## Saturday, February 7, 2015

### The Midgard Serpent: Why It Would and Wouldn't Work

A few weeks ago, I hastily wrote up and posted an idea for an absurdly mega-engineered energy project. Since then I've had a chance to check my figuring and do some more calculations, in an effort to determine whether or not it could work in principle or in practice.

Here's what I've come up with so far.

### Reasons That Are Not Reasons It Wouldn't Work

Yes they do.

Yes they would.

#### No, really. Tidal forces are tricky and hard to understand. Even many textbooks get their descriptions of how they work wrong. If you think the Serpent will be pulled around the earth because the moon's gravity is tugging on it, that's wrong.

Okay. Yes, I looked carefully (though hastily, at first) at the physics involved, but in the post I was trying to mimic the style of a science article in the popular press, so I didn't attempt the difficult task of explaining how it works with any precision.

The earth is affected by the moon's gravitational field. But the earth as a whole is in free-fall with respect to that field, so no one on earth feels the moon's pull. What we do feel (or would, if they were large enough to actually feel) are the variations in the moon's gravitational field over the volume of space the earth takes up. The lunar tidal force at any given point on (or in) the earth is the difference between the moon's pull at that particular point, and the moon's "average" pull on the entire earth. Due to the mathematics of how gravitation works, we can also say, with even more precision, that the lunar force is the difference between the moon's pull at the particular point in question, and the moon's pull at the center of the earth. That difference is felt as a pull itself, the "tidal differential" or "tidal force." A mass at that location, if it were freely able to move, would be accelerated by that pull.

The much larger and more familiar gravitational pull of the earth itself, at the earth's surface, causes an acceleration of 9.8 meters per second per second, straight down toward the earth's center. That value is also called 1g.

The lunar tidal pull at the point on the earth's surface closest to the moon is much smaller. It's about 1.13 x 10-7g, a little more than one ten-millionth of a g, and its direction is straight up toward the moon.

But that pull is different, and pulls in different directions, at other places on the earth's surface. To understand why those variations have the values and directions they do  takes a lot of explaining and/or a lot of mathematics, but the result is as shown in the diagram in the previous post. On the side of the earth farthest from the moon, the pull is directly away from the moon. At the equator ninety degrees from the earth-moon axis, the tidal differential is not toward the moon at all, but toward the center of the earth, with an acceleration of 5.65 x 10-8 g, which is exactly half of the previously mentioned upward pull. At 54.7° from the earth-moon axis, the pull is horizontal; that is, tangential to the earth's surface.

In the last post, I said the point where the pull is horizontal was at 45°, so consider this a correction. Also, I used 1x10-7g as the magnitude of that pull. I'm still refining the calculations on that, but the true value is about 20% less, about 8x10-8g. That decreases the energy output of the Midgard Serpent by at least that value, unless we compensate by making the vehicle denser or larger.

There's another problem: that value for the horizontal pull only applies at the point on the Serpent that's in that ideal 54.7° position. Everywhere else along the Serpent gets less. If the Serpent is thousands of miles long, its "head" and "tail" experience very little horizontal pull. There is at least some horizontal pull everywhere between zero degrees and ninety degrees, but it trails off toward zero at those extremes.

That being the case, how long should the Serpent be? The longer it is (up to about 6,000 miles), the more power it can produce in total, but the less power it produces per meter of its length. Given the expense of building the tunnel, it would probably make the most sense to make the Serpent as long as possible, up until the point where additional length would cause more power loss to additional friction than it would add in power produced. But that depends on the relative cost of the Serpent compared to its tunnel. A shorter Serpent could be more cost-effective.

In any case, if I keep the design as 5,000-mile-long Serpents, I have to reduce the estimate of the average tidal force on it by about half. So to keep it producing the amount of power described in the previous post, it would have to be twice as heavy. For instance, just under a mile and half in diameter instead of a mile.

That said, the main point is that the basic concept does work. The Serpent does get accelerated westward in the tunnel by the lunar tidal forces, and this could be used to generate power.

For more detailed information about the physics and mathematics of tides, see this white paper by Mikolaj Sawicki. Other treatments of the subject can be found here (by Donald E. Simanek) and here (by C. Johnson).

