© 2006 All Rights Reserved. Do not distribute or repurpose this work without written permission from the copyright holder(s).
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About four hundred years ago—sometime in the latter half of the 17th century—Isaac Newton received a letter from the brilliant British scientist and inventor Robert Hooke. In this letter, Hooke outlined the mathematics governing how objects might fall if dropped through hypothetical tunnels drilled through the Earth at varying angles. Though it seems that Hooke was mostly interested in the physics of the thought experiment, an improbable yet intriguing idea fell out of the data: a dizzyingly fast transportation system.
Hooke’s calculations showed that if the technology could be developed to bore such holes through the Earth, a vehicle with sufficiently reduced friction could use such a tunnel to travel to another point anywhere on the on Earth within three quarters of an hour, regardless of distance. Even more amazingly, the vehicle would require negligible fuel. The concept is known as the Gravity Train, and though it seems inconceivably difficult to construct, it has received some serious scientific attention and research in the intervening centuries.
The basic concept behind the gravity train is straightforward: At each end of the tunnel, an observer looking into the hole would see a downhill slope. If a train at one end of the tunnel were to release its brakes, the force of gravity would immediately pull the train downhill and cause the train to accelerate much like a roller coaster. Steeper slopes would result in more speed, with the highest acceleration occurring in the straight-down tunnels which cross the Earth’s center. The train would continue to accelerate until reaching the halfway point, at which time its inertia would be at odds with gravity and it would begin to decelerate. As Hooke’s data indicates, if the train operated in a frictionless environment it would reach the surface on the opposite end of the tunnel at the exact moment that its speed reached zero. Naturally, a gravity train operating in a real-world environment would need to bring along enough horsepower to make up the friction loss.
One interesting property of the Gravity Express is that its transit time would always be very, very close to forty-two minutes regardless of the distance travelled. In fact, if the Earth were a perfect sphere, the trip time would always be exactly forty-two minutes and twelve seconds. Greater distances would be traversed in the same amount of time as short ones because the train’s maximum speed would be increased enough to exactly make up the difference. Due to nature of gravity, this forty-two minute trip time would be consistent for any size of vehicle.
Consider a hypothetical Gravity Express station in Spain which connects to a sister station in New Zealand. The tunnel would be straight down because its route would intersect with the Earth’s center, making for an interesting departure as the train entered sudden free-fall. The vehicle would accelerate to a maximum velocity of about 17,670 miles per hour before beginning to decelerate, and it would travel in a straight line for 7,920 miles—a trip which would be 12,440 miles on the surface. Forty-two minutes after their stomach-turning departure, the train and its passengers would pull to a gentle stop at their destination on the other side of the world.
Though Robert Hooke and Isaac Newton corresponded on the subject of objects falling through the Earth, they did so merely as an intellectual exercise. The first serious suggestion to build a gravity train wasn’t put forward until the 1800s, presented to the Paris Academy of Sciences by a group of scientific optimists. Unsurprisingly, the Academy opted to defer the ambitious suggestion. The concept was lost to obscurity until the 1960s, when physicist Paul Cooper published a paper in the American Journal of Physics suggesting that gravity trains be considered for a future transportation project. Though the article sparked some lively debate, the proposal was not taken very seriously.
While friction does put a damper on the gravity train concept, clearly the biggest technical hurdle would be in creating such massive tunnels in the first place. A hole with a ten foot radius which passed through the Earth’s center would displace over twelve billion cubic feet of rock, all of which would need to be hauled away somewhere. Furthermore, the Earth’s mantle and core writhe with extreme pressure and heat, so any tunnel would have to be lined with a protective shield to keep it intact. Unfortunately no currently known materials can even withstand the hostile environment, let alone insulate the tunnel from the intense heat. Due to these extreme temperatures, the trip may never be survivable by humans. But the technology would be extremely useful for rapid, unmanned cargo delivery between continents, essentially becoming a massive global dumbwaiter.
Those who find sport in reflecting on such wild ideas have suggested that the tunnel could be evacuated of air to eliminate wind resistance, though such a feat would prove almost as challenging as the drilling itself. Some have also postulated that such a train could be magnetically levitated to eliminate friction in situations where the tunnel does not pass through the Earth’s center; though if electromagnets were used, the amount of energy consumed by the apparatus would rise drastically. A more viable location for the gravity train would be on a celestial body which is not troubled by an atmosphere, plate tectonics, and magma, such as the Earth’s moon. The concept would be the same, though a planet with a density different from that of Earth would also have a different standard trip length.
Though the Gravity Express may seem impossible—or at best absurdly impractical—it is appealing to consider the possibility of extremely rapid transit across the planet with very little expenditure of energy per trip. Certainly the creation and reinforcement of such tunnels is well beyond the reach of our current technology, but the future is full of surprises.
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That would be one hell of ride :)
I have always wanted to drill a hole through the earth’s core and jump into it…i think that due to the friction, after going up then down then up then down that i would eventually end up in the exact centre of the earth…i can imagine thinking…”uh oh…i dug the hole a bit too deep”
I’ve thought about this question myself. If a person were to be in the exact center of the earth in a hypothetical sphere protected by the elements would that person float or would gravity force them into a little ball? My best guess is that with such a huge amount of mass around a person that they would simply float in the middle being that gravity is relative to mass.
What I want to see is a tunnel like that connected to a space elevator of sorts with a hole through the earth at the bottom. Then what you do is wench the craft up into a tower say 20 miles high and fire thrusters straight toward the ground. Then all you do is let the added momentum blow you out into space on the other side. Hey a man can dream of putting a space elevator type thing and a hole through the earth together now can’t he?
Puppeto said: “I’ve thought about this question myself. If a person were to be in the exact center of the earth in a hypothetical sphere protected by the elements would that person float or would gravity force them into a little ball? My best guess is that with such a huge amount of mass around a person that they would simply float in the middle being that gravity is relative to mass.
No, you would be effectively weightless. Since the planet is surrounding you, the gravity is pulling at you equally in all directions at the same time, and it would all cancel each other out.
Consider.. there is a considerable portion of the earths mass that is not directly below you, in fact, most of it. You don’t get pulled to the side though, or experience gravity from a different direction than straight down to the earths core, simply due to the fact that this mass is equal on all sides, and all sides cancel each other out, leaving only a net pull downward.
Interesting stuff, but completely infeasible for use on earth due to the plate tectonics, rotation, and the general hotter than hell status of 99% of the earths volume. However, if we ever colonize the moon in a big way, or another body that has a solid core, this could be doable(though the question must be asked why would we build settlements that are far apart there in the first place.. ).
Here’s what troubles me — I’ve read more than a few sci-fi and horror novels in which a world or worlds are honeycombed with tunnels and labyrinths. It *always* ends badly.
Now, if I remember my boyhood folklore, don’t all holes dug deep enough come out in China?
cutterjohn said: “(though the question must be asked why would we build settlements that are far apart there in the first place.. ).”
I guess for the same reason settlements are built far apart here on Earth… we’ve run low on places in Europe and Asia to live, so we moved some people over to the New World. Sure, we’ll start out in one compact place on the moon, but when we have enough people there, they won’t want to be so close to the neigbors, and having your own pool up there would really be a blast… a 200 lb person would only weigh 33.2 lbs on the moon.
BTW, good job clarifying the gravity question at the center.
You don’t need to drill through the earths middle, or even drill at all, in order to get negligible fuel consumption: you just need to have both ends of the ‘tracks’ be enough higher than the middle portion, the friction sufficiently low, and no train stops in between. I put tracks in quotes, because you need something a lot better than modern tracks to reduce the friction enough for negligible fuel.
Of course, the travel time will not be that nice constant 42 minutes.
While I am not aware of any serious work on drilling that deep through the earth, there is serious work being done on vacuum tunnels for high speed trains.
If I recall correctly, there is a part of the core of the Earth that spins at a different rate than the suface (creating the Earth’s magnetic field?). So any tunnel that deep would experience shear effects, making it unpassable.
Welcome back! As always, great brain food. The more good minds studyting the problem of gravity, the sooner its physical effects will be overcome for both local and space transportation.
Here’s a thought which has interested me since my youth.
Imagine the floating in the middle of an earth transmigratory tunnel situation. As somone suggested before,
Now consider digging a tunnel, say, halfway to the center of the earth and, for the purposes of palpability, one then tunnelled horizontally a perceivable amount.
A this point you’ll probably need a rest.
However, will the shovel in your hand appear lighter on account of both the reduced amount of planet beneath you, and the additional pull from the body above you?
In short: Are miners slightly lighter when at work than at home?
