You can do a similar calculation for any altitude you wish to reach using the exponential decrease in atmospheric density with altitude. However we suggest that you do not actually do this. At least one person has died trying to duplicate Larry's stunt.*
Balloons on Other Planets
Of course, now that you understand the basics, you can extrapolate to other situations. Suppose you're on Mars and you have an urge to go for a balloon ride. You don't have to worry about the FAA, since they haven't reached Mars yet. But you have to figure out what gas will float your balloon in the Martian atmosphere.
The atmosphere on Mars is mostly carbon dioxide—compared with the air here on Earth, which is a mixture of seventy-eight percent nitrogen and twenty-one percent oxygen with argon, carbon dioxide, ozone and everything else making up only about one percent. ("But wait!” you say, being the astute sort of reader we expect here in the pages of Fantasy & Science Fiction. “What about the water vapor?” Well, we're giving the composition of dry air. Water vapor varies from nearly zero percent to nearly four percent depending on place and time.)
To float your balloon on Mars, you need a gas that's lighter than the carbon dioxide—and Avogadro's law will help you figure out what gases might qualify. Back in 1811, Amedeo Avogadro hypothesized that equal volumes of ideal gases, at the same temperature and pressure, contain the same number of particles, or molecules.
Real gases behave pretty much like ideal gases for our purposes. Since two identical volumes of two different gases at the same temperature and pressure contain the same number of molecules,you can figure out which one will be lighter by comparing the weights of the molecules. And you can do that easily enough by consulting the Periodic Table of the Elements and knowing just a little bit about gas molecules.
On the Periodic Table, you'll see that oxygen has an atomic weight of about sixteen (that's eight protons and eight neutrons). An oxygen molecule is made of two atoms, for a molecular weight of thirty-two. Carbon dioxide is two oxygen atoms and a carbon atom (which has an atomic weight of twelve) for a total molecular weight of forty-four.
Look on the table to see if you can find a lighter gas, and you'll see the same ones that work well on Earth. Helium has an atomic and a molecular weight of four. (It's an atomic gas—just one atom per molecule.) Hydrogen has an atomic weight of one, and it has two atoms per molecule, making it a molecular lightweight at two.
Since helium and hydrogen are both lighter than carbon dioxide, they would work fine. You might be reluctant to use hydrogen for lift on Earth (remembering the unfortunate fate of the Hindenburg), but hydrogen requires oxygen to burn. In the Martian carbon-dioxide atmosphere, you'd be fine.
Now suppose you decided to go ballooning on Jupiter. There, the atmosphere is mostly hydrogen and helium. A glance at the periodic table reveals that those gases are the lightest ones around.
So what do you do? You remember that Avogadro's law applies to identical volumes of gases at the same temperature and pressure. On Jupiter, we suggest you consider a hot-air balloon. When you heat a gas, the molecules bounce around faster, spreading out and taking up more space. The density of the gas drops—perfect for ballooning!
Submarine Ballooning
So far we've been considering balloons that are filled with air and float in air. In both science and science fiction, it's interesting to consider what happens if you take a commonplace situation and make just one change.
You can think of the atmosphere as an ocean of air and a balloon as a bubble floating upward in that ocean. Suppose you changed that ocean of air into an ocean of water. What would you put inside your balloon if you wanted to start at the bottom of the ocean and float to the top?
In science and science fiction, one change leads to other changes. Maybe you think you could fill your submarine balloon with air—after all, air is less dense than water.
But there's a problem. At the bottom of the sea, the pressure of the water would crush the gas. That's fine down to a certain depth. But when you reach the level where the volume of the gas has been reduced so much that your craft's weight exactly matches the weight of the water it displaces, the craft becomes neutrally buoyant. That means it doesn't rise and it doesn't sink.
What happens when you go below that point of neutral buoyancy? The water pressure goes up and the volume of the gas that serves as your balloon goes down. Now the craft weighs more than the water it displaces and you're sinking with no way to get back to the surface. Not a good situation.