#### You'd have to expend energy to keep the Serpent magnetically levitated, so it would use more energy than it produced.

It takes energy to lift something by any means, whether by a crane or by magnetism. In the case of the Serpent, it would take a large amount of energy to lift it even the fraction of an inch it would be magnetically levitated. (Though it's a tiny amount of energy compared with the energy needed to get the Serpent up to operating speed—more on that later—so we can disregard it as a detail.)
But once something is lifted, it doesn't necessarily take energy to keep it lifted. It does, if it's a helicopter rotor or human muscle holding the thing up. But it doesn't, if the thing is kept lifted by setting it on a platform or hanging it from a cable or putting it into a stable orbit around the earth.

Ordinary electromagnets do require continuous power to hold an object in position.  (Permanent magnets, of course, do not.) Those giant electromagnets used to pick up cars in junkyards need 4.000 Watts or so. (Additional power, of course, is needed to lift the car once the magnet has grabbed it.) That power is needed because the electric current through the wire coils of the magnet that creates the magnetic field meets resistance in the wire and generates waste heat.

Superconducting magnets have no resistance and don't generate waste heat. So, once the Serpent is levitated to its operating height anywhere in the tunnel, no power is needed to maintain the magnetic fields that keep it levitated. Power is needed to keep the superconducting magnets cold, but that's a fixed amount that is in no way proportional to the amount of time or distance over which the Serpent remains levitated.

#### It would slow down the earth's rotation too much.

The previous post stated that the energy produced by the Midgard Serpent is extracted from both the rotational kinetic energy of the earth and the kinetic energy of the revolution of the moon around the earth. It also states that the energy loss would slowly increase the distance from earth to moon. That is incorrect. It turns out that the Midgard Serpent would actually add energy to the moon's orbit around the earth. Note the direction of the moon's revolution in the diagram. The gravity of the mass of the serpent at point A in the diagram attracts the moon by a small amount more so than the empty tunnel in the symmetrical position west of the earth-moon axis (up, in the diagram). That attraction pulls the moon ahead in its orbit.

The same would be true in the analogy of tying the moon to a train on a track around the equator with a long rope. The earth's surface rotates around its center in a twenty-eighth the time it takes the moon to revolve around the earth's center, in the same direction. So the rope connecting the moon to the train drags the train westward against the earth's rotation, and it drags the moon eastward in the direction of its revolution.

So, the operation of the Serpent would gradually add energy to the moon's orbit. It's that addition of energy, not a subtraction, that would cause the moon to move farther away from earth. The ocean tides do the same thing, and already cause the moon's distance from earth to increase by about an inch and a half per year.

That energy ultimately comes from the rotational energy of the earth. So does all the useful energy the Midgard Serpent produces. So what we really need to worry about is, what effect does this have on the rotation of the earth? Even though many people complain about not having enough time in a day to get everything done, slowing down the earth's rotation sounds like a really bad idea.

Let's imagine, then, that we've built not one but a number of Midgard Serpents, enough to generate power for a future population of ten billion people, all using the average power present-day Americans use. So we need, not fifteen terawatts, but 110 terawatts. Let's say that the Midgard Serpents are only 25% efficient, so to generate those 110 terawatts we actually have to extract 440 terawatts from the earth's rotational kinetic energy. And let's say we use that power continuously for 10,000 years.

How much longer would a day be, at the end of those 10,000 years?

The absolute amount of energy extracted during that time turns out to be 1.01 x 10^26 Joules. The earth's rotational kinetic energy is, at the start, 2.13 x 10^29 Joules. So the rotational energy is reduced by just under one fifteenth of one percent. Because the earth's rotation speed is proportional to the square of that energy, that decreases the rotation speed by about one thirtieth of one percent, adding twenty-eight seconds to each day.

Horologists will not be pleased by this, but it's hard to imagine that such a change spread out over ten millennia would have many adverse environmental effects. Compared with doubling the atmosphere's carbon dioxide content, which we're already well on the way to doing in a fiftieth of that time, it seems downright benign.