OMG… Douglas Adams was right!!!
“A hole with a ten foot radius which passed through the Earth’s center would displace over twelve billion cubic feet of rock, all of which would need to be hauled away somewhere. “
…maybe so, but you can’t take any earth out of hole that has a 10 foot radius and is 7290 miles long. The hole is already empty!
I must apologize, I think I forgot to replace close a tag… any better?
What would the G-forces be when one is going that fast? Or would they be cancelled out by the reduced gravity? And wouldn’t the Mole People be *mighty* upset if we started destroying their natural habitat?
Do those figures add up? I’m *incredibly* rusty when it comes to physics equations but acceleration is velocity over time, yeah? Wouldn’t that make the acceleration less than the normal 10m/s2?
I had visions of people being squelched into their seats for 20 minutes or so but I guess I could be wrong… :)
.g
Aside from the impossibility of the shifting tectonic plates, magma, hole-boring, friction, etc, if the tunnel network was extensive enough it would easily be able to replace almost every transportation device out there. If I have to take a train 2 hours to get to work in the morning, it would be faster for me to go to the other side of the planet in 42 minutes and then catch another grav train back to where I need to go in another 42. Seeing as how we’re already talking the impossible on a massive scale, you’d only have to bore a few “master” tunnels, and then have “switch-tunnels” to divert grav trains to different locations. This of course would also require more energy for cornering g forces and loss of speed, but as long as we’re talking about a fantasy, I also get a black unicorn with red eyes that shits candy.
If this was built it wouldn’t be long before it was nicknamed the gravy train.
Another froot-loopy idea that will be replaced by something practical. For example, the originally proposed mail rockets versus electronic mail of various kinds. (Look up the history of the FAX; it’s older than you think.)
Gravity, at the earth’s surface, provides enough force to accelerate objects at 9.8 m/s^2. As you start falling down the gravity train’s tunnel, you would feel weightless – zero G’s, if the tunnel goes straight down. So it’s not a bone-crushing g-force; quite the opposite, actually. It’s free-fall.
If the tunnel is a shorter trip that only goes partway through the earth (this would be a “chord” for a 2D circle; I’m not sure what the name is for a sphere), you accelerate at something less than freefall. The math works out such that each and every trip takes 42 minutes, whether you’re going from Spain to New Zealand or New York to Chicago.
However, as you fall down, your acceleration slows, as the mass “above” you (or “behind” … adjectives are difficult in this circumstance) starts tugging backwards. As you near the center of the earth, your acceleration gets slower and slower. You feel a minimum of force in the center of your trip: if your trip is through the center of the earth, your minimum weight is zero. For “chord trips”, your minimum weight is the square of the ratio (distance to center of earth / radius of earth).
So fundamentally, yes, miners weight slightly less when they’re at work.
Puppeto, your first thought was answered by cutterjohn. On your second point:
Puppeto said: …
“What I want to see is a tunnel like that connected to a space elevator of sorts with a hole through the earth at the bottom. Then what you do is wench the craft up into a tower say 20 miles high and fire thrusters straight toward the ground. Then all you do is let the added momentum blow you out into space on the other side. Hey a man can dream of putting a space elevator type thing and a hole through the earth together now can’t he?”
That would not be of any use. As the article described, the effect of the “tunnels” would be like a pendulum. While you would gain all the the potential energy (from gravity) of dropping down the tunnel to the Earth’s core, you would then have to release all of it to travel back out the other side (and this climb back out of the gravitational field). The net result would be a zero gain in energy/momentum – just like a pendulum at either end of its swing.
I am amused by how badly everyone here needs to take a physics class (some exceptions, of course).
The significance of “42” has not escaped my attention…
cutterjohn said:
Consider.. there is a considerable portion of the earths mass that is not directly below you, in fact, most of it. You don’t get pulled to the side though, or experience gravity from a different direction than straight down to the earths core, simply due to the fact that this mass is equal on all sides, and all sides cancel each other out, leaving only a net pull downward.
This would only be true if the earth were a perfect sphere, it is not, it is more of an “egg” shape.
Maybe i also need to take a physics class, but what if you dug a tunnel that bent upwards again? With i.e. a maglev vacuum train your acceleration and deceleration would be provided by gravity. (no fuel and brakes required) and you don’t need to go through the magma.
thermopile said: “If the tunnel is a shorter trip that only goes partway through the earth (this would be a “chord” for a 2D circle; I’m not sure what the name is for a sphere), … “
…would you be willing to accept…”a chord-oroid”?
Screw the gravity train think about the gravity generator. Fill the tunnel with wire coils and send a magnet through the tunnel and reap the rewards of practically free energy. The only cost would be would be the energy required to overcome resistance forces. If done correctly the machine would use energy it created ifself to keep popping 50ft. or so out of each end. This would be done with MagLev or lasers, technology we already have. Perpetual Motion Machine?
lockedout said: “Perpetual Motion Machine?”
And therein lies the problem. There ain’t no such thing as a free lunch, which in this is expressed by the fact that generating energy with electromagnetic coils creates “back pressure” in your generator system. The motion of the permanent magnet will be slowed by the slight removal of energy at each coil by electromagnetic induction. Thus the magnet would be slowed so that its motion would resemble a damped harmonic oscillator (it would pass the Earth’s core to some distance, turn ’round and come back, pass the Earth’s core at a lesser distance…). The degree of damping would depend on the mass of the object emplaced in the tunnel.
The net result is that the energy you would harvest would be exactly equivalent to the potential energy of an object from here to the the Earth’s core. This is a relatively simply calculus-based physics problem that requires integration but not too much else. If you could somehow manufacture magnets at the Earth’s surface and keep dropping them down after clearing your tunnel of the previous magnet, you could indeed make energy. But, you have to clear the tunnel which means you’ve spent a huge amount of energy increasing the potential energy of the entire bulk of the tunnel mass.
So, like all such Perpetual Motion Machine designs, it seems an elegant concept but the strict laws of physics prevent it from working. The longer a PMM runs, the lower its energy production capabilities, but you can never achieve more energy than you put in.
Coherent said: “I am amused by how badly everyone here needs to take a physics class (some exceptions, of course).”
Wouldn’t it be cool if we hadan elevator to the moon instead of using a rocket?? I want one in my backyard!!!
Anthony Kendall said: “And therein lies the problem. There ain’t no such thing as a free lunch, which in this is expressed by the fact that generating energy with electromagnetic coils creates “back pressure” in your generator system. The motion of the permanent magnet will be slowed by the slight removal of energy at each coil by electromagnetic induction. Thus the magnet would be slowed so that its motion would resemble a damped harmonic oscillator (it would pass the Earth’s core to some distance, turn ’round and come back, pass the Earth’s core at a lesser distance…). The degree of damping would depend on the mass of the object emplaced in the tunnel.
The net result is that the energy you would harvest would be exactly equivalent to the potential energy of an object from here to the the Earth’s core. This is a relatively simply calculus-based physics problem that requires integration but not too much else. If you could somehow manufacture magnets at the Earth’s surface and keep dropping them down after clearing your tunnel of the previous magnet, you could indeed make energy. But, you have to clear the tunnel which means you’ve spent a huge amount of energy increasing the potential energy of the entire bulk of the tunnel mass.
So, like all such Perpetual Motion Machine designs, it seems an elegant concept but the strict laws of physics prevent it from working. The longer a PMM runs, the lower its energy production capabilities, but you can never achieve more energy than you put in.”
Hi, I’m new here, and I saw you were talking about PMM’s, and I have been trying to make one of these for quite a while, only to find out that it does not work again. But I have come up with a new design which I cannot figure out why it would not work, and I think it may be a possible way to gain “free energy” note: it’s not free, I can explain where most of the energy is coming from, it’s more of a way of magnifying the energy created. In order to understand the creation you have you understand it’s key points first. The main key points are that Boiling Point is determined by pressure. So if you were to lower the pressure drasticlly, you could alter water’s boiling point and lower it so far that it will boil at room temperature. Now if you did this to a large container which was filled with water, and sealed this container, the pressure would remain constant inside the container( when the water boils it will re-pressurize the container, but not too much)
So now you have a sealed container in which water boils at room temperature in. The water that is boiling rises( since hot air rises) and is fed into a generators fans, causing them to turn and create electricity. the rising air then goes up a pipe further where it is cooled just enough to recondense it at which point it lands back in the bottom of the holding tank. I believe that the energy created from the generator would be enough to alter to water a few degrees, making it hotter or colder as needed, with still extra energy. Here is a picture that I made like 3 months ago of it: http://i12.photobucket.com/albums/a250/banmeihack/model1.jpg
now I know this has nothing to do with the gravity train, and its not exactly perpetual motion, but I think its a pretty good idea, and this seemed like the best place to tell people about it.
