## Fun Fact - Fly on a Fan

My fan is on almost all the time, summer and winter, because I run hot. Even as a kid I had fans in my bedroom, and oh the games I would play: singing into the fan (that's pretty universal), flipping the switch from high forward to high reverse (stressing out the motor), stopping the fan by grabbing the stem (not recommended), and shoving foreign objects into the spinning blades (also not recommended). The fan would shred a piece of paper very nicely, making satisfying thwacking sounds as the paper bits flew about inside the housing. One day I inserted a stick into the blades. Remember, fans in the 1970's had stiff metal blades, not the wimpy plastic blades you see today. The resulting clatter reverberated throughout the house. My Mother, who rarely used profanity, exclaimed, "What the hell is going on up there?!" Oops. Perhaps the only thing I didn't do was stop the blades with my tongue, as a guest did on David Letterman on February 26, 1987, in his popular segment Stupid Human Tricks. watch No matter what you do, there's always somebody who is doing something crazier.

Fast forward 30 years, and I thought of a fan experiment that I can't perform in reality, so let's do it in our minds. What if a fly went for a ride on the tip of one of the fan blades? What would that be like?

Well he'd fly off of course, so we have to put him in a cage. It has to be a light cage, so it doesn't unbalance the blades and cause the fan to wabble. Let's assume this has been done.

The blades of my fan are about a foot across, or a third of a meter. I have no idea how fast the blades spin, so I found a few examples on the Internet (see below). Let's assume my fan is typical, and spins at 6 revolutions per second (low), 9 rps (medium), and 12 rps (high). These are conservative speeds; some tabletop fans run faster. If the radius r is a sixth of a meter, then the circumference, 2πr, is, conveniently, one meter. Hurray for round numbers! The previous article, shooting a bullet around the moon, introduced the formula for circular acceleration as v2/r. At 6 rps, the tip of the blade moves at 6 meters per second, and similarly for 9 and 12. 6 meters per second doesn't sound like much, the speed of a bicycle, but when the motion is in a tight circle it creates a substantial force. Apply the formula and get 216 meters per second squared. Divide by 9.8 to get 22 times the force of gravity, or 22 Gs. Turn the fan up to medium and produce 50 Gs, or 88 Gs on high. Could a fly survive that?

The froghopper bug, king of acceleration, experiences 400 Gs as it jumps from plant to plant. Even an ordinary housefly, swatted in mid air, experiences from 200 to 400 Gs, and is unharmed. It's looking good for our insecta friends. But of course there is a limit. Recall Peter Gabriel's words, "I'm hovering like a fly, waiting for the windshield on the freeway." That impact is 10,000 Gs, and is not survivable, even by an insect. Splat!

Well these events are all instantaneous, or nearly so. How would an insect fair under forces lasting a minute or more? Remember that a fly has a beating heart, and a few drops of liquid inside, so 400 Gs over ten minutes would probably do some damage. However, 22 Gs is certainly survivable, even for an hour. If a small cat can hold up to these forces (see below), then an insect certainly can. Thus a ride on the fan at low speed would cause no trouble. As for 88 Gs, well, I don't really know. It is probably at the upper limit of an insect's long-term tolerance.

If the fan was oriented horizontally, blowing air up to the ceiling, that would be the end of the story. However, the fan is vertical, and the blades spin within the gravity well of the earth. At the bottom of the circle, there is an extra G from the pull of the earth's gravity; at the top there is 1 G less. 6 times a second the G forces oscillate from 21 to 23. The fly is plastered against the bottom of his cage, but he is also shaken, vigorously, 6 times a second, or 12 times a second if the fan is on high. I'm not sure if these low frequency high amplitude vibrations cause any harm. Perhaps not, when compared to the 22 Gs that hold him fast to the floor, but if the fly were self-aware I'm sure he would complain about the organ jostling vibrations.

What about a human in a rapidly spinning Ferris wheel? The Great Wheel in Seattle is 50 meters across, or 25 meters in radius. Place a human in a gondola, lying flat on his back (the optimal position for high G forces), then crank up the speed. What would that be like?