### Reasons That Might Be Reasons It Won't Work

#### Friction

The lateral tidal force that pushes the Serpent is minuscule compared to the weight of the Serpent. With my revised numbers, the pushing force averages about a half of a hundred-thousandth of a percent of the weight. A ratio of 5 x 10^-8 to 1.

Now, it's pretty clear that if the frictional and drag forces on the Serpent equal or exceed the pushing force, it won't generate any power. In fact, those forces must be significantly less, or else all the power the Serpent generates (or more) will be needed to get rid of the waste heat that friction and drag would cause. If a coefficient of friction (the friction and drag forces, as a fraction of the weight) less than about 1 x 10^-8 can't be achieved, then we might as well give it up, and to get reasonably close to the expected power output, we want to be closer to 5 x 10^-9. The Midgard Serpent will have to be an extraordinarily slippery beast, gliding through its tunnel with nary a rattle, whoosh, or squeal.

Can that be achieved? It seems possible. Coefficients of friction about 1 x 10^-8 have been reported for superconducting magnetically levitated bearings operating in vacuum. But those are small devices that rotate. There are good reasons to expect that a vastly larger machine, operating at high speeds but low accelerations, would experience considerably less friction and drag per unit of its mass. Friction and drag, including the exotic effects such as magnetic eddy currents that affect magnetic bearings, occur at surfaces and at places where the magnetic fields are changing. The Midgard Serpent has a lot of volume and a lot of length. Resistance from residual gas molecules in the tunnel would occur mostly at the Serpent's head, and magnetic field changes would occur mostly at its head and tail. Other sources of drag, such as the effect of the weight of the Serpent flexing the tunnel floor downward by a small amount, would follow that same pattern. The head and tail are such small portions of the overall length of the Serpent that the net effects on the whole mass would be small. For reasons analogous to the reasons a longer ship experiences less water drag relative to the size of the ship, the Midgard Serpent would indeed be extremely slippery overall.

However, this needs to be verified and tested. Analogy isn't proof. Friction could still be a show-stopper if I've overlooked anything.

#### Structural strength

If there's one aspect of the Midgard Serpent that uses verbal sleight of hand to make the impossible sound possible, it's the "mile in diameter" dimension (or worse, the "mile and a half" alternative mentioned above). That doesn't sound so big, especially compared to the miles-long starships (some of which can hover over entire cities doing no damage until they open fire) and miles-tall towers of our popular science fiction, or compared to the extreme length of the Serpent itself. Heck, compared to the Death Star or a Ringworld, the entire Serpent is miniscule.

But in reality, a cylinder of dense material a mile in diameter is huge. The problem is its height. How is it going to hold up under its own weight? What is going to support it from underneath?

The magnetic levitation makes no difference to these questions. Being levitated doesn't make it weightless. It still must hold up under its own weight, and whatever is underneath the magnets that levitate it must still support that weight as well. And the magnets themselves, in between, have to withstand the pressure as well, which could be a major problem given that most known superconducting materials are not very structurally strong.

The problem is, nothing that large and dense, no matter what it's made of, can be considered as completely solid. It would tend to deform under its own weight. Nothing stacked a mile high, except perhaps diamond, could stand. We can build skyscrapers a half a mile high or so, and it's believed to be possible to build them a mile high. But those are open frameworks filled mostly with air. Fill any skyscraper with solid rock and it would collapse. Stone or concrete or steel will deform under that weight. Even Egyptian pyramids bulge out on their sides due to the weight of the upper part pressing downward and outward on the base. (A pyramid built too steep can collapse, as most historians believe occurred with the pyramid at Medium, Egypt. It might seem strange that a tapered pile of blocks of stone could collapse, but if the sides start bulging, blocks near the base can shift out of place, allowing blocks above them to fall, resulting in a landslide-like progressive collapse of much of the structure.) And the Great Pyramid is a toy compared to a mile-diameter Midgard Serpent. You'd have to stack eleven and a half Great Pyramids on top of each other to reach a mile high.

