(yells) - This would be a pretty bad
situation to find yourself in. That is, unless you had
the properties necessary to be able to survive
a fall from any height. Let's get technical and quickly! (techno music) (Kyle yells) Throughout more recent human history, you can find some incredible
stories of human survival. People falling from thousands of feet, usually from an airplane
due to an accident or, like, a world war and
living to tell the tale. These are amazing stories,
and they are very unusual, but they usually involve some
very special circumstances like having a pillow of
snow to break your fall or the embrace of tree branches
to mitigate your deadness. There are organisms, though, on this planet that need no such luck. They can fall from theoretically
any height and survive. But how? Oh, that's a horse! Okay. First, what is actually
dangerous about a fall? Well, you may have heard the phrase it's not the fall that kills
you, it's the sudden stop, so let's put some
variables to that verbiage. The force on an object is equivalent to the product of that object's mass and the acceleration imposed upon it. We get that from smart boy Isaac Newton, and we can expand it. Acceleration is equivalent to a change, this delta symbol here indicates change, a change in velocity over time. So the sudden stop of a
fall, the impact force, is directly related to your mass going from some velocity
to basically zero velocity in a very short amount of time. So if you wanted to be
technical, which we always do, you could say well, actually, it's not the fall that kills
you, it's the M delta V over T. Oh! When falling from a
sufficiently scary height, there's not a whole lot
you can do about your mass, and your impact time is always going to be more or less instantaneous, and so the only way to soften
your fall realistically is to reduce your impact velocity. And at least here there is a limit. When you're on Earth, the planet's mass imposes a
gravitational force on you, which accelerates your own mass. If you're near the Earth's surface, that acceleration is
around 10 meters per second every single second. Because of this relatively
substantial acceleration, if you were to fall from the edge of what you humans call space with nothing to get in the way, by the time you hit the ground, you'd be traveling at over Mach 4. But of course there is
something to get in the way. Oh, oh! (yells) And that something is air, atoms and molecules with
their own mass and momentum that your body has to push
out of the way when falling. And these trillions of tiny impacts stealing velocity from
you can be a real drag. Literally. (yells) The opposing force that keeps
you from falling to Earth at the speed of sound is drag. When falling, your body has a drag force acting on it the entire time, but at some point the drag force will be equal and opposite
to what's pulling you down. Your weight. At that point, you'll
have no net force on you, therefore no net acceleration. Your velocity will stop changing. At this point you have
reached terminal velocity. It's the fastest anything will go when freefalling through the
air from a sufficient height. Everything has a terminal velocity, from you to a cat to a
horse to your original TI-89 calculator you used
in engineering school, and this value will exactly determine what will happen to an
object during an impact. Will it survive, or won't it? Drag determines velocity, and
velocity determines force, so if we want to know what will survive a fall from any height, we should first calculate a human drag. And I'm not just talking about your Twitter timeline, either. Mathematically speaking, the force of drag is
equivalent to one half times the density of the air
an object is falling through, multiplied by the coefficient of drag, which is just a unitless coefficient that depends on the object's shape, multiplied by the area that that object is presenting to the air,
how it's pushing through it, multiplied by the velocity
it's traveling at, squared. To calculate the terminal
velocity of a human, then, we would want to set our drag equation equal to weight so that the
velocity will be terminal, and then we can look up some average values
for all these variables and rearrange this whole
equation to solve for V. And if we use my mass of 72 kilograms, this should be easy enough for us to do. For you to do. Right now. Right now, pop quiz! Using all these numbers, what
would be my terminal velocity? I want you to try to
calculate it right now. When you get the right
answer, it feels really good. (organ music) Oh, wait a second. I know I'm kinda asking you to do math out of nowhere and you might be rusty, so that equation that we need to rearrange should look like this. You can even write it down if you need to. Like right now. (organ music) I'll assume that you did it. The correct answer is B, 55 meters per second. About 120 miles per hour for someone falling like a skydiver. Did you get it? Well, either way, now how would we slow this
terminal velocity down if we wanted to land
