The Fatal Physics of Falling Objects

What would happen if you dropped a penny off the Empire State Building? Could it kill someone walking on the sidewalk below? What does it take to create a deadly projectile? Well, I'm gonna put this to the test with original MythBuster, Adam Savage. He's going up in a helicopter to throw pennies at me. No one hasn't heard that story. When you talk about it, people are like, oh yeah, the penny from the Empire State Building. And when we went to the Empire State Building, every ledge below the observation deck is filled with change. I just love the idea of all these people. They're not murderers, but they're like, it's probably not true. They're like throwing pennies over the side thinking it's probably not true. A penny weighs around two and a half grams, which is about half to a quarter the weight of a bullet. If you ignore air resistance, a penny dropped from the Empire State Building, which is 443 meters to the very top, would accelerate to over 300 kilometers per hour by the time it hits the ground. That's around half as fast as a typical bullet. The MythBusters made contraptions to shoot pennies at each other. Stephen Colbert shot me in the ass with it a few times. How did it feel? It's a baseball pitcher throwing a penny hard at you. Yeah. It'll sting. But they never tried the ultimate test, dropping pennies from the height of the Empire State Building onto someone below. And that's what we're gonna do here with Adam. That'd be great watching it bounce off your body. Yeah. I say this thinking it's always been my body up till now. First one, I'll drop the pennies. We'll see where they're gonna land. You're gonna walk there. I'll throw a second one. That's good for you. And then you're ready for the full dump. Yeah. Helicopter, where Adam Savage is gonna drop a whole bunch of pennies on me. What are we even doing? I know I agreed to do this and I didn't think I'd get hurt, but as I'm walking out onto the helicopter, I started to think no one has actually done this. We planned for pennies falling through still air, but the helicopter creates a huge downdraft to support its weight. And three. I start to imagine pennies gouging into my shoulders. You can see how tense my body looks. Ah! One hit my helmet. And three. Ah! That hit my shoulder. Ah! Really good. And three, two, one. They feel like tiny little bullets. I feel like I'm gonna be bruised after this. Oh boy. Here we go, doing the whole thing. And three, two, one. Ah! Yeah! Unbelievable. There you have it. A penny dropped from the Empire State Building is not gonna hurt. I mean, it hurts a little, but not a lot. You'll be all right. That was great. I saw little dust clouds all around you. Amazing. Tell me what it was like down here. I was terrified. I got out there and the rotor wash is so heavy. I'm like, maybe we haven't calculated for rotor wash. It stung to get hit by pennies falling that far, but it certainly wasn't fatal. So why aren't pennies more dangerous? Well, the reason is air resistance. And I'll drop the two of them here and hopefully they'll hit the ground at the same time. Take the classic experiment of a hammer and feather dropped simultaneously on the moon. In the near vacuum of the moon's surface, both objects speed up at the same rate due to the moon's gravity. And they're both still accelerating when they hit the ground at the same time. How about that? Repeat the experiment on earth. And of course, the hammer lands way before the feather. If you watch the feather closely, you'll notice that it doesn't speed up as it falls. For most of its journey, it's moving at a constant speed known as its terminal velocity. Terminal velocity is reached when the force of gravity pulling an object down is equal to the force of air resistance pushing it up. In this case, which object, the hammer or the feather, experiences a greater force of air resistance? Well, I bet most people would say the feather because its motion is clearly affected by drag. But the answer is actually the hammer. Air resistance is proportional to speed squared and the hammer gets going much faster than the feather, so it experiences the larger force of air resistance. But its weight is so much greater that drag is negligible in comparison. And that's why the hammer keeps speeding up while the feather reaches terminal velocity early and just stays at that speed. It all comes down to the ratio of weight to air resistance. Every object has its own terminal velocity, the maximum speed it will reach in free fall through still air. And I went indoor skydiving to experience this firsthand. That was so amazing. That was totally wild. Objects that have the same size and shape experience the same air resistance. But if one is heavier, here I've got two identical balls, but this one has water added to it, so it's heavier, then it has a higher terminal velocity, so it doesn't float at the same wind speed as the lighter object. Conversely, some objects are very different in size and shape, like a person and a lacrosse ball. And obviously they have very different weights, but they also experience very different forces of air resistance. And the key thing is that the ratio of their weight to air resistance is the same for both bodies. So they have the same terminal velocity, which means they will both float together in the tunnel. If you transported the skydiver and lacrosse ball to the stratosphere, they would continue to fall together, but their joint terminal velocity would be much faster. In 2012, Felix Baumgartner jumped from a helium balloon 39 kilometers above sea level. After just 40 seconds of free fall, he reached a terminal velocity over 1300 kilometers per hour. It was 25% faster than the speed of sound, making him the first person to break the sound barrier outside of a vehicle. What allowed him to do this was the lack of air at that