Again sorry for posting in the wrong section
Thanks for any feedback :)
banmeihack said: “So now you have a sealed container in which water boils at room temperature in. The water that is boiling rises( since hot air rises) “
Therein lies the problem, though. The water vapor isn’t hot, it’s still room temperature in your pressurized container.
That’s a neat idea. Would the lack of air make it harder for the steam to rise? Convection requires a medium to work (I hope that’s the right word). There may be steam in the air but it doesn’t necessarily mean that it carries the same amount of energy. That might be why it’s easier to boil; because it takes less energy to make the water evaporate. hmmm… is that right? oh well, atleast I have my pie. Interesting banmeihack. I personally think that the best form of energy out there is nuclear energy, it’s incredibly abundant and safe when done properly. I wonder why so many people fear it. I think there’s only been one melt down in the world. (Chernobyl, another DI article).
But yeah, I love newtons gravity train idea. It’s too bad that we have to live with friction and that pesky molten core. Great article!
Oh! I like the comment on induction by Anthony. I’d quote it but it’s huge. Induction is really cool. It makes our lives work. It’d be cool to drop a really huge magnet down one of those shafts and watch it float down like an elevator. mhmm
I wonder how soon somebody will create a safe, practical cold-fusion generator (if that is even possible)?
Until then, we should really increase our reliance on the sun. It vomits out an absurd amound of energy every second. It’s clean, it’s abundant, and it’s free.
banmeihack said: “Thanks for any feedback :)”
There are many working generator systems that use the same principle you note here: namely room-temperature boiling of a fluid. In fact, your refrigerator has that system running in reverse as a condensor.
Now, the reason that system will not generate any more energy than is input, and significantly less is this: the amount of power generated by the turbine will never be any more than is required to boil your pressure-reduced water. If you don’t input any heat into the system, eventually it will merely settle to the point where the temperature and pressure are uniform throughout. If you extract energy from the turbine outside of that system, without reheating the fluid then equilibrium will be arrived at very very quickly.
If you add heat from outside the system, by say allowing the water to boil at room temperature, then the vapor pressure within the system will rise sufficiently to increase the boiling point beyond room temperature, thus there will be no change in state from vapor->fluid to drive the turbine.
The study of your idea is known as Thermodynamics and is a very robust and well-founded branch of physics and engineering. One of the principal tenents of thermodynamical cycles like that which you describe is that the maximum efficiency in a power generation system can never exceed a limit set by the temperature difference between the high temperature state, and the low temperature one. Thus, surrounded by an atmosphere at room temperature, the efficiency of an engine is exactly 0: no power is generated. This, combined with the first law of thermodynamics, completely prevents anything more efficient than the “Carnot Cycle”, which typically operate at about 30-40% efficiency and are very similar to the cycle within an automobile engine.
So, while the system you describe could be very useful in certain situations because of the low boiling point involved, it is far more useful as a refrigerator than as a power generation system, and will never be capable of generating more energy than is input via heat, chemical reactions, nuclear reactions, or other such inputs.
http://xkcd.com/c123.html
Isnt it possible to have a tunnel that doesnt go through the core. Instead it just goes to the side of it. Like for example from New York to Seattle. That wouldnt have the problem of pressure and heat yet i dont know if it would be as fast then. Ill look it up and please help out!
HarleyHetz said: “This would only be true if the earth were a perfect sphere, it is not, it is more of an “egg” shape.”
You are correct, but grossly overexaggerating how much earth is out of round. The diameter of the earth at the equator is only ~43km greater than the diameter of the earth from pole to pole. This, of course, is due to centrifugal force from the earths rotation.
Anyway, for all intents and purposes, the earth is a perfect sphere. a 43km difference when the earths diameter is ~12,700km is miniscule, and the net effect on gravity is negligable.
Actually, according to wiki, the earth is rounder than the tolerance for billiard balls.
This website is excellent! will there be a forum in the future so i can chat to like minded people here?
Didoka said: “Isnt it possible to have a tunnel that doesnt go through the core. Instead it just goes to the side of it. Like for example from New York to Seattle. That wouldnt have the problem of pressure and heat yet i dont know if it would be as fast then. Ill look it up and please help out!”
Sure, it’s (theoretically) possible to have a chord-line tunnel. [It’s a chord, regardless of whether it’s present in a circle or a sphere.] There would be a problem with friction, though, since you would be sliding along the floor of the tunnel rather than falling freely through it (which would be possible only in a tunnel along a diameter).Much more importantly, there would still be a problem with pressure and heat even in a New York-Seattle tunnel, since the midpoint of the ride would be 180 miles (290 km) below the surface. This is far enough into the mantle that, even if you could make a lining for the tunnel that would not collapse under the pressure there, getting rid of the >1600°F(870°C) heat would be a big problem.
rats…I wanted to put some line-breaks in there. Is there some way to edit these after posting?
Am I the only one who feels wary of putting exhaust vents into the earth’s core, or will our hypothetical super-lining keep all that heat where it belongs (inside the earth)? What about a breach? One crack could potentially lower the core temperature of the earth ever-so-slightly and (correct me if I’m wrong) muck with the earth’s magnetic field…and I have problems with sunburn now!
Also, how will we deal with rain water, or worse, flooding? I can’t imagine it would take that long for such a tunnel to fill with water, and either option of running a train through it or pumping it up a ~3,000 mile vertical shaft would be somewhat inefficient, no?
Quite a DI idea, but the logistics are mind boggling ;)
Marius said: “Now, if I remember my boyhood folklore, don’t all holes dug deep enough come out in China?”
Only in Bugs Bunny cartoons
davidmcw said: “Only in Bugs Bunny cartoons”
No, in Bugs Bunny cartoons the tunnels come up in the dessert instead of the beach!!
A quick note about the perpetual motion stuff: If you can design it, it doesn’t work. If your design says it works, then you made a mistake.
I can say this because I’m using the word “design” in an engineering sense: To designate an arrangement of components that will work a certain way according to certain known principles. The problem is that all of the known principles conserve energy. This is a statement of mathematical fact. At this point in the development of physical science, all physical principles that do not conserve energy are at best ill defined and highly speculative (and at worst, absolute nonsense). They’re not the kinds of “known principles” you can use for designing things.
Because this is a mathematical fact, I can say this: If you have specified an arrangement of components that seems (according to known engineering principles) to not conserve energy, then you’ve made a mistake in your analysis. It may be an interesting exercise to find out where the error is, but mathematically there must be an error. I can say this even if I don’t take the time to find out where the error is. It’s as if someone went through a long derivation showing 1+1=3. I can tell them right away that they made an error. Scientists that seem to have a knee-jerk reaction condemning any proposed perpetual motion machine aren’t actually being unreasonable; they’re just being parsimonious, as they’re aware of the mathematics.
Such a tunnel could probably be used as a space vehicle launcher. From insertion on side A you simply keep on accelerating slightly so that by the time you come out side B you still have sufficient escape velocity speed left.
Unfortunately, elifint is correct by the laws of thermodynamics: You can’t win, you can’t break even, and you can’t get out of the game.
For any non-scientist this basically means that you can’t finish with more energy than you started, you can’t end with the same amount of energy, and you can’t get to absolute zero (although this is less relevant).
Losses, however small, will always occur.
The degree of damping would depend on the mass of the object emplaced in the tunnel.
Not to be nitpicky, but it would depend on the air resistance (If there is any) and how much energy you are taking out per cycle for electrical generation. The mass term is separate from the damping term in the differential equation for the system.
banmeihack said: “The main key points are that Boiling Point is determined by pressure. So if you were to lower the pressure drasticlly, you could alter water’s boiling point and lower it so far that it will boil at room temperature. Now if you did this to a large container which was filled with water, and sealed this container, the pressure would remain constant inside the container( when the water boils it will re-pressurize the container, but not too much)”
This won’t work. Actually, when steam engines were first invented, they tried this exact technique (Using alcohol and other low boiling-point liquids). I won’t bore anyone with the details, but it’s basically where the idea of conservation of energy was solidified. Any thermodynamics book will explain the details pretty clearly, although I think Anthony explained it just fine.
Dave Group said: “What would the G-forces be when one is going that fast? Or would they be cancelled out by the reduced gravity? And wouldn’t the Mole People be *mighty* upset if we started destroying their natural habitat?”
