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Green Cows

If cows could photosynthesize, how much less food would they need?

Green Cows

If cows could photosynthesize, how much less food would they need?

—Anonymous

In a way, they already do. A field of grass sits there all day soaking up energy from the sun and storing it chemically. A grazing animal can then come along and absorb weeks of accumulated energy in a matter of minutes.

cows absorbing energy

A Jersey cow presents in the neighborhood of nearly two square meters of usable space to the sun if it stands right. (Cows would have to be trained to stand optimally, but we might not have too far to go; research suggests they already align themselves north-south.

Chlorophyll photosynthesis extracts 3%-6% of the total energy from sunlight. If we figure on any given day the cow gets the equivalent of about six hours of peak sunlight, it works out to less than two million joules of usable energy each day.

grass giving cows energy

Is that a lot? Well, a 450-kilogram cow just wandering around in a field might eat about 10 kilograms of dry matter a day, extracting on the order of 50 million joules of metabolic energy. So photosynthesis could only make up about 4% of the required intake—saving only a few handfuls of grain.

If we could equip cows with solar panels, which can be several times more energy-efficient than photosynthesis, we could improve that number—but not by much.

cow with a solar panel on its back

The basic problem facing cows is the same one facing solar cars—they're too small. If you saw the world's cattle population in silhouette, they'd have an overall cross-sectional area of about two thousand square kilometers. This means that if they were migrating through the air over Rhode Island (biology is not my strong suit), they'd blot out the sun over barely half the state. They'd only catch enough sunlight to produce a daily average of about 40 gigawatts of power (two megayodas).

By contrast, about 3% of the world's surface area is cultivated, which means that (given rough estimates of geographic distribution of farmland) our crops easily intercept over a thousand times more sunlight than our cattle—which is why grazing is a good strategy.

I'd like to conclude with this quote, which I found in the Cedara Agricultural Development Institute's Applied Ruminant Nutrition for Dairy Cows:

Cows on a typical dairy ration can produce 80 to 100 litres of saliva per day.

This has nothing to do with photosynthesis, but I wanted to share anyway.

bottles... of cow saliva... ew.

Today's topic: Lightning

How dangerous is it, really, to be in a pool during a thunderstorm?

Today's topic: Lightning

How dangerous is it, really, to be in a pool during a thunderstorm?

—Jay Gengelbach

What would happen if you were taking a shower when you were struck by lightning? Or standing under a waterfall?

—same3chords

What would happen if you were in a boat or a plane that got hit by lightning? Or a submarine?

—SoobNauce

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?

—Danny Wedul

What would happen if lightning struck a bullet in midair?

—Timothy Campbell

What if you were flashing your BIOS during a thunderstorm and you got hit by lightning?

—njsg

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 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/

Ok. With that out of the way ...

To answer these questions, 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.

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 Mt. Everest. But does it find the tallest person in a crowd? The tallest person I know is probably Ryan North (paleontologists estimate he stood nearly five meters tall at the shoulder). Should I try to hang around him for lightning safety reasons? What about other reasons? (This is probably why you people ask the questions on this blog, not me.)

But how does lightning pick its targets?

This video, captured by Tom A. Warner, might be the single coolest piece of footage I’ve ever seen. It shows a bolt of lightning recorded at 7,207 frames per second. The 33-second video represents barely a tenth of a second of real time. There are lots of slow-motion videos of lightning, but this is by far the best I’ve found.

Tom’s video gives an idea of how lightning moves. It starts with a branching bundle of charge—the “leader”—descending from the cloud. This is what you see in the first part of the video. 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—all within a single frame of that video.

(Technical detail: while it’s called a “return stroke”, charge is still flowing downward. However, the discharge appears to propagate upward. This effect similar to how when a traffic light turns green, or whatever color, the cars in front start moving, then the cars in back, so the movement appears to spread backward.)

So the place on the ground where we see a bolt “strike” is the spot where the leader first makes contact with the surface. The leader moves down through the air in little jumps. It’s ultimately feeling its way toward the (usually) positive charge in the ground. However, it only “feels” charges within a few tens of meters of the tip. 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.

lightning makes a series of steps down toward ryan north

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 (for safety reasons, do not use a real sphere). This sphere climbs up over trees and buildings without passing through anything (or rolling it up). Places the surface makes contact—treetops, fenceposts, 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.

a sphere of radius 30 meters rests on the ground next to a man on a platform with a flag

The shadow is the area where the leader is likely to hit the tall object instead of the ground around it:

[ ext{Shadow Radius}=sqrt{-h(h-2r)}]

Now, that doesn’t mean you’re safe on the ground around it—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 so far this year, 13 were standing under or near trees.

With all this in mind, let’s look at possible lightning paths for the scenarios in the questions.

How dangerous is it, really, to be in a pool during a thunderstorm?

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 further 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?

lightning strikes two people, one standing in an inside waterfall and one standing in an outside 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.

What would happen if you were in a boat or a plane that got hit by lightning? Or a submarine?

lightning hits a boat, another boat, and a plane. it does not hit the submarine because the ocean is in the way.

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).

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?

lightning strikes a person on a tower, then flows into the tower to the ground. another bolt passes through someone doing a backflip. a person stands in a graphite field (?). a person looks at a lightning bolt which is hitting them in the eyes.

What would happen if lightning struck a bullet in midair?

The bullet won't affect the path the lightning takes. You'd have somehow to 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.

a bullet passes through the ionized channel of a lightning bolt. as it reaches the center, it glows very brightly. it is still going brightly as the bullet exits undamaged.