with less of an impact? Well, there's not much we can do about the density of the air, and you can't really change your mass. The only thing you can
really have an effect over in this case is your area that you present to the air that you're falling through. A much smaller area has much
smaller drag and vice versa. This is why skydivers falling
in a pencil-like position can fall much faster
and can fall much slower when they dramatically increase this area with something like a parachute. However. Oh. Not gonna get me this-- (yells) Without a parachute or
a really lucky landing, humans basically always achieve
fatal terminal velocity. In fact, in one study in 2013, they found that the average height for a fall-related fatality
was just 6.6 meters, under 22 feet, not very high at all. Humans are fragile beings. But for some beings, terminal
velocity is never terminal. (yells) Drag may not be able to save us, but it will save the
majority of life on Earth. In his famous essay titled
On Being the Right Size, biologist J.B.S. Haldane
observed a relationship between the mass and the surface
area of falling creatures. Please consider the
following cube creature. I said creature. Thank you. Let's imagine that this cubular organism has sides that are each 10 units long. If that's the case, then our
creature here has a volume, which is directly related to its mass, of a thousand cubic units. And each side has a surface
area of a hundred square units. Now, what happens if
we dramatically reduce the size of our organism here? If we were to equally shrink the sides of our creature
by, say, a factor of 10, then doing the same math we
find a volume of one cubic unit and a surface area per
side of one square unit. The volume has been reduced
by a factor of a thousand, but the sides that are being
presented to freefalling through the air is only
reduced by a factor of 100. In other words, as a creature shrinks, the surface area and therefore the drag stays a lot more relevant
and becomes more relevant than the volume and therefore
the creature's mass. That's why in general smaller creatures have much smaller terminal velocities, and why, in Haldane's own words,
a man is broken by a fall, but you can drop a mouse down
a thousand-yard mineshaft, his words, and when it hits the ground,
it's more or less fine. Less velocity, less force. Just gonna step over the void there. There is a right size for
surviving a fall from any height. So you know what that means, of course. We're gonna make a tier
list of what will survive and what will basically explode on impact. The majority of complex
life on this planet, at least in terms of sheer
numbers, are the insects. And thanks to a combination
of very low mass, relatively higher surface
area, and robust exoskeletons, insects can theoretically
survive a fall from any height. You could go to the observation deck on the Empire State Building
and throw an ant off, and it would theoretically survive. But don't do that. S tier! Moving up in mass, as Haldane pointed out, creatures about the size of
mice are very robust and, interestingly enough, so too are cats. A recent study found a
90% survival rate in cats falling from terminal velocity height, given that they also get
some medical treatment. A tier! Again, it's possible that even
larger creatures like humans can survive falls from harrowing heights, but more often than not, they are completely shattered on impact, as are dogs and deer and,
I don't know, crocodiles? D tier! Finally, animals much larger than humans are just probably not going to survive a brush with terminal velocity. I'm pretty sure that if you
pushed a horse or an elephant or a whale out of a cargo
plane to see what would happen, they would basically explode. E tier. Not that anyone should ever
try that to find it out. Leave falling up to the
professionals, okay? (yells) Ah! So how do you survive
a fall from any height? Well, having an irregular
shape helps, as does a, relatively speaking, low
mass and high surface area. You want to maximize drag while minimizing terminal velocity. We have to do this artificially with something like a parachute, but, say, an ant can do so naturally and hit the ground at
just four miles per hour instead of a hundred and twenty. If you are the right size,
life is like a video game, and you're immune to fall damage. Because science. (techno music) Freefalling isn't always
just a jumble or a mess. Many animals have ways to
harness the power of drag or not. For example, cats, if you drop a cat, you can try this at home. (laughs) If you drop a cat from
a height high enough, they will spread out their arms and legs, theoretically to increase the drag and lower the terminal velocity, so when they hit the
ground it's not as fast. And something like the peregrine falcon makes its body shape in
such a way and controls the surface drag of its shape,
its coefficient of drag, that it can go, like, 200
miles an hour during a dive and then basically come
to a stop using its wings. It is a master of whatever we were just talking about for 10 minutes. (light fanfare)