There would be no G-forces. The force of acceleration that you feel is caused by whatever object is pushing against you to accelerate you. The force of gravity that you feel on Earth is the ground pushing up against you to resist gravity. People pass out while making high-G turns because blood gets accelerated (relative to the person) while the rest of their body is pushed by the turning machine to stay in place.
Since there’s nothing resisting, and gravity acts on each particle of your body equally, the entire trip would feel like being in space – free fall. I shudder at the thought of people barfing in such an environment, I guess astrounaughts receive a lot of anti-voimet training.
FORTY-TWO minutes! Can you hear that?!
Does this mean ‘the natural trip time from one side of the earth to another’ is the Ultimate Question that Earth has been built for?
My dad is 64 years old, has never used a credit card, uses a rotary phone and loves DI….I print it and use the pony express to get it to his cave. Welcome back…more than worth the wait.
Tunnels wouldn’t necessarily need to be straight lines either, would they? If I remember my physics right, if friction was negated, the only work done on the train would be the vertical forces of gravity, allowing for more U, or V-Shaped tunnels, letting closer cities also be linked by this system. This would also reduce the 42 minute trip time between these cities.
If I’ve remembered incorrectly, please correct me.
pyrhho said: “Tunnels wouldn’t necessarily need to be straight lines either, would they? If I remember my physics right, if friction was negated, the only work done on the train would be the vertical forces of gravity, allowing for more U, or V-Shaped tunnels, letting closer cities also be linked by this system. This would also reduce the 42 minute trip time between these cities.
If I’ve remembered incorrectly, please correct me.”
As has been mentioned in the article and several times in the comments, yes, this is possible. However, the 42 minute trip time is constant, regardless of the distance. This occurs because with a shorter distance, less velocity will be attained in the downwards portion of the trip before beginning to decelerate again with the upward portion.
Donlaudanny said:” Since there’s nothing resisting, and gravity acts on each particle of your body equally, the entire trip would feel like being in space – free fall. I shudder at the thought of people barfing in such an environment, I guess astrounaughts receive a lot of anti-voimet training.”
ie The Vomit Comet
Alternately, couldnt these tunnels begin use as vastly oversized geothermal tunnels? Even supply free heat to countries far from the equator. Geothermal heating isnt a new idea even. They have “Houses of the future” where the earth’s temprature constant (around 72 I think) is used to maintain steady tempratures in these houses. Couldnt these tunnels provide a way in which to sap heat into a main line where it would be transported like water lines thru the cities and towns? It would surely be a vast undertaking, and plate techtonics would be an issue depending on the region.
While this may not solve the heat problem of the vomit comet, it grants it multifunctionality required for a project so large. After all, if you’re going to be going to so much effort then its important to make the most out of it.
At the very least, regions with low plate activity could serve as a proving grounds for the technology. It could be supplimented at first with regular mag lev technology and mining techniques so that it would not dive as deeply into the earth. Consequently, by limiting the range to withing the same plate and region it would be more feasible than trying to link together two moving plates and going thru magma. At least more feasible than tunneling thru the center of the earth. I think everyone at least agrees that it would be a vast undertaking, and need lots and lots of surveying.
Sorry for the double-post, but…
Or, if the tunnels were dug in a way, such as this.
The train could gain some momentum, then coast frictionless, until it ascends again at it’s destination. This would alleviate the need to drill very far into the earth. The downside is, the speed would be greatly decreased. Or has my physics completely escaped me?
HarleyHetz said: “No, in Bugs Bunny cartoons the tunnels come up in the dessert instead of the beach!!”
Only because he didn’t turn left at Albuquerque.
cspariah said: “Here’s what troubles me — I’ve read more than a few sci-fi and horror novels in which a world or worlds are honeycombed with tunnels and labyrinths. It *always* ends badly.”
I know nothing about physics, but it seems that all of the tunnels would make the Earth into a whiffle ball — easily batted around the universe…
What I want to see is a tunnel like that connected to a space elevator of sorts with a hole through the earth at the bottom. Then what you do is wench the craft up into a tower say 20 miles high and fire thrusters straight toward the ground. Then all you do is let the added momentum blow you out into space on the other side. Hey a man can dream of putting a space elevator type thing and a hole through the earth together now can’t he?”
That sounds like a cool idea, but there are flaws. Since any momentum you gain from gravity will be lost due to gravity, you’d have the same exact momentum going into the hole as you would when you come out, if not less due to friction and air resistance. This renders the entire “hole through Earth” part is useless, at best. The only momentum you would have would be from the extra height and thrusters on the starting side. You would have to drop from a height sufficient for instantaneous freefall velocity upon entering the hole to be equal to or greater than Earth’s escape velocity, approximately 25,000 miles per hour, which is absolutely absurd. Since terminal velocity would be a problem, the tower would need to be a vacuum tunnel that is completely frictionless with no air resistance whatsoever in order for the craft to possibly have enough momentum when it comes out through the other side of Earth to escape Earth’s gravitational pull.
It’s definitely a cool idea, but physically it doesn’t work. The thrusters will definitely be needed. With what I’ve figured, the required additional push from the thrusters will be large; why not just launch straight off the surface of the Earth? Or better, just launch vehicles off of the top of the tower, where Earth’s gravity plays a significantly lesser role.
pyrhho said: “Sorry for the double-post, but…
Or, if the tunnels were dug in a way, such as this.
The train could gain some momentum, then coast frictionless, until it ascends again at it’s destination. This would alleviate the need to drill very far into the earth. The downside is, the speed would be greatly decreased. Or has my physics completely escaped me?”
This would probably be a feasible idea. Your physics is correct, but only for a perfect world with no friction or air resistance. The law of conservation of energy, kinetic energy equals potential energy, shows that the train would start with a potential energy equal to its weight times its height from the bottom. If it can coast frictionlessly, it’ll lose no energy due to nonconservative forces (friction). Then, when it reaches the point of ascension, it will already have a kinetic energy equivalent to its starting potential energy, sufficient to allow it to travel to the surface and coast to a stop right at the top at a height equal to where it started.
This would only work if we could eliminate ALL nonconservative forces; friction, air resistance, etc. Unforunately, we can’t, but they can perhaps be reduced enough so that the train would only have to expend a small amount of energy to make the final ascent.
Thanks for the replies :)
I have long believed that it would be impossible to make, and many have said so, but with little reason, You guys really can explain it quite well. So then I will move on to a new idea, and one day once I come up with it, I will post it and see what you guys think.
Use the displaced dirt to add to Japan’s landmass. They need it….of course, every coastal city on the planet would pay for that. I’d kinda like to know what the displacement of all the atmosphere that would go into the hole would do to the planet. Forget the technical problems of building it. The global consquences haven’t been well thought out if you ask me.
cutterjohn said: “No, you would be effectively weightless. Since the planet is surrounding you, the gravity is pulling at you equally in all directions at the same time, and it would all cancel each other out.
So, one quick way to loose some weight would be to go down in a mine? OK, a really deep mine.
First of all, there’s no such thing as centrifugal force. Period. I used to be convinced there was, there isn’t. It took me a good friend, and a long time to realize that “Centrifugal Force” is an imaginary force that people assume is pushing things outward from a rotational axis. Again, this force never really existed. Things only go “outward” from the axis (again, also not true at all) because they want to go in a straight line. CentriPEDAL force exists, which is simply an inward force keeping things from traveling in a straight line, thereby confining them to a circle of motion around the axis.
Just thought there were too many people, today in particular, that mentioned the so-called “Centrifugal Force.” sorry if it felt like I was picking on you Cutterjohn. (by the way, the billiard ball comment was an awesome little factoid)
It also took me a long time to give up on perpetual motion, too. The only one that I can think of is maybe an atom or the universe (kinda poetic, in a way) but I’m not even sure about those.
One thing I AM sure about, though, I am definitely going to have an obsession with 42minutes 12 seconds now. That will be the timer set for my snooze alarm from now on, and confuse my roommate.
How big is that 12 billion cubic feet of rock, exactly? Compared to a mounatin, perhaps? a city? what could we do with all that dirt?
Misfit,
I recall from my article about the Yellowstone Supervolcano that the largest volcanic eruptions are about 1,000 cubic kilometers of material. Mt. St. Helens was about 3 cubic kilometers (sources vary on the exact amount). Doing the unit conversions, 12 billion cubic feet of rock from the tunnel converts to about 0.33 cubic kilometers. So the tunnel would displace about 1/10th the volume of a medium-sized volcanic eruption. For a feeling of how much material that is, compare the first picture to the second on the Mt. St. Helens wikipedia page.