John Stapp, a colonel in the United States Air Force, became the willing subject in a number of G force experiments in the 1940's and 50's. Some of these produced broken limbs, a detached retina, and burst blood vessels in his eyes, which led to lifelong vision impairment. Since such experiments will never be repeated, John Stapp's records will almost certainly stand for all time, including his unimaginable body slam at 46.2 Gs. How did he walk away from that one?? Once again, these are instantaneous forces, as a pilot might experience during a crash landing, thus the rationale for the experiments under the auspices of the Air Force. This is quite different from sustained forces such as those felt by astronauts during ascent and reentry. Indeed, three astronauts, from Russia, the United States, and South Korea, endured an unexpected load of 8 Gs during reentry on April 19, 2008, when their Soyuz capsule hit the atmosphere at a steeper trajectory than planned. The Soyuz landed almost 300 miles off target, but was quickly located by GPS. All three astronauts were unharmed. Peggy Whitson remarked, "Gravity's not really my friend right now, and 8 Gs was especially not my friend." The reentry glitch was not fatal, because a trained astronaut can survive 8 Gs for several minutes if necessary. Still, this is pushing the limit, even for a person lying on his back. Beyond 12 Gs, the heart is unable to pump the sluggish blood about the body, and breathing becomes impossible as the rib cage collapses under its own weight. Our hapless victim dies in short order.

With this in mind, let's spin the Ferris wheel up to 8 Gs. We're looking for an acceleration of 80 meters per second squared, and with a radius of 25 meters, we find a velocity of 45 meters per second, or 0.285 revolutions per second. The Ferris wheel, no longer a pleasant ride, turns once every 3.5 seconds. That doesn't sound like much, but with those long arms, the force on the rider is 8 Gs.

Don't forget the milkshake effect. Since the rotations are slower than the fan, the effect is not as dramatic. Your organs are not shaken violently as though you were in a blender. Still, the force rises and falls every 3.5 seconds, in a manner that probably gives you a queasy feeling inside. Every 3.5 seconds the G force rises to 9 at the bottom of the circle, and decreases to 7 at the top. Take your breaths at the top, under 7 Gs, when the elephant standing on your chest is not as heavy, then hold your breath at the bottom, under 9 Gs - and ask for your money back when the ride is over.

If you want a greater milkshake effect, then lie down inside a barrel, 1 meter in radius, spinning 1.1 times per second. Forces will osscilate from 4 to 6 Gs and back again in less than a second. That should jostle your stomach. For a different effect, slow the spin rate down to ½ rps, and experience 2 Gs at the bottom, and weightlessness at the top, in a cycle that repeats every 2 secondes.

As mentioned earlier, an extreme rotational experiment was performed, sadly, and unintentionally, on a small cat named Natasha. Bob (not his real name) was doing laundry, and when he stepped away to get a few more clothes, Natasha jumped in and sat happily atop the pile of clothes. Bob returned, tossed in one more item, lowered the lid, and pressed start. Natasha should have meowed loudly at this point, but she didn't. Bob walked away, and the cat endured a full 35-minute wash cycle. Fortunately, the dial was set for cold, else Natasha would have scalded to death. Still, it's amazing she didn't drown, nor did she succumb to the G forces of the spin cycle. A wash tub is considerably wider than a fan, but it spins a bit slower, perhaps 4 rps. As a rough estimate, the forces at the outer edge are about 20 Gs. Perhaps a thick layer of clothing cushioned Natasha, and reduced her radius somewhat. Still, she must have endured 15 to 20 Gs for several minutes. Imagine her small mammalian heart trying to move the blood around her little furry body, while her lungs gasped for air, as she was plastered flat against the padded wall of the spinning tub. Bob lifted the lid, discovered the bedraggled cat, and rushed her to the vet. She was suffering from hypothermia and shock. The vet dried her and warmed her up, and declared Natasha to be the most pleasant smelling pet he had ever treated. Natasha returned home, and was her usual active self - though she now stays far away from the washing machine.

In summary, survivable G forces, over several minutes, are approximately 10 Gs for a human, 20 Gs for a small cat, and 100 Gs for an insect.