Surprisingly, the bullet handles it pretty well. If it were sitting still, the current would quickly heat and melt the metal. But it’s moving along so quickly that it exits the channel before it can be warmed by more than a few degrees. It continues on to its target relatively unaffected. There are 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 changed the overall picture very much.

What if you were flashing your BIOS during a thunderstorm and you got hit by lightning?

the tempest installs microsoft bob (gateway 2000 edition)

Mariana Trench Explosion

What if you exploded a nuclear bomb (say, the Tsar Bomba) at the bottom of the Marianas Trench?

Mariana Trench Explosion

What if you exploded a nuclear bomb (say, the Tsar Bomba) at the bottom of the Marianas Trench?

—Evin Sellin

Surprisingly little—especially compared to what would happen if you put it just under the surface.

Evin isn’t the first person to think of setting off nuclear weapons underwater. In fact, we’ve actually tried it a bunch of times. This is what it looks like.

Most of the tests, however, involved either small bombs or shallow water. Evin’s scenario concerns neither.

At 53 megatons, the Tsar Bomba was the most powerful nuclear weapon ever detonated, and at 11 kilometers, the Mariana(s) Trench is the deepest part of the ocean. No underwater test has involved bombs anywhere near that size, nor depths anywhere near that deep.

In 1962, physicist Freeman Dyson wrote a memo discussing eight possible novel weapon systems, all of which looked like they’d be possible in the near future, and outlined the potential military uses and dangers of each. This memo has been declassified, but was never published. Freeman’s son, science historian George Dyson, got a paper copy of the memo from his father, and was kind enough to show it to me.

In the memo, one of the eight ideas Freeman discusses is the use of gigaton nuclear weapons as wave generators. It includes this rather terrifying passage describing the detonation of a submerged gigaton mine off the North American coast: “Quantitative study of the destructive effects has not been made. Rough estimates indicate that the inundation would reach to a height of 200-300 feet above sea level, or a distance of 200-300 miles inland, whichever limit is reached first.”

a map showing a thing happening in the atlantic ocean and then another thing happening to the east coast of north america

Luckily for the coast, later research paints a less dire picture.

The seminal work in the field of nuclear ocean waves is Water Waves Generated By Underwater Explosions, a sprawling 400-page report produced for the Department of Defense by Bernard Le Mehaute and Shen Wang. The report, published in 1996, exhaustively examines and summarizes all available research about the ocean waves created by nuclear explosions.

The report outlines how when a nuclear weapon goes off underwater, it produces a cavity of hot gasses, which then collapses. If the explosion happens near the surface, it can create some pretty big waves—under some circumstances, they can be hundreds of feet high near ground zero.

a bubble forms and rises out of the water, creating waves.

Or is it ocean zero?

Fortunately for the coast, these waves are fundamentally different from tsunamis. It turns out that if the waves are very large, they break early, and expend most of their energy creating a narrow surf zone on the continental shelf. This is potentially hazardous to some ships, but much less catastrophic than a direct nuclear attack. When they reached the coast, the waves would be no worse than those from a bad storm.

But those are waves from an explosion close to the surface. A nuke set off deep underwater acts a bit differently.

The explosion at the bottom of the Mariana Trench will create a quickly-expanding spherical cavity of hot steam. To figure out how big it gets, we can try a formula from the 1971 paper Evaluation of Various Theoretical Models For Underwater Explosion:

[ ext{Radius} = left ( rac{3}{4pi} ight ) ^ rac{1}{3}left ( rac{40% imes 53 ext{ megatons of TNT}}{ ext{Mariana Trench pressure}+ ext{1 ATM}} ight )^ rac{1}{3}approx580 ext{ meters}]

The bubble grows to about a kilometer across in a couple of seconds. The water above bulges up, though only slightly, over a large area. Then the pressure from that six miles of water overhead causes it to collapse. Within a dozen or so seconds, the bubble shrinks to a minimum size, then ‘bounces’ back, expanding outward again.

It goes through three or four cycles of this collapse and expansion before disintegrating into, in the words of the 1996 report, “a mass of turbulent warm water and explosion debris.” According to the report, as a result of such a deep-water closed bubble creation and dissipation, “no wave of any consequence will be generated.”

That “turbulent warm water” is actually quite substantial. The rising column of heat creates a hot spot in the ocean—many degrees warmer than the surrounding water—that lingers for some time.

 tropical cyclone passes over the mariana trench

Earlier this year, Severe Tropical Storm Sanvu passed over the Mariana Trench. The column of deep, hot water from our nuke could conceivably have been enough to strengthen it into a typhoon, much as the deep warm waters of the Gulf of Mexico’s Loop Current sometimes cause hurricanes to rapidly intensify. In addition to the heat energy from the water, Sanvu could whip up a spray containing fallout from the blast, and approach Iwo Jima as a radioactive whirlwind.

Of course, that’s getting a little far-fetched. In the absence of an improbable typhoon interaction, the overall effect of the bomb isn’t quite as dramatic as Evin might have imagined.

... But.

All that changes when this cat enters the equation:

a man in a hat holds up a cat

Literally.

Let’s say that when I’m typing the above equation, the cat hops onto my desk and steps on the “0” key, which inserts six extra zeroes:

[ ext{Radius} = left ( rac{3}{4pi} ight ) ^ rac{1}{3}left ( rac{40% imes 53000000 ext{ megatons of TNT}}{ ext{Mariana Trench pressure}+ ext{1 ATM}} ight )^ rac{1}{3}approx35 ext{ miles}]

If there was enough water, and if the model held up, this blast would expand into a bubble 70 miles across.

In reality, the oceans aren’t that deep. Instead, it blows a hole in the Earth’s crust dozens of miles across, leaving a hole through which briefly glows the magma of the mantle.