More FYI, as I mentioned in my article on Artificial Islands, the Kansai International airport was one of the largest manmade island projects in terms of volume of material. In the construction there, about 0.02 cubic kilometers were excavated and moved, so the tunnel would be about 10 times that volume again. Not a small undertaking, especially considering Alan’s article about drilling to the Moho discontinuity and the fact that the Soviets found that rocks get kind of flowy and semi-liquid down even at 10 km. Never mind going down almost 6,000 km!
I did a little googling and mathing, and 12 billion cubic feet of rock would be approximately 35,000 Mt. Everests. Be warned, this is a TOTAL approximation, but at least it gives you an idea of the scale. I used my rudimentary math skills once again, to see how fast a train, plane, or whatever would have to go to get somewhere in 42 minutes along the surface of the Earth. To get halfway around the world in 42 minutes, your train would have to go a little faster than the space shuttle at cruising altitude, assuming instant acceleration and deceleration – that is, almost 18,000 mph. To get from New York to Seattle in 42 minutes, you would have to go over 2.5 times the top speed of the Concorde. So, you would have to go about 3,500 mph. Come on, people – this whole thing is a thought experiment. You don’t have to prove how it couldn’t work with all your physics that you don’t even understand. I think no matter how advanced our technology becomes, the gravity train will never be feasible. We will invent instant teleportation before we ever build a tunnel through the Earth’s core, or even 180 miles down. Beam me up, Scotty.
Whoah, I’m an idiot. I told you I had rudimentary math skills. Just save it. Please. I know I screwed up, Anthony posted while I was writing mine. He obviously has a much better grasp of numbers than me. I’m not worthy. Even though my volume calculation was WAY off, by several magnitudes, let me know if my velocity calculations were anywhere close to correct. I’d like to think my high school physics taught me Something … I really liked that teacher. Peace.
I have one of these birds. i think if enough of these birds were strung up in unison, they could power a generator that could power the whole world! http://serioustoyz.com/OptiArt/auctionart/WINTER'05AUCTIONLARGE/drinkingbirdMIBL.jpg
Apart from the scientific theory of this project, i believe it would never go ahead regardless. Not until around 2015 at least. The reasoning behind my conclusion is due to the multitude of existing tunnels that most of us are unaware of, even after countless stories, tales and lore that alot of us have heard. Many people in the excavation/mining/construction industries have encountered many tunnels in their time, some rough cave-like tunnels, others mysteriously carved through stone and bedrock using some sort of advanced laser-like cutting device (many believe sound is used rather than light, much like the megalith/pyramid stone theory). I’ve heard of stories of this calibre my entire life from many sources, some smooth-carved tunnels are reported to have tracks with carts travelling automatically through them, with no known origin or destination.
As most of us only know of people that live on land, there are many noted civilizations that live beneath our feet in caverns and tunnels, and the fact that not everyone on earth knows about these cultures states that we’re not supposed to know of them – perhaps for fear of people leaving their taxable lives to live with them (many reported to be beneviolent, only few are reported malicious in nature).
So the reason why this wouldnt work is because the construction of this project will interfere with the existing infrastructure of tunnel systems that people are occupying at present.
And the reason i believe this wouldnt take off until around 2015 is due to the upcoming evident unvieling of many of these secrets of our planet/universe/selves which is due to occur in the upcoming age of revealing, expected in 2012. Once we learn of the things that are currently (selfishly) kept from us, and once we accept them, we might then have a chance of using their tunnels (and technology) to travel around the world in true style without the need for boring more tunnels.
So we can play with mathematical theories all we like, but keep in mind that we’re still playing with variables within the constraints of our collective knowledge. And unless we delve into the texts and tales of the people who lived here before the world turned into an ugly, concrete jungle, we’re still looping in an endless cycle of scientific masturbation.
awesome
TrueBeliever said: “…”
No shit! Is there anything you don’t believe?
There is much i dont believe in, the majority being the laws of the apparent understanding of our sciences, and i do not believe in what 100 (or one million) scientists would have us believe that contradicts literally thousands of documents, artifacts and eyewitness accounts regarding said theories.
We have found that science is merely speculative, and expands with our understanding of the universe. Can you even sit and count the number of people that objected to the inventions and discoveries that we all take for granted today? How can anyone even object to a possibility? How about objecting to a possibility that hundreds of thousands of people worldwide fully support due to spoken accounts and stolen artifacts (usually from Harvard Research) regarding such claims?
You’ll find that we always look back in time many years later at the misfits, visionaries and anyone that fought for what they believe in only to find that they were right on the money in most cases. Their dreams which they perhaps couldnt execute back in their time have since been invented, and we’re finding that our technological advances are only limited by our imagination.
Now think for a moment to a different civilization that didnt have such hurdles of objection and skepticism, but greeted every idea with an open mind. You might then realise how little we ourselves have come in comparison to our beloved technology.
If you guys want to discover “real” science, then check out Dan Winter amongst a few others who risk their careers (and lives) every day by putting it all on the line for the sake of connecting all sciences together, modern and ancient, physical and metaphysical. People like Dan will continue to work in the face of ridicule from many others, and we’ll most likely be collectively praising him years after he passes like so many great men before him.
http://www.soulinvitation.com/indexdw.html
And if you dont believe that great men with great ideas are being silenced all around the world for merely telling people what they believe in, then look around, its still happening to this day. David Icke is on the same boat these days. Have you seen Nicola Tesla’s ideas of free energy being utilized anywhere?
These great people wake up every day and challenge the norm for our own benefit, and we treat them this way coz oil companies dont wanna lose a buck…. Aint life grand….
I’d like to propose a new scientific law called Sparky’s Law. Basically it states: “The longer a single webpage is, the more crazy the person running it is.”
Seriously, that page is in league with Timecube.
TrueBeliever said: stuff
The mole men are real? ive been living a lie!
Just don’t build it anywhere in California,
it shakes eno-ou-ou-ugh!
Have the sceenwriters for The Core
read this article yet? They could call it,
The Lucifer Project.
TrueBeliever said: “The reasoning behind my conclusion is due to the multitude of existing tunnels that most of us are unaware of, even after countless stories, tales and lore that alot of us have heard.”
Demonstrate this multitude of tunnels, please. Do not simply make wild claims, because to do so is simply to waste time.
“Many people in the excavation/mining/construction industries have encountered many tunnels in their time, some rough cave-like tunnels, others mysteriously carved through stone and bedrock using some sort of advanced laser-like cutting device (many believe sound is used rather than light, much like the megalith/pyramid stone theory). “
(1) Bedrock is stone; no need to draw a distinction. (2) “Some sort of advanced laser-like cutting device” is just hand-waving. It sounds neat, but it has no substance. (3) If sound is used, then the device is not “laser-like”.
“I’ve heard of stories of this calibre my entire life from many sources, some smooth-carved tunnels are reported to have tracks with carts travelling automatically through them, with no known origin or destination.”
Umm…would it be at all possible to follow (or otherwise track) these mysterious automatic carts to their origin or destination, so as to learn something (instead of just indulging in more hand-waving)?
“…there are many noted civilizations that live beneath our feet in caverns and tunnels…”
If they’re “noted” civilizations, that means that (surface) people are aware of them, and in a broad and significant way. Such awareness does not abound, which militates strongly against the notion. Provide hard data, not mysterious allusions!
“And the reason i believe this wouldnt take off until around 2015 is due to the upcoming evident unvieling of many of these secrets of our planet/universe/selves which is due to occur in the upcoming age of revealing, expected in 2012.”
Expected by whom, and for what sound reason(s)? How do you, for instance, know of this “age of revealing”? What special knowledge do you have, and how can the rest of us obtain it?
“There is much i dont believe in, the majority being the laws of the apparent understanding of our sciences,”
Which laws of nature do you disbelieve? The law of gravity? The laws of thermodynamics? The law of least action? The law of conservation of charge? Others?
“We have found that science is merely speculative,”
Dead wrong. Science is investigative. It proceeds sometimes from speculation, but it is not chiefly characterized thereby. Science would not be science if it were just speculation–it would be philosophy instead.
“How about objecting to a possibility that hundreds of thousands of people worldwide fully support due to spoken accounts and stolen artifacts (usually from Harvard Research) regarding such claims?”
So, are we to understand that Harvard Research gets all the good stuff–and that they are thus targeted for the majority of thefts of reprisal? How is it that Harvard got into such an unusual position?
“If you guys want to discover “real” science, then check out Dan Winter amongst a few others who risk their careers (and lives) every day by putting it all on the line for the sake of connecting all sciences together, modern and ancient, physical and metaphysical.
