Science For Everyone - Terminal Velocity

Copyright © Karl Dahlke, 2022

The "terminal velocity" is the maximum speed that an object can fall here on earth. Hold a balloon over your head and let go; by the time it reaches your chest it is falling as fast as it can, about 5 miles an hour. At this speed, the air resistance exactly balances the weight of the balloon. It has to push the air out of the way as it falls, and it's light, so it falls slowly to earth. Drop a balloon off the Empire State Building and it floats down to the ground at 5 miles an hour, all the way down.

The terminal velocity of a penny is 25 mph, or 40 kph, which is more than a balloon, true, but a penny is still relatively light. It tumbles and flutters on the way down, displacing air across its surface. A mythd that floated around when I was a kid was that a penny tossed off a skyscraper could kill a person, drilling into the skull. Not true. 25 mph isn't all that fast, and the light penny would bounce harmlessly, (but painfully), off your head.

A raindrop falls at 20 mph, or 32 kph. A hailstone falls at 31 mph, or 50 kph. A golf ball falls at 72 mph, or 115 kph. A bowling ball falls at 285 mph, or 460 kph. Multiply the radius of a ball by r, and its mass increases by r cubed, while its cross sectional area increases by r squared. The terminal velocity increases as the size of the ball increases, assuming it is made of the same stuff.

Many have, playfully, shot live rounds into the air, but that's not a great idea. A bullet falls back to earth with a terminal velocity that depends on its orientation, and the caliber of the bullet, but can reach 200 mph, or 320 kph. This won't kill a hapless bystander, but could inflict serious injury.

How about a human? If you are falling in a horizontal position, your terminal velocity is 120 mph, or 190 kph. You can jump from 8 miles high, as the Byrds would say, and still you will land at 120 mph. If you can keep yourself in a head down position, without tumbling, you can push this velocity up to 160 mph, or 255 kph. Well, when you hit the ground, either velocity is terminal. 😁

Now here's the fun part. Some day we will have a colony on Titan, the largest moon of Saturn. The atmosphere is thicker than ours,almost half again as thick, and the gravity lighter, about one seventh of our gravity. Combine the thick air and the weak gravity, and terminal velocity for a human is a modest 19 mph, or 30 kph. That is the same as falling from a height of 15 feet here on earth. You wouldn't jump off a 15 foot ledge, but if you did, you would survive. Oh you might break a leg, or sprain an ankle, but you would survive. With some training, you might learn to walk away from such a fall. So imagine - you jump off the top of a one mile sky scraper on Titan, and fall through the air, down and down, spread out to maintain a steady 19 mph, down and down, and execute a perfect tuck&roll, and stand up and walk away. How cool is that‽

Can we really walk away from this fall? The military provides impact training, going all the way back to World War I, when some of our brave paratroopers jump behind enemy lines. While falling through the sky, they are helpless targets for the enemy, like a skeet shoot. A faster descent means they are harder to hit, and they spend less time in the air. Of course the impact is more dangerous, and nobody wants to break a leg behind enemy lines. The military has determined the maximum speed for a descent into enemy territory, about 16 mph, assuming the soldier is trained to tuck and roll. In other words, the soldier, with his gear and his parachute, has a terminal velocity of 16 mph.

With the aforementioned military training, a healthy adult might be able to sustain a 19 mph landing on Titan. He could fall from any height, with nothing but his outstretched arms to moderate his descent, and suffer only modest ijuries, if that.

I'm glossing over some details here. The temperature on Titan is -180 degrees c, or -290 degrees f. That kind of cold is unimaginable. Exposed flesh would freeze in seconds, and an inhalation would freeze the lungs, and render them useless. One breath on Titan, and death is inevitable. We don't need a pressurized space suit on Titan, but a full body suit is required, withseveral centimeters of insulation covering every part of the body. This suit adds to the weight of our freefaller, but it also adds to his surface area. Furthermore, the padding might cushion his fall.

There is no oxygen on Titan. The oxygen canaster must be kept inside the suit, or otherwise heated. This adds additional weight, though probably not much. Now, properly dressed and equipped, our intrepid explorer can walk around Titan, and if he happens to fall off a cliff, he might be ok.

There is no terminal velocity on an airless world like the moon. An object falls faster and faster, until it hits the ground. Galileo predicted this in the 1600's, when he famously said that a feather and a hammer would fall at the same rate, if there were no air. Astronaut David Scott, of Apollo 15, proved Galileo correct, when he performed this very experiment on the moon.