Around the early 1990s, scientists started discovering jumbled fields of petrified wood mixed with sand buried beneath the Louisiana and Texas coast. These turned out to be the remains of North American forests swept out to sea by a massive tsunami. The culprit was a comet or asteroid hitting the Yucatan—the impact that killed most of the dinosaurs. The debris played a key role in identifying the 65-million-year-old Chicxulub impact site—this book provides a wonderful account of the unraveling of that mystery.

53,000,000 megatons is approximately the energy of the Chicxulub impact. A blast this size in the Mariana Trench creates kilometer-high waves that engulf the forests of Indonesia, California, and the Pacific Northwest, along with most of coastal China and the rest of the Pacific rim.

Huge volumes of rock and water are blasted into space. The debris takes less than an hour to encircle the Earth. As the chunks of rock fall back into the atmosphere, they heat to a glow—like meteors—igniting global firestorms. The hole fills in, with huge columns of steam and great convulsions.

The Mariana Trench is gone, and with it Guam and the Mariana Islands. The area is now marked by a 100-kilometer-wide scar of magma sizzling beneath the waters of the Pacific.

The majority of the world’s plants die and the food chain collapses completely. Between the famine and the fires, most life on Earth is wiped out.

Stupid cat.

the cat which just destroyed the planet licks its paw

Short Answer Section

In today’s article, I give short answers to several reader questions.

How long would the Sun last if a giant water hose were focused upon it? My sixth grade brother, Adam, asked me this.

Short Answer Section

In today’s article, I give short answers to several reader questions.

How long would the Sun last if a giant water hose were focused upon it? My sixth grade brother, Adam, asked me this.

—Austin Dickey

Your brother might be surprised to learn that the water would actually make the Sun hotter!

austin's sixth grade brother, adam, waters the sun

Water is made of hydrogen and oxygen, which is fuel for the Sun’s fusion. But more importantly, the extra mass also makes the Sun heavier. This crushes it together more tightly and makes fusion happen faster. This means it will burn more brightly and run through its fuel more quickly.

As you keep adding water, the Sun will go through a lot of wacky fusion phases. (During one phase, called a helium flash, the reaction rate is proportional to the 40th power of the temperature—which is probably the largest exponent I’ve ever seen in a physics equation!)

But one way or another, eventually the whole thing will collapse in on itself, blow off its outer layers, and become a black hole. This black hole will keep soaking up water, spraying off X-rays in the process, until finally the municipal water department notices what you’ve been doing and shuts off your service.

What if you shined a flashlight (or a laser) into a sphere made of one-way mirror glass?

—Chase Montgomery

Believe it or not, you’ve been lied to all your life—there’s no such thing as one-way mirror glass.

Glass either lets light through or reflects it, but there’s no glass that lets light through one way and reflects it the other way. The glass in police shows is partially reflective (on both sides).  The key is that the room on the prisoner’s side is brightly lit, so the reflection washes out the small amount of light from the observers’ side.

two people in a dark room look through one way glass at one person in a light room.

If Michael Phelps could hold his breath indefinitely, how long would it take for him to reach the lowest point in the ocean and back if he swam straight down and then straight back up?

—Jimmy Morey

He’d most likely black out and die somewhere between 100 and 400 meters.

michael phelps is unable to swim upward because his gold medals are too heavy.

The human body handles pressure remarkably well. With the right preparation, we can survive pressures over a dozen atmospheres. Different body systems break down at different depths, but one of the trickiest limits is created by High Pressure Nervous Syndrome. Below about 100 meters, divers become jittery and excitable (especially if the pressure increase is rapid), and at the same time begin slipping in and out of sleep. The reason may be direct pressure on the brain.

But let’s suppose Michael Phelps were immune to all those things. In that case, it simply becomes a question of speed.

There aren’t very many records for underwater swimming, but based on how quickly this guy completed the 50m backstroke, it would probably take Michael about ...

[ 2 imes ext{Depth of Marianas Trench} imes rac{23.1 extrm{ seconds}}{50 extrm{ meters}}approx3 extrm{ hours} ]

… to make the trip.

In the first Superman movie, Superman flies around Earth so fast that it begins turning in the opposite direction. This somehow turns back time [... ] How much energy would someone flying around the Earth have to exert in order to reverse the Earth's rotation?

—Aidan Blake

Someone recently blew my mind by telling me I’d been misinterpreting that scene all my life. I like their take on it way better:

Superman wasn't exerting a force on the Earth. He was just flying fast enough to go back in time. (Faster than light, I guess? Comic book physics.) The Earth changed direction because we were watching time run backward as he traveled. It didn't actually have anything to do with the direction he was flying.

Now that I see it, it makes a lot more sense. I mean, as much sense as a red-cape-and-outside-underwear time traveler can make.

A discussion of the reversal of the Earth’s spin—and what that even means—will have to wait for another article.

How fast would you have to go in your car to run a red light claiming that it appeared green to you due to the Doppler Effect?

—Yitzi Turniansky

[ rac{ ext{Red light wavelength}}{ ext{Green light wavelength}}=sqrt{ rac{1+ rac{ ext{Your speed}}{ ext{Speed of light}}}{1- rac{ ext{Car speed}}{ ext{Speed of light}}}} ]

[ extrm{Car speed}= rac{ extrm{Speed of light} imesleft ( extrm{Red light wavelength}^2- extrm{Green light wavelength}^2 ight )}{ extrm{Green light wavelength}^2+ extrm{Red light wavelength}^2} ]

What would happen if you opened a portal between Boston (sea level) and  Mexico City (elev. 8000+ feet)?

—Jake G.