Your use of quotes around “real”, there, is revealing. You seem to not realize that that use of quotes denotes irony, not emphasis. Here’s a good way to illustrate that proper usage: ‘The detective watched Mr. Smith checking into the hotel with his “wife”.’Tell us, also, how Dan Winter is truly risking his life by publishing such…interesting…assertions as this: “Why Fractal Charge Compression (& Then Hyper-efficient + Faster Than Light Charge Propagation)
– is both the CAUSE and the RESULT of:
a) Human Attention, b) Gravity , and c) Electrical Nourishment of DNA.
“..In other words: Charge fractality IS THE SECRET OF LIFE ITSELF.”This sounds like someone who is impressed with fractals but has no real understanding of them. For one thing, charge is incompressible. For another, FTL propagation of anything is, as far as we can tell–and yes, we have researched this very thoroughly–impossible. Even if you wave fractals at it.For another thing, charge does not cause gravity.For yet another thing, charge does not cause human attention (except in the sense of charge transport across neurons’ membranes, so that such neuronal action can be involved in the mental state of ‘paying attention’).For still another thing, DNA has no need of nourishment, electrical or otherwise.
“People like Dan will continue to work in the face of ridicule from many others,”
I have no doubt.
“and we’ll most likely be collectively praising him years after he passes like so many great men before him.”
I have doubt.
“Have you seen Nicola Tesla’s ideas of free energy being utilized anywhere?”
Have you read that even the great Tesla (and truly great he was!) had some crackpot ideas, including that of free energy?
I wasn’t going for the possibility factor at all when combining the tunnel and space elevator. Just saying it’d be a hell of a theme park ride. I would call it “through heaven and hell” and charge $4 billion a ticket. :)
Getting a little off topic here. Would it not be possible to build a completely straight ramp around 4 to 5,000 miles long that uses the curvature of the earth to lift a craft above the ground. This way the spacecrafts rides this ramp and “jumps” into space if it were long enough. I’m too tired right now to figure out the math and I’d have to look up the formula, I know it’s pretty simple to find out. The distance would have to be huge however. At that kind of distance you could also use earth’s rotation to slingshot the craft off the end of the ramp.
Just another crazy thought for a 400 trillion dollar space ramp. :) I’ll shut up now.
Silverhill, don’t you think your efforts might be better spent NOT disproving something so wildly ridiculous?
Puppeto:
Yes, you could, but it’s not practical. Even if it were feasible to build a ramp like this, you would have friction with the wheels and the surface of the ramp. Even if you ignore friction, you are using exactly the same amount of energy to launch it over the ramp than if you just launched it straight up. The momentum gained from the rotation of the earth is also used if you launch straight up (Haven’t you ever wondered why rocket launches try to be close to the equator?) The only advantage to a ramp is that you can reduce the power impulse to launch, but you could do the same thing with an incredibly tall tower (Space elevator).
donlaudanny said: “Silverhill, don’t you think your efforts might be better spent NOT disproving something so wildly ridiculous?”
Hey! I was going to say that!
This is the greatest thing for all of mankind since Al Gore invented the Internet. I have never seen so much info from so many that actually know stuff and even paid attention in English class. One question remains. Why wonder so much and waste so much grey matter when the answers are already there? How many tunnel boring machines are abandoned or idle? Drill a hole ten miles long and see how well a gravity vehicle would work. Do not write to my congressman. He would not understand.
What’s with the picture of Space Mountain on the page? What does it have to do with the tunnel?
donlaudanny said: “Silverhill, don’t you think your efforts might be better spent NOT disproving something so wildly ridiculous?”
Well, someone needs to make the effort to challenge the patently absurd… ;-)Seriously, there is so much ignorance out there–and the Internet facilitates ignorance even better than it does education, in too many cases–that we educators feel a responsibility to try to stem the tide by presenting facts in counter to the fantasies.
SparkyTWP said: “I’d like to propose a new scientific law called Sparky’s Law. Basically it states: “The longer a single webpage is, the more crazy the person running it is.”
Seriously, that page is in league with Timecube.”
Hahahaha … Timecube is nowhere near the same league. I checked out both pages, just to see what the fuss was about. Timecube is the most hateful idiotic thing I’ve ever come across on the ‘net. I can’t believe anyone would even give this guy the satisfaction of responding to his diseased brain. This Dan Winters guy, on the other hand, seems like a reasonably smart guy that took a few too many thousands of doses of LSD. Sacred Geometry and fractals are definitely interesting topics, but there’s no need to make wild extrapolations when there is so much to discover in a scientific manner. Anyways, I don’t know what this has to do with hypothetical gravity tunnels. And kudos to Silverhill – it’s amazing how these people disappear when presented with reasoned arguments. It’s much more effective than attacking them on a personal level, even though it might take some more brain power. Peace.
This is a tangent (pardon the weak pun), but there is a problem similar to “free energy” that is nonetheless tantalizingly “solveable”: reaction mass.
When I was taking Spacecraft Propulsion in a previous life, the problem was always that you can’t go forward without spitting something out the back end. If you want your propulsion system to work for a long time (say to travel between stars), you have three choices: take a huge amount of reaction mass with you, accelerate the reaction mass you have to near-light velocities to make the most of the little you have (ion engines, etc.), or “steal” reaction mass from your surroundings (solar sail, hydrogen ramjet).
The goal is to convert every bit of available energy into force, which can only happen when all the *possible* mass/energy conversion takes place, which occurs only in a matter/antimatter reaction. Unfortunately, the reaction mass needed to make use of the energy is several orders of magnitude greater than the mass needed for energy generation. So… if someone could figure out a way to use the energy from, say, a fusion reaction, to propel a spacecraft forward *without* losing reaction mass, they could make a MILLION DOLLARS (to paraphrase Dr Evil). The benefits would be astronomical (pardon again), since your spacecraft would be a fraction of the total mass of any other, and that mass would stay almost constant for the entire trip, minus the mass lost in energy conversion.
This seems as impossible as free energy, though, since any closed system zeros all forward force with an equal backward force. If you accelerate a mass forward, you will get a backwards thrust, but if your system is closed, that mass must either come back or stop, causing your spaceship to oscillate at best. You could theoretically create ship that was made up of two balls connected by a very long (lightyears) spring, and magnetize the spring, repelling the balls in opposite directions, until one found anchor on a planet somewhere, and the other snapped back.
Anyway, I don’t know if y’all are interested in this line of thought. I have an idea for a solution. I’m sure it will also zero out, but it’s good for a thought experiment:
1) Build an large particle accelerator in the shape of a race track, with two long legs and two short curves.
2) On leg A, accelerate particles to relativistic velocities, enough that their mass increases.
3) On leg B, decelerate the particles to the original speed, so that the mass decreases.
Thus, you have “found” some extra reaction mass, and recycled it on the return. You will have net forward thrust on both leg A and B. UNFORTUNATELY, all of that net thrust is lost by the net force on the two curves (“centrifugal force”, that misnomered bugger).
Anyhoo, that’s my story, and maybe someone much better at the math involved can either find a way to make it work, or conclusively prove it won’t.
Thanks
Rinson Drei said: “2) On leg A, accelerate particles to relativistic velocities, enough that their mass increases.3) On leg B, decelerate the particles to the original speed, so that the mass decreases.
Thus, you have “found” some extra reaction mass, and recycled it on the return. You will have net forward thrust on both leg A and B. UNFORTUNATELY, all of that net thrust is lost by the net force on the two curves (“centrifugal force”, that misnomered bugger).
Unfortunately, TANSTAAFL. (“There Ain’t No Such Thing As A Free Lunch.”)The force experienced by the particles will be matched by the reaction force on the accelerating (and decelerating) equipment. Even in a perfect system (with no loss of energy due to dissipative effects, such as electric resistance and magnetic hysteresis), there would be no net gain of force or energy; and in a real system, there will be such losses. :-(Now, concerning centrifugal “force”–it really is a force, if you look at it in the proper way. The math works out the same way, whether you treat the force as pulling outward or pulling inward; you just have to use the appropriate coordinate system. (It is still more “proper”, though, to use the coordinate system that shows an inward-pulling force. The momentum of the object being pulled has a vector component directed outward, so it feels as though there is an outward force.)
anamexis said: “As has been mentioned in the article and several times in the comments, yes, this is possible. However, the 42 minute trip time is constant, regardless of the distance. This occurs because with a shorter distance, less velocity will be attained in the downwards portion of the trip before beginning to decelerate again with the upward portion.”
