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XKCD QA (What If?): Sunless Earth

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Sunless Earth

What would happen to the Earth if the Sun suddenly switched off?

—Many, many readers

This is probably the single most popular question submitted to What If.

Part of why I haven’t answered it is that it's been answered already. A Google search for what if the Sun went out turns up a lot of excellent articles thoroughly analyzing the situation.

However, since my recent articles on sunsets, the rate of submission of this question has risen even further, so I’ve decided to do my best to answer it.

If the Sun went out ...

We won’t worry about exactly how it happens. We'll just assume we figured out a way to fast-forward the Sun through its evolution so that it becomes a cold, inert sphere. What would the consequences be for us here on Earth?

Let's look at a few:

Reduced risk of solar flares: In 1859, a massive solar flare and geomagnetic storm hit the Earth.[1] Magnetic storms induce electric currents in wires. Unfortunately for us, by 1859 we had wrapped the Earth in telegraph wires. The storm caused powerful currents in those wires, knocking out communications and in some cases causing telegraph equipment to catch fire.[2]

Since 1859, we've wrapped the Earth in a lot more wires. If the 1859 storm hit us today, the Department of Homeland Security estimates the economic damage to the US alone would be several trillion dollars[3]—more than every hurricane which has ever hit the US combined.[4] If the Sun went out, this threat would be eliminated.

Improved satellite service: When a communications satellite passes in front of the Sun, the Sun can drown out the satellite's radio signal, causing an interruption in service.[5] Deactivating the Sun would solve this problem.

Better astronomy: Without the Sun, ground-based observatories would be able to operate around the clock. The cooler air would create less atmospheric noise, which would reduce the load on adaptive optics systems and allow for sharper images.

Stable dust: Without sunlight, there would be no Poynting–Robertson drag, which means we would finally be able to place dust into a stable orbit around the Sun without the orbits decaying. I’m not sure whether anyone wants to do that, but you never know.

Reduced infrastructure costs: The Department of Transportation estimates that it would cost $20 billion per year over the next 20 years to repair and maintain all US bridges.[6] Most US bridges are over water; without the Sun, we could save money by simply driving on a strip of asphalt laid across the ice.

Cheaper trade: Time zones make trade more expensive; it's harder to do business with someone if their office hours don't overlap with yours.[7] If the Sun went out, it would eliminate the need for time zones, allowing us to switch to UTC and give a boost to the global economy.

Safer Children: According to the North Dakota Department of Health, babies younger than six months should be kept out of direct sunlight.[8] Without sunlight, our children would be safer.

Safer combat pilots: Many people sneeze when exposed to bright sunlight. The reasons for this reflex are unknown, and it may pose a danger to fighter pilots during flight.[9] If the Sun went dark, it would mitigate this danger to our pilots.

Safer parsnip: Wild parsnip is a surprisingly nasty plant. Its leaves contain chemicals called furocoumarins, which can be absorbed by human skin without causing symptoms ... at first. However, when the skin is then exposed to sunlight (even days or weeks later), the furocoumarins cause a nasty chemical burn. This is called phytophotodermatitis.[10] A darkened Sun would liberate us from the parsnip threat.

In conclusion, if the Sun went out, we would see a variety of benefits across many areas of our lives.

Are there any downsides to this scenario?

We would all freeze and die.


XKCD QA (What If?): Extreme Boating

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Extreme Boating

Question:What would it be like to navigate a rowboat through a lake of mercury? What about bromine? Liquid gallium? Liquid tungsten? Liquid nitrogen? Liquid helium? By:–Nicholas Aron Let's take these one at a time. Bromine and mercury are the only known pure elements that are liquid at room temperature. Rowing a boat on a sea of mercury just might be possible. **Mercury** is so dense that [steel ball bearings float on the surface](http://www.youtube.com/watch?v=EGv_YVQHu7U). Your boat would be so buoyant that you'd barely make a dent in the mercury, and you'd have to lean your weight into the paddle to get the end of it below the surface. Image:boat_mercury.png:'Michael, row the boat ashore.' 'I'm TRYING!' In the end, it certainly wouldn't be easy, and you wouldn't be able to move *fast*. But you could probably row a little bit. You should probably avoid splash fights. **Bromine** is about as dense as water, so a standard rowboat could in theory float on it. However, Bromine is awful. For one thing, it smells terrible; the name "bromine" comes from the ancient Greek "brōmos", meaning "stench". If that weren't enough, it [violently reacts](http://www.youtube.com/watch?v=uCwHzTsx5yY) with a lot of materials. Hopefully, you're not in an aluminium rowboat. Imageboat_bromine_aluminium.png:The mercury one was going to be the least deadly, wasn't it. If that's not incentive enough to avoid it, the [Materials Safety Data Sheet on bromine](http://avogadro.chem.iastate.edu/MSDS/Br2.htm) includes the following phrases: - "severe burns and ulceration" - "perforation of the digestive tract" - "permanent corneal opacification" - "vertigo, anxiety, depression, muscle incoordination, and emotional instability" - "diarrhea, possibly with blood" You should not get in a splash fight on a bromine lake. **Liquid gallium** is weird stuff. Gallium melts just above room temperature, like butter, so you can't hold it in your hand for too long. It's fairly dense, though not anywhere near as dense as mercury, and would be easier to row a boat on. However, once again, you'd better hope the boat isn't made of aluminium, because aluminium (like many metals) absorbs gallium like a sponge absorbs water. The gallium spreads throughout the aluminium, dramatically changing its chemical properties. The modified aluminium is so weak it can be [pulled apart like wet paper](http://www.youtube.com/watch?v=FaMWxLCGY0U). This is something gallium has in common with mercury—both will [destroy aluminium](http://www.youtube.com/watch?v=Z7Ilxsu-JlY). Like my grandma used to say, don't sail an aluminium boat on a gallium lake. (My grandma was a little strange.) **Liquid tungsten** is really hard to work with. Tungsten has the highest melting point of any element. This means there's a lot we don't know about its properties. The reason for this—and this may sound a little stupid—is that it's hard to study, because we can't find a container to hold it in. For almost any container, the material in the container will melt before the tungsten does. There are a few compounds, like tantalum hafnium carbide, with slightly higher melting points, but no one has been able to make a liquid tungsten container with them. To give you an idea of how hot liquid tungsten is, I could tell you the exact temperature that it melts at (3422°C). But a better point might be this: *Liquid tungsten is so hot, if you dropped it into a lava flow, the lava would freeze the tungsten.* Needless to say, if you set a boat on a sea of liquid tungsten, both you and the boat would rapidly combust and be incinerated. **Liquid nitrogen** is very cold. Liquid helium is colder, but they're both closer to absolute zero than to the coldest temperatures in Antarctica, so to someone floating on them in a boat, the temperature difference is not that significant. A [Dartmouth engineering page on liquid nitrogen safety](http://engineering.dartmouth.edu/microeng/ln2.html) includes the following phrases: - "violent reactions with organic materials" - "it will explode" - "displace oxygen in the room" - "severe clothing fire" - "suffocation without warning" Liquid nitrogen has a density similar to that of water, so a rowboat would float on it, but if you were in it, you wouldn't survive for long. If the air above the nitrogen was room temperature when you started, it would cool rapidly, and you and the boat would be smothered in a thick fog as the water condensed out of the air. (This is the same effect that causes steam when you pour out liquid nitrogen.) The condensation would freeze, quickly covering your boat in a layer of frost. The warm air would cause the nitrogen on the surface to evaporate. This would displace the oxygen over the lake, causing you to asphyxiate. If the air (or the nitrogen) were both cold enough to avoid evaporation, you would instead develop hypothermia and die of exposure. **Liquid helium** would be worse. For one thing, it's only about one-eighth as dense as water, so your boat would have to be eight times larger to support a given weight. Imageboat_large.png:Frankly, what they needed was a smaller shark. But helium has a trick. When cooled below about two degrees kelvin, it becomes a superfluid, which has the odd property that it crawls up and over the walls of containers by capillary forces. It crawls along at about 20 centimeters per second, so it would take the liquid helium less than 30 seconds to start collecting in the bottom of your boat. This would, as in the liquid nitrogen scenario, cause rapid death from hypothermia. If it's any consolation, as you lay dying, you would be able to observe an odd phenomenon. Superfluid helium films, like the one rapidly covering you, carry the same types of ordinary sound waves that most materials do. But they also exhibit an additional type of wave, a slow-moving ripple that propogates along thin films of helium. It's only observed in superfluids, and has the mysterious and poetic name "[third sound](http://www.physics.berkeley.edu/research/packard/current_research/schechter's%20web/page2.html)." Your eardrums may no longer function, and wouldn't be able to detect this type of vibration anyway, but as you froze to death in the floor of a giant boat, your ears would be filled—literally—with a sound no human can ever hear: The third sound. And that, at least, is pretty cool. Imageboat_cool.png:Worth it.

XKCD QA (What If?): Free Fall

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Free Fall

What place on Earth would allow you to freefall the longest by jumping off it? What about using a squirrel suit?

—Dhash Shrivathsa

The largest purely vertical drop on Earth is the face of Canada's Mount Thor, which is shaped like this:

To make things a little less gruesome, let's put a pit at the bottom of the cliff filled with something fluffy, like cotton candy, to safely break your fall. (Would this work? Hmm ...)

A human falling with arms and legs outstretched has a terminal velocity in the neighborhood of 55 meters per second. It takes a few hundred meters to get up to speed, so it would take you a little over 26 seconds to fall the full distance.

How long is that?

It's long enough to finish the first level of the original Super Mario.[1]

Sprint's ring cycle—the time the phone rings before going to voicemail—is 23 seconds.[2] (For those keeping score, Wagner's is 2,350 times longer.)

This means that if someone called your phone, and it started ringing the moment you jumped, it would go to voicemail three seconds before you reached the bottom.

On the other hand, if you jumped off Ireland's 210-meter Cliffs of Moher, you would only be able to fall for about eight seconds—nine, if you jumped upward.

That's not very long, but according to River Tam, it would be enough time to drain all the blood from your body given adequate vacuuming systems. (So much for making things less gruesome.)

But you don't have to drop vertically.

Even without any special equipment, a skilled skydiver—once they get up to full speed—can glide at almost a 45-degree angle.[3] By gliding away from the base of the cliff, you could conceivably extend your fall substantially.

It's hard to say exactly how far; it all depends on your clothes. As a comment on a BASE jumping records wiki puts it,

The record for longest [fall time] without a wingsuit is hard to find since the line between jeans and wingsuits has blurred since the introduction of more advanced tracking apparel.

Which brings us to wingsuits.

Wingsuits are what you get when you take the average of parachute pants and parachutes.

One wingsuit operator posted tracking data from a series of jumps.[4] It shows that in a glide, a wingsuit can lose altitude as slowly as 18 meters per second.

Even ignoring horizontal travel, that would stretch out our fall to over a minute. That's long enough for a chess game. It's also long enough to sing the first verse of—appropriately enough—REM's It's the End of the World as We Know It followed by—less appropriately—the rap breakdown from the end of the Spice Girls' Wannabe.

When we include horizontal glides, the times get even longer.

There are a lot of mountains that could probably support very long wingsuit flights. For example, Nanga Parbat, a mountain in Pakistan, has a drop of more than three kilometers at a fairly steep angle.[5] (Surprisingly, a wingsuit still works fine at those altitudes,[6] though the jumper needs oxygen and glides a little faster than normal.)