Bernoulli’s principle gives us this estimate of the air flow rate:

[ ext{Flow rate}=sqrt{2 imes rac{ ext{Sea level pressure}- ext{Mexico City pressure}}{ ext{Density of air}}}=440 extrm{ mph} ]

That’s fast enough to strip up the pavement from a parking lot. I suggest we put it in Kendall Square—the MIT folks are probably used to dealing with this kind of thing.

When my wife and I started dating she invited me over for dinner at one time. Her kitchen had something called Bauhaus chairs, which are full of holes, approx 5-6 millimeters in diameter in both back and seat. During this lovely dinner I was forced to liberate a small portion of wind and was relieved that I managed to do so very discretely. Only to find that the chair I sat on converted the successful silence into a perfect, and loud, flute note. We were both (luckily) amazed and surprised and I have often wondered what the odds are for something like that happening. We kept the chairs for five years but despite laborious attempts it couldn't be reproduced.

—R. D.

This ... isn’t actually a question.

i don't know how all these words got on my screen.

But thank you for sharing!

Laser Pointer

If every person on Earth aimed a laser pointer at the Moon at the same time, would it change color?

Reposted bynichimtaktsqampydanielbohrernilsfFreXxXdingens

Laser Pointer

If every person on Earth aimed a laser pointer at the Moon at the same time, would it change color?

—Peter Lipowicz

Not if we use regular laser pointers.

The first thing to consider is that not everyone can see the Moon at once. We could gather everyone in one spot, but we learned our lesson about that a few weeks ago. Instead, let’s just pick a time when the Moon is visible to as many people as possible. Since about 75% of the world’s population lives between 0°E and 120°E, we should try this while the Moon is somewhere over the Arabian Sea.

We can try to illuminate either a new moon or a full moon. The new moon is darker, making it easier to see our lasers. But the new moon is a trickier target, because it’s mostly visible during the day—washing out the effect.

Brightness aside, an ideal time would probably be 2:00 PM EST on December 27th, 2012, when a full moon will be high in the sky above Mumbai and Islamabad. At that point, the Moon will be visible to approximately five billion people—most of Asia, Europe, and Africa—about as many as can ever see it at one time.

But let’s pick a quarter moon instead, so we can see the effect on the dark side. We’ll avoid the December 21st quarter moon to avoid encouraging any Mayan nonsense, and pick the one on January 4th, 2013, half an hour after midnight (GMT). It’ll be day in East Asia but night in Africa and Europe.

Here’s our target:

the moon, half lit by light from the sun and half dark because the moon is in the way

The typical red laser pointer is about 5 milliwatts, and a good one has a tight enough beam to actually hit the Moon—though it’d be spread out over a large fraction of the surface when it got there. The atmosphere would distort the beam a bit, and absorb some of it, but most of the light would make it.

a dotted line shows that a laser pointer's beam would cover part of the moon's face

Let’s assume everyone has steady enough aim to hit the Moon, but no more than that, and the light is spread evenly across the surface.

At half an hour after midnight (GMT), everyone aims and presses the button.

This is what happens:

people aim laser pointers at the moon. there is no visible effect.

Well, that’s disappointing.

It makes sense, though. Sunlight bathes the Moon in a bit over a kilowatt of energy per square meter. Since the Moon’s cross-sectional area is around 10^13 square meters, it’s bathed in about 10^16 watts of sunlight—ten petawatts, or two megawatts per person—far outshining their five milliwatt laser pointer. There are varying efficiencies in each part of this system, but none of it changes that basic equation.

a man in a hat suggests trying more power.

5 milliwatts is wimpy. We can do better.

A 1-watt laser is an extremely dangerous thing. It’s not just powerful enough to blind you—it’s capable of burning skin and setting things on fire. Obviously, they’re not legal for consumer purchase in the US.

Just kidding! You can pick one up for $300.

So suppose we spend the $2 trillion to buy one-watt green lasers for everyone. (Memo to presidential candidates: this policy would win my vote.) In addition to being more powerful, green laser light is nearer to the middle of the visible spectrum, so the eye is more sensitive to it and it seems brighter.

Here’s the effect:

people aim more powerful laser pointers at the moon. there is no visible effect.

Dang.

The laser pointers we’re using put out about 150 lumens of light (more than most flashlights) in a beam 5 arc-minutes wide. This lights up the surface of the Moon with about half a lux of illumination—compared to about 130,000 lux from the sun. (Even if we aimed them all perfectly, it would only manage half a dozen lux over about 10% of the Moon’s face.)

By comparison, the full moon lights up the Earth’s surface with about one lux of illumination—which means that not only would our lasers be too weak to see from Earth, but if you were standing on the Moon, the laser light on the landscape would be fainter than Moonlight is to us on Earth.

a man in a hat suggests trying more power.

With advances in lithium batteries and LED technology over the last ten years, the high-performance flashlight market has exploded. But it’s clear that flashlights aren’t gonna cut it. So let’s skip past all of that and give everyone a Nightsun.

You may not recognize the name, but chances are you’ve seen one in operation: It’s the searchlight mounted on police and Coast Guard helicopters. With an output on the order of 50,000 lumens, it’s capable of turning a patch ground from night to day.

The beam is several degrees wide, we’ll want some focusing lenses to get it down to the half-degree needed to hit the Moon.

Here’s the effect:

people aim Nightsuns at the moon. there might be a visible effect. it's hard to say.

It’s hard to see, but we’re making progress! The beam is providing 20 lux of illumination, outshining the ambient light on the night half by a factor of two! However, it’s quite hard to see, and it certainly hasn’t affected the light half.

a man in a hat suggests trying more power.

Let’s swap out each Nightsun for an IMAX projector array—a 30,000-watt pair of water-cooled lamps with a combined output of over over a million lumens.

people aim IMAX projectors with lenses on them at the moon. there's little visible effect.

