The bottom line is that in the range of 150–300 mph, a typical sedan would lift off the ground, tumble, and crash . . . before you even hit the bump.
BREAKING: Child, Unidentified Creature in Bicycle Basket Hit and Killed by Car
If you kept the car from taking off, the force of the wind at those speeds would strip away the hood, side panels, and windows. At higher speeds, the car itself would be disassembled, and might even burn up like a spacecraft reentering the atmosphere.
What’s the ultimate limit?
In the state of Pennsylvania, drivers may see $2 added to their speeding ticket for every mile per hour by which they break the speed limit.
Therefore, if you drove a car over a Philadelphia speed bump at 90 percent of the speed of light, in addition to destroying the city . . .
. . . you could expect a speeding ticket of $1.14 billion.
1Like 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 answer in anything but miles per hour; it’s just been burned into my brain. Sorry!
2Just Google “hit a curb at 60.”
3There are cars everywhere. Go outside with a ruler and check.
4At 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.
Lost Immortals
Q. If two immortal people were placed on opposite sides of an uninhabited Earthlike planet, how long would it take them to find each other? 100,000 years? 1,000,000 years? 100,000,000,000 years?
—Ethan Lake
A. We’ll start with the simple, physicist-style1 answer: 3000 years.
That’s about how long it would take two people to find each other, assuming that they were walking around at random over a sphere for 12 hours per day and had to get within a kilometer to see each other.
We can immediately see some problems with this model.2 The simplest problem is the assumption that you can always see someone if they come within a kilometer of you. That’s possible under only the most ideal circumstances; a person walking along a ridge might be visible from a kilometer away, whereas in a thick forest during a rainstorm, two people could pass within a few meters without seeing each other.
We could try to calculate the average visibility across all parts of the Earth, but then we run into another question: Why would two people who are trying to find each other spend time in a thick jungle? It would seem to make more sense for both of them to stay in flat, open areas where they could easily see and be seen.3
Once we start considering the psychology of our two people, our spherical-immortal-in-a-vacuum model is in trouble.4 Why should we assume our people will walk around randomly at all? The optimal strategy might be something totally different.
What strategy would make the most sense for our lost immortals?
If they have time to plan beforehand, it’s easy. They can arrange to meet at the North or South Pole, or—if those turn out to be unreachable—at the highest point on land, or the mouth of the longest river. If there’s any ambiguity, they can just travel between all the options at random. They have plenty of time.
If they don’t have a chance to communicate beforehand, things get a little harder. Without knowing the other person’s strategy, how do you know what your strategy should be?
There’s an old puzzle, from before the days of cell phones, that goes something like this:
Suppose you’re meeting a friend in an American town that neither of you have been to before. You don’t have a chance to plan a meeting place beforehand. Where do you go?
The author of the puzzle suggested that the logical solution would be to go to the town’s main post office and wait at the main receiving window, where out-of-town packages arrive. His logic was that it’s the only place that every town in the US has exactly one of, and which everyone would know where to find.
To me, that argument seems a little weak. More importantly, it doesn’t hold up experimentally. I’ve asked that question to a number of people, and none of them suggested the post office. The original author of that puzzle would be waiting in the mailroom alone.
Our lost immortals have it tougher, since they don’t know anything about the geography of the planet they’re on.
Following the coastlines seems like a sensible move. Most people live near water, and it’s much faster to search along a line than over a plane. If your guess turns out to be wrong, you won’t have wasted much time compared to having searched the interior first.
Walking around the average continent would take about five years, based on typical width-to-coastline-length ratios for Earth land masses.5
Let’s assume you and the other person are on the same continent. If you both walk counterclockwise, you could circle forever without finding each other. That’s no good.
A different approach would be to make a complete circle counterclockwise, then flip a coin. If it comes up heads, circle counterclockwise again. If tails, go clockwise. If you’re both following the same algorithm, this would give you a high probability of meeting within a few circuits.
The assumption that you’re both using the same algorithm is probably optimistic. Fortunately, there’s a better solution: Be an ant.
Here’s the algorithm that I would follow (if you’re ever lost on a planet with me, keep this in mind!):
If you have no information, walk at random, leaving a trail of stone markers, each one pointing to the next. For every day that you walk, rest for three. Periodically mark the date alongside the cairn. It doesn’t matter how you do this, as long as it’s consistent. You could chisel the number of days into a rock, or lay out rocks to plot the number.
If you come across a trail that’s newer than any you’ve seen before, start following it as fast as you can. If you lose the trail and can’t recover it, resume leaving your own trail.
You don’t have to come across the other player’s current location; you simply have to come across a location where they’ve been. You can still chase one another in circles, but as long as you move more quickly when you’re following a trail than when you’re leaving one, you’ll find each other in a matter of years or decades.
And if your partner isn’t cooperating—perhaps they’re just sitting where they started and waiting for you—then you’ll get to see some neat stuff.