Fortunately, the Serpent doesn't have to stand on a flat surface. It will be completely cradled in its tube, supported (by the levitating magnets) not just at the bottom but all around the lower half of its circumference. If the tube were similarly resting on the bedrock of the tunnel, there might not be a problem. The outward pressure generated by the weight of the Serpent would be balanced by the inward pressure of the weight of the bedrock around it. In fact, we'd have to worry about the opposite problem: the tube, during the times the Serpent isn't passing through it, being lighter than the surrounding bedrock and thus tending to gradually "float" upward.

However, as we'll see in the next section, there are reasons we'll probably have to support the tube inside a somewhat larger tunnel, with space between the outside of the tube and the walls of the tunnel. That's a problem because there's nothing strong enough to hold the tube up that way.

There is a solution, though: change the shape of the Serpent. The cylindrical shape sounds good and is convenient for some calculations, but the shape doesn't actually matter; only the total mass does. And because the toughest structural problems are caused by the height (the higher it is, the more pressure it exerts per unit area of its magnetic "tracks"), a flatter shape would solve many problems. A "tapeworm" version of the Serpent with a rectangular cross-section 415 feet high and ten miles wide would have the same mass for its length as a mile-diameter cylinder. Make it twenty miles wide, and it has the mass needed (with the revised figures above) to generate the 34 terawatts of power originally described. Multiple parallel smaller tunnels with two separate Serpents in each one could also be used, as long as the total mass comes out the same.

#### Plate Tectonics

Whatever the shape of its cross-section, the Midgard Serpent requires a tube that's essentially flawless, perfectly flat and smooth and regular. So much force would be required to cause it to make even the slightest turn (aside from the downward turn it's constantly making to follow the surface of the earth) that any wiggle in the tunnel could start a cascade of effects that would destroy the thing. (More on that later!)

The problem is, the earth's surface doesn't sit still. The path of the Serpent around the equator must pass through regions where continental plates are spreading apart, crunching together, and sliding past each other. These movements are usually very slow, a few centimeters per year, but the Serpent's sublimely slippery track can't be even a centimeter out of true, and we want it to run practically forever. (It has to run for years even to get up to operating speed. More on that later, too.)

This means the tunnel must, as mentioned above, be larger than the tube, and the tube must be supported within the tunnel with struts that can be gradually adjusted when the tunnel walls start shifting. Regular maintenance would have to include cutting away more tunnel wall wherever it tends to "drift" toward the tube.

That assumes, however, that the movements occur slowly and steadily. What if there are sudden movements instead? That is to say, earthquakes?

Earthquakes appear to be Midgard-Serpent-killers. All that mass just cannot be laterally shaken without potentially massive damage. However, a two-pronged strategy might be sufficient to address this problem: first, make the struts that support the tube within the tunnel shock absorbers. And second, release lubricant on the surface of the Serpent when unexpected accelerations occur. Normally such lubricant would be useless, because the Serpent doesn't touch the tube, But the lubricant would minimize the heat generated from friction if the Serpent did touch the tube due to vibrations during an earthquake, for the few seconds or minutes the earthquake is going on.

#### Its Own Tidal Effects

Consider what I said above about the portion of the Serpent positioned near 54.7° experiencing the most tidal acceleration, while the head and the tail experience less. That means the middle is being driven forward, and is actually pushing the head forward more than the head would be pushed by the tidal force alone. And it's also pulling the tail forward more than the tail would be pulled by the tidal force alone. As a result, the front half of the Serpent experiences compressive forces, while the back half is in tension.

Does this sound familiar? It should, because this is another example of tidal forces. And we have to account for them, because even though the acceleration differences are small, the amount of mass involved is large.

These forces do not pull the earth apart, because the earth has its own gravity pulling it together much more strongly. But that's not true of the long thin Serpent. And earth's gravity doesn't help pull the Serpent together, because it's in a nearly frictionless tube deliberately designed to minimize the effects of earth's gravity on it. As far as these particular tidal stresses on the Serpent are concerned, it might as well be floating in space by itself at earth's distance from the moon. Bodies that float in space near planets and moons aren't shaped like threads a mile wide and thousands of miles long, because such bodies would be broken apart by tidal forces.