Still barely visible.

a man in a hat suggests trying more power.

At the top of the Luxor Hotel in Las Vegas is the most powerful spotlight on Earth. Let’s give one of them to everyone.

a battery of luxor hotels fires beams of light at the moon. the light is slightly visible on the dark side.

Oh, and let’s add a lens array to each so the entire beam is focused on the Moon:

a battery of luxor hotels with lenses fires beams of light at the moon. the dark side is visibly illuminated.

Our light is definitely visible, so we’ve accomplished our goal! Good job, team.

a man in a hat suggests trying more power.

… Well.

The Department of Defense has developed megawatt lasers, designed for destroying incoming missiles in mid-flight.

The Boeing YAL-1 was a megawatt-class chemical oxygen iodine laser mounted in a 747. It was an infrared laser, so it wasn’t directly visible, but we can imagine building a visible-light laser with similar power. Let’s give one to everyone.

a fleet of aircraft fire megawatt lasers at the moon. the dark side is nearly as bright as the light side.

Finally, we’ve managed to match the brightness of sunlight!

We’re also drawing five petawatts of power, which is double the world’s average electricity consumption.

a man in a hat suggests trying more power.

Ok, let’s mount a megawatt laser on every square meter of the surface of Asia. Powering this array of 50 trillion lasers would use up Earth’s oil reserves in approximately two minutes, but for those two minutes, the Moon would look like this:

a field of megawatt lasers covering asia fires at the moon

The Moon shines as brightly as the midmorning sun, and by the end of the two minutes, the lunar regolith is heated to a glow.

a man in a hat suggests trying more power.

Ok, let’s step even more firmly outside the realm of plausibility.

The most powerful laser on Earth is the confinement beam at the National Ignition Facility, a fusion research laboratory. It’s an ultraviolet laser with an output of 500 terawatts. However, it only fires in single pulses lasting a few nanoseconds, so the total energy delivered is about equivalent to a quarter-cup of gasoline.

Let’s imagine we somehow found a way to power and fire it continuously, gave one to everyone, and pointed them all at the Moon. Unfortunately, the laser energy flow would turn the atmosphere to plasma, instantly igniting the Earth’s surface and killing us all.

But let’s assume that the lasers somehow pass through the atmosphere without interacting.

Under those circumstances, it turns out Earth still catches fire. The reflected light from the Moon would be four thousand times brighter than the noonday sun. Moonlight would become bright enough to boil away Earth’s oceans in less than a year.

But forget the Earth—what would happen to the Moon?

The laser itself would exert enough radiation pressure to accelerate the Moon at about one ten millionth of a gee. This acceleration wouldn’t be noticeable in the short term, but over the years, it adds up to enough to push it free from Earth orbit.

… If radiation pressure were the only force involved.

40 megajoules of energy is enough to vaporize a kilogram of rock. Assuming Moon rocks have an average density of about 3 kg/liter, the lasers would pump out enough energy to vaporize four meters of lunar bedrock per second:

[ rac{5 ext{ billion people} imes 500 rac{mathrm{terawatts}}{ ext{person}}}{pi imes ext{Moon radius}^2} imes20 rac{mathrm{megajoules}}{mathrm{kilogram}} imes 3 rac{mathrm{kilograms}}{mathrm{liter}}approx4 rac{mathrm{meters}}{ ext{second}}]

However, the actual lunar rock won’t evaporate that fast—for a reason that turns out to be very important.

When a chunk of rock is vaporized, it doesn’t just disappear. The surface layer of becomes a plasma, but that plasma is still blocking the path of the beam.

Our laser keeps pouring more and more energy into the plasma, and the plasma keeps getting hotter and hotter. The particles bounce off each other, slam into the surface of the Moon, and eventually blast away into space at a terrific speed.

This flow of material effectively turns the entire surface of the Moon into a rocket engine—and a surprisingly efficient one, too. Using lasers to blast off surface material like this is called laser ablation, and it turns out to be a promising method for spacecraft propulsion.

The Moon is massive, but slowly and surely the rock plasma jet begins to push it away from the Earth. (The jet would also scour clean the face of the Earth and destroy the lasers, but we’re pretending for the moment that they’re invulnerable.) The plasma also physically tears away the lunar surface, a complicated interaction that’s tricky to model.

But if we make the wild guess that the particles in the plasma exit at an average speed of 500 kilometers per second, then it will take a few months for the Moon to be pushed out of range of our laser. It will keep most of its mass, but escape Earth’s gravity and enter a lopsided orbit around the sun.

Technically, the Moon won’t become a new planet, under the IAU definition of a planet. Since its new orbit crosses Earth’s, it will be considered a dwarf planet like Pluto. This Earth-crossing orbit will lead to periodic unpredictable orbital perturbation.  Eventually it will either be slingshotted into the Sun, ejected toward the outer Solar System, or slammed into one of the planets—quite possibly ours. I think we can all agree that in this case, we’d deserve it.

Scorecard:

everyone fires 500-terawatt lasers at the moon. the moon leaves.

And that, at last, is enough power.

Raindrop

What if a rainstorm dropped all of its water in a single giant drop?

Raindrop

What if a rainstorm dropped all of its water in a single giant drop?

—Michael Mcneill

It’s midsummer. The air is hot and heavy. Two old-timers sit on the porch in rocking chairs.

two old people sitting on a porch that is attached to a house that is on the ground

On the horizon to the southwest, ominous-looking clouds begin to appear. The towers build as they draw closer, the tops spreading out into an anvil shape.

dark clouds emerge in the the corner of the sky (above the house)

They hear the tinkling of wind chimes as gentle breeze picks up. The sky begins to darken.