altitude. Air resistance is directly proportional to the density of air you're moving through. And at that altitude, the air is 60 times less dense than at sea level. As he continued falling into thicker atmosphere, the increasing air density reduced his terminal velocity. And by two and a half kilometers above sea level, he had slowed to 200 kilometers per hour, at which point he opened his parachute. Now, rain also falls kilometers, but through the thicker air of the troposphere. One of the coolest things in the wind tunnel was to see water floating. Poured from a jug, it quickly breaks up into droplets, the same size as raindrops, from around 0.5 to four millimeters in diameter. And standing there, you can experience what it would be like to fall with raindrops. They have a low terminal velocity of just 25 kilometers per hour. And that's what the wind speed was set to for this demonstration. And what you can see is that raindrops aren't shaped like cartoon raindrops. They are closer to spherical, but a bit flatter on the bottom where they encounter oncoming air. If a raindrop gets too big, it flattens out, caves in in the middle, and briefly resembles a little parachute before breaking up into smaller droplets. So raindrops aren't damaging, but it's a different story for hail. Every year in the US, hail injures around 20 people. And since 2000, it's caused four fatalities. That's because hail can reach terminal velocities of over 200 kilometers per hour. That's around 10 times the terminal velocity of rain. But why is its terminal velocity so much higher, even though ice itself is slightly less dense than liquid water? The main thing is that hail can get much bigger than a raindrop. Hailstones have been measured up to 20 centimeters in diameter. Now, drag is proportional to cross-sectional area. So it scales with radius squared, whereas weight scales with radius cubed. So the bigger the hailstone, the faster its terminal velocity. It also has more mass, so it carries even more kinetic energy and packs a bigger punch when it hits something. Pennies reach terminal velocity after falling only around 15 meters. You can see in this shot, the average speed of the pennies in the top of the frame is the same as at the bottom of the frame. They aren't speeding up, they've reached terminal velocity. So it wouldn't matter if pennies were dropped on you from 15 meters or 300 meters or 3,000 meters, it would feel the same because they would be going the same speed. In fact, we didn't take the helicopter all the way up to Empire State Building height because that wouldn't have increased the speed of the pennies at all. And it would have just made aiming much harder. By the end, I'm throwing to account for this secondary air current that's moving between you and the helicopter. And so the pennies are making this like 12-foot arc all the way over and then coming back. One of the reasons pennies are so hard to aim is because they flutter and tumble as they fall. This tumbling behavior means pennies don't actually have a single terminal velocity. A penny actually has two terminal velocities and it oscillates between them. So it's got one on its face and one on its edge. I've got a wind tunnel that can show you exactly how that works. It's really beautiful. I gotta see that. Yeah, it's really neat. Throw to that. Adam built a custom wind tunnel to witness this for himself. So I went to San Francisco to his cave to check it out. This is literally like my MythBusters origin story, this device. I'm so delighted to fire this up again. It's like looking at a piece of history. How old is this? 19 years old now. It's old enough to drive and vote, but not during. There's people watching this video, you know? Yeah. Who weren't alive when you were making this. Because of the holes, which allow air to escape, this wind tunnel has a gradient of wind speeds from around 100 kilometers per hour at the bottom up to 25 kilometers per hour at the top. This creates a little bit of back pressure, the tongue depressors up here, and that back pressure is relieved by these holes enough so that the penny spins. If a penny really has two different terminal velocities, it should oscillate up and down in this wind tunnel as a result. I know! The fact that it goes up and down and then comes back up again, it was just like on its flat face. It was just hanging out like that. When, in 2003, I dropped the penny in the top and it went up and down, like, I'm still, every single time I tell that story, I get goosebumps, because I remember that feeling of like, oh, wow! We made a separate video on Adam's channel that discusses the wind tunnel in more detail, so check it out after this. So the reason pennies aren't dangerous is because their terminal velocity is, at most, about 80 kilometers per hour. Yeah, it's not gonna hurt you. That's busted. Right. That's a start. I think I'm allowed to say that. Like old habit. But something more aerodynamic would have a higher terminal velocity, and this has led some to suggest ballpoint pens falling from a skyscraper, like the Empire State Building, could be lethal. But supposedly- Yeah, a pen, a ballpoint pen. Is as dangerous as a penny is mythically dangerous? Yeah, yeah. Like that is meant to actually be lethal. It's worth really trying. These pens weigh about twice as much as a penny, and they have a smaller cross-sectional area. So this will increase the ratio of weight to drag, but will it be enough? Now, because I'm not sure what will happen, I'm not putting my body on the line for this one. Instead, we'll use a ballistics gel dummy. Here we go, in three, two, one! I'm not getting in. The second to last drop, we had almost no crosswinds at all. So they dropped perfectly down and kind of hit right below where we were, and they were all cattywampus. If the myth was true, I would expect to see this everywhere. Right. Right? That's