linear function and we can find the slope. Here is that plot.

This fit gives a slope of 0.64 m2/kg and an intercept of 0.62 m2. It looks nice except it doesn’t seem to fit very well with the smaller mass birds. We could probably get a better function, but this will do for now.

PREDICTING THE WINGSPAN OF A HUMAN

If a human was a bird, what kind of wingspan would this Big Bird have? Let us take a grown human

male with a mass of 70 kg. If we put 70 kg in for the mass in function, we get a wingspan of 6.7

meters. Sure that is big, but possible. Right? Well, how much do we think 6.7 meter long wings would weigh? We may doubt that wing mass is negligible. If we built them out of balsa wood, how much mass would it add? Let’s just estimate an average wing thickness of 1 cm and a width of 2 meters.

This would be a balsa-wood volume of 0.134 m3. Balsa wood has a density of about 160 kg/m3. This

would give a wing-mass of 21 kg. AH HA. But now we need bigger wings. We could keep playing this game until we find wings that would work – but here we see the problem.

The problem is that if we have 7 meter long wings, we really aren’t going to be able to easily fit them in your car. And that is why humans can’t fly.

BONUS BIRD

Can Big Bird fly? We have never seen that. What would Big Bird look like with correct sized wings? First, need to guess his mass. This is tough since he isn’t really human. Let us ball park his mass at 90 kg (since Wikipedia lists his height at 2.49 meters). This would be a wingspan (if his mass included the wings) of 7.6 meters. Let us redraw Big Bird with wings this size. Now when we can’t fly , we are to make ourselves satisfied with the powered flight and this is the only way, we can fly…

AUTHOR:

Mr. Deepak Juneja

(Assistant Professor  & Head of Mechanical Engineering Department)

(Geeta Engineering College, Panipat)