Chutes And Landers

From: Robin Feder <rjfeder@fortleenj.com>
To: Sy Moire <sy@moirestudies.com>
Subj: Questions

Hello again, Mr Moire. Kalif and I have a question. We were talking about falling out of stuff and we wondered how high you have to fall out of to break every bone in your body. We asked our science teacher Mr Higgs and he said it was something that you or Randall Munroe could answer and besides he (Mr Higgs) had to get ready for his next online. Can you tell us? Sincerely, Robin Feder


From: Sy Moire <sy@moirestudies.com>
To: Robin Feder <rjfeder@fortleenj.com>
Subj: Re: Questions

Hello again, Robin. You do take after your Dad, don’t you? Please give my best to him and to Mr Higgs, who has a massive job. Mr Munroe may already have answered your question somewhere, but I’ll give it a shot.

You’ve assumed that the higher the fall, the harder the hit and the more bones broken. It’s not that simple. Suppose, for instance, that your fall is onto the Moon, whose gravity is 1/6 that of Earth. For any amount of impact, however high the fall would have been on Earth, it’d be six times higher on the Moon. So the answer depends where you’re falling.

But the Moon doesn’t have an atmosphere worth paying attention to. That’s important because atmospheres impose a speed limit, technically known as terminal velocity, that depends on a whole collection of things

  • the Mass of the falling object
  • the local strength of Gravity
  • the Density of the atmosphere
  • the object’s cross‑sectional Area in the direction of fall

The first two produce the downward pull of gravity, the others produce the upward push of air resistance. Fun fact — in Galileo’s “All things fall alike” experiments, he always used spheres in order to cancel the effects of air resistance in his comparisons.

Let’s put some numbers to it. Suppose someone’s at Earth’s “edge of space” 100 kilometers up. From the PE=m·g·h formula for gravitational potential energy and dividing out their mass which I don’t know, they have 9.8×105 joules/kilogram of potential energy relative to Earth’s surface. Now suppose they convert that potential to kinetic energy by falling to the surface with no air resistance. Using KE=m·v² I calculate they’d hit at about 1000 meters/second. But in real life, the terminal velocity of a falling human body is about 55 meters/second.

That Area item is why parachutes work. Make a falling object’s area larger and it’ll have to push aside more air molecules on its way down. Anyone wanting to survive a fall wants as much area as they can get. A parachute’s fabric canopy gives them a huge area and a big help. Parachute drops normally hit at about 5 meters/second. Trained people walk away from that all the time. Mostly.

Which gets to the matter of how you land. Parachute training schools and martial arts dojos give you the same advice — don’t try to stop your fall, just tuck in your chin and twist to convert vertical kinetic energy to rolling motion. Rigid limbs lead to bones breaking, ligaments tearing and joints going out of joint.

So let’s talk bones. Adults have about 210 of them, about 90 fewer than when they were a kid. Bones start out as separate bony patches embedded in cartilage. The patches eventually join together as boney tissue and the cartilage proportion decreases with age. Bottom line — kid bones are bendy, old bones snap more easily. For your question, breaking “every bone in your body” is a bigger challenge if you’re young.

But all bones aren’t equal — some are more vulnerable than others. Sesamoid bones, like the ones at the base of your thumb, are millimeter‑sized and embedded in soft tissue that protects them. The tiny “hammer, anvil and stirrup” ear bones are buried deep in hard bony tissue that protects them, too. Thanks to bones and soft tissues that would absorb nearly all the energy of impact, these small bones are almost invulnerable.

To summarize, no matter how high up from Earth you fall from, you can’t fall fast enough to hit hard enough to break every bone in your body. Be careful anyhow.

Regards,
Sy Moire.

~~ Rich Olcott

  • Thanks to Xander and Lucas for their input.