what I would expect to see. And I don't see a single one, and I didn't after we dropped them all. Are you going to call it? Wow, I will, sure. I'll come back at a retirement to say busted. Pens are not dangerous falling from tall objects. Ballpoint pens with their caps off. Yeah. Narrow metal pens might still be dangerous, but these plastic ones still seem to have too much drag relative to their weight for them to achieve a high terminal velocity. One of the curious things about air resistance is that it depends not only on the cross-sectional area of the object, but also on its overall shape. This dependence is captured in a dimensionless number known as the drag coefficient. The drag coefficient is all about how smoothly air can flow around an object without creating vortices. The word bullet comes from the French boule, meaning ball. So a boulette is a small ball, exactly what the earliest bullets were. But the drag coefficient of a sphere is 0.5. So people modified the shape to reduce drag, and eventually they settled on the modern bullet shape, which has a drag coefficient between 0.1 and 0.3. So drag coefficient is the reason a bullet is no longer a boulette. So what would happen if you dropped a bullet from a skyscraper? Not what you'd expect. Instead of falling pointy side down, a bullet would tumble and likely end up falling on its side. The thing is that cylinders tend to fall on their sides if given enough chance. Really? But the object falls in relation to the highest resistance. It chooses, it ends up finding the highest resistance as the most stable. Why doesn't it fall on the lowest resistance? I know. That seems intuitive. Bullets, if you let them, they'll fall and make bullet-shaped holes. On their side? A bullet fired straight up slows down as its kinetic energy is turned into gravitational energy. And at its highest point, which could be up to three kilometers high, it stops and then falls back down. At that moment, it's just like dropping a bullet from a really tall building. As it starts to fall, it will tumble. And so it experiences far more air resistance than on the way up. And so it's not gonna get back a lot of that energy that went into its height, which means that by the time it reaches the ground, it will be much slower than it was shot. Now, if the bullet isn't fired completely vertical, then it poses much greater danger. At the peak of its trajectory, only the vertical component of velocity is zero. It still maintains its horizontal velocity. And that, combined with the spin imparted to the bullet by the grooves inside the gun barrel, keep it moving pointy end forwards. And so as the bullet comes back to the ground, it speeds up to a significant fraction of its launch speed. There are hundreds of cases of people being struck and killed by celebratory gunfire from all over the world. Now, this is accidental, but the concept of dropping deadly projectiles on enemies is almost as old as aircraft. In World War I, these little pieces of metal were dropped out of planes. And they look like nails with little feathers on the back to make sure they fall straight. They're called flechettes, which is French for little arrow, but some were up to 15 centimeters long. That is great. I totally wanna make a thing that shoots these. And how big were these things? About the size of a dart, a little heavier than a standard pub dart. And there were like endless different shapes. From a military perspective, the advantages were they didn't require any explosives and they were cheap to produce and deploy at scale. They could pierce helmets leading to enemy casualties and some nasty injuries. They found darts that had gone through a rider and his horse. That's insane. But I also just love the idea of a guy in an open cockpit, cloth and wood plane, just hurling handfuls of darts out. That is like a 10-year-old's idea of warfare. Right? Then I'm gonna hit him with darts. Later, the US created similar weapons called lazy dogs, which were a bit heftier, used in the Korean and Vietnam wars. The damage they inflicted was indiscriminate and unpredictable, but at least they didn't leave unexploded ordinances in the field. And militaries continue to use kinetic projectiles to this day. For example, to make precision strikes on terrorist leaders. Falling objects are also dangerous in civilian life. Nearly 700 Americans die each year by being struck by a falling object. These range from loose tiles and bricks to falling construction tools, falling rocks and tree branches, and even icicles. Death by icicle is rare, but they were a serious enough concern that in the winter of 2014, streets around New York's One World Trade Center were closed due to the danger caused by icicles hanging on the building. So which projectiles are lethal and which aren't? Honestly, a lot of them are. The lower limit of the energy required to fracture a human skull is around 68 joules. So anything that has kinetic energy greater than that is very likely to kill you. A raindrop at terminal velocity with its tiny mass will only deliver two thousandths of a joule. A falling penny has about a fifth of a joule. But a baseball and the largest hailstone measured deliver more than 80 joules. That is plenty to crack your skull. In 2014, a man was killed when he was hit by a falling measuring tape that had fallen 50 stories. And this is just calculating for blunt force trauma. The energy stored in a falling flechette is not enough to crack your skull, but it can apply a large force to a very small area. So yeah, a penny falling from the Empire State Building won't kill you. A pen likely won't either. Anything that weighs a few grams and isn't aerodynamic isn't going to be fatal. But objects that weigh more than a few hundred grams traveling at terminal velocity are likely to be deadly. 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