Putting the ?terminal? in terminal velocity
The impact crater left by a penny that fell out of an airplane and achieved terminal velocity, probably? Photo by Dave Herring.
Once, on a family vacation when I was a child, we went to New York City. Wandering through Manhattan left an impression in my young mind of vastness, huge buildings that stretched so far up into the sky that, when trying to see their tops, I was in danger of falling over backwards on the sidewalk.
How could a building be so tall? What would the world look like from the top?
And, perhaps most important to a small child wandering around at the base of the building, what if something fell off the top and hit me, standing way down at the bottom?
The fear grew more detailed when I heard about people, pranksters and tricksters, throwing pennies off the top of the Empire State Building. What if one of those pennies hit me?
Could it kill me? Could something as common, everyday, and nonthreatening as a penny prove lethal?
Terminal Velocity Is Not the Speed Where Something Becomes Deadly
When we talk about an object falling from a great height, we usually discuss its terminal velocity. This sounds like a term out of the Final Destination movies (are those too long ago? Am I dating myself with that reference?), but it?s a concept from physics.
Unless you?re on a racetrack, your car never (and should never) reach terminal velocity. Photo by toine G.
Terminal velocity describes the maximum speed that an object can attain in a given environment, usually in our atmosphere. It?s different for each object.
Imagine that you went sky-diving. When you first jump out of the plane, you?re briefly floating, before you start dropping towards the ground, for a split second!
After that instant, however, gravity pulls you down, and you accelerate towards the earth, at a rate of 9.81 meters per second. But you don?t build up more and more speed until you hit the ground at a million miles per hour!
Instead, the air resistance pushes back against you, until eventually you can?t fall any faster than you currently are. For a falling person, this is about 200 km/hr (120 mph) if your arms and legs are spread out. Tucking yourself into a more streamlined shape can increase your terminal velocity up to 290 km/hr (180 mph).
And if you?re jumping out of a plane, you hit terminal velocity at around 6 seconds; 200 km/hr is equal to 55.6 meters per second. Your maximum speed (55.6 m/s) divided by your acceleration rate (9.81 m/s) means that you reach max falling speed after 5.7 seconds.
So if you fall out of a plane, don?t worry ? you only hit the ground at around 120 miles per hour if you spread out! Totally fine!
But we?re not throwing humans off the top of the Empire State Building; there are laws against that sort of thing. We?re chucking off pennies.
And it turns out that pennies have a pretty low terminal velocity ? about 40?50 miles per hour, just slightly faster than a ping-pong ball. Getting hit by a penny at 50 mph will certainly leave a welt, but it?s not going to break bones or kill.
But what if it went faster?
The Penny Gun, Still In Prototyping
Thankfully, I don?t need to go out and build a gun that?s been specially modified to fire pennies? because none other than the Mythbusters, two of the most well-known scientific/engineering TV personalities, have done it already in an episode of their titular show.
In the video above, the Mythbusters prove through experimentation what I showed with math ? a penny traveling at terminal velocity, like one thrown off the top of a building, just isn?t going fast enough to kill someone. They even fire it at Adam?s hand, where it bounces off without breaking the skin.
Not content with these results, they rig up a rifle that fires a blank cartridge?s power at a penny, accelerating it to nearly 3,000 feet per second. Even at this speed, however, a penny won?t be as deadly as using a regular old bullet:
Penny weight: 1.5 grams
.22 long round bullet weight: 2.5 grams
Because it weighs less, it won?t fly as far or carry as much energy, making it less lethal. Additionally, a flat disc is not a very aerodynamic shape, so a penny fired from a gun would be inaccurate and would quickly lose speed when facing air resistance (slowing down to terminal velocity).
So all in all, it?s pretty hard to kill someone with a single penny.
What about a lot of pennies?
It Takes a Lot of Pennies to Kill Someone ? Like 50
We can?t kill someone for $0.01, even with the Empire State Building as our weapon. But what about for $0.50?
Calculating terminal velocity means we need to know the mass, surface area, and drag coefficient (how much resistance there is from the air, based on its shape). A roll of pennies contains 50 coins, which means that it weighs around 75 grams. The surface area of a penny is around 61 square millimeters, and the drag coefficient of a cylinder is around 1.2.
Put it all together, and we get a terminal velocity of 286 mph, or 128 m/s. But because the object is much heavier, it?s got a lot more force ? which means it will hit with more impact and be deadlier.
Assuming that our penny roll weighs around 75 grams, some back-of-the-envelope calculations show that it hits with around 550 joules of force ? which is more than enough to break a human skull, which fractures at 15?68 joules of force on average.
So if you see someone heading up to the top of a skyscraper with a handful of loose change, you?re fine ? but watch out if that change is still in rolls!
(On a less joking note, this is why hard hats are so vital at construction sites. A falling bolt may weigh 50 or 60 grams, which could crack a skull ? but will bounce harmlessly off a hard hat.)
Pennies as weapons? Not individually, but like people, when they come together, they can accomplish great, or terrible things.
My childhood fears of being hit by a penny falling from a skyscraper were unfounded, but shifting the numbers a bit does show why it?s important, if visiting a construction site or anywhere else that things could fall from the sky, to protect your noggin with a hard hat. Just a bit of extra weight on a falling object can mean the difference between ?bounces off harmlessly? to ?cracks a skull.?
Pennies are next to useless when it comes to commerce (except for the four pennies you give me when you read one of my articles on Medium ? thank you!), but they aren?t going to be of much use as a bullet replacement, either.
Sam Westreich holds his PhD in genetics, focusing on methods for studying the gut-associated microbiome. He believes that you are worth far more than four cents. You?re the whole dollar, baby. Follow on Medium, or on Twitter at @swestreich.
Also, I used to link another article down here ? but a recent post on Medium suggested removing the call-to-action. If there had been another of my articles linked here, would you have clicked on it?