So far, the record for longest wingsuit BASE jump is held by Dean Potter, who jumped from the Eiger—a mountain in Switzerland—and flew for three minutes and twenty seconds.[7]

Joey Chestnut and Takeru Kobayashi are the world's top competitive eaters.

If we can find a way for them to operate wingsuits while eating at full speed, and they jumped from the Eiger, they could—in theory—finish as many as 45 hot dogs between them before reaching the ground ...

... making them the joint holders of what just might be the strangest world record of all time.

XKCD QA (What If?): Bouncy Balls

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Bouncy Balls

What if one were to drop 3,000 bouncy balls from a seven story parking structure onto a person walking on the sidewalk below? Should the person survive, what would be the number of bouncy balls needed to kill them? What injuries would occur and what would the associated crimes be?

—Ginger Bread

After falling from seven stories, the mass of bouncy balls would be moving at about 20 meters per second.

20 meters per second is about how fast an average person with a good arm could throw a bouncy ball. Therefore, to determine the result of an impact, we can make use of what Einstein called a gedankenexperiment, or "thought experiment":

In science, it's important that results be repeatable, so let's try that again:

The tricky thing about this scenario is that 3,000 one-inch bouncy balls is not as many as you probably think—it'd be enough to fill a large bucket.

This bucket would weigh about as much as a small child, which leads us to another gedankenexperiment:

Of course, in reality, the average person can't throw a small child as fast as they can throw a bouncy ball.[citation needed] Furthermore, they won't all fall in one clump. If you poured the balls from a container, they would bounce around and spread out as they fell, and most of them would probably miss the target.

This effect was demonstrated in an experiment by Utah State University students, who poured 20,000 bouncy balls from a helicopter as part of their Geek Week. The balls fell as a cloud, rather than a single mass.

If you wanted to be sure of killing someone, you'd need a lot more balls. 3,000,000 of them—enough to fill a large room—would be be enough to guarantee that the target would either be crushed to death by the impact or buried too deep to dig themselves out.

To your last question, if someone just happened to walk underneath when you dropped the bouncy balls, and they were killed by the impact, you'd most likely be guilty of some form of manslaughter.

However, by asking this question, you've shown your intent to cause harm to the victim, demonstrating clear malice aforethought. By writing in to this blog, you've probably upgraded your charge to murder.

All in all, you should probably stick to gedankenexperiments.

XKCD QA (What If?): Drain the Oceans

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Drain the Oceans

How quickly would the ocean's drain if a circular portal 10 meters in radius leading into space was created at the bottom of Challenger Deep, the deepest spot in the ocean? How would the Earth change as the water is being drained?

–Ted M.

I want to get one thing out of the way first:

According to my rough calculations, if an aircraft carrier sank and got stuck against the drain, the pressure would easily be enough to fold it up[1] and suck it through. Cooool.

Just how far away is this portal? If we put it near the Earth, the ocean would just fall back down into the atmosphere. As it fell, it would heat up and turn to steam, which would condense and fall right back into the ocean as rain. The energy input into the atmosphere alone would also wreak all kinds of havoc with our climate, to say nothing of the huge clouds of high-altitude steam.

So let's put the ocean-dumping portal far away—say, on Mars. (In fact, I vote we put it directly above the Curiosity rover; that way, it will finally have incontrovertible evidence of liquid water on Mars's surface.)

What happens to the Earth?

Not much. It would actually take hundreds of thousands of years for the ocean to drain.

Even though the opening is wider than a basketball court, and the water is forced through at incredible speeds,[2] the oceans are huge. When you started, the water level would drop by less than a centimeter per day.

There wouldn't even be a cool whirlpool at the surface—the opening is too small and the ocean is too deep.[3] (It's the same reason you don't get a whirlpool in the bathtub until the water is more than halfway drained.)

But let's suppose we speed up the draining by opening more drains. (Remember to clean the whale filter every few days), so the water level starts to drop more quickly.

Let's take a look at how the map would change.

Here's how it looks at the start:

And here's the map after the oceans drop 50 meters:

It's pretty similar, but there are a few small changes. Sri Lanka, New Guinea, Great Britain, Java, and Borneo are now connected to their neighbors.

And after 2000 years of trying to hold back the sea, the Netherlands are finally high and dry. No longer living with the constant threat of a cataclysmic flood, they're free to turn their energies toward outward expansion. They immediately spread out and claim the newly-exposed land.

When the sea level reaches (minus) 100 meters, a huge new island off the coast of Nova Scotia is exposed—the former site of the Grand Banks.

You may start to notice something odd: Not all the seas are shrinking. The Black Sea, for example, shrinks only a little, then stops.

This is because these bodies are no longer connected to the ocean. As the water level falls, some basins cut off from the drain in the Pacific. Depending on the details of the sea floor, the flow of water out of the basin might carve a deeper channel, allowing it to continue to flow out. But most of them will eventually become landlocked and stop draining.

At 200 meters, the map is starting to look weird. New islands are appearing. Indonesia is a big blob. The Netherlands now control much of Europe.

Japan is now an isthmus connecting the Korean peninsula with Russia. New Zealand gains new islands. The Netherlands expand north.

New Zealand grows dramatically. The Arctic Ocean is cut off and its the water level stops falling. The Netherlands cross the new land bridge into North America.

The sea has dropped by two kilometers. New islands are popping up left and right. The Caribbean Sea and the Gulf of Mexico are losing their connections with the Atlantic. I don't even know what New Zealand is doing.

At three kilometers, many of the peaks of the mid-ocean ridge—the world's longest mountain range—break the surface. Vast swaths of rugged new land emerge.

By this point, most of the major oceans have become disconnected and stopped draining. The exact locations and sizes of the various inland seas are hard to predict; this is only a rough estimate.

This is what the map looks like when the drain finally empties. There's a surprising amount of water left, although much of it consists of very shallow seas, with a few trenches where the water is as deep as four or five kilometers.

Vacuuming up half the oceans would massively alter the climate and ecosystems in ways that are hard to predict. At the very least, it would almost certainly involve a collapse of the biosphere and mass extinctions at every level.

But it's possible—if unlikely—that humans could manage to survive. If we did, we'd have this to look forward to:

XKCD QA (What If?): Bouncy Balls

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Bouncy Balls

What if one were to drop 3,000 bouncy balls from a seven story parking structure onto a person walking on the sidewalk below? Should the person survive, what would be the number of bouncy balls needed to kill them? What injuries would occur and what would the associated crimes be?

—Ginger Bread

After falling from seven stories, the mass of bouncy balls would be moving at about 20 meters per second.

20 meters per second is about how fast an average person with a good arm could throw a bouncy ball. Therefore, to determine the result of an impact, we can make use of what Einstein called a gedankenexperiment, or "thought experiment":

In science, it's important that results be repeatable, so let's try that again:

The tricky thing about this scenario is that 3,000 one-inch bouncy balls is not as many as you probably think—it'd be enough to fill a large bucket.

This bucket would weigh about as much as a small child, which leads us to another gedankenexperiment:

Of course, in reality, the average person can't throw a small child as fast as they can throw a bouncy ball.[citation needed] Furthermore, they won't all fall in one clump. If you poured the balls from a container, they would bounce around and spread out as they fell, and most of them would probably miss the target.

This effect was demonstrated in an experiment by Utah State University students, who poured 20,000 bouncy balls from a helicopter as part of their Geek Week. The balls fell as a cloud, rather than a single mass.

If you wanted to be sure of killing someone, you'd need a lot more balls. 3,000,000 of them—enough to fill a large room—would be be enough to guarantee that the target would either be crushed to death by the impact or buried too deep to dig themselves out.

To your last question, if someone just happened to walk underneath when you dropped the bouncy balls, and they were killed by the impact, you'd most likely be guilty of some form of manslaughter.

However, by asking this question, you've shown your intent to cause harm to the victim, demonstrating clear malice aforethought. By writing in to this blog, you've probably upgraded your charge to murder.

All in all, you should probably stick to gedankenexperiments.

XKCD QA (What If?): Random Sneeze Call

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Random Sneeze Call

If you call a random phone number and say “God bless you”, what are the chances that the person who answers just sneezed? On average, not just in spring or fall.

–Mimi

It's hard to find good figures, but it's probably about 1 in 40,000.

Before you pick up the phone, you should also keep in mind that there's roughly a 1 in 1,000,000,000 chance that the person you're calling just murdered someone.[1]Based on a murder rate of 4 per 100,000, the average in the US but on the high end for industrialized countries. You may want to be careful when you hand out blessings.

However, given that sneezes are far more common than murders,[2]Citation: You are alive. you're still much more likely to get someone who sneezed than to catch a killer, so this strategy is not recommended:

(Mental note: I'm going to start saying that when people sneeze.)

Compared with the murder rate, the sneezing rate doesn't get much scholarly research. The most widely-cited figure for average sneeze frequency comes from a doctor interviewed by ABC News, who pegged it at 200 sneezes per person per year.[3]Cari Nierenberg, The Perils of Sneezing, ABC News, Dec. 22, 2008

One of the few scholarly sources of data is a study which monitored the sneezing of people undergoing an induced allergic reaction.[4]Werner E. Bischoff, Michelle L. Wallis, Brian K. Tucker, Beth A. Reboussin, Michael A. Pfaller, Frederick G. Hayden, and Robert J. Sherertz, “Gesundheit!” Sneezing, Common Colds, Allergies, and Staphylococcus aureus Dispersion, J Infect Dis. (2006) 194 (8): 1119-1126 doi:10.1086/507908 To estimate the average sneezing rate, we can ignore all the real medical data they were trying to gather and just look at their control group. This group was given no allergens at all; they just sat alone in a room for a total of 176 20-minute sessions.[5]For context, that's 490 repititions of the song Hey Jude.

The subjects in the control group sneezed four times during those 58 or so hours,[6]Over 58 hours of research, four sneezes were the most interesting data points. I might've taken the 490 Hey Judes. which—assuming they only sneeze while awake—translates to about 400 sneezes per person per year.

Google Scholar turns up 5,980 articles from 2012 that mention "sneezing".[7]Google Scholar search for "sneezing" If half of these articles are from the US, and each one has an average of four authors, then if you dial the number, there's about a 1 in 10,000,000 chance that you'll get someone who just that day published an article on sneezing.

On the other hand, about 60 people are killed by lightning in the US every year.[8]Lightning fatalities by country That means there's only a 1 in 10,000,000,000,000 chance that you'll call someone in the 30 seconds after they've been struck and killed.

Lastly, let's suppose that, on the day this article was published, five people who read it decide to actually try this experiment. If they call numbers all day, there's about a 1 in 30,000 chance that at some point during the day, one of them will get a busy signal because the person they've called is, themselves, calling a random stranger to say "God bless you."

And there's about a 1 in 10,000,000,000,000 chance that two of them will simultaneously call each other.

At this point, probability will give up, and they'll both be struck by lightning.

XKCD QA (What If?): Restraining an Airplane

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Restraining an Airplane

If you wanted to anchor an airplane into the ground so it wouldn't be able to take off, what would the rope have to be made out of?

—Connor Childerhose

Ah, the Just Cause 2 scenario.

At takeoff, a 747's four engines can each generate 281.57 kN of thrust. I have no real sense for what that number means, so let's put it in different terms:

A 747 with all engines at full could roughly balance the weight of a dangling blue whale.

With all that weight, how thick would the cable need to be?

Surprisingly, not all that thick! A cable a little over an inch in diameter would do it.[1]Bethlehem Wire Rope General Purpose Catalog

Let's suppose you don't have a cable lying around. What else could you use?