So you need to fill your submarine balloon with something that doesn't compress under pressure. Marine mammals have solved this problem with a fatty layer of blubber. Not only does blubber insulate these animals from cold water, it also serves as an incompressible buoyancy device—sort of like a built-in life vest. Taking a tip from the whales, you could fill your balloon with fat. A big balloon full of lard would keep your craft buoyant.
Alas—as far as we know, no one has yet created a lard-based buoyancy control. The Bathyscaphe Trieste, a deep-diving research vessel with a crew of two people, solved the problem by filling its float chamber (an underwater balloon, if you will) with gasoline. Gasoline is less dense than water. Like other liquids, it doesn't compress significantly even at extreme pressures, making it as effective (though perhaps not as absurd) as a float chamber filled with lard.
You've probably heard of a bathysphere: a spherical deep-sea submersible that is lowered into the depths on a cable. A bathysphere isn't an undersea balloon. It's more like an undersea rock. It sinks and, when the adventurers aboard are done, it's hauled back to the surface. Unfortunately, using a cable to lower and raise a craft limits its range. The bathysphere's maximum was about 900 meters (or around 3,000 feet) down.
The bathyscaphe, on the other hand, is not limited by a connection to the surface. Because of its gasoline-filled float chamber, the Trieste could free dive in the water. In 1960, the bathyscaphe reached a depth of about 10,900 meters (35,761 feet), in the Mariana Trench, breaking every previous record and establishing a record that has not yet been matched.
Water balloons
Talking about underwater balloons got Pat thinking about water balloons.
Well, to tell the truth, Pat started out thinking about water balloons. We were working on this story during a rare heat wave here in San Francisco and she needed an excuse to spend an hour tossing water balloons out the window. ("It's science,” she says. The neighbors wonder about that.)
She started thinking about water balloons when she took a look at a few of the many online videos that show a water balloon popping in slow motion. Just go to YouTube and search for “water balloon” and “slow motion.” A slow-motion video lets you see aspects of an event that you never noticed before.
Our favorite videos show someone popping a water balloon with a pin or knife. The moment after a pin pricks the balloon, the rubber vanishes, speedily contracting to a fraction of its stretched size. For an instant, you'll see the water without the balloon, a beautiful crystal clear shape Then gravity takes over, pulling the water down down down.
That moment when you see the water without the balloon is an interesting one. As we mentioned in the discussion of the gasoline-filled submarine balloon, liquids don't compress much, even under pressure. So the water is contained but not compressed by the stretched balloon. Remove the balloon and the water stays put.
Equally amazing are the videos of water balloons that do NOT explode, but bounce. Paul likes to create such super strong water balloons by putting one balloon inside another to make a double-strength balloon. Watching a water balloon (or a tennis ball) deform when it hits the ground and bounces back is seeing conservation of energy in action. Energy, say the physicists, can neither be created nor destroyed.
Suppose you hold a water balloon a foot from your driveway. That balloon has potential energy. It has the potential to fall, pulled downward by gravity. As the balloon falls, the potential energy becomes the kinetic energy of motion.
When the balloon hits the ground, it either breaks or bounces. If it breaks, its kinetic energy becomes the kinetic energy of water flying all over the place. (That's Pat's favorite part.)
But if it bounces, that kinetic energy goes into deforming the balloon—squashing it flat. The balloon membrane stretches, momentarily storing energy in the stretch. Some of the energy is lost to friction (which becomes heat), but most goes to restoring the balloon to its original shape and sending it springing back into the air.
When Pat was tossing water balloons and meditating on the conservation of energy, she noticed that balloons filled with air made a loud bang when she popped them. But when a water balloon popped, there wasn't much of a sound, other than the splash of the water and the yelps of the people who had been doused. Why, she asked Paul, didn't water balloons pop with a bang?
