Hole through the earth
April 23, 2003 6:00 AM Subscribe
Have you ever wondered... Just how long would it take to travel through a theoretical hole to the other side of the earth? Apparently 42 minutes.
Alternatively...
Interestingly enough, for a tunnel that reaches from one point to another point on the earth's surface but does not pass through the center of the planet, the travel time would still be about 42 minutes.
Well that explains the delays in the Holland, Lincoln, Midtown, and Brooklyn-Battery tunnels in NYC.
posted by riffola at 6:05 AM on April 23, 2003 [1 favorite]
Interestingly enough, for a tunnel that reaches from one point to another point on the earth's surface but does not pass through the center of the planet, the travel time would still be about 42 minutes.
Well that explains the delays in the Holland, Lincoln, Midtown, and Brooklyn-Battery tunnels in NYC.
posted by riffola at 6:05 AM on April 23, 2003 [1 favorite]
I just did some very shallow excavation work while expanding my driveway. All that dirt had to go somewhere. How much slag would be left over from a tunnel that long?
posted by gimonca at 6:53 AM on April 23, 2003
posted by gimonca at 6:53 AM on April 23, 2003
Odd coincidence: I just finished reading the new Jasper Fforde novel, Lost in a Good Book (for those who don't know him, it's a kind of whimsical, quasi-Hitchhiker's Guide fantasy/adventure/extended joke, the second in the series which began with The Eyre Affair). In the alternate world of Fforde's book, there are "shuttles" which utilize holes just like this one. Interestingly, he not only matches the travel time mentioned in the article, but also includes the datum that the time it takes to "fall" from London to Auckland winds up being the same 40+-minutes as a shorter journey by the same method between two closer points. So he must have done his homework.
Of course, he ignores all the other physics objections to the idea (how you get frictionless travel, how you drill and maintain the hole), but then, this is a book that features time travel, cloned Dodos as housepets, and people popping in and out of the great works of literature. So I suppose physics is a quibble.
posted by BT at 6:55 AM on April 23, 2003
Of course, he ignores all the other physics objections to the idea (how you get frictionless travel, how you drill and maintain the hole), but then, this is a book that features time travel, cloned Dodos as housepets, and people popping in and out of the great works of literature. So I suppose physics is a quibble.
posted by BT at 6:55 AM on April 23, 2003
Fall through the Earth? But wait, wouldn't you stop somewhere in the middle? Because after you pass through the core of the Earth, you'd be falling up, right? I mean, your kinetic energy would be high since you'd be falling at about 180 mph (free-fall), so maybe you'd go another hundred feet or so, but then you'd fall back like a yo-yo to the center. Actually, you'd probably not even hit free-fall speeds, since you'd most likely slow down as you approach the center.
I'd just like to add that this is all pure speculation on my part. If anyone has any actually scientific knowledge to back this up or refute this, or perhaps a good link to an explanation, the CommunityFilter would probably appreciate it.
posted by Civil_Disobedient at 6:59 AM on April 23, 2003
I'd just like to add that this is all pure speculation on my part. If anyone has any actually scientific knowledge to back this up or refute this, or perhaps a good link to an explanation, the CommunityFilter would probably appreciate it.
posted by Civil_Disobedient at 6:59 AM on April 23, 2003
If there were no friction, there would be no energy loss so our traveler could oscillate into and out of the tunnel.
How fun would that be?
posted by gottabefunky at 7:04 AM on April 23, 2003
How fun would that be?
posted by gottabefunky at 7:04 AM on April 23, 2003
Civil: The article states no friction. The terminal velocity that you list at 180mph is the free fall speed of a human through air. The no friction stated in the problem would mean that there was also no air....thus you would accelerate all the way to the center and decelerate all the way to the surface at the other end.
posted by Odi et Amo at 7:11 AM on April 23, 2003
posted by Odi et Amo at 7:11 AM on April 23, 2003
(Civil Disobedient) - They ignore friction, so there wouldn't be a terminal velocity, you'd just keep accellerating to the middle and then slow down all the way back. Quickly doing the maths, the tunnel is 12,756 kilometers long and you do it in 42 mins, so your average speed is 18223 kph.
And gimonca, if the tunnel was 1 metre in diameter you'd get 12,756,000 x 3.14 x 0.5 x 0.5 = 10,013,460 metres cubed of rubble (would make a cube 215 metres on the side)
posted by jonvaughan at 7:15 AM on April 23, 2003
And gimonca, if the tunnel was 1 metre in diameter you'd get 12,756,000 x 3.14 x 0.5 x 0.5 = 10,013,460 metres cubed of rubble (would make a cube 215 metres on the side)
posted by jonvaughan at 7:15 AM on April 23, 2003
Ah, sorry, didn't notice no friction. That'd be pretty neat, though I still prefer the world of friction and all of its unstated conveniences and pleasures.
posted by Civil_Disobedient at 7:35 AM on April 23, 2003
posted by Civil_Disobedient at 7:35 AM on April 23, 2003
Just like in college when you were able to ignore friction....
posted by Cool Alex at 7:51 AM on April 23, 2003
posted by Cool Alex at 7:51 AM on April 23, 2003
would make a cube 215 metres on the side
Or a 'pile' about 400 meters high and getting on towards a kilometer across the base... depending on the steepness of the sides of course. That's a fairly respectable slag heap but it's not really much of a hill by geographic standards.
posted by adamt at 8:00 AM on April 23, 2003
Or a 'pile' about 400 meters high and getting on towards a kilometer across the base... depending on the steepness of the sides of course. That's a fairly respectable slag heap but it's not really much of a hill by geographic standards.
posted by adamt at 8:00 AM on April 23, 2003
expanding the scope of this thread to the other stuff on the site linked to, i call bullshit on the "scientific" answer to this question.
Fancy pants Scientific American says that the direction of swirling water going down the drain is not governed by the hemisphere you're in, because local effects (residual currents in the water pre-draining, or imperfections in the shape of the drain) overwhelm the rotational effect of the earth. I spent a slow evening once trying to make the water drain the other way. EVERY drain in my house drains one way (I forget which), no matter how much I push the water around to try and encourage swirling the opposite direction. What's more, everyone I know born in the northern hemisphere has a head swirl going in