There are two possible solutions to the stresses on the Serpent caused by differential tidal forces along its own length. One is to make the Serpent strong enough to handle those forces. The other is to adjust the dynamic magnetic braking that keeps the Serpent in position (and generates power), so that more braking is applied to the portions of the Serpent that experience the most tidal pull, which would even out the tidal forces. (During the period when the Serpent is being accelerated up to operating speed, a similar adjustment has to be made by providing the electromagnetic push in a way that balances the current tidal forces.)

That settled, there's another issue we have to consider. The mass of the Serpent itself is sufficient to cause a slight but noticeable gravitational attraction. (Similarly, the gravitational attraction of mountain ranges affects surveying instruments enough that surveyors have to take that phenomenon into account.)

So, imagine a Serpent speeding along in its tunnel beneath an ocean. As it passes, it attracts water toward it, causing a slight rise in the water level toward the rear of the Serpent. Once the Serpent passes, the water will flow away again, but this will take some time. So, the Serpent ends up essentially being followed by a mound of higher water that piles up behind it. That extra water, in turn, pulls gravitationally on the Serpent more than the lower water in front of it does, slowing the Serpent down. We can call this phenomenon the Serpent's "tidal wake." Like ordinary wake from a ship, this will extract energy from the Serpent, making it less efficient.

How much effect does the tidal wake have? That's a rather complex calculation, but we can get some idea by just looking at the strength of the Serpent's gravitational field. We can calculate that fairly accurately, and simply, by assuming that the Serpent is an infinitely long line of mass, which (as long as you're much closer to the Serpent than the Serpent's length) is a very close approximation of the truth. The formula that then applies is, g = 2Gd/r, where d is the mass per meter of Serpent length, G is the universal gravitational constant, r is the distance in meters from the Serpent, and g is the strength of the gravitational pull at that distance.

For the heavier version of the Serpent, 1.42 miles in diameter, at a 1.75 mile distance from the center of the serpent (or, about 1 mile from the tunnel wall), the Serpent's own gravitational pull is about half of a ten-millionth of a g, which is about the same as the average lunar gravitational pull on the Serpent itself, and about the same as the forces causing the ocean tides. So the Serpent will have a gravitational wake. But will it be large enough to impede the Serpent significantly?

The answer appears to be no. The lunar tides can cause the oceans to rise and fall by meters or more, but only because they act across thousands of miles of ocean simultaneously. Large lakes like the Great Lakes in the U.S., that experience the same kinds of forces, have very small tides that are usually not noticeable at all. The gravitational pull from the Serpent is comparable to the lunar tidal pull when the Serpent is right nearby, but it falls off with distance. Ten miles from the tunnel, the pull is only a tenth of the lunar pull. A hundred miles away, it's only a hundredth. That's not enough of a pull to attract a lot of water toward the Serpent in the time it takes the Serpent to pass by.

### The Real Reason the Serpent Doesn't Work

It's too big to build.

Let's consider some of the numbers. First of all, suppose the Serpents and the tunnel are completely built and ready, sitting in their tunnels, and it's time to get them up to speed. Let's say we have as much power available to put into accelerating the Serpents as the Serpents will eventually generate (which, keep in mind, is supposed to be the entire world's power needs). And let's say the process is an unrealistic 100% efficient. (Note that, until a Serpent is fully up to speed and in position, tidal forces don't help it to accelerate. They sometimes boost it a bit, and sometimes hold it back a bit, and those influences over time will average out to zero.) How long does it take to get the Serpents moving at the needed speed?

The answer is, fourteen years, plus a few months.

Is that for the original Serpent or the heavy Serpent? It turns out, it doesn't matter, as long as the power used to rev up the Serpent to operating speed is the same as the power it generates. If you allow for realistic inefficiencies and losses in both processes, it'll be more like thirty years.

If you don't have that much power to spare (and if you did, why would you need a Midgard Serpent?), then you can accelerate the Serpent up to speed more slowly, or you could power up a lighter version of the Serpent using proportionally less power, and then bootstrap from there, using the power the Serpent generates to accelerate more mass and add it to the Serpent in stages. Of course, adding mass to an already running Serpent inside its vacuum tunnel would require a rather complicated subsystem.