Not with a whimper, but a bang
So why does popping a toy balloon make such a satisfying “BANG!"?
First, we'd better talk about what that noise is. The human ear and brain perceive sound when there is a pressure change outside the eardrum. A popping balloon creates a sudden pressure change.
Inside an air-filled balloon, air is trapped and squeezed. The air pressure inside the balloon is higher than the surrounding atmospheric pressure. When you prick the balloon with a pin, the stretchy latex of the balloon splits open. If you could somehow color the air inside the balloon, you would see a region of compressed colored air hanging where the balloon used to be, just like the water in the water balloon.
But unlike the water, the air is under pressure. Once it's released from its latex prison, the compressed air expands outward. The air in the center of the balloon pushes the air closest to the balloon's surface outward. The expanding air reaches maximum speed when the pressure of the air that was originally in the center of the balloon matches atmospheric pressure. The outwardly expanding air sends a compression wave spreading out at the speed of sound. When this compression wave passes your ears, the compression pushes on your eardrum and you hear a bang.
But wait—there's more! When the air that was inside the balloon reaches atmospheric pressure, it's still rushing outward. It overshoots, creating a lower pressure region where the balloon used to be. So then the air rushes back to fill that lower pressure area. This creates an expansion wave of low pressure, which follows the compression wave. This alternation of compression and expansion makes a sound with a given pitch.
Of course, it doesn't stop there. The air rushes back, overshoots, then rushes out, overshoots, and so on, getting a little closer to equilibrium each time. Depending on the size and initial pressure in the balloon, the oscillation between compression and expansion takes different times. That's why popping different balloons produces different pitches. Larger balloons produce lower pitched pops than smaller balloons with the same pressure.
Going out with the biggest bang
Once you have a loud explosive noise, it's only human nature to try to make that noise louder. We will be continuing our investigation of balloons with hands-on experiments into ways to get the biggest bang. Since the loudness of the pop increases with increased air pressure inside the balloon, we will be testing balloons to find the ones that maximize the internal pressure. We are also looking for an ideal balloon-popping environment. A large interior space with plenty of hard surfaces and no padding to absorb the sound (an empty gymnasium or a concrete stairwell) offers the best potential for echoes.
We invite you to join the investigation—in empty gymnasiums or concrete stairwells, with balloons of your choice. And if anyone complains about the noise, remember: you're not just popping balloons. It's science.
The Exploratorium is San Francisco's museum of science, art, and human perception—where science and science fiction meet. Paul Doherty works there. Pat Murphy used to work there, but now she works at Klutz (www.klutz.com), a publisher of how-to books for kids. Pat's latest novel is The Wild Girls. To learn more about Pat Murphy's writing, visit her website at www.brazenhussies.net/murphy. For more on Paul Doherty's work and his latest adventures, visit www.exo.net/~pauld.
*For people who prefer to experience a trip like Larry's more safely through the magic of fiction, we refer you to “The View from On High” by Steven R. Boyett, from our Aug. 2000 issue. You'll find the story reprinted on our website this month.
[Back to Table of Contents]
Novelet: The Price of Silence by Deborah J. Ross
Longtime readers might recall the stories “Madrelita” (Feb. 1992) or “Javier, Dying in the Land of Flowers” (Jan. 1996) by one Deborah Wheeler. Ms. Wheeler now goes by her birth name and we're pleased to welcome Ms. Ross back into F&SF. Deborah has by no means been inactive during the past thirteen years—according to www.deborahjross.co , much of her creative energy has gone into the Darkover world created by her friend Marion Zimmer Bradley and she's currently writing a novel entitled Hastur Lor. Here she regales us with a tight, compelling science fiction story of life aboard the Juno.
Because he had joined the crew at the last minute and because he was still very young, Devlin felt awkward, not quite accustomed to no longer having a last name, but being only “Devlin of Juno.” During the last stretch of space flight to the planet December, he explored the various work areas, practicing maneuvering in zero-gee, until he found Shizuko, Juno's engineer, and Verity, the pilot, in the galley. The room was roughly spherical, the walls studded with storage bins.