1Assuming a spherical immortal human in a vacuum . . .
2Like, what happened to all the other people? Are they okay?
3Although the visibility calculation does sounds fun. I know what I’m doing next Saturday night!
4Which is why we usually try not to consider things like that.
5Of course, some areas would present a challenge. Louisiana’s bayous, the Caribbean’s mangrove forests, and Norway’s fjords would all make for slower walking than a typical beach.
Orbital Speed
Q. What if a spacecraft slowed down on reentry 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
Q. 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
Q. 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
A. The answers to these questions all hinge on the same idea. It’s an idea I’ve touched on in other answers, but right now I want to focus on it specifically:
&nb
sp; 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:
Not actual size.
Space is like this:
You know what, sure, actual size.
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 is easy.1 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 rocket the size of a telephone pole. The X-15 aircraft reached space just by going fast and then steering up.2,3
You will go to space today, and then you will quickly come back.
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 percent 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 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 orbital speed while carrying enough fuel to slow back down would be completely impractical.5
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 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 the International Space Station could cross the length of the field before the bullet traveled 10 yards.8
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 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 2 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.
You’d be moving at about 15 subway stops per minute.
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, and the ISS is moving at 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 1000 miles.
1Specifically, low Earth orbit, which is where the International Space Station is and where shuttles could go.
2The X-15 reached 100 km on two occasions, both when flown by Joe Walker.
3Make sure to remember to steer up and not down, or you will have a bad time.
4It’s a little less if you’re in the higher region of low Earth orbit.
5This exponential increase is the central problem of rocketry: The fuel required to increase your speed by 1 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 × 1.4 × 1.4 × 1.4 × 1.4 × 1.4 × 1.4 × 1.4 ≈ 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.
6There are some good apps and online tools to help you spot the station, along with other neat satellites.
7Either kind.
8This type of play is legal in Australian rules football.
9Using song beats to help measure the passage of time is a technique also used in CPR training, where the song “Stayin’ Alive” is used.
FedEx Bandwidth
Q. When–if ever–will the bandwidth of the Internet surpass that of FedEx?
—Johan Öbrink
Never underestimate the bandwidth of a station wagon full of tapes hurtling down the highway.
–Andrew Tanenbaum, 1981
A. If you want to transfer a few hundred gigabytes of data, it’s generally faster to FedEx a hard drive than to send the files over the Internet. This isn’t a new idea—it’s often dubbed “SneakerNet”—and it’s even how Google transfers large amounts of data internally.
But will it always be faster?
Cisco estimates that total Internet traffic currently averages 167 terabits per second. FedEx has a fleet of 654 aircraft with a lift capacity of 26.5 million pounds daily. A solid-state laptop drive weighs about 78 grams and can hold up to a terabyte.
That means FedEx is capable of transferring 150 exabytes of data per day, or 14 petabits per second—almost a hundred times the current throughput of the Internet.
If you don’t care about cost, this 10-kilogram shoebox can hold a lot of Internet.
We can improve the data density even further by using microSD cards:
Those thumbnail-sized flakes have a storage density of up to 160 terabytes per kilogram, which means a FedEx fleet loaded with microSD cards could transfer about 177 petabits per second, or 2 zettabytes per day—a thousand times the Internet’s current traffic level. (The infrastructure would be interesting—Google would need to build huge warehouses to hold a massive card-processing operation.)
Cisco estimates Internet traffic is growing at about 29 percent annually. At that rate, we’ll hit the FedEx point in 2040. Of course, the amount of data we can fit on a drive will have gone up by then, too. The only way to actually reach the FedEx point is if transfer rates grow much faster than storage rates. In an intuitive sense, this seems unlikely, since storage and transfer are fundamentally linked—all that data is coming from somewhere and going somewhere—but there’s no way to predict usage patterns for sure.
While FedEx is big enough to keep up with the next few decades of actual usage, there’s no technological reason we can’t build a connection that beats them on bandwidth. There are experimental fiber clusters that can handle over a petabit per second. A cluster of 200 of those would beat FedEx.
If you recruited the entire
US freight industry to move SD cards for you, the throughput would be on the order of 500 exabits—half a zettabit—per second. To match that transfer rate digitally, you’d need to take half a million of those petabit cables.
So the bottom line is that for raw bandwidth of FedEx, the Internet will probably never beat SneakerNet. However, the virtually infinite bandwidth of a FedEx-based Internet would come at the cost of 80,000,000-millisecond ping times.
Free Fall
Q. What place on Earth would allow you to free-fall the longest by jumping off it? What about using a squirrel suit?
—Dhash Shrivathsa
A. The largest purely vertical drop on Earth is the face of Canada’s Mount Thor, which is shaped like this:
Source: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
To make this scenario a little less gruesome, let’s suppose there’s a pit at the bottom of the cliff filled with something fluffy—like cotton candy—to safely break your fall.
Would this work? You’ll have to wait for book two . . .
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.
What If? Page 14