Either method would multiply the time it would take to get the Serpent generating power usable for something else. For instance, you could devote a fourth of the world's power to accelerating a one-quarter-full Serpent for thirty years, and then use all the Serpent's power over the next sixty years to double its mass twice over. After that, the Serpent would be producing abundant available power. Or, you could use a quarter of the world's power for 120 years.

That might seem like a long time, but it's probably a lot less time than it would take to build the tunnel in the first place. Machines that bore conventional tunnels achieve about ten meters per day under ideal conditions, but let's say we have one immense machine that can somehow cut a tunnel with an opening 17,000 times larger (or we have a fleet of 17, 000 smaller machines, the size of today's largest tunnel borers) at an unprecedented hundred meters a day. With no holidays, breakdowns, or labor strikes, it would take about 400,000 days to excavate the tunnel. or 1,100 years.

The good news is that there would be plenty of removed rubble to sift through to find all the iron and other materials needed to build the tube and the Serpents. (Some portion of the excavated stone can be used to provide most of the Serpents' mass. The rest could be used, perhaps, to create a chain of equatorial islands for use as maintenance stations.) The bad news is that the energy needed to drill (or blast) the tunnel, lift and transport it, and smelt the necessary steel and other metals, again dwarfs the energy the Serpent would generate over a few centuries.

Then there's building the Serpents themselves. Let's suppose we somehow come up with a way to drill a little over a kilometer (1,100 meters) a day (perhaps, using eleven fleets of tens of thousands of machines each, working on different sectors simultaneously, or maybe using nuclear blasts or something), reducing the tunnel building time to a mere 100 years. To complete two Serpents in that same time period, we'd need to build about 275 meters of Serpent a day. Each meter of the heavy (160 trillion tons total) Serpent has the volume of 1.6 Great Pyramids. So, we'd need to build the equivalent of 440 Great Pyramids every day to complete the Serpents in a century.

It's barely imaginable that by devoting a large portion of the world's resources and mechanized equipment to the task, we could build one Great Pyramid per day (most likely, in some sort of assembly line fashion, so that a few hundred are under construction at a time, and one is completed per day on average). Multiplying that by 100 or more, to complete a Serpent in a few centuries, is out of the question.

For the civilizations of science fiction, that have the scale of power sources needed to maneuver miles-long spaceships around like they were biplanes, building a Midgard Serpent might be child's play. But for anyone who actually needs the power the Serpent would generate, it's a (somewhat literal) pipe dream.

### By the way, what happens if it crashes?

That is a really interesting question. There's really nothing that we're familiar with that makes a good model for intuitive understanding of what happens if the Midgard Serpent were to escape its tunnel. Types of crashes that physicists have modeled in detail are all either much bigger (colliding planets, continental plates), much smaller (avalanches; artillery fire; plane crashes; progressive collapses of buildings), much slower or shorter distances (building collapses, continental plates, earthquakes, road and rail accidents), or much faster (asteroid impacts, colliding planets, colliding black holes).

Could a Midgard Serpent crash? Certainly. Imagine, for example, if some part of the tunnel collapsed. There would be no way to stop the Serpents in the tunnel, or even slow them down significantly, before one of them hit the obstruction (and eventually, got rear-ended by the other).

But it doesn't take that much. Imagine if the magnetic levitation fails. The friction of the Serpent on the floor of the tunnel would suddenly become enormous. Friction generates heat; the friction of a vehicle weighing as much as mountains against whatever surface it started grinding against would generate enough heat to instantly destroy any tunnel material and any support systems.

So, the Serpent grinds to a halt, doing enormous amounts of damage to a few hundred miles of tunnel, right? Well, no. The amount of kinetic energy in a full-speed Serpent is enormous. It's the mass of a major mountain range moving at the speed of a fighter plane. The kinetic energy is comparable to the kinetic energy of a 4-mile diameter asteroid striking the earth.

But it's not moving at a comparable speed. It's much slower. Physicists have a convenient shortcut for figuring out the effects of an asteroid impact. The collision is so rapid that nearly all the kinetic energy turns into heat all at the same time at the collision point. So, it's only necessary to determine the effects of that amount of heat being released. The original solid material of the asteroid becomes all but irrelevant. Most of it will vaporize, without the heat required to do that making a dent in the amount of heat released.