I think you may have missed the point. If the tunnel isn’t straight, the time can be a lot less than 42 minutes. Look at skateboarders on a half-tube. By following a curved path and minimizing friction, they can let gravity move them like 10 meters in just a few seconds. If the path were perfectly straight and there were absolutely no friction, they’d make the same trip in 42 minutes, under the (unrealistic) assumptions of the model.
Anyway, the constant-42-minutes thing isn’t quite true. It assumes not just that the earth is spherically symmetric but also that it has constant density. It doesn’t, though, and the center is a lot denser than the crust. This means that the gravitational field isn’t linear with radial position, you don’t have a simple harmonic oscillator, and different orbits (where in this case an orbit is actually inside the earth) can have different periods. It also means that the gravitational field is not (as one might expect) strongest at the surface of the earth, but rather it is strongest at a depth rather deep inside the earth.
Another thing–going from point to point on the equator, you’d actually miss the center of the earth. Why? Coriolis effect. Or conservation of angular momentum; two different ways of thinking of the same thing, in this case.
By the way, did anyone notice that the 84 minute round trip time is the same time as it takes to do a low-earth orbit? This isn’t a coincidence; in fact it’s pretty easy to prove mathematically, when you realize that the gravitational field is a continuous function.
Lastly–The argument about whether centrifugal force is “really” a force or not is spurious. It’s just a choice of terminology, with no physical content.
Rinson Drei said: Anyway, I don’t know if y’all are interested in this line of thought. I have an idea for a solution. I’m sure it will also zero out, but it’s good for a thought experiment:
1) Build an large particle accelerator in the shape of a race track, with two long legs and two short curves.
2) On leg A, accelerate particles to relativistic velocities, enough that their mass increases.
3) On leg B, decelerate the particles to the original speed, so that the mass decreases.
Thus, you have “found” some extra reaction mass, and recycled it on the return. You will have net forward thrust on both leg A and B. UNFORTUNATELY, all of that net thrust is lost by the net force on the two curves (“centrifugal force”, that misnomered bugger).
“
Here’s a spot where the unfortunate use of confusing (and nonstandard) teminology in some intrductory science texts is really clouding the issue. Something you should know: The way (the vast majority of) actual practicing physicists use the word “mass,” the statement that mass increases as velocity increases is bogus. Energy increases. Momentum increases. Mass doesn’t. I know your book says otherwise; for some reason this little terminology distinction (which was settled on decades ago among physicists) never seems to reach the ears of the textbook writers. Worse, a lot of physicists deliberately use the confusing (and, really, technically incorrect) terminology when writing popular books.
Anyway, the short answer is that the relevant quantity you want is not mass but momentum. And as the thing goes around the racetrack, the total momentum you give it as it goes around the back side is exactly equal and opposite to the total momentum you give it as it goes around the front side. No net change in momentum, no net impulse, no propulsion.
Thanks for the reax. As I indicated, I knew it was flawed from the get-go (ME 101). Now, if there were only some way to “push” on the aether in space, like a propeller does with air… ;^) I guess we’ll just have to build our spaceships with huge fuel tanks after all, maybe using the outer shell of rotating tanks for artificial gravity, like a colony ship, unless someone can make that long spring out of nanotubes.
As for TANSTAAFL: Don’t try to wow me with those fancy German words, Mr. Heinlein :^) There are, in fact, free lunches everywhere, but only if you like liverworst and collard greens. But I’m willing to pay full price, I just wanted a tax break.
Elifint: if you noticed, I accelerate on one leg, and decelerate on the other. Like a game of catch, the momentum exchange on both legs is in the same direction, so judging by the legs alone, there is a net forward thrust. It’s the net imbalance going round the bends that zeros it all out. Maybe a Mobius strip would do the trick. ;^)
btw, did y’all here that Kim Jung Il tried to reach the moon with a fan-powered rocket. It was working great until he ran out of extension cord. (wah, wah, waaaaaaahhh)
The idea of using the hole to aid in orbital launches is actually quite clever. IF such a frictionless straight hole could be made, a rocket would have a longer distance/time to accelerate, allowing lower-thrust, higher-specific impulse rockets. Such a rocket would be cheaper, smaller, and much safer than our present guvmint-pork-powered shuttles.
As for the hole itself: Unless you drilled it straight through the axis (and managed to stop the axis from wobbling), OR you stopped the Earth’s rotation, you’ll find that anything dropped would follow one trajectory, and the hole follow another, I believe (haven’t done the math, but I’m pretty sure). Thus, the object would have to have frictionless wheels even if the hole passes through the center, because on both the down and up segments it will be grazing the walls. It would be like trying to run in a straight line through a revolving pipe.
Sorry, I see elifint already made my second point (coriolis), and more elegantly than me.
I have a great idea. What if we make those tunnels not going through the core. We make get all the air out of there. Then we put in tracks for a maglev train. The train would then have no friction. It would have one cart thats just full of oxygen so the passengers can breathe. Once accelerated that thing could go REALLY FAST for a really long time.
I’m just off into the garden to test this idea out.
This is dumb. The initial energy to get any vehicle up to speed is not all that considerable. It is friction that in almost all vehicles (save rockets) results in the most energy demand. If there were no friction or energy losses, you could move at any rate you want and if you had a perfect battery you could get all the energy back when you decide to stop. I am way smarter than everybody in the world. People should be like me because I know things. If everybody were as smart as me, the world would be a trivial place and people like you would have nothing to think about because all of your problems would be solved for you.
And a toast, Alan, to the dreams of Arthur C Clarke! As a child I read Fountains and I always believed that someday man would learn how to make such technology possible. As an adult I just wish the dreams of my childhood had come true.
However I do see promise in the field of synthetics. I even have worked with composites and the results keep getting stronger and better. I’ll bet that $400 billion dollars could accomplish such a feat of superb engineering as this. Maybe the next president of my nation will decide to reach for the stars like Kennedy did… We Have The Technology!!!
12000000000 is about 700metre wide cube isnt
Not so, not by a pretty wide margin. A cube with a volume of 12,000,000,000 m^3 would have an edge of about 2290 m; a 700-m cube has a volume of only 343,000,000 m^3 (1/35 of the bigger cube).
700metres x 3.3ish = 2300. 2300ft cubed is 12 167 000 000 smack on. am i missing something?
oh your doing m^3, the problem is in ft^3
Wow, it takes me more than 42 minutes just to get to the city on the train to go to school (60km, not sure how many miles…someone please tell me how to convert km to miles?) (And that’s without the extra train trip and tram trip (1/2 hour) when i get to the city) I wonder how long it would take to get me to school at that speed?
To convert kilometers to miles, divide by 1.6, because they are very nearly in an 8:5 ratio. 60 km is therefore 37 miles (to the nearest mile).
An excellent website for converting nearly anything to most everything is Online Conversion: http://www.onlineconversion.com
Silverhill said: “An excellent website for converting nearly anything to most everything is Online Conversion: http://www.onlineconversion.com“
You can also go to Google and enter “60 kilometers in miles“. It works for many kinds of conversions, like “14 cups in teaspoons“, or “14 British pounds in US dollars“. Quite handy, indeed.
denki said: “This of course would also require more energy for cornering g forces and loss of speed, but as long as we’re talking about a fantasy, I also get a black unicorn with red eyes that shits candy.”
I love it!!!
nutramistic said: “This is dumb. The initial energy to get any vehicle up to speed is not all that considerable. It is friction that in almost all vehicles (save rockets) results in the most energy demand. If there were no friction or energy losses, you could move at any rate you want and if you had a perfect battery you could get all the energy back when you decide to stop. I am way smarter than everybody in the world. People should be like me because I know things. If everybody were as smart as me, the world would be a trivial place and people like you would have nothing to think about because all of your problems would be solved for you.”
The reason noone is repling is because
A. You’re stating the obvious
B. You’re conceited
C. You’re dumb
Scharneeigh you’re goin little less than 52 mph.
Also, about converting km to miles, I would just like to say that when you run around the track 4 times, you didn’t run a mile, you have 9.7 meters left because a mile is 1609.7m, and one time around the track is 400m.
It takes you more than 51 minutes to
another viewpoint said: “”A hole with a ten foot radius which passed through the Earth’s center would displace over twelve billion cubic feet of rock, all of which would need to be hauled away somewhere. “
…maybe so, but you can’t take any earth out of hole that has a 10 foot radius and is 7290 miles long. The hole is already empty!”
no; there isn’t a “hole” in the Earth until someone takes OUT the rock inside, and then THAT rock would need to be put somewhere.