Air holds water. If you walled off a column of air, from the ground up to the top of the atmosphere, and then cooled the column of air down, the moisture it contained would condense out as rain. If you collected the rain in the bottom of the column, it would fill it to a depth of anywhere between zero and a few dozen centimeters. That depth is what we call the air’s total precipitable water.

a diagram showing two views of a column connecting the ground and space. the clouds trapped in the column turn to rain, which fills up the bottom of the column.

Normally, the TPW is one or two centimeters.

Satellites measure this water vapor content for every point on the globe, producing some truly beautiful maps.

We’ll imagine our storm measures 100 kilometers on each side and has a high TPW content of 6 centimeters. This means the water in our rainstorm would have a volume of:

[100 extrm{km}^2 imes6 extrm{cm}=0.6 extrm{km}^3]

That water would weigh 600 million tons (which happens to be about the current weight of our species). Normally, a portion of this water would fall, scattered, as rain—at most, 6 centimeters of it.

In this storm, all that water instead condenses into one giant drop, a sphere of water over a kilometer in diameter. We’ll assume it forms a couple kilometers above the surface, since that’s where most rain condenses.

a diagram showing, from bottom to top: ground, air, cloud, and a sphere of water two kilometers up, within the cloud

The drop begins to fall.

For five or six seconds, nothing is visible. Then, the base of the cloud begins to bulge downward. For a moment, it looks a little like a funnel cloud is forming. Then the bulge widens, and at the ten-second mark, the bottom of the drop emerges from the cloud.

the edge of the sphere of water pokes out of the bottom of the cloud

The drop is now falling at 90 meters per second (200 mph). The roaring wind whips up the surface of the water into spray. The leading edge of the droplet turns to foam as air is forced into the liquid. If it kept falling for long enough, these forces would gradually disperse the entire droplet into rain.

Before that can happen, about 20 seconds after formation, the edge of the droplet hits the ground. The water is now moving at over 200 m/s (450 mph). Right under the point of impact, the air is unable to rush out of the way fast enough, and the compression heats it so quickly that the grass would catch fire if it had time.

Fortunately for the grass, this heat lasts only a few milliseconds because it’s doused by the arrival of a lot of cold water. Unfortunately for the grass, the cold water is moving at over half the speed of sound.

the edge of the sphere of water touches the ground

If you were floating in the center of this sphere during this episode, you wouldn’t have felt anything unusual up until now. It’d be pretty dark in the middle, but if you had enough time (and lung capacity) to swim a few hundred meters out toward the edge, you’d be able to make out the dim glow of daylight.

a person floats in darkness

As the raindrop approached the ground, the buildup of air resistance would lead to an increase in pressure that would make your ears pop. But seconds later, when the water contacted the surface, you’d be crushed to death—the shock would briefly create pressures exceeding those at the bottom of the Marianas Trench.

The water plows into the ground, but the bedrock is unyielding. The pressure forces the water sideways, creating a supersonic omnidirectional jet that destroys everything in its path.

supersonic omnidirectional jets (of water) shoot out from the base of the droplet in all directions

The wall of water expands outward kilometer by kilometer, ripping up trees, houses, and topsoil as it goes. The house, porch, and old-timers are obliterated in an instant. Everything within a few kilometers is completely destroyed, leaving a pool of mud down to bedrock. The splash continues outward, demolishing all structures out to distances of 20 or 30 kilometers. At this distance, areas shielded by mountains or ridges are protected, and the flood begins to flow along natural valleys and waterways.

The broader region is largely protected from the effects of the storm, though areas hundreds of kilometers downstream experience flash flooding in the hours after the impact.

News trickles out into the world about the inexplicable disaster. There is widespread shock and puzzlement, and for a while, every new cloud in the sky causes mass panic. Fear reigns supreme as the world fears rain supreme, but years pass without any signs of the disaster repeating.

Atmospheric scientists try for years to piece together what happened, but no explanation is forthcoming. Eventually, they give up, and the unexplained meteorological phenomenon is simply dubbed a “Skrillex Storm”—because, in the words of one researcher, “It had one hell of a drop.”

Droppings

If you went outside and lay down on your back with your mouth open, how long would you have to wait until a bird pooped in it?

Droppings

If you went outside and lay down on your back with your mouth open, how long would you have to wait until a bird pooped in it?

—Adrienne Olson

Answer:

[ ext{Period}= rac{1}{ ext{Frequency}}= rac{1}{ rac{300 ext{ billion birds}}{4pi imes ext{Earth radius}^2} imes 1 rac{ rac{ ext{poop}}{ ext{bird}}}{ ext{hour}} imes16 rac{ ext{hours}}{ ext{day}} imes 1 rac{ ext{mouth}}{ ext{poop}} imes 15 rac{ ext{ cm}^2}{ ext{mouth}}}=195 ext{ years}]

Unit cancellation is weird.

Of course, that equation makes a few simplifying assumptions.

It assumes there are 300 billion birds in the world. This number comes from the best-titled source ever—“How many birds are there?”, an actual academic paper published in 1996 in the journal Biodiversity and Conservation.

The equation also assumes birds are randomly distributed across the Earth’s surface (they’re not) and that they poop an average of once an hour at a random location (they don't, although having owned a bird, I can tell you that’s probably more accurate than you might think). In the real world, the time would vary tremendously. For example, if the spot you pick is in a park under a tree, it could turn out to be a matter of hours.

the questioner awaiting bird poop.

However long it takes, though, one thing is certain: Given the relative areas of your mouth and your body, by the time they do finally get your mouth, the rest of you will have been hit an average of several hundred times.