If you're into fishing, you might have some fishing line. A typical line for saltwater fishing might have a 50-100 lb strength,[2]West Marine: Selecting Fishing Line so it would take a brigade of several thousand people armed with fishing rods to restrain the plane.

If you don't have fishing line, there's one thing you probably do have: Hair.

While hair isn't as strong as steel, it's just about the strongest material in your body,[3]Examples of the Tensile Strength of Materials with a tensile strength rivaling or exceeding that of bone.[4]Properties of Textile Fibers

This tensile strength is why performers are able to hang by their hair at the circus. In fact, from a materials standpoint, it's actually more impressive that performers are able to hang by their arms.

Based on these hair strength figures, a piece of hair three inches in diameter would be strong enough to restrain a 747.[5]If you wanted to measure the strength of a strand of hair, you could use the device described by US Patent #4628742A, "Tensile strength tester for hair"

Hairs that big around are hard to come by.[6]... I hope. Since most of us have many small hairs, instead of one big hair ...

... we'd need to get a lot of hairs and bundle them together. Given that individual hairs can support about 50 grams of weight, we'd need roughly 20 heads of hair to restrain the aircraft.

Conclusion: Restraining a plane with a cable would be pretty easy.

Further conclusion: Blue whales are not typically covered in hair,[8]Although they are mammals, most whales do not have coats of hair like land mammals typically do but if we transplanted the hair from at least 20 human heads onto a blue whale ...

... it would have enough hair to perform acrobatics at a circus.


XKCD QA (What If?): Dropping a Mountain

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Dropping a Mountain

What if a huge mountain—Denali, say—had the bottom inch of its base disappear? What would happen from the impact of the mountain falling 1 inch? What about 1 foot? What if the mountain's base were raised to the present height of the summit, and then the whole thing were allowed to drop to the earth?

John-Clark Levin

The one-inch gap would take about 70 milliseconds to close. Don't stick your hand in.

The impact could trigger an earthquake. Denali (also known as Mount McKinley) is a mountain in Alaska that sits just to the south of a major fault line.[1]Roger A. Hansen, Earthquake and Seismic Monitoring in Denali National Park, National Park Service This fault is active,[2]Alaska Earthquake Information Center, M 7.9 Denali Fault earthquake of November 3, 2002 and we know that drilling can trigger earthquakes.[3]Van der elst NJ, Savage HM, Keranen KM, Abers GA. Enhanced remote earthquake triggering at fluid-injection sites in the midwestern United States. Science. 2013;341(6142):164-7. Earthquakes can happen at any time, so there's always a chance that dropping a mountain any distance could trigger one. So could kicking a tree. The only way to find out for sure would be to try it.[4]This article has an awful lot of citations.

Assuming it didn't trigger an earthquake, the impact wouldn't be all that dramatic. If you were standing on the mountain when it happened, you'd definitely feel a jolt, but it probably wouldn't even be enough to knock you down.

When the mountain hit the ground, the rock under it would be damaged, but only a little. The granite base is strong enough to hold up under the tremendous resting weight of a mountain;[5]Citation: The rock was holding up a mountain when you got there. the shockwave from dropping it an inch doesn't add too much pressure on top of that, and the rock would survive with a little minor cracking.

People nearby would definitely feel the impact, and probably hear it; the sound would likely resemble the crack of a lightning strike (if you were standing near the mountain) fading into a long, deep rumble.[6]Citation: A dream I had once. The vibration would be equivalent to that of a 3.5-magnitude earthquake[7]For more on the specific seismic details, see Stein, Seth, and Michael Wysession. "Earthquakes." An Introduction to Seismology, Earthquakes, and Earth Structure. Malden, MA: Blackwell Pub., 2003. 241. Print.; at worst, it would knock a few pictures off the wall if you happened to be living next to the mountain. Frankly, I'd be more worried about debris flying out of the gap.[8]If your magical mountain-cutter put air in the space where the rock used to be, you should avoid standing near the crack when it falls. The air will come jetting out from the closing crack, spraying rocks and dust at speeds approaching, or even—thanks to some fun heat-related effects—exceeding, Mach 1.

Oh. You again.

Ok.

Dropping from a height of one foot wouldn't be all that different.

The mountain would hit the ground at 2.5 m/s, or roughly walking speed. The shockwave from that impact would be in the range of 50 megapascals of pressure,[9]You can calculate the peak pressure of the compressive strain wave in the rock using the Joukowsky equation, which says that the peak pressure of the compressive wave in a material is (material's density)x(speed at impact)x(the speed of sound in the material). This equation is is normally used in fluid mechanics, but it works fine here, too! which granite can handle without too much trouble.[10]Bhat HS, Sammis CG, Rosakis AJ. The Micromechanics of Westerley Granite at Large Compressive Loads. Pure Appl. Geophys. 2011;168(12):2181-2198. [11]"... for a plane shock wave ... granite will stand a compressive stress of 3000-4000 MPa elastically before failing." Persson, Per-Anders, Roger Holmberg, and Jaimin Lee. Rock Blasting and Explosives Engineering. Boca Raton, FL: CRC, 1994. 5-6. Print.

Ok. Let's jump straight to the end of John-Clark's question:

After falling from summit height to base height—about 5 kilometers—the mountain would be moving at roughly the speed of sound.

The last two impacts were pretty minor. This one wouldn't be. The jolt to the ground would be as violent as in a magnitude 7 earthquake.[12]In addition, there's a good chance that a shock this large will release some existing seismic energy; see: U.S. Congress, Office of Technology Assessment, Seismic Verification of Nuclear Testing Treaties, P. 715, OTA-ISC-361 (Washington, DC: U.S. Government Printing Office, May 1988). There wouldn't exactly be a crater, but the mountain would definitely not be shaped like it used to be. The pressure from the impact would be high enough to produce some unusual geologic strutures. If you put a lump of coal under the meteor, the impact would be enough to convert it to diamond (and, unfortunately, smash it to bits).[13]French B. M. (1998) Traces of Catastrophe: A Handbook of Shock-Metamorphic Effects in Terrestrial Meteorite Impact Structures., Chapter 4, LPI Contribution No. 954,Lunar and Planetary Institute, Houston. 120 pp

The good news is that, the last time a magnitude 7+ earthquake hit Denali, no one was killed.[2]Alaska Earthquake Information Center, M 7.9 Denali Fault earthquake of November 3, 2002 Let's just hope nobody is on the mountain itself when we do this.

Ok. Last one.

We'd need to lift the mountain out of the atmosphere, out past the orbit of the GPS satellites, to the very outer limits of the Earth's gravity well. Then we let go.

It would hit Alaska at 10 kilometers per second.

The Last Frontier would not fare well. A 50-mile-wide crater would have obliterated Denali National Park. Anchorage would be buried under three meters of gravel.[14]Purdue University ImpactEarth asteroid impact simulator The shaking, combined with the debris falling into the ocean, would cause tsunamis across the Pacific. Across North America, the ground would tremble. A wind would sweep in from the northwest. The sky would darken.

In 1815, Mount Tambora erupted in the largest volcanic event in recorded history. The resulting global veil of aerosols made 1816 the "year without a summer". Snow fell in Massachusetts in June, ice formed on rivers in Pennsylvania in August, and frost killed most of the spring crops. The cooling effects lingered for several years.

The Alaska impact would be far worse. Over the next few months, the skies around the globe fill with dust. Summer is canceled and winter arrives. Global temperatures would drop by 5 to 20 degrees Celsius and stay that way for a year or more.[15]Covey, C, S Thompson, P Weissman, and M Maccracken. "Global Climatic Effects Of Atmospheric Dust From An Asteroid Or Comet Impact On Earth." Global and Planetary Change 9, no. 3-4 (1994): 263-273.

On the plus side, we would not be engulfed in a global firestorm. When the Chicxulub comet hit the Yucatan peninsula 65 million years ago, it blasted molten debris into space. This debris fell back to Earth around the world, heating the atmosphere and igniting global firestorms. These may have played a role in the mass extinctions.[16]I don't have a citation for this. But, c'mon, it's a 'global firestorm'. Can you really imagine that every species made it through unscathed?

However, our mountain would carry only about 10% of the energy of the Chicxulub impactor, which means that it wouldn't be capable of igniting global firestorms.[17]Osinski, G. R., and E. Pierazzo. "Environmental Effects of Impact Events." In Impact Cratering Processes and Products.. Chicester: Wiley, 2012. 151. The firestorms would, in fact, only cover some of North America. So that's a relief.

The northern hemisphere would be covered in ice, but our species would probably manage to limp through. Civilization, on the other hand, might well collapse. A total collapse of modern civilization would be a serious blow to the already sluggish economy, and the economic damage could amount to $80 trillion per year (the total value of all human goods and services). All in all, it would have serious implications for the upcoming elections.

And that's that. We've dropped the mountain from as high as it can be dropped, and I hope John-Clark is proud of the resulting devastation. Thanks for reading, and—

No, that doesn't actually make sense. The Earth's gravitational pull doesn't—

Dropping it from higher up won't do anything; there won't be enough force pulling it toward the—

Ok. Fine. You win. We'll try it.

Oops.

XKCD QA (What If?): Orbital Speed

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Orbital Speed

What if a spacecraft slowed down on re-entry to just a few miles per hour using rocket boosters like the Mars-sky-crane? Would it negate the need for a heat shield?

—Brian

Is it possible for a spacecraft to control its reentry in such a way that it avoids the atmospheric compression and thus would not require the expensive (and relatively fragile) heat shield on the outside?

—Christopher Mallow

Could a (small) rocket (with payload) be lifted to a high point in the atmosphere where it would only need a small rocket to get to escape velocity?

—Kenny Van de Maele

The answers to these questions all hinge on the same idea. It's an idea I've touched on in other articles, but today I want to focus on it specifically:

The reason it's hard to get to orbit isn't that space is high up.

It's hard to get to orbit because you have to go so fast.

Space isn't like this:

Space is like this:

Space is about 100 kilometers away. That's far away—I wouldn't want to climb a ladder to get there—but it isn't that far away. If you're in Sacramento, Seattle, Canberra, Kolkata, Hyderabad, Phnom Penh, Cairo, Beijing, central Japan, central Sri Lanka, or Portland, space is closer than the sea.

Getting to space[1]Specifically, low Earth orbit, which is where the International Space Station is and where the shuttles could go. is easy. It's not, like, something you could do in your car, but it's not a huge challenge. You could get a person to space with a small sounding rocket the size of a telephone pole. The X-15 aircraft reached space[2]The X-15 reached 100 km on two occasions, both when flown by Joe Walker. just by going fast and then steering up.[3]Make sure to remember to steer up and not down, or you will have a bad time.

But getting to space is easy. The problem is staying there.

Gravity in low Earth orbit is almost as strong as gravity on the surface. The Space Station hasn't escaped Earth's gravity at all; it's experiencing about 90% the pull that we feel on the surface.

To avoid falling back into the atmosphere, you have to go sideways really, really fast.

The speed you need to stay in orbit is about 8 kilometers per second.[4]It's a little less if you're in the higher region of low Earth orbit. Only a fraction of a rocket's energy is used to lift up out of the atmosphere; the vast majority of it is used to gain orbital (sideways) speed.

This leads us to the central problem of getting into orbit: Reaching orbital speed takes much more fuel than reaching orbital height. Getting a ship up to 8 km/s takes a lot of booster rockets. Reaching orbital speed is hard enough; reaching to orbital speed while carrying enough fuel to slow back down would be completely impractical.[5]This exponential increase is the central problem of rocketry: The fuel required to increase your speed by one km/s multiplies your weight by about 1.4. To get into orbit, you need to increase your speed to 8 km/s, which means you'll need a lot of fuel: $ 1.4\times1.4\times1.4\times1.4\times1.4\times1.4\times1.4\times1.4\approx 15$ times the original weight of your ship.

Using a rocket to slow down carries the same problem: Every 1 km/s decrease in speed multiplies your starting mass by that same factor of 1.4. If you want to slow all the way down to zero—and drop gently into the atmosphere—the fuel requirements multiply your weight by 15 again.

These outrageous fuel requirements are why every spacecraft entering an atmosphere has braked using a heat shield instead of rockets—slamming into the air is the most practical way to slow down. (And to answer Brian's question, the Curiosity rover was no exception to this; although it used small rockets to hover when it was near the surface, it first used air-braking to shed the majority of its speed.)

How fast is 8 km/s, anyway?

I think the reason for a lot of confusion about these issues is that when astronauts are in orbit, it doesn't seem like they're moving that fast; they look like they're drifting slowly over a blue marble.

But 8 km/s is blisteringly fast. When you look at the sky near sunset, you can sometimes see the ISS go past ... and then, 90 minutes later, see it go past again.[6]There are some good apps and online tools to help you spot the station, along with other neat satellites. My favorite is ISS Detector, but if you Google you can find lots of others. In those 90 minutes, it's circled the entire world.

The ISS moves so quickly that if you fired a rifle bullet from one end of a football field,[7]Either kind. the International Space Station could cross the length of the field before the bullet traveled 10 yards.[8]This type of play is legal in Australian rules football.

Let's imagine what it would look like if you were speed-walking across the Earth's surface at 8 km/s.

To get a better sense of the pace at which you're traveling, let's use the beat of a song to mark the passage of time.[9]Using song beats to help measure the passage of time is a technique also used in CPR training, where the song "Stayin' Alive" is used to . suppose you started playing the 1988 song by The Proclaimers, I'm Gonna Be (500 Miles). That song is about 131.9 beats per minute, so imagine that with every beat of the song, you move forward more than two miles.

In the time it took to sing the first line of the chorus, you could walk from the Statue of Liberty all the way to the Bronx:

It would take you about two lines of the chorus (16 beats of the song) to cross the English Channel between London and France.

The song's length leads to an odd coincidence. The interval between the start and the end of I'm Gonna Be is 3 minutes and 30 seconds,[10]Based on timing from the official Youtube video and the ISS is moving is 7.66 km/s.

This means that if an astronaut on the ISS listens to I'm Gonna Be, in the time between the first beat of the song and the final lines ...

... they will have traveled just about exactly 1,000 miles.

XKCD QA (What If?): Updating a Printed Wikipedia

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Updating a Printed Wikipedia

If you had a printed version of the whole of (say, the English) Wikipedia, how many printers would you need in order to keep up with the changes made to the live version?

Marein Könings

This many:

That's surprisingly few printers! But before you try to create a live-updating paper Wikipedia, let's look at what those printers would be doing ... and how much they'd cost.

Printing Wikipedia

People have considered printing out Wikipedia before. A few years ago, student Rob Matthews printed every Wikipedia featured article, creating a book several feet thick.

Of course, that's just a small slice of the best of Wikipedia; the entire encyclopedia would be a lot bigger. Wikipedia user Tompw has set up a page for calculating the size of the whole English Wikipedia in printed volumes. It would currently fill a lot of bookshelves.

Keeping up with the edits would be harder.

Keeping up

The English Wikipedia currently receives about 125,000 to 150,000 edits each day, or 90-100 per minute.[1]ToolServer: Edit rate

We could try to define a way to measure the "word count" of the average edit, but that's hard bordering on impossible. Fortunately, we don't need to—we can just estimate that each change is going to require us to reprint a page somewhere. Many edits will actually change multiple pages—but many other edits are reverts, which would let us put back pages we've already printed.[2]The filing system for this would be staggering. One page per edit seems like a reasonable middle ground.

For a mix of photos, tables, and text typical of Wikipedia, a good inkjet printer might put out 15 pages per minute. That means you'd only need about six printers running at any given time to keep pace with the edits.

The paper would stack up quickly. Using Rob Matthews' book as a starting point, I did my own back-of-the-envelope estimate for the size of the current English Wikipedia. Based on the average length of featured articles vs. all articles, I came up with an estimate of 300 cubic meters for a printout of the whole thing.[3]That's a little larger than Tompw's estimate, but I'm assuming they're printed straight from the browser, which is less compact and includes images.

By comparison, if you were trying to keep up with the edits, you'd print out 300 cubic meters every month.

$500,000 per month

Six printers isn't that many, but they'd be running all the time. And that gets expensive.

The electricity to run them would be cheap—a few dollars a day.

The paper would be about one cent per sheet, which means you'll be spending about a thousand dollars a day.

You'd want to hire people to manage the printers 24/7, but that would actually cost less than the paper.

Even the printers themselves wouldn't be too expensive, despite the terrifying replacement cycle.

But the ink cartridges would be a nightmare.

Ink

A study by QualityLogic[4]QualityLogic: Cost of Ink Per Page Analysis, June 2012 found that for a typical inkjet printer, the real-life cost of ink ran from 5 cents per page for black-and-white to around 30 cents per page for photos. That means you'd be spending four to five figures per day on ink cartridges.

You definitely want to invest in a laser printer. Otherwise, in just a month or two, this project could end up costing you half a million dollars:

But that's not even the worst part.

If, someday, Wikipedia decides to go dark again, and you want to join the protest ...

You'll have to get a crate of markers and color every page solid black yourself.

I would definitely stick to digital.

XKCD QA (What If?): Signs of Life

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Signs of Life

If you could teleport to a random place of the surface of the Earth, what are the odds that you'll see signs of intelligent life?

Borislav Stanimirov

The surface of the Earth is about 70% water, so you'll usually plop down into the ocean.

But even there, you could find signs of human habitation.

But first, we'll start with ...

The big stuff

In one way or another, humans have altered every square meter of this planet. But we'll start with the obvious: Roads, houses, and fields.

To get an idea of how often Borislav would stumble across such obvious structures, I loaded up a sample of random geographic coordinates[1]Generating uniform points on a sphere is tricky—you can't just pick a random latitude and a random longitude. The solution is to either do a bunch of math or use something like GeoMidpoint's Random Point Generator. in Google Earth.

Most of the points were over open ocean, out of sight of any land. Once you get away from the major ports, the odds of having a ship in view are not that good, so I continued sampling until I had 50 land coordinates.

Based on Google Earth imagery, Borislav would definitely see clear signs of human activity in about 10 of those 50 points. Six of them were actually in cultivated fields (in Poland, Argentina, Brazil, Pakistan, and Kazakhstan). Another point was in a highway cut along the coast of French Guiana. One was in a small town deep in the Amazon, and another on a road in the Australian outback.

In another five or ten cases, Borislav might be able to see something if you looked carefully or walked a short distance; it's hard to be sure without actually visiting the points to find out what you can see. Included in this list of marginal points was the only US location on the list, a spot in the woods outside in Keachi, Louisiana—a town which, during the American Civil War, saw the creation of a contingent of 'Highlanders' complete with government-issued kilts and plaids.

Most of the points were in the middle of deserts, barren mountains, tropical jungles. or—in one case—central Antarctica. All in all, it seems like the odds of landing somewhere with human artifacts in view are about one in four to one in three—and that artifact will usually be either a field of crops or a dirt road.

Look down

If you find yourself on a beach, check the sand. Sand all over the world contains tiny grains of plastic, mostly from industrial spillage into the oceans.[2]Patricia L. Corcorana, Mark C. Biesinger, Meriem Grifi, Plastics and beaches: A degrading relationship. Even if you land in the water, you might still be able to spot bits of plastic debris; the ocean is covered with them, which leads to heartbreaking consequences.

Sample the air

If you have a CO2 meter—and you know Earth's atmospheric history—you can also detect the changes we've made to the air around you. Over the past hundred years, we've rapidly increased CO2 concentrations from less than 300 parts per million to over 400—higher than they've been in millions of years. It's not proof of technological activity, but it's a pretty good tip-off that something weird is going on.

More sensitive testing could detect human-generated aerosols, or—by testing the soils—detect the alterations we've made to the global nitrogen cycle.[3]'Although carbon dioxide may get more press, “the nitrogen cycle has been altered more than any other basic element cycle,” says John Aber, vice president for research and public service at the University of New Hampshire.' Scott Fields, Global Nitrogen: Cycling out of Control

Look up

Depending on the humidity, you may have a good chance of seeing jet contrails. Under the right conditions, these water vapor trails from planes can linger for hours. In many parts of the world, they're a common sight. However, in areas with fewer flight paths—central Africa, South America, and Australia, in particular—they might be less easy to spot.

But even if you find yourself in the middle of the Algerian desert, the Peruvian Amazon, or the Arctic cliffs of Transfiguration Island, there's an easy way to see evidence of intelligent life:

Wait for nightfall.[4]And then go crazy and burn down your civilization when you see the stars for the first time.

At any given time, there are hundreds of satellites in the sky. Most of them are too faint to see, but if you're in an area without much light pollution, and you look carefully enough, there's virtually always a satellite visible. Their rapid motion across the sky and various highly inclined orbits make them unlikely to be anything but artificial.

It's often said that the Great Wall of China is the only human artifact that can be seen from space. This is wrong.

But in my opinion, the real problem with this factoid isn't that it's wrong—it's that it overlooks a much cooler point. The Great Wall of China may not be the only artifact on Earth that you can see from a satellite ... but our satellites are the only human artifacts that you can see from everywhere on Earth.

Want to see signs of intelligent life? Just look up.

XKCD QA (What If?): Speed Bump

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Speed Bump

How fast can you hit a speed bump while driving and live?

Myrlin Barber

Surprisingly fast.

First, a disclaimer: After reading this article, don't try to drive over speed bumps at high speeds. Here are some reasons:

• You could hit and kill someone.
• It can damage or destroy your tires, suspension, and potentially your entire car.
• Have you read any of the other articles on this blog?

If that's not enough, here are some quotes from medical journals on spinal injury from speed bumps:

Examination of the thoracolumbar X-ray and computed tomography displayed compression fractures in four patients ... Posterior instrumentation was applied ... All patients recovered well except for the one with cervical fracture.[1]Speed bump–induced spinal column injury

L1 was the most frequently fractured vertebra (23/52, 44.2%)[2]Speed hump spine fractures: injury mechanism and case series

Incorporation of the buttocks with realistic properties diminished the first vertical natural frequency from ~12 to 5.5 Hz, in agreement with the literature.[3]Source: The 2nd American Conference on Human Vibration.

(That last one isn't directly related to speed bump injuries, but I wanted to include it anyway.)

Regular little speed bumps probably won't kill you

Speed bumps are designed to make drivers to slow down. Going over a typical speed bump at 5 miles per hour[4]Like anyone with a physics background, I do all my calculations in SI units, but I've gotten too many US speeding tickets to write this article in anything but miles per hour; it's just been burned into my brain. Sorry! results in a gentle bounce, while hitting one at 20 delivers a sizable jolt. It's natural to assume that hitting a speed bump at 60 would deliver a proportionally larger jolt, but it probably wouldn't.

As those quotes attest, it's true that people are occasionally injured by speed bumps. However, nearly all of those injuries happen to a very specific category of people: Those sitting in hard seats in the backs of buses, riding on poorly-maintained roads.

When you're driving a car, the two main things protecting you from bumps in the road are the tires and the suspension. No matter how fast you hit a speed bump, unless the bump is particularly large, enough of the jolt will be absorbed by these two systems that you probably won't be hurt.

Absorbing the shock won't necessarily be good for those systems. In the case of the tires, they may absorb it by exploding.[5]Citation: Just Google "hit a curb at 60". If the bump is large enough, it may permanently damage a lot of important parts of the car.

The typical speed bump is between three and four inches tall. That's also about how thick an average tire's cushion is (the separation between the bottom of the rims and the ground).[6]Citation: There are cars everywhere. Go outside with a ruler and check. This means that if a car hits a small speed bump, the rim won't actually touch the bump; the tire will just be compressed.

The typical sedan has a top speed of around 120 miles per hour. Hitting a speed bump at that speed would, in one way or another, probably result in losing control of the car and crashing.[7]At high speeds, you can easily lose control even without hitting a bump. Joey Huneycutt's 220 mph crash left his Camaro a burned-out hulk. However, the jolt itself probably wouldn't be fatal.

If you hit a larger speed bump—like a speed hump or speed table—your car might not fare so well.[8]Youtube: Speed bump in Dubai + flying Gallardo

How fast would you have to go to definitely die?

Let's consider what would happen if a car went were going faster than its top speed.

The average modern car is limited to a top speed of around 120 mph, and the fastest can go about 200.[9]The Bentley Continental Flying Spur has a top speed of 199.64 miles per hour.

While most passenger cars have some kind of artificial speed limits imposed by the engine computer, the ultimate physical limit to a car's top speed comes from air resistance. This type of drag increases up with the square of speed; at some point, a car doesn't have enough engine power to push through the air any faster.

If you did force a sedan to go faster than its top speed—perhaps by re-using the magical accelerator from the relativistic baseball—the speed bump would be the least of your problems.

Cars generate lift. The air flowing around a car exerts all kinds of forces on it.

The lift forces are relatively minor at normal highway speeds, but at higher speeds they become substantial.

In a Formula One car equipped with airfoils, this force pushes downward, holding the car against the track. In a sedan, they lift it up.[10]Parker, Barry R.. "Aerodynamic Design." In The Isaac Newton school of driving: physics and your car. Baltimore, MD: Johns Hopkins University Press, 2003. 155.

Among NASCAR fans, there's frequently talk of a 200-mph "liftoff speed" if the car starts to spin.[11]The Myth of the 200-mph "Lift-Off Speed" Other branches of auto racing have seen spectacular[12]Youtube: Porsche 911 GT2 (or GT1) crash backflip crashes[13]Youtube: Mercedes CLR-GTR Le Mans Flip when the aerodynamics don't work out as planned.

The bottom line is that at somewhere in the range of 150-300 mph, a typical sedan will lift off the ground, tumble, and crash ... before you even hit the speed bump.

If you kept the car from taking off, the force of the wind at those speeds would strip away the the hood, side panels, and windows. At higher speeds, the car itself would be disassembled, or even burn up like a spacecraft reentering the atmosphere.

What's the ultimate limit?

In the state of Pennsylvania, drivers may have $2 added to their speeding ticket for every mile per hour by which they break the speed limit.[14]NHTSA, Summary of State Speed Laws, 2007

Therefore, if you drove a car over a Philadelphia speed bump at 90% of the speed of light, in addition to destroying the city ...

... you could expect a speeding ticket of $1.14 billion.

XKCD QA (What If?): Falling With Helium

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Falling With Helium

What if I jumped out of an airplane with a couple of tanks of helium and one huge, un-inflated balloon? Then, while falling, I release the helium and fill the balloon. How long of a fall would I need in order for the balloon to slow me enough that I could land safely?

Colin Rowe

As ridiculous as it sounds, this is—sort of—possible.

Falling from great heights is dangerous.[citation needed] A balloon could actually help save you, although a regular helium one from a party obviously won't do the trick.

If the balloon is large enough, you don't even need the helium. A balloon will act as a parachute, slowing your fall to non-fatal speeds.

Avoiding a high-speed landing is, unsurprisingly, the key to survival. As one medical paper[1]De Haven H. Mechanical analysis of survival in falls from heights of fifty to one hundred and fifty feet. Injury Prevention. 6(1):62-b-68. put it,

It is, of course, obvious that speed, or height of fall, is not in itself injurious ... but a high rate of change of velocity, such as occurs after a 10 story fall onto concrete, is another matter.

... which is just a wordy version of the old saying, "It's not the fall that kills you, it's the sudden stop at the end."

To act as a parachute, a balloon filled with air, rather than helium, would have to be 10 to 20 meters across—far too big to be inflated with portable tanks. A powerful fan could be used to fill it with ambient air, but at that point, you may as well just use a parachute.

Helium

The helium makes things easier.

It doesn't take too many helium balloons to lift a person. In 1982, Larry Walters flew across Los Angeles in a lawn chair lifted by weather balloons, eventually reaching several miles in altitude. After passing through LAX airspace, he descended by shooting some of the balloons with a pellet gun.

On landing, Walters was arrested, although the authorities had some trouble figuring out what to charge him with. At the time, an FAA safety inspector told the New York Times, "We know he broke some part of the Federal Aviation Act, and as soon as we decide which part it is, some type of charge will be filed."[2]ARMCHAIR AIRMAN SAYS FLIGHT FULFILLED HIS LIFELONG DREAM, New York Times, July 4, 1982

A relatively small helium balloon—certainly smaller than a parachute—will suffice slow your fall, but it still has to be huge by party balloon standards. The biggest consumer rental helium tanks are about 250 cubic feet, and you'd need to empty at least 10 of them to put enough air in the balloon to support your weight.

You'd have to do it quickly. The compressed helium cylinders are smooth and often quite heavy, which means they have a high terminal velocity. You'll only have a few minutes to use up all the cylinders. (As soon as you emptied one, you could drop it.)

You can't get around this problem by moving your starting point higher. Since the upper atmosphere is pretty thin, anything dropped from the stratosphere up will accelerate to very high speeds until it hits the lower atmosphere, then fall slowly the rest of the way. This is true of everything from small meteors[3]By the time meteors hit the Earth, they have slowed down to a few hundred miles per hour. to Felix Baumgartner.[4]Jason Martinez, Falling Faster than the Speed of Sound, Wolfram Blog, October 24, 2012

But if you inflated the balloons quickly, possibly by connecting many canisters to it at once, you'd be able to slow your fall. Just don't use too much helium, or you'll end up floating at 16,000 feet like Larry Walters.

While researching this article,[5]Additionally, while researching impact speeds for this article, I came across a discussion on the Straight Dope Message Boards about survivable fall heights. One poster compared a fall from height to being hit by a bus. Another user, a medical examiner, replied that this was a bad comparison:

"When hit by a car, the vast majority of people are not run over; they are run under. The lower legs break, sending them into the air. They usually strike the hood of the car, often with the back of the head impacting the windshield, "starring" the windshield, possibly leaving a few hairs in the glass. They then go over the top of the car. They are still alive, although with broken legs, and maybe with head pain from the nonfatal windshield impact. They die when they hit the ground. They die from head injury."

The lesson: Don't mess with medical examiners. They're apparently pretty hardcore.
I managed to lock up my copy of Mathematica several times on balloon-related differential equations, and subsequently got my IP address banned from Wolfram|Alpha for making too many requests. The ban-appeal form asked me to explain what task I was performing that necessitated so many queries, so this is what I put:

I hope they understand.

XKCD QA (What If?): Google's Datacenters on Punch Cards

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Google's Datacenters on Punch Cards

If all digital data were stored on punch cards, how big would Google's data warehouse be?

James Zetlen

Google almost certainly has more data storage capacity than any other organization on Earth.

Google is very secretive about its operations, so it's hard to say for sure. There are only a handful of organizations who might plausibly have more storage capacity or a larger server infrastructure. Here's my short list of the top contenders:

Honorable mentions:

  • Amazon (They're huge, but probably not as big as Google.)
  • Facebook (They're on the right scale and growing fast, but still playing catch-up.)
  • Microsoft (They have a million servers,[1]Data Center Knowledge: [Ballmer: Microsoft has 1 Million Servers although no one seems sure why.)

Let's take a closer look at Google's computing platform.

Follow the money

We'll start by following the money. Google's aggregate capital expenditures–spending on building stuff[2]I'm excluding the cost of an extremely expensive building they bought in New York.—adds up to somewhere over $12 billion dollars.[3]Data Center Knowledge: Google’s Data Center Building Boom Continues: $1.6 Billion Investment in 3 Months Their biggest data centers cost half a billion to a billion dollars, so they can't have more than 20 or so of those.

On their website,[4]Data center locations Google acknowledges that they have datacenters in the following locations:

  1. Berkeley County, South Carolina
  2. Council Bluffs, Iowa
  3. Atlanta, Georgia
  4. Mayes County, Oklahoma
  5. Lenoir, North Carolina
  6. The Dalles, Oregon
  7. Hong Kong
  8. Singapore
  9. Taiwan
  10. Hamina, Finland
  11. St Ghislain, Belgium
  12. Dublin, Ireland
  13. Quilicura, Chile

In addition, they appear to operate a number of other large datacenters (sometimes through subsidiary corporations), including:

  1. Eemshaven, Netherlands
  2. Groningen, Netherlands
  3. Budapest, Hungary
  4. Wrocław, Poland
  5. Reston, Virginia
  6. Additional sites near Atlanta, Georgia

They also operate equipment at dozens to hundreds of smaller locations around the world.

Follow the power

To figure out how many servers Google is running, we can look at their electricity consumption. Unfortunately, we can't just sneak up to a datacenter and read the meter.[5]Actually, wait, can we? Somebody should try that. Instead, we have to do some digging.

The company disclosed that in 2010 they consumed an average of 258 megawatts of power.[6]Google used 2,259,998 MWh of electricity in 2010, which translates to an average of 258 megawatts. How many computers can they run with that?

We know that their datacenters are quite efficient, only spending 10-20% of their power on cooling and other overhead.[7]Google: Efficiency: How we do it To get an idea of how much power each server uses, we can look at their "container data center" concept from 2005. It's not clear whether they actually use these containers in practice—it may just have been a now-outdated experiment—but it gives an idea of what they consider(ed) reasonable power consumption. The answer: 215 watts per server.

Judging from that number, in 2010, they were operating around a million servers.

They've grown a lot since then. By the end of 2013, the total amount of money they've pumped into their datacenters will be three or four times what it was as of 2010. They've contracted to buy over three hundred megawatts of power at just three sites,[8]Google: Purchasing clean energy which is more than they used for all their operations in 2010.

Based on datacenter power usage and spending estimates, my guess would be that Google is currently running—or will soon be running—between 1.8 and 2.4 million servers.

But what do these "servers" actually represent? Google could be experimenting in all kinds of wild ways, running boards with 100 cores or 100 attached disks. If we assume that each server has a couple[9]Anywhere from 2 to 5 of 2 TB disks attached, we come up with close to 10 exabytes[10]As a refresher, the order is: kilo, mega, giga, tera, peta, exa, zetta, yotta. An exabyte is a million terabytes. of active storage attached to running clusters.

10 Exabytes

The commercial hard disk industry ships about 8 exabytes worth of drives annually.[12]IDC: Worldwide External Disk Storage Systems Factory Revenue Declines for the Second Consecutive Quarter Those numbers don't necessarily include companies like Google, but in any case, it seems likely that Google is a large piece of the global hard drive market.

To make things worse, given the huge number of drives they manage, Google has a hard drive die every few minutes.[11]Eduardo Pinheiro, Wolf-Dietrich Weber and Luiz Andre Barroso, [Failure Trends in a Large Disk Drive Population This isn't actually all that expensive a problem, in the grand scheme of things—they just get good at replacing drives—but it's weird to think that when a Googler runs a piece of code, they know that by the time it finishes executing, one of the machines it was running on will probably have suffered a drive failure.

Google tape storage

Of course, that only covers storage attached to running servers. What about "cold" storage? Who knows how much data Google—or anyone else—has stored in basement archives?

In a 2011 phone interview with Paul Mah of SMB Tech, Simon Anderson of Tandberg Data let slip[13]SMB Tech: Is Tape Still Relevant for SMBs? that Google is the world's biggest single consumer of magnetic tape cartridges, purchasing 200,000 per year. Assuming they've stepped up their purchasing since then as they've expanded, this could add up to another few exabytes of tape archives.

Putting it all together

Let's assume Google has a storage capacity of 15 exabytes, or 15,000,000,000,000,000,000 bytes.

A punch card can hold about 80 characters, and a box of cards holds 2000 cards:

15 exabytes of punch cards would be enough to cover my home region, New England, to a depth of about 4.5 kilometers. That's three times deeper than the ice sheets that covered the region during the last advance of the glaciers:

That seems like a lot.

However, it's nothing compared to the ridiculous claims by some news reports about the NSA datacenter in Utah.

NSA datacenter

The NSA is building a datacenter in Utah. Media reports claimed that it could hold up to a yottabyte of data,[14]CNET: NSA to store yottabytes in Utah data centre which is patently absurd.

Later reports changed their minds, suggesting that the facility could only hold on the order of 3-12 exabytes.[15]Forbes: Blueprints Of NSA's Ridiculously Expensive Data Center In Utah Suggest It Holds Less Info Than Thought We also know the facility uses about 65 megawatts of power,[16]Salt-Lake City Tribune: NSA Bluffdale Center won’t gobble up Utah’s power supply which is about what a large Google datacenter consumes.

A few headlines, rather than going with one estimate or the other, announced that the facility could hold "between an exabyte and a yottabyte" of data[17]Dailykos: Utah Data Center stores data between 1 exabyte and 1 yottabyte ... which is a little like saying "eyewitnesses report that the snake was between 1 millimeter and 1 kilometer long."

Uncovering further Google secrets

There are a lot of tricks for digging up information about Google's operations. Ironically, many of them involve using Google itself—from Googling for job postings in strange cities to using image search to find leaked cell camera photos of datacenter visits.

However, the best trick for locating secret Google facilities might be the one revealed by ex-Googler talentlessclown on reddit:[18]reddit: Can r/Australia help find Google's Sydney data center? Seems like a bit of a mystery...

The easiest way to find manned Google data centres is to ask taxi drivers and pizza delivery people.

There's something pleasing about that. Google has created what might be the most sophisticated information-gathering apparatus in the history of the Earth ... and the only people with information about them are the pizza delivery drivers.

Who watches the watchers?

Apparently, Domino's.


XKCD QA (What If?): Rising Steadily

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Rising Steadily

If you suddenly began rising steadily at one foot per second, how exactly would you die? Would you freeze or suffocate first? Or something else?

Rebecca B.

Did you bring a coat?

A foot per second isn't that fast—it's substantially slower than a typical elevator.[1]Otis: About Elevators It would take you 5-7 seconds to rise out of arms' reach, depending how tall your friends are.

After 30 seconds, you'd be 30 feet—9 meters—off the ground. Judging from What-If #44, this is getting close to your last chance for a friend to throw you a sandwich or water bottle or something.[2]Not that it will help, ultimately.

After a minute or two you would be above the trees. You'd still be about as comfortable as you were on the ground. If it's a breezy day, it will probably get chillier thanks to the steadier wind above the treeline.[3]For this article, I'm going to assume a typical atmosphere temperature profile. It can, of course, vary quite a bit.

After 10 minutes you would be above all but the tallest skyscrapers, and after 25 minutes you'd pass the spire of the Empire State Building.

The air at these heights is about 3% thinner than it is at the surface. Fortunately, your body handles air pressure changes like that all the time. Your ears may pop, but you wouldn't really notice anything else.

Air pressure changes quickly with height. Surprisingly, when you're standing on the ground, air pressure is even measurably lower at your head than at your feet. If your phone has a barometer in it, as a lot of new Android phones do, you can download an app and actually see the pressure difference between your head and your feet.

A foot per second is pretty close to a kilometer per hour, so after an hour, you'll be about a kilometer off the ground. At this point, you definitely start to get chilly. If you have a coat, you'll still be ok, though you might also notice the wind picking up.

At about two hours and two kilometers, the temperature would drop below freezing. The wind would also, most likely, be picking up. If you have any exposed skin, this is where frostbite starts to become a concern.[4]National Weather Service: Wind Chill Temperature Index

Starting at this point, the air pressure would drop below what you'd experience in an airliner cabin,[5]... which are typically kept pressurized at about 70%-80% of sea level pressure, judging from the barometer in my phone. and the effects would start to become more significant, but unless you had a warm coat, the temperature would be a bigger problem.

Over the next two hours, the air would drop to below-zero[6]Either unit.[7]Not Kelvin, though. temperatures. Assuming for a moment that you survived the oxygen deprivation, at some point you'd freeze to death. But when?

The scholarly authorities on freezing to death seem to be, unsurprisingly, Canadians. The most widely-used model for human survival in cold air was developed by Peter Tikuisis and John Frim for the Defence and Civil Institute of Environmental Medicine in Ontario.[8]Prediction of Survival Time in Cold Air—see page 24 for the relevant tables.

According to their model, the main factor in the cause of death would be your clothes. If you were nude, you'd probably succumb to hypothermia somewhere around the five hour mark, before your oxygen ran out.[9]And frankly, this really raises more questions than it answers. If you were bundled up, you may be frostbitten, but you would probably survive ...

... long enough to reach the Death Zone.

Above 8,000 meters—above the tops of all but the highest mountains—the oxygen content in the air is too low to support human life. Near this zone, you would experience a range of symptoms, possibly including confusion, dizziness, clumsiness, impaired vision, and nausea.

As you approach the Death Zone, your blood oxygen content would plummet. Your veins are supposed to bring low-oxygen blood back to your lungs to be refilled with oxygen. But in the Death Zone, there's so little oxygen in the air that your veins lose oxygen to the air instead of gaining it.[10]Linda D. Pendleton, When Humans Fly High: What Pilots Should Know About High-Altitude Physiology, Hypoxia, and Rapid Decompression

The result would be a rapid loss of consciousness and death. This would happen around the seven hour mark; the chances are very slim that you would make it to eight.

And two million years later, your frozen body, still moving along steadily at a foot per second, would pass through the heliopause into interstellar space—the same boundary that Voyager just crossed.[11]Again.

Clyde Tombaugh, the astronomer who discovered Pluto, died in 1997. A portion of his remains were placed on New Horizons spacecraft, which will fly past Pluto and then continue out of the Solar System.

It's true that your hypothetical foot-per-second trip would be cold, unpleasant, and rapidly fatal. But when the Sun becomes a red giant in four billion years and consumes the Earth, you and Clyde would be the only ones to escape.

So there's that.

XKCD QA (What If?): Twitter Timeline Height

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Twitter Timeline Height

If our Twitter timelines (tweets by the people we follow) actually extended off the screen in both directions, how tall would they be?

Anonymous

This is a surprisingly tricky question. The answer involves German tanks, human extinction, and the most disputed statistics problem on the internet.

But first, Twitter.

Lots of tweets

The answer obviously depends who you follow. Some people tweet a lot more than others.

@JephJacques, the author of Questionable Content, tweets a lot. His contribution to your timeline will be 36,000 tweets and rising. On the other hand, if you follow people who don't tweet very much, it's possible your timeline to date could fit on a single screen.

According to an analysis by Diego Basch, as of last year the "average" Twitter account had tweeted 307 times and was following 51 people.[1]Diego Basch, Some Fresh Twitter Stats (as of July 2012, Dataset Included) (Dataset not included.) But averages can be deceptive;[2]If Larry Ellison, who made $96 million last year, moves into a typical town of 3,000 people, the average income in that town will double overnight. most Twitter accounts had never even tweeted at all, or have only one follower.

To get an idea of the typical timeline, I asked some friends to take a snapshot of their Twitter homepages and count the rate of tweets at that particular moment. The results covered a wide range—some were seeing 20 tweets per minute, some 20 tweets per month.

Correcting[3]Multiplying by a random number between 0.5 and 1 for the time of day and extrapolating[4]Filling a spreadsheet with numbers until I ran out of columns backward based on Twitter's growth rate, this suggested some timelines currently contain hundreds of tweets and some contain millions.

On my computer's monitor, the average tweet is about 2.4 centimeters high.[5]Citation: I just measured. You can measure, too, but you'll have to use your computer instead of mine. I'm using mine now to type this, so I need to be able to see the screen. This suggests that Jeph Jacques' tweet tower is 900 meters tall—taller than the tallest building—and still growing.

However, Jeph has nothing on @YOUGAKUDAN_00, who tweets many times per minute—usually binary, but sometimes actual words. @YOUGAKUDAN_00 has accumulated 37 million tweets, enough to reach into low Earth orbit.

Combining Diego's July 2012 estimate with the current rate of tweets per day suggests there have been a total of about 345 billion tweets as of October 2013. That means that if you followed every Twitter user, your timeline would be eight million kilometers high. For comparison, here's the Earth, with your Twitter timeline next to it:

Of course ... that's just the part of the timeline below the screen. What about the whole timeline?

Someday, the last person you follow will tweet for the last time. When will that be?

The future

Our timelines aren't really as tall as skyscrapers—even virtually–because Twitter limits the number of past tweets you can see by scrolling. But can we estimate how tall our timelines will eventually be?

Based on human lifespans, it seems likely that most of the accounts you follow will stop tweeting within a century. On the other hand, accounts like @big_ben_clock could keep going for millennia.

But will Twitter last that long?

It's obviously impossible to predict for sure, but there's a strange tool from statistics that might help.[6]Predict the end of Twitter with this 1 weird old tip!

Or might not. It depends who you talk to.

German tank problem

Suppose you're transported to an alternate universe. You open IMDb and load a random page, and the movie that comes up is The Land Before Time XXVII.[7]27

Based only on the title, how many Land Before Time movies do you think there are in this universe? Clearly there are at least 27, and probably more.

Allied troops faced a version of this problem in World War II.[8](A flood of Axis-produced Land Before Time sequels.) German tank parts had serial numbers, many of which were sequential (1, 2 ... N). Suppose they captured a random tank. If they determined it was Tank #27, then they can be sure that the Germans had made at least 27 tanks. It also told them there probably weren't millions of tanks; if there were, they would have been unlikely to get a two-digit serial number.

Of course, the enemy can foil this plan by giving their tanks random large serial numbers. The US actually did that in 1981—the Navy named its elite counterterrorism unit "Seal Team Six" to confuse Soviet spies into thinking there must be at least five other teams out there.[9]Pfarrer, Chuck. "Team Jedi." In SEAL target Geronimo: the inside story of the mission to kill Osama Bin Laden. New York: St. Martin's Press, 2011. Loc 594/3898.

Assuming the numbers are sequential, using clever Bayesian math, you can guess the actual number from a sample of tanks pretty reliably.[10]In addition to the Wikipedia article, there are good discussions of the solution on Statistics Blog and Event Horizon

If you have only a few samples, the math gets a little trickier.[11]The problem is that you're forced to select a "prior"—an initial hypothesis about how likely each number of tanks is. Usually, people just assume there's an equal chance of every number of tanks. But mathematically, this assumption plays fast and loose with the math. The idea of having "an equal chance of getting every number from 1 to infinity" doesn't work in probability; technically speaking, it violates Kolmogorov's Second Axiom. With one sample—as in our Land Before Time problem—the best strategy is probably to take the number you've seen and double it. This suggests that there are probably about 54 Land Before Time Movies.

The idea is that you're likely to be somewhere in the middle of the range—there's only a small chance that you're looking at one of the first or one of the last movies.

Things get weird

If we apply the German tank problem to humans, we can argue that our species will go extinct by the year 2807.

Here's the argument:

Humans will go extinct someday. Suppose that, after this happens, aliens somehow revive all humans who have ever lived. They line us up in order of birth and number us from 1 to N. Then they divide us divide them into three groups—the first 5%, the middle 90%, and the last 5%:

Now imagine the aliens ask each human (who doesn't know how many people lived after their time), "Which group do you think you're in?"

Most of them probably wouldn't speak English, and those who did would probably have an awful lot of questions of their own. But if for some reason every human answered "I'm in the middle group", 90% of them will (obviously) be right. This is true no matter how big N is.

Therefore, the argument goes, we should assume we're in the middle 90% of humans. Given that there have been a little over 100 billion humans so far, we should be able to assume with 95% probability that N is less than 2.2 trillion humans. If it's not, it means we're assuming we're in 5% of humans—and if all humans made that assumption, most of them would be wrong.

To put it more simply: Out of all people who will ever live, we should probably assume we're somewhere in the middle; after all, most people are.

If our population levels out around 9 billion, this suggests humans will probably go extinct in about 800 years, and not more than 16,000.

This is the Doomsday Argument.

Yeah, but that's stupid

Almost everyone who hears this argument immediately sees something wrong with it.

The problem is, everyone thinks it's wrong for a different reason. And the more they study it, the more they tend to change their minds about what that reason is.

Since it was proposed in 1983, it's been the subject of tons of papers refuting it, and tons of papers refuting those papers.[14]Nick Bostrom, A Primer on the Doomsday Argument There's no consensus about the answer; it's like the airplane on a treadmill problem, but worse.

What does this mean for Twitter?

Let's assume the Doomsday argument is valid and apply this reasoning to Twitter. Since there have been 345 billion tweets so far, then the best guess about Twitter's total lifetime is that there will be 690 billion tweets.

At the current rate of 400 million tweets per day, this argument says Twitter has about five years left. And it suggests that there's a 95% chance Twitter will disappear within 45 years.

This certainly sounds reasonable—given the rate of technological change, there's no reason to expect an internet service to stay popular for more than 10 or 20 years.

But ... is the Doomsday argument valid?

If we see Twitter activity winding down in 2018, then will that be evidence in favor of the Doomsday argument? And if so, does it suggest that humanity has only two centuries left?

Probably not. But it depends which statisticians you ask.

On the plus side, they seem to have stopped making The Land Before Time sequels in 2007, so at least we stand a good chance of avoiding that particular scenario.

XKCD QA (What If?): 500 MPH

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500 MPH

If winds reached 500 mph, would it pick up a human?

Grey Flynn, age 7, Stoneham, MA

Absolutely!

Some things don't work like they do in the movies. Getting shot doesn't really make someone fly backward. The vacuum of space doesn't make your skin explode.

But high wind can definitely pick up a person. In fact, if you were standing in the parking lot, the wind wouldn't just pick you up—it would also peel the pavement from the ground!

It wouldn't be strong enough to peel your skin off. Humans can survive blasts of 500 mph wind, which is important because pilots sometimes need to eject from airplanes at those speeds.

In the 1940s, the US government put pilots in wind tunnels to learn how they reacted to high winds. Have you ever been curious what happens to a person's face in 457 mph winds? Well, you can watch a video of one of those wind tunnel tests here. (That test was conducted at NASA Langley Research Center, where I worked before I started drawing internet comics for a living.)

It doesn't look very comfortable—I didn't know cheeks could flap like that—but the pilot appears to stay alive.

Luckily, he's strapped into that chair. He wouldn't be able to stand up in those winds! If he tried, he would go flying backward down the tunnel.

High wind is really powerful. In a paper in the journal Weather, J. F. R. McIlveen showed how to calculate the force of wind on the human body.[1]McIlveen, J. F. R.. "The Everyday Effects Of Wind Drag On People." Weather 57, no. 11 (2002): 410-413. The calculations on page 2 show how far you'd have to lean to stay upright in wind of various speeds.

When wind speed rises above about 120 mph, it's no longer possible to stay upright no matter how far you lean; you'll start to slide backward across the ground,[2]When Hurricane Isabel hit Virginia in 2003, I had the bright idea of standing on a skateboard with a poncho held up like a sail, so the wind would blow me down the street. But the moment I got the sail up, the wind fell quiet.

Later, I learned that people die from doing that. Oops.
then quickly go head over heels and start to tumble.

You wouldn't necessarily be thrown very high. If the wind were perfectly level, you'd tumble along the surface, bouncing against the ground. However, if there were any updrafts, you could easily be lifted up and carried away.

The good news is that 500 mph winds are rare. The strongest hurricanes have wind speeds around 200 mph with gusts up to 250.[3]Courtney, J.; Buchan, S.; Cerveny, R.S.; Bessemoulin, P.; Peterson, T.C.; Rubiera Torres, J.M.; Beven, J.; King, J.; Trerwin, B.; Rancourt, K.. 2012 "Documentation and verification of the world extreme wind gust record: 113.3 m s–1 on Barrow Island, Australia, during passage of tropical cyclone Olivia." Australian Meterological and Oceanographic Journal, 62 (1). 1-9. Tornadoes can reach 300 mph.[4]It's difficult to get accurate measurements of surface winds since those tornadoes destroy most measuring equipment! 300 is a far cry from 500; the force from a 500 mph wind is several times stronger than the force from a 300 mph wind.

There are a few ways you could experience wind speeds faster than 500 mph. One is to stand on top of a volcano when it erupts. When Mount St. Helens exploded in 1980, the column of ash was blasted outward at 700 mph, which is close to the speed of sound.[5]Kieffer, S. W., 1981, Fluid dynamics of the May 18 blast at Mount St. Helens, in Lipman, P.W., and Mullineux, D.R., eds., The 1980 Eruptions of Mount St. Helens, Washington: U.S. Geological Survey Professional Paper 1250, p. 379-400.

Another way to experience 500 mph winds is to trigger a hypercane.[6]Limits on Hurricane Intensity A hypercane is an exotic type of hurricane with 500 mph winds spinning in a very tight vortex just a few miles across.

Hypercanes can't exist on Earth right now. To form, they require ocean temperatures of about 50°C. No matter how much we warm the planet, we're not going to get the temperature that high any time soon.

However, there's one way these storms might happen.

When an asteroid or comet—coincidentally, one about the size of the recently-named 4942 Munroe—hit Mexico 65 million years ago, it punched a hole in the crust and left behind a sea of lava.[7]Christeson, Gail L., Gareth S. Collins, Joanna V. Morgan, Sean P.S. Gulick, Penny J. Barton, and Michael R. Warner. "Mantle Deformation Beneath The Chicxulub Impact Crater." Earth and Planetary Science Letters 284, no. 1-2 (2009): 249-257. When water flowed back in to fill the hole, it would have been heated by contact with the molten rock. This might have created the conditions for hypercanes to form, and one paper suggests that these storms could have lifted a large amount of dust and debris into the upper atmosphere—thus contributing to a global winter and extinction of the dinosaurs.[8]Emanuel, Kerry A., Kevin Speer, Richard Rotunno, Ramesh Srivastava, and Mario Molina. "Hypercanes: A Possible Link In Global Extinction Scenarios." Journal of Geophysical Research 100, no. D7 (1995): 13755-13765.

In short, the answer to Grey's question is yes—500 mph winds would send you flying through the air. But don't worry about that. Instead, worry about is the thing that created the 500 mph winds. Odds are, that's what's going to kill you.

XKCD QA (What If?): Expanding Earth

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Expanding Earth

How long would it take for people to notice their weight gain if the mean radius of the world expanded by 1cm every second? (Assuming the average composition of rock were maintained.)

Dennis O'Donnell

The Earth is not, currently, expanding.[1]Yes, I have a citation for this.

"In conclusion, no statistically significant present expansion rate is detected by our study within the current measurement uncertainty of 0.2 mm yr−1."

Wu, X., X. Collilieux, Z. Altamimi, B. L. A. Vermeersen, R. S. Gross, and I. Fukumori (2011), Accuracy of the International Terrestrial Reference Frame origin and Earth expansion, Geophys. Res. Lett., 38, L13304, doi:10.1029/2011GL047450.

People have long suggested that it might be. Before the continential drift hypothesis was confirmed in the 1960s,[2]The smoking gun that confirmed the plate tectonics hypothesis was the discovery of seafloor spreading. The way seafloor spreading and magnetic pole reversal neatly confirmed each other is one of my favorite examples of scientific discovery at work. people had noticed that the continents fit together. Various ideas were put forward to explain this, including the idea that the ocean basins were rifts that opened in the surface of a previously-smooth Earth as it expanded. This theory was never very widespread,[3]It turns out it's kind of dumb. although it still periodically makes the rounds on YouTube.

To avoid the problem of rifts in the ground, let's imagine all the matter in the Earth, from the crust to the core, starts expanding uniformly. To avoid another Drain the Oceans scenario, we'll assume the ocean expands, too.[4]As it turns out, the ocean is expanding, since it's getting warmer. This is (currently) the main way global warming is raising the sea level. All human structures will stay.

t = 1 second:

As the Earth started expanding, you'd feel a slight jolt, and might even lose your balance for a moment. This would be very brief. Since you're moving steadily upward at 1 cm/s, you woudn't feel any kind of ongoing acceleration. For the rest of the day, you wouldn't notice much of anything.

t = 1 day:

After the first day, the Earth would have expanded by 864 meters.

Gravity would take a long time to increase. If you weighed 70 kilograms when the expansion started, you'd weigh 70.01 at the end of the day.

What about our roads and bridges? Eventually, they would have to break up, right?

Not as quickly as you might think. Here's a puzzle I once heard:

Imagine you tied a rope tightly around the Earth, so it was hugging the surface all the way around.
Now imagine you wanted to raise the rope one meter off the ground.
How much extra length will you need to add to the rope?

Though it may seem like you'd need miles of rope, the answer is 6.28 meters. Circumference is proportional to radius, so if you increase radius by 1 unit, you increase circumference by 2π units.

Stretching a 40,000-kilometer line an extra 6.28 meters is pretty negligible. Even after a day, the extra 5.4 kilometers would be handled easily by virtually all structures. Concrete expands and contracts by more than that every day.[5]Lawrence Grybosky, Thermal Expansion and Contraction

After the initial jolt, one of the first effects you'd notice would be that your GPS would stop working. The satellites would stay in roughly the same orbits, but the delicate timing that the GPS system is based on would be completely ruined within hours. GPS timing is incredibly precise; of all the problems in engineering, it's one of the only ones in which engineers have been forced to include both special and general relativity in their calculations.

Most other clocks would keep working fine. However, if you have a very precise pendulum clock, you might notice something odd—by the end of the day, it would be three seconds ahead of where it should be.

t = 1 month:

After a month, the Earth would have expanded by 26 kilometers—an increase of 0.4%—and its mass would have increased by 1.2%. Surface gravity would only have gone up by 0.4%, rather than 1.2%, since surface gravity is proportional to radius.[6]Mass is proportional to radius cubed, and gravity is proportional to mass times inverse square of radius, so radius3 / radius2 = radius.

You might notice the difference in weight on a scale, but it's not a big deal. Gravity varies by this much between different cities already. This is a good thing to keep in mind if you buy a digital scale. If your scale has a precision of more than two decimal places, you need to calibrate it with a test weight—the force of gravity at the scale factory isn't necessarily the same as the force of gravity at your house.

While you might not notice the increased gravity just yet, you'd notice the expansion. After a month, you'd see a lot of cracks opening up in long concrete structures and the failure of elevated roads and old bridges. Most buildings would probably be ok, although those anchored firmly into bedrock might start to behave unpredictably.[7]Just what you want in a skyscraper.

At this point, astronauts on the ISS would start getting worried. Not only would the ground (and atmosphere) be rising toward them, but the increased gravity would also cause their orbit to slowly shrink. They'd need to evacuate quickly; they'd have at most a few months before the station reentered the atmosphere and deorbited.

t = 1 year:

After a year, gravity would be 5% stronger. You'd probably notice the weight gain, and you'd definitely notice the failure of roads, bridges, power lines, satellites, and undersea cables. Your pendulum clock would now be ahead by five days.

What about the atmosphere?

If the atmosphere isn't growing like the land and water are, air pressure would start dropping. This is due to a combination of factors. As gravity increases, then air gets heavier. But since that air is spread out over a larger area, the overall effect would be decreasing air pressure.

On the other hand, if the atmosphere is also expanding, surface air pressure would rise. After years had passed, the top of Mt. Everest would no longer be in the "death zone".[8]See What-If #64. On the other hand, since you'd be heavier—and the mountain would be taller—climbing would be more work.

t = 5 years:

After five years, gravity would be 25% stronger. If you weighed 70 kg when the expansion started, you'd weigh 88 kg now.

Most of our infrastructure would have collapsed. The cause of the collapse would be the expanding ground below them, not the increased gravity. Surprisingly, most skyscrapers would hold up fine under much higher gravity.[9]Although I wouldn't trust the elevators. For most of them, the limiting factor isn't weight, but wind.

t = 10 years:

After 10 years, gravity would be 50% stronger. In the scenario where the atmosphere isn't expanding, the air would become thin enough to be difficult to breathe even at sea level. In the other scenario, we'd be ok for a little while longer.

t = 40 years:

After 40 years, Earth's surface gravity would have tripled.[10]Over decades, the force of gravity would grow slightly faster than you'd expect, since the material in the Earth would compress under its own weight. The pressure inside planets is roughly proportional to the square of their surface area, so the Earth's core would be squeezed tightly. At this point, even the strongest humans would only be able to walk with great difficulty. Breathing would be difficult. Trees would collapse. Crops wouldn't stand up under their own weight. Virtually every mountainside would see massive landslides as material sought out a shallower angle of repose.

Geologic activity would also accelerate. Most of the Earth's heat is provided by radioactive decay of minerals in the crust and mantle,[12]Although some radioactive elements, like uranium, are heavy, they get squeezed out of the lower layers because their atoms don't mesh well with the rock lattices at those depths. For more, see this chapter and this article. and more Earth means more heat. Since the volume expands faster than the surface area, the overall heat flowing out per square meter will increase.

It's not actually enough to substantially warm the planet—Earth's surface temperature is dominated by the atmosphere and the Sun—but it would lead to more volcanoes, more earthquakes, and faster tectonic movement. This would be similar to the situation on Earth billions of years ago, when we had more radioactive material and thus a hotter mantle.

More active plate tectonics might be good for life. Plate tectonics play a key role in stabilizing the Earth's climate, and planets smaller than Earth (like Mars) don't have enough internal heat to sustain long-term geologic activity. A larger planet would allow for more geologic activity, which is why some scientists think that exoplanets slightly larger than Earth ("super-Earths") could be more friendly to life than Earth-sized ones.[11]Sasselov, Dimitar D.. The life of super-Earths: how the hunt for alien worlds and artificial cells will revolutionize life on our planet. New York: Basic Books, 2012.

t = 100 years:

After 100 years, we'd be experiencing over six gees of gravity. Not only would we be unable to move around to find food, but our hearts would be unable to pump blood to our brains. Only small insects (and sea animals) would be physically able to move around. Perhaps humans could survive in specially-built controlled-pressure domes, moving around by keeping most of our bodies submerged in water.

Breathing in this situation would be difficult. It's hard to suck in air against the weight of the water, which is why snorkels can only work when your lungs are near the surface.

Outside of low-pressure domes, the air would become unbreathable for a different reason. At somewhere around 6 atmospheres, even ordinary air becomes toxic.[13]R.M. Franz and P.C. Schutte, Barometric hazards within the context of deep-level mining, The Journal of The South African Institute of Mining and Metallurgy Even if we'd managed to survive all the other problems, by 100 years, we'd be dead from oxygen toxicity. Toxicity aside, breathing dense air is difficult simply because it's heavy.

Black hole?

When would the Earth eventually become a black hole?

It's hard to answer that, because the premise of the question is that the radius is steadily expanding while the density stays the same—whereas a black hole, the density increases.

The dynamics of really huge rocky planets aren't often analyzed, since there's no obvious way that they could form; anything that large will have enough gravity to gather hydrogen and helium during planet formation and become a gas giant.

At some point, our growing Earth would reach the point where adding more mass causes it to contract, rather than expand. After this point, it would collapse into something like a sputtering white dwarf or neutron star, and then—if its mass kept increasing—eventually become a black hole.

But before it gets that far ...

t = 300 years:

It's a shame humans wouldn't live this long, because at this point, something really neat would happen.

As the Earth grows, the Moon would, like all our satellites, gradually spiral inward.[14]Plummer, H. C., Note on the motion about an attracting centre of slowly increasing mass, Monthly Notices of the Royal Astronomical Society, Vol. 66, p.83 After several centuries, it would be close enough to the swollen Earth that the tidal forces between Earth and the Moon would be stronger than the gravitational forces holding the Moon together.

When the Moon passed this boundary—called the Roche limit—it would gradually break apart ...

... and Earth would, for a short time, have rings.

XKCD QA (What If?): Little Planet

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Little Planet

If an asteroid was very small but supermassive, could you really live on it like the Little Prince?

Samantha Harper

Last week, we looked at at life on a giant world. This week, let's look at a small one.

The Little Prince, by Antoine de Saint-Exupéry, is a story about a traveler from a distant asteroid. It's simple and sad and poignant and memorable.[1]For another take on the Petit Prince, scroll down to the last section of this wonderful piece by Mallory Ortberg. It's ostensibly a children's book, but it's hard to pin down who the intended audience is. In any case, it certainly has found an audience; it's among the best-selling books in history.

It was written in 1942. That's an interesting time to write about asteroids, because in 1942 we didn't actually know what asteroids looked like. Even in our best telescopes, the largest asteroids were only visible as points of light. In fact, that's where their name comes from—the word asteroid means "star-like."

We got our first confirmation of what asteroids looked like in 1971, when Mariner 9 visited Mars and snapped pictures of Phobos and Deimos.[2]Here's a picture of Phobos looking like the archetypical asteroid. The archived images from the mission are at the NASA Space Science Data Center, but strangely, the NSSDC refers readers to someone's personal Tripod page to browse the actual images. These moons, believed to be captured asteroids,[3]Ironically, while Phobos and Deimos look like asteroids, new research suggests they're not. See Craddock, Robert A.. "Are Phobos And Deimos The Result Of A Giant Impact?". Icarus (2010) solidified the modern image of asteroids as cratered potatoes.

Before the 1970s, it was common for science fiction to assume small asteroids would be round, like planets.[4]Not always; plenty of people had a good idea of what they would look like. And there were stranger ideas ...

The Little Prince took this a step further, imagining an asteroid as a tiny planet with gravity, air, and a rose. There's no point in trying to critique the science here, because (1) it's not a story about asteroids, and (2) it opens with a parable about how foolish adults are for looking at everything too literally.

So rather than trying to take things away from the story, let's see what strange new pieces science can add. If there really were a superdense asteroid with enough surface gravity to walk around on, it would have some pretty surprising properties.

If the asteroid has a radius of 1.75 meters, then in order to have Earth-like gravity at the surface, it would need to have a mass of about 500 million tons. This is roughly equal to the combined mass of every human on Earth.

If you stood on the surface, you'd experience tidal forces. Your feet would feel heavier than your head, which you'd feel as a gentle stretching sensation. It would feel like you were stretched out on a curved rubber ball, or were lying on a merry-go-round with your head near the center.

The escape velocity at the surface would be about 5 meters per second. That's slower than a sprint, but still pretty fast. As a rule of thumb, if you can't dunk a basketball, you wouldn't be able to escape by jumping straight up.

However, the weird thing about escape velocity is that it doesn't matter which direction you're going.[5]... which is why it should really be called "escape speed"—the fact that it has no direction (which is the distinction between "speed" and "velocity") is actually very significant here. If you go faster than the escape speed, as long as you don't actually go toward the planet, you'll escape. That means you might be able to leave our asteroid by running horizontally and jumping off the end of a ramp.

If you didn't go fast enough to escape the planet, you'd go into orbit around it. Your orbital speed would be roughly 3 meters per second, which is a typical jogging speed.

But this would be a weird orbit.

Tidal forces would act on you in several ways. If you reach your arm down toward the planet, it would be pulled much harder than the rest of you. And if you reach down with one arm, the rest of you gets pushed upward, which means other parts of your body feel even less gravity. Effectively, every part of your body would be trying to go in a different orbit.

A large orbiting object under these kinds of tidal forces—say, a moon—will generally break apart into rings. This wouldn't happen to you. However, your orbit would become chaotic and unstable.

These types of orbits were investigated in an interesting paper by Radu D. Rugescu and Daniele Mortari.[6]Rugescu, Radu D., Mortari, Daniele, "Ultra Long Orbital Tethers Behave Highly Non-Keplerian and Unstable", WSEAS Transactions on Mathematics, Vol. 7, No. 3, March 2008, pp. 87-94. Their simulations showed that large, elongated objects follow strange patterns around their central bodies. Even their centers of mass don't move in the traditional ellipses; some adopt pentagonal orbits, while others spin chaotically and crash into the planet.

This type of analysis could actually have practical applications. There have been various proposals over the years to use long, whirling tethers to move cargo in and out of gravity wells—a sort of free-floating space elevator. Such tethers could transport cargo to and from the surface of the Moon, or to pick up spacecraft from the edge of the Earth's atmosphere. The inherent instability of many tether orbits poses an interesting challenge for this kind of project.

As for the residents of our superdense asteroid, they'd have to be careful; if they ran too fast, they'd be in serious danger of going into a tumble and losing their lunch.

Fortunately, vertical jumps would be fine.

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