I remember this from high school physics. I think I almost made my teacher cry when I raised my hand and asked with a very serious look, “What would they do with all the dirt?” I was yanking his chain at the time, but I knew that it was a practical concern and one he wasn’t interested in, as this was not a practical discussion :)
It made me happy to see it addressed in the article. Take that, Mr. Chapman~! (I loved that guy’s class, he was the best teacher I ever had)
I am wondering about the math that leads to the 42 minute travel time. Was that calculated using a standard 1 g acceleration and deceleration, or was there thought given to the fact that the 1 g would lessen during the course of the fall to the center as more and more mass moves relatively behind and/or above the craft as it descends? Or would it not matter as the effect would cancel itself out after passing the midpoint?
As far as producing energy, if the tube were left filled with air rather than a vacuum, would it be possible to take advantage of the differential in air pressure? Say you have a descending object the same diameter as the tube. Couldn’t you use the accumulating air pressure in front of the craft to turn turbines at one end of the tunnel, and the resulting decrease in air pressure behind the craft to turn turbines by pulling air into the tunnel at the origin. Then repeat the process when the craft switches directions.
I realize that, eventually, you are left hauling the craft out of the center of the tunnel. I guess the main question then is would you be producing enough energy to be able to retrieve the craft and still have enough left for other uses to make it all worthwhile?
Gee you would think there’d be a way to slingshot with gravity without having to bore through good old mother earth. Hea- but nice horror movie stuff anyhow.
Banmeihack, altering the pressure of your fluid is not necessary with compounds used in air conditioning and refridgeration. I think you will find this article interesting. An MIT Peace Corp student is using just your idea to provide energy for poor developing countries:
http://www.technologyreview.com/read_article.aspx?ch=biztech&sc=&id=17169&pg=2
The efficiencies touted sound impressive. Coupled with some cheap fresnel lenses, I could see how this could easily provide home energy in a small foot print (less household cooling and air heating needs). Of course thermal battery home designs could solve these problems. I’ve been working on that idea for a while now.
Personally, I’ve always liked solar. Much more so than wind or ocean power. But I’m afraid ugly fuels like nuclear, coal and oil are going to be necessary for a long time.
The recent commitiment to creating wonder crops with great caloric potential is a bit of a horror movie also. This perhaps to fuel our cars and automobiles while still keeping the traditional market forces over energy production and distributuion.
Lets hope those new crops aren’t flammable and don’t destroy too much soil.
I wonder if you have consider the internal dynamics of the earth, as it would seem that the last thing you want to do is drill a hole, if you could, to the center of the earth. The result would be a very big explosion.
Yes, I know, gravity is supposed to increase toward the center of the earth, but does it and does such an idea make the slightest bit of sense.
Has no one considered that the internal and external dynamics of the earth must be inversely proportional to maintain a balanced relatively stable structure. If so gravity decreases from the surface curve to the center of the earth, just as it decreases isometrically from the surface curve.
So the whole idea of a tunnel through the earth is not a reasonable idea at all.
You only have to consider the deepest hole ever drilled which is in Siberia to see that a hole to the center of the earth is not feasible, as the energy of the earth increases with depth the drill simply stops cutting.
Of course a hole in the ground simply extends the external dynamics inward without accessing the internal dynamics which always remain on the inside.
A fun idea the gravity express, but not very realistic. But if gravity is your passion you might want to check out the 7 chapters of a book called Unity at http://www.gravitycontrol.org
Some interesting thoughts on gravity for sure.
The Gravy Train is not a viable transportation mode. I have poured it on the floor (gravity) and sat on it for hours…..nothing. Also, if you drilled a bunch of holes through the earth, it would make an annoying whistling sound as it hurtled through space, pissing off aliens….or are WE the aliens. HMMM.
Essentially impossible on earth, but one hell of a cool idea.
Ok lets say there was a tunnel through the earth couldn’t we just use geothermal energy to convert something like water to steam and use the pressure to counteract the forces of friction and possibly even get there faster than 42 minutes? I hold no degrees in this, but it seems to me that such a temperature difference could more than propel a vehicle from point A to B regardless how deep the tunnel is cut as long as it hot enough underground and cool enough at surface.
It also occurred to me that rather than using magnets and/or electromagnets to reduce friction just use a cushion of gas. If i remember correctly heat can destroy magnets by rearranging the atoms but don’t quote me on that.
I seriously believe that the concept of gravity trains is possible. All have already talked a lot about physics, I need not add volumes to it. However, I think there can be an altogether different approach to the gravity trains.
We have been discussing till now that we need to dig deep straight, reach the earth crust and come up exactly upwards on the opposite direction. Say, the Newzealand and Spain example which are geographically the opposite and straight if we travel through earth’s core.
But what if we never think of reaching the earth core and travel rather shorter distances. All’s well, the gravitaional force, the air pressure, the frictional forces come into much consideration when we have to ACTUALLY REACH THE EARTH’S CORE.
WHAT IS WE NEVER REACH THE EARTH’S CORE? Imagine a circle, rather than a sphere for a moment. Uptil now we have been talking about travelling as a diameter of a circle thus we reach the two extreme points of the circle. What if we consider different chords of the circle and travel from one point of the circle and reach another, much closer point not reaching the core. This will leave us of some considerations of physics be it the gravitional forces, etc.
Naturally, the gravitational force acting at the earth’s core is the maximum so we never need to consider the extreme force. Imagine a place China, if we go straight, we will land on Argentina on the other side, but we are passing the core in this way. Instead, imagine travelling from China to North America, that will make a chord in the circle have shorter distance.
Now imagine going from North America in a different tunnel straight, this will open somewhere in the Indian Ocean. Rather, imagine going to Australia from North America, this will make the 2nd chord of the circle. Now imagine the 3rd chord from Australia to China, short distance thought but just for the sake of connecting places.
If you imagine these THREE CHORDS inside earth’s sphere, you will come to realize that none of these have actualled travelled throught the earth’s core. I am no man of physics but I am sure this will create less troublesome gravity train routes, some which we might believe to be true.
Once a 15th century man thought that we might one day land on moon. People laughed at him, but our great great grand fathers and forefathers never thought we would one day be using cell phones.
Yeah, well it will not be then that easy that it will be a theorotical friction less travel, some kind of energy…..electromagnetic may be required to push and pull the train.
Either of your suggested “chords”, while not touching the earth’s core directly, will penetrate deep into the earths Mantle, which begins only 35 km beneath the surface.
http://en.wikipedia.org/wiki/Structure_of_the_Earth
Down there we have temperatures between 500 and 900°C and pressures above 1 million atmospheres. I find it hard to imagine that the energy needed to build and maintain a tunnel through THAT will be offset by the poential savings in transportation costs.
Also I believe that we’ll see the first few Space Elevators long before such a project will even be technologically feasible for us.
Interesting as the idea of a gravity train may be, it would be much more so if it were backed by empirical evidence. Since the period of oscillation depends only on the sphere’s density and Newton’s constant, G, a scaled down version is possible. The demonstration could be done in an Earthbased laboratory using a modified Cavendish balance.
If only for the sake of completeness, this experiment ought to be performed. To me it seems a glaringly huge gap in our knowledge of gravity that we do not really know how objects fall through the centers of other massive objects. In all known cases, radial falling motion always ends with a collision. Why not let one body fall radially into another body to see what happens when there is no collision?
At the website GravitationLab.com other reasons are given for wanting to do the experiment.
Couldn’t shorter U-shape tunnels work in a low friction environment? I suppose the point where you have to do more of the work than gravity does would mean it would no longer be a ‘Gravity Train’ and more a ‘Gravity-Assisted Train’.
So interesting! And some funny comments. ;)
I want to know what would theoretically happen if someone bored through the earth and came up on the ocean side. All the water would rush down to the hot core and…….? What? The whole ocean turn to steam? Would any water reach the other side? What would happen to the earth’s orbit with all that water gone? Etc…..
With enough lubrication anything is possible!
As an Engineer and free energy opportunist this is my contribution to the tunnel design. We all agree that the closer to the core the hotter, then we can use this free heat energy to suppliment the kinetic energy gained during the drop due to gravity and any losses. We can use water boilers to generate superheated steam at very high pressures. With steam jet nozzles directed at the rear end of this train, say when we are aproaching the center where acceleration due to gravity is negligble we can the open the steam jets to continue accelerating through the center and until we gain suffiecient momentum to guarantee an exit on the other end. All this very much depends on our material science developments and financing. If we have the materials withstanding the pressures, forces and the temperatures this may no longer be a far fetched dream after all.