I have to say—from a dimensional analysis standpoint, ”poops” is one of the strangest units I’ve ever tried to cancel in an equation. But there’s another case of odd unit cancellation, common in everyday life, which is—in a way—even weirder: Gas mileage.

In the US, we measure fuel economy in miles/gallon—which could just as easily be written as gallons/mile. (This reciprocal form has some advantages. It’s popular in Europe, where it’s expressed as liters per 100 kilometers.)

But regardless of which units you use, there’s something strange going on here. Miles are units of length, and gallons are volume—which is ( ext{length}^3). So gallons/mile is ( rac{ ext{length}^3}{ ext{length}}). That’s just ( ext{length}^2).

Gas mileage is measured in square meters.

You can even plug it into Wolfram|Alpha, and it’ll tell you that 20 MPG is about 0.1 square millimeters (roughly the area of two pixels on a computer screen).

Unit cancellation is weird.

Ok, so what’s the physical interpretation of that number? Is there one?

It turns out there is! If you took all the gas you burned on a trip and stretched it out into a thin tube along your route, 0.1 square millimeters would be the cross-sectional area of that tube.

a diagram showing a tube of gas stretched along a car's route.

In conclusion:

If the average bird produces half a fluid ounce of poop a day, and Americans drive about 3 trillion miles a year, then in order to satisfy US demand, cars that ran on bird poop would need to get a minimum of:

[ rac{300 ext{ billion birds} imes 0.5 rac{ ext{fluid oz}}{ ext{day}}}{3 ext{ trillion} rac{mathrm{miles}}{ ext{year}}}=0.335 mathrm{ mm}^2 = 13 ext{ miles per gallon}]

Unit cancellation is weird.

Cassini

What would the world be like if the land masses were spread out the same way as now - only rotated by an angle of 90 degrees?

Cassini

What would the world be like if the land masses were spread out the same way as now - only rotated by an angle of 90 degrees?

—Socke

It would profoundly alter our biosphere in general and public radio in particular.

Socke asks what would happen if the Earth’s surface were slid around by 90 degrees, putting our current North and South Poles on the equator. We’re not changing the tilt of the Earth’s axis; we’re just imagining that the surface were arranged differently.

a diagram showing the new location of the equator and the poles

We’ll pick the Greenwich meridian for our new equator, putting the new North and South poles in the Indian ocean (0N, 90E) and off the coast of Ecuador (0N, 90W). India, Indonesia, and Ecuador would become polar, while Europe, Antarctica, and Alaska would become tropical.

Where would the deserts and forests be? What areas would get better or worse?

This stuff is complicated. In a moment, we'll start using wild speculation to reshape the face of the planet. But first, a brief story to illustrate just how mind-bogglingly complicated this stuff is:

In Chad, on the southern outskirts of the Sahara, there’s valley called the Bodélé Depression. It was once a lakebed, and the dry dust in the valley floor is full of nutrient-rich matter from the microorganisms that lived there.

From October to March, winds coming in from the east are pinched between two mountain ranges. When the surface winds climb over 20 mph, they start picking up dust from the valley. This dust is blown westward, all the way across Africa, and out over the Atlantic.

That dirt—from one small valley in Chad—supplies over 50% of the nutrient-rich dust that helps fertilize the Amazon rainforest.

At least, according to that one study. But if it's right, it wouldn’t be a crazy anomaly. This kind of complexity is found everywhere. The basic building blocks of our world are crazy.

This is why we can be so certain about large-scale patterns like global warming, where we understand the overall physics pretty well—energy comes in, less energy goes out, so the average temperature rises—but have a harder time predicting how it will affect any particular place or specific species.

So even if I were a climate expert—which I’m definitely not—there’d be no way to answer this question with certainty. There are just too many variables. Instead, think of what follows as a rough sketch of some of the things this alternate Earth could contain.

To start, here’s a map of our reshuffled world:

a map of the reshuffled earth, with asia, africa, and most of antarctica north of the equator and north and south america south of it.

(An equirectangular projection, by the way. This type of equirectangular projection, centered on a north-south meridian instead of the equator, is specifically called a Cassini projection, so a good name for our alternate Earth might be "Cassini".)

Let’s imagine that this alternate Earth develops over millions of years, with ecosystems and climate zones settling out. Then one day we wake up to find our current civilization has been magically transported there—cities and all. What would they find?

The climate on the rotated Earth would depend heavily on the details of ocean and atmospheric heat circulation. We'll guess at some of that, but for now, let's assume this world has extremes which are similar to ours.

So let's add some ice and permafrost near the poles and in mountainous areas:

a map showing ice near the poles and mountainouse areas, shown with a light blue color

Next, we should fill in some green areas and deserts. The locations of these depend heavily on rainfall, so we’ll need to sketch out some winds.

The main driver of our weather is the sun, which heats air near the equator more than at the poles. Hot air rises at the equator and then flows poleward, and cooler air moves in across the surface toward the equator. This circulation is called a Hadley cell.

illustration of a hadley cell

Hadley cells shift north and south of the Equator with the seasons. At this time of year on our Earth, the sun is directly overhead at about 10°N, which is why hurricanes are forming near that latitude right now.

Because of the Coriolis effect, the surface winds in a Hadley cell flow from east to west. Further north, for most of the temperate zones, the prevailing surface winds are west to east. (At times, there are also east-to-west winds circulating around the poles.)

So let’s fill in some wind patterns—keeping in mind that in reality things would be further complicated by land interactions and the location of persistent high and low pressure systems.

a map with the new wind patterns

Sinking air is cool and dry, so land under the outer edges of the Hadley cells tends to be arid. These regions, lying a bit poleward of 30 degrees, are known as the horse latitudes.

map showing air movement with horse latitudes labeled

The rising air at the equator carries moisture from the ocean, which then condenses into rain, so tropical areas are usually wet and thick with growth. Areas near the equator are sometimes dominated by a seasonal monsoon cycle.

