I later learned that the reason the sparks didn’t hurt him was that they were tiny; the heat they carried could be absorbed into the body without warming anything more than a tiny patch of skin.
The hot molecules in space are like the sparks in my dad’s machine shop; they might be hot or cold, but they’re so small that touching them doesn’t change your temperature much.1 Instead, your heating and cooling is dominated by how much heat you produce and how quickly it pours out of you into the void.
Without a warm environment around you radiating heat back to you, you lose heat by radiation much faster than normal. But without air around you to carry heat from your surface, you also don’t lose much heat by convection.2 For most human-carrying spacecraft, the latter effect is more important; the big problem isn’t staying warm, it’s keeping cool.
A nuclear submarine is clearly able to maintain a livable temperature inside when the outer hull is cooled to 4°C by the ocean. However, if the submarine’s hull needed to hold this temperature while in space, it would lose heat at a rate of about 6 megawatts while in the shadow of the Earth. This is more than the 20 kilowatts supplied by the crew—and the few hundred kilowatts of apricity3 when in direct sunlight—so they’d need to run the reactor just to stay warm.4
To get out of orbit, a submarine would need to slow down enough that it hit the atmosphere. Without rockets, it has no way to do this.
Okay—technically, a submarine does have rockets.
Unfortunately, the rockets are pointing the wrong way to give the submarine a push. Rockets are self-propelling, which means they have very little recoil. When a gun fires a bullet, it’s pushing the bullet up to speed. With a rocket, you just light it and let go. Launching missiles won’t propel a submarine forward.
But not launching them could.
If the ballistic missiles carried by a modern nuclear submarine were taken from their tubes, turned around, and placed in the tubes backward, they could each change the submarine’s speed by about 4 meters per second.
A typical de-orbiting maneuver requires in the neighborhood of 100 m/s of delta-v (speed change), which means that the 24 Trident missiles carried by an Ohio-class submarine could be just enough to get it out of orbit.
Now, because the submarine has no heat-dissipating ablative tiles, and because it’s not aerodynamically stable at hypersonic velocities, it would inevitably tumble and break up in the air.
If you tucked yourself into the right crevice in the submarine—and were strapped into an acceleration couch—there’s a tiny, tiny, tiny chance that you could survive the rapid deceleration. Then you’d need to jump out of the wreckage with a parachute before it hit the ground.
If you ever try this, and I suggest you don’t, I have one piece of advice that is absolutely critical:
Remember to disable the detonators on the missiles.
1This is why, even though matches and torches are about the same temperature, you see tough guys in movies extinguish matches by pinching them but never see them do the same with torches.
2Or conduction.
3This is my single favorite word in the English language. It means the warmth of sunlight in winter.
4When they moved into the Sun, the sub’s surface would warm, but they’d still be losing heat faster than they’d be gaining it.
Short-Answer Section
Q. If my printer could literally print out money, would it have that big an effect on the world?
—Derek O’Brien
A. You can fit four bills on an 8.5" × 11" sheet of paper.
If your printer can manage one page (front and back) of full-color high-quality printing per minute, that’s $200 million dollars a year.
This is enough to make you very rich, but not enough to put any kind of dent in the world economy. Since there are 7.8 billion $100 bills in circulation, and the lifetime of a $100 bill is about 90 months, that means there are about a billion produced each year. Your extra two million bills a year would barely be enough to notice.
Q. What would happen if you set off a nuclear bomb in the eye of a hurricane? Would the storm cell be immediately vaporized?
—Rupert Bainbridge (and hundreds of others)
A. This question gets submitted a lot.
It turns out the National Oceanic and Atmospheric Administration—the agency that runs the National Hurricane Center—gets it a lot, too. In fact, they’re asked about it so often that they’ve published a response.
I recommend you read the whole thing,1 but I think the last sentence of the first paragraph says it all:
“Needless to say, this is not a good idea.”
It makes me happy that an arm of the US government has, in some official capacity, issued an opinion on the subject of firing nuclear missiles at hurricanes.
Q. If everyone put little turbine generators on the downspouts of their houses and businesses, how much power would we generate? Would we ever generate enough power to offset the cost of the generators?
—Damien
A. A house in a very rainy place, like the Alaska panhandle, might receive close to 4 meters of rain per year. Water turbines can be pretty efficient. If the house has a footprint of 1500 square feet and gutters 5 meters off the ground, it would generate an average of less than a watt of power from rainfall, and the maximum electricity savings would be:
The rainiest hour on record as of 2014 occurred in 1947 in Holt, Missouri, where about 30 centimeters of rain fell in 42 minutes. For those 42 minutes, our hypothetical house could generate up to 800 watts of electricity, which might be enough to power everything inside it. For the rest of the year, it wouldn’t come close.