The Serpent is much more massive, but much slower, than an asteroid. It doesn't have enough kinetic energy to cause most of it to vaporize, or even melt.

But it also won't stop. Not quickly, not in a short distance like a mere few hundred or few thousand miles. Anything that tries to make it stop, anything that gets in its way, including any part of itself that does so, will be quickly pushed out of the way or crushed or melted or vaporized from the friction and pressure. Whatever is necessary to happen, for the rest of the Serpent's mass to keep going, will happen. Eventually, the second Serpent will catch up with the stricken one from behind, adding its own length and mass to the juggernaut. No matter what the front of the Serpent encounters, from hitting water if the tunnel floods to hitting solid rock, the massive inertia of the thousands of miles behind it will keep driving forward. So essentially, if it goes out of control, the Serpent becomes an enormous thermal-kinetic drill.

Does it destroy the world? In a word, no.

The reason it doesn't is because, as big as it is, it's very small compared with the world. My diagram depicted it as the width of a worm in a large apple. The caption does say "width [of the tunnel] not to scale," but it's hard to imagine how far out of scale it is. If you model the earth as a globe two and a half feet in diameter, the cylinder-shaped version of the Midgard Serpent, in the same scale, is the thickness of a human hair.

(That's why the scale of the Midgard Serpent is difficult to fathom. On the scale of human artifacts, including iconic monuments like the Great Wall of China or the Great Pyramid of Giza or even entire modern cities, the Midgard Serpent is so much larger that we can't really compare them. But on the planetary scale, it's still so much smaller than the earth that we can't really compare them in that way either.)

But even though it won't devastate the earth, a crashed Midgard Serpent could do a lot of damage. Or very little. We'd need to run some elaborate simulations to figure out which, and it might also depend on exactly where and how it goes wrong.

The most likely possibility is that the Serpent continues to follow its tunnel, even after the tunnel has been severely damaged, until it grinds to a halt. The tunnel is likely to remain the path of least resistance. If that happens, all the kinetic energy of the Serpent will be turned directly into heat, except for causing minor tremors as it grinds its way along. That heat will end up distributed all along the thousands of miles of tunnel, rather than being concentrated in any one place, so the oceans won't boil and new volcanoes won't suddenly erupt all around the equator.

That's close to the best case scenario, though. A slightly better case might be if the Serpent grinds its way through the bottom of the tunnel and, under its own enormous weight, burrows deep into the earth.

However, there's another possibility that's just as likely. Though the Serpent is very heavy, it's not denser than the bedrock beneath it. So it wouldn't necessarily sink downward. Instead, depending on chance, it might drill its way upward, until it reaches the sea bed or the land surface.

If it emerges in the sea bed, it would be much like an undersea volcano, extruding hot (but not all molten) stone and metal that will pile up into a massive new island. The total mass of the Serpent is that of a major mountain range, so the island would likely rise above the ocean surface.

That much material spilling into an ocean all at once would be more than enough displacement  to cause devastating tsunamis in all directions, but it wouldn't emerge all at once. It would take several hours, unlike the rapid fault movements and landslides that normally cause tsunamis. Hours of earth tremors as this was going on would probably cause some problems in the surrounding coastal cities, but would not destroy them.

If the Serpent emerges on land, it would be the most spectacular geological event since perhaps the asteroid strike at the end of the Cretaceous period. It would burst out like Silly String scaled up to ridiculous proportions. A stream of land the size of mountains would erupt from the ground at supersonic speed, traveling for miles, possibly (depending on the angle) hurtling miles into the air, shaking the ground, continuing hour after hour, piling up a new major mountain range (or perhaps several smaller ones). Anything and anyone in its way, across (at least) thousands of square miles, would be so thoroughly destroyed and so deeply buried that Indiana Jones would be hard-pressed to find any trace of them afterward.

The total kinetic energy of the Serpents corresponds to the energy released by an earthquake measuring between 8,7 and 8.8 on the Richter scale. But it's difficult to compare the two, because an earthquake of that magnitude would release that energy over several minutes' time, while the Serpent would take at least several hours. The shaking would be less intense but more sustained.

When it was all over, the earth's rotation would be increased by a small but measurable fraction of a second.