Heads close together, knees hooked around stabilization bars, the two women were sipping bulbs of what looked like real coffee. Spirals of plum blossoms covered Shizuko's micropore skins from one arm to the opposite shoulder, leaving the rest of her slender body shimmering silver. Verity's thunderbolts jagged across a field of palest yellow. Despite his medical training, Devlin's pulse rate jumped. The skins clung almost as closely as the real thing, revealing every line of muscle and bone, breasts round and soft without the pull of gravity.
"Ohé, Devlin!” Shizuko beckoned him to join them. “Hungry?"
Devlin fitted himself into the frame, banging his knees and one elbow in the process. The natural tone of his postural muscles kept his body pressed against the bars, holding him in place.
Verity smothered a smile and handed Devlin two bulb containers and a flat packet. He bit off the tip of one, expecting the standard reconstitute paste. Instead, the mixture was subtly spiced, with a lingering warmth of ginger. He chewed the accompanying bread, fluffy dough layered with potato and garbanzo filling. The second dish was a spirulina pudding that looked like pale green gelatin but tasted of limes.
"This is good!"
"Araceli's cooking.” Unlike the other crew, Verity didn't shave her head, but braided her black hair in scalp-hugging spirals. With her milky skin, he thought her beautiful but hard-edged.
A shadow shifted at the edge of Devlin's vision. Archaimbault March floated at the entrance, like a silent panther in his jumpsuit of unallayed black. Archaimbault March, like Devlin, had joined Juno at TerraBase, neither passenger nor crew, his mission as well as his military rank never stated. Devlin assumed he was a high-ranking security officer; with his restless gaze and opaque expression, the man reeked of covert power.
"Was there something you wanted?” Shizuko said.
"Your captain tells me you are investigating the lack of communication with the December authorities."
"That's true,” she replied, without a hint of defensiveness. “But it's not unexpected, given the recent stellar flares. We're still on the other side of the sun from the planet."
December was a Stage Three planet, with a breathable atmosphere and generous supplies of water. Its five principal continents hosted pristine forests, plains, and deserts, all abundant in compatible biology. It had been colonized and then abandoned ten thousand years ago by an alien race whose enigmatic ruins dotted the temperate zones.
The planet had passed the rigorous process of robotic exploration, followed by years of painstaking Stage Two surv
ey. The first wave of colonists had been there for more than a decade local time, enough to establish a viable agricultural community. Sometimes dangerous conditions didn't show up right away, but planets usually didn't make it this far in the colonization process without some indication of trouble.
"I will run diagnostics on our own equipment to make sure the problem isn't reception,” Shizuko added.
From the faint tightening around Archaimbault March's eyes, he doubted her reassurance. “Very well. Inform me as soon as you obtain any results."
"You'll be the second to know,” she said, her voice carefully neutral. Then added, “After Fidelio."
Once Archaimbault March had left, Devlin muttered, “He's sure got a comet stuck up his ass."
"I don't trust him, either,” Shizuko said. “Why would TerraBase dispatch someone like him to an agricultural colony?"
Verity looked at Devlin slantwise. “Do all military personnel set you off, or just this particular idiot?"
"Anything in a uniform. It's a good thing you—we—don't wear them."
Shizuko laughed in such a friendly way that Devlin relaxed. “Oh, Devlin, you're not what we expected.” Her lips drew together like softly rounded petals. Devlin wondered what it would be like to kiss her.
"What did you expect, that I'm not it?"
Shizuko tilted her head, a gesture that substituted for a shrug. “We're used to being a world unto ourselves. Dirtsiders brush past us like mayflies. But we're out of balance now. You know that Aimer jumped ship at our last TerraBase refit?"
"He was your previous physician, wasn't he?” Devlin said.
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