If the generator rig cost $100, residents of the rainiest place in the US—Ketchikan, Alaska—could potentially offset the cost in under a century.
Q. Using only pronounceable letter combinations, how long would names have to be to give each star in the universe a unique one-word name?
—Seamus Johnson
A. There are about 300,000,000,000,000,000,000,000 stars in the universe. If you make a word pronounceable by alternating vowels and consonants (there are better ways to make pronounceable words, but this will do for an approximation), then every pair of letters you add lets you name 105 times as many stars (21 consonants times 5 vowels). Since numbers have a similar information density
—100 possibilities per character
—this suggests the name will end up being about as long as the total number of stars:
The stars are named Joe Biden.
I like doing math that involves measuring the lengths of numbers written out on the page (which is really just a way of loosely estimating log10x). It works, but it feels so wrong.
Q. I bike to class sometimes. It’s annoying biking in the wintertime, because it’s so cold. How fast would I have to bike for my skin to warm up the way a spacecraft heats up during reentry?
—David Nai
A. Reentering spacecraft heat up because they’re compressing the air in front of them (not, as is commonly believed, because of air friction).
To increase the temperature of the air layer in front of your body by 20 degrees Celsius (enough to go from freezing to room temperature), you would need to be biking at 200 meters per second.
The fastest human-powered vehicles at sea levels are recumbent bicycles enclosed in streamlined aerodynamic shells. These vehicles have an upper speed limit near 40 m/s—the speed at which the human can just barely produce enough thrust to balance the drag force from the air.
Since drag increases with the square of the speed, this limit would be pretty hard to push any further. Biking at 200 m/s would require at least 25 times the power output needed to go 40 m/s.
At those speeds, you don’t really
have to worry about the heating from the air—a quick back-of-the-envelope calculation suggests that if your body were doing that much work, your core temperature would reach fatal levels in a matter of seconds.
Q. How much physical space does the Internet take up?
—Max L
A. There are a lot of ways to estimate the amount of information stored on the Internet, but we can put an interesting upper bound on the number just by looking at how much storage space we (as a species) have purchased.
The storage industry produces in the neighborhood of 650 million hard drives per year. If most of them are 3.5-inch drives, that’s 8 liters (2 gallons) of hard drive per second.
This means the last few years of hard-drive production—which, thanks to increasing size, represents the majority of global storage capacity—would just about fill an oil tanker. So, by that measure, the Internet is smaller than an oil tanker.
Q. What if you strapped C4 to a boomerang? Could this be an effective weapon, or would it be as stupid as it sounds?
—Chad Macziewski
A. Aerodynamics aside, I’m curious what tactical advantage you’re expecting to gain by having the high explosive fly back at you if it misses the target.
1Search for “Why don’t we try to destroy tropical cyclones by nuking them?” by Chris Landsea.
Lightning
Before we go any further, I want to emphasize something: I am not an authority on lightning safety.
I am a guy who draws pictures on the Internet. I like it when things catch fire and explode, which means I do not have your best interests in mind. The authorities on lightning safety are the folks at the US National Weather Service:
http://www.lightningsafety.noaa.gov/
Okay. With that out of the way . . .
To answer the questions that follow, we need to get an idea of where lightning is likely to go. There’s a cool trick for this, and I’ll give it away right here at the start: Roll an imaginary 60-meter sphere across the landscape and look at where it touches.1 In this section, I answer a few different questions about lightning.
They say lightning strikes the tallest thing around. That’s the kind of maddeningly inexact statement that immediately sparks all kinds of questions. How far is “around”? I mean, not all lightning hits Mount Everest. But does it find the tallest person in a crowd? The tallest person I know is probably Ryan North.2 Should I try to hang around him for lightning safety reasons? What about other reasons? Maybe I should stick to answering questions rather than asking them.
So how does lightning pick its targets?
The strike starts with a branching bundle of charge—the “leader”—descending from the cloud. It spreads downward at speeds of tens to hundreds of kilometers per second, covering the few kilometers to the ground in a few dozen milliseconds.
The leader carries comparatively little current—on the order of 200 amps. That’s still enough to kill you, but it’s nothing compared to what happens next. Once the leader makes contact with the ground, the cloud and the ground equalize with a massive discharge of more like 20,000 amps. This is the blinding flash you see. It races back up the channel at a significant fraction of the speed of light, covering the distance in under a millisecond .3
The place on the ground where we see a bolt “strike” is the spot where the leader first made contact with the surface. The leader moves down through the air in little jumps. It’s ultimately making its way toward the (usually) positive charge in the ground. However, it “feels” charges within only a few tens of meters of its tip when it’s deciding where to jump next. If there’s something connected to the ground within that distance, the bolt will jump to it. Otherwise, it jumps out in a semi-random direction and repeats the process.