In temperate zones, things are more variable. Weather there is dominated by the movement of jet streams and fronts, and depends heavily on geography. Most of the United States is in this type of region.

With all that in mind, let’s fill in some arid and lush areas:

the same map filled in with various lush (green) and arid (yellow) areas

(Climates can be hard to predict—for example, in our world, Somalia and French Guiana both sit on the equator, at the eastern coast of a continent, and seem like they should both receive a tropical sea breeze. But coastal French Guiana is dense rain forest while coastal Somalia is an arid desert. The explanation involves the monsoon cycle.)

And just for fun, here’s a wild guess as to where the hurricane basins would be:

the same map with swaths of red to show where hurricanes might occur

Let’s take a closer look at each continent.

North America has a range of climates similar to what it had before, but flipped north-south. The Arctic Canadian provinces are now tropical, while Central America is icy and polar. Hurricanes threaten Greenland, Baffin Island, and the Maritimes. Tropical moisture from Baffin Bay and the northwest (formerly north) Atlantic mixes with cool air flowing down through the US from the Rockies, creating a new Tornado Alley in the prairies inland from Hudson Bay.

South America looks sort of like the old Europe. It's cool and temperate along the Brazilian coast, with boreal forests and grasslands across much of its width. In the south, the boreal vegetation gives way to polar tundra, and eventually to the massive icebound Andes, which cut the continent off from the frozen polar waters. The Amazon, which in our world carries more water than the next seven largest rivers put together, is reduced to something akin to the Mississippi.

Asia is flipped in the same way North America was, with the Siberian coast facing an enclosed tropical sea. The Indian subcontinent and north (formerly southeast) Asia form the new Siberia. The Gobi Desert is no longer in the rain shadow of the Himalayas, but doesn't exactly become tropical.

Europe resembles the old southeast Asia. Great Britain and Ireland look like the Indonesian islands of Sumatra and Borneo. Iceland resembles our Philippines. Central Europe is the new New Guinea, with the Alps the only place on the Equator with permanent glaciers.

Africa is rotated 90 degrees, with south (formerly west) Africa becoming tropical rainforest and north (formerly east) Africa an arid desert. On our Earth, North America is the only continent where tornadoes are common, but in this world, they're frequent in East Africa as well.

Australia is cooler and wetter, with forests across the northern (formerly western) regions.

Antarctica is a clear winner. Without its ice cap, it’s a bit smaller than we remember, but most of it is blanketed with highland rainforest. There are alpine zones around the mountains to the south and west. The researchers at McMurdo and Scott Base on Ross Island wake up to a tropical paradise. If any of them find they miss the frozen wastelands, they can always put in for a transfer to Costa Rica.

Now, let’s see how the world’s largest cities fare:

the same map showing where some maor cities would now be located

Some cities get colder.

Mexico City, high in the polar mountains, is buried beneath an ice sheet.

Jakarta is the new Svalbard—a desolate coastal rock too far north even for most Norwegians.

Kolkata and Delhi are icebound, sealed off from the warmer world by the Himalayas.

Hong Kong, Manila, Karachi, and Mumbai are similar to our world’s Anchorage or Reykjavik—the ocean isn’t frozen, but it sure is cold.

A few cities remain perfectly habitable, albeit with some changes:

Seoul, Osaka, Tokyo, Shanghai, and New York City are among the least-affected cities, with climates roughly similar to their previous ones. Shanghai does get colder, but seasonal extremes in all five cities get milder—particularly in Seoul—and substantially wetter.

Cairo is moved slightly south. It’s now surrounded by coastal savannah, with spots of rain forest found around the mouth of the Nile. Though it moves closer to the equator, it doesn’t actually get hotter.

São Paulo and Buenos Aires cool down a bit. They’re now on the northern coast of a South America, which occupies a Canadalike range of latitudes. Their climate is somewhere between that of our New England and that of our Regular England.

Los Angeles is cool and mild. The steady sea breeze carrying moisture up into the San Gabriel mountains makes LA one of the rainiest places in the new US. It closely resembles a wetter version of our Seattle.

And a few cities get much hotter.

Moscow is extremely hot and very dry, with a climate somewhere between our Phoenix and our Baghdad. Russians, who have been surviving in Russia for centuries, shrug with resignation.

London sits in a steamy jungle straddling the equator, with a climate generally resembling Manila's. The food is still bland, the Thames is full of piranha, and it's the only place on Earth where tigers apologize as they attack you.

At the beginning, I mentioned the impact on public radio. To explain, let’s consider one more scenario. Namely, what if this change were made on our Earth, over a fairly short time?

We’re assuming that all the material is magically shifted around, so there are no massive tsunamis or earthquakes. Even so, it would definitely still be a catastrophe. For starters, the ice caps would melt long before new ones could develop, pushing the ocean up by a few hundred feet. The reshuffling of climate zones would come as a huge shock to the biosphere, leading to collapse of the food chain and eventually to mass extinctions at every level.

But if the shift happened just right—and Michael Bay were telling the story—then as the waters of the Gulf of Mexico began to cool and the Mississippi slowed and became an estuary, the region’s wildlife would spread inland.

And one morning, Minnesotans would wake up to the sight of floating rafts of fire ants, followed by five million lost, hungry alligators …

the same map showing arrows labeled 'alligators' moving north into minnesota

… leading a harrowing, surprisingly bloody “News from Lake Wobegon” segment on what would become the final, fatal broadcast of A Prairie Home Companion.

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