This is where the 60-meter sphere comes in. It’s a way to imagine what spots might be the first thing the leader senses—the places it might jump to in its next (final) step.
To figure out where lightning is likely to hit, you roll the imaginary 60-meter sphere across the landscape.4 This sphere climbs up over trees and buildings without passing through anything (or rolling it up). Places the surface makes contact—treetops, fence posts, and golfers in fields—are potential lightning targets.
This means you can calculate a lightning “shadow” around an object of height h on a flat surface.
The shadow is the area where the leader is likely to hit the tall object instead of the ground around it:
Now, that doesn’t mean you’re safe within the shadow—often, it means the opposite. After the current hits the tall object, it flows out into the ground. If you’re touching the ground nearby, it can travel through your body. Of the 28 people killed by lightning in the US in 2012, 13 were standing under or near trees.
With all this in mind, let’s look at possible lightning paths for the scenarios in the following questions.
Q. How dangerous is it, really, to be in a pool during a thunderstorm?
A. Pretty dangerous. Water is conductive, but that’s not the biggest problem—the biggest problem is that if you’re swimming, your head is poking up from a large flat surface. But lightning striking the water near you would still be bad. The 20,000 amps spread outward—mostly over the surface—but how much of a jolt it will give you at what distance is hard to calculate.
My guess is that you’d be in significant danger anywhere within a minimum of a dozen meters—and farther in fresh water, because the current will be happier to take a shortcut through you.
What would happen if you were taking a shower when you were struck by lightning? Or standing under a waterfall?
You’re not in danger from the spray—it’s just a bunch of droplets of water in the air. It’s the tub under your feet, and the puddle of water in contact with the plumbing, that’s the real threat.
Q. What would happen if you were in a boat or a plane that got hit by lightning? Or a submarine?
A. A boat without a cabin is about as safe as a golf course. A boat with a closed cabin and a lightning protection system is about as safe as a car. A submarine is about as safe as a submarine safe (a submarine safe is not to be confused with a safe in a submarine—a safe in a submarine is substantially safer than a submarine safe).
Q. What if you were changing the light at the top of a radio tower, and lightning struck? Or what if you were doing a backflip? Or standing in a graphite field? Or looking straight up at the bolt?
A.
Q. What would happen if lightning struck a bullet in midair?
A. The bullet won’t affect the path the lightning takes. You’d have to somehow time the shot so the bullet was in the middle of the bolt when the return stroke happened.
The core of a lightning bolt is a few centimeters in diameter. A bullet fired from an AK-47 is about 26 mm long and moves at about 700 millimeters every millisecond.
The bullet has a copper coating over a lead core. Copper is a fantastically good conductor of electricity, and much of the 20,000 amps could easily take a shortcut through the bullet.
Surprisingly, the bullet would handle it pretty well. If it were sitting still, the current would quickly heat and melt the metal. But since it would be moving along so quickly, it would exit the channel before it could be warmed by more than a few degrees. It would continue on to its target relatively unaffected. There would be some curious electromagnetic forces created by the magnetic field around the bolt and the current flow through the bullet, but none of the ones I examined would change the overall picture very much.
Q. What if you were flashing your BIOS during a thunderstorm and you got hit by lightning?
A.
1Or a real one, for that matter.
2Paleontologists estimate he stood nearly 5 meters tall at the shoulder.
3While it’
s called a “return stroke,” charge is still flowing downward. However, the discharge appears to propagate upward. This effect is similar to how when a traffic light turns green, the cars in front start moving, then the cars in back, so the movement appears to spread backward.
4For safety reasons, do not use a real sphere.
weird (and worrying) questions from the what if? INBOX, #4
Q. Would it be possible to stop a volcano eruption by placing a bomb (thermobaric or nuclear) underneath the surface?
—Tomasz Gruszka
Q. A friend of mine is convinced that there is sound in space. There isn’t, right?
—Aaron Smith
Human Computer
Q. How much computing power could we could achieve if the entire world population stopped whatever we are doing right now and started doing calculations?How would it compare to a modern-day computer or smartphone?
—Mateusz Knorps
A. On one hand, humans and computers do very different types of thinking, so comparing them is like comparing apples and oranges.
On the other hand, apples are better.1 Let’s try directly comparing humans and computers at the same tasks.
It’s easy, though getting harder every day, to invent tasks that a single human can do faster than all the computers in the world. Humans, for example, are probably still far better at looking at a picture of a scene and guessing what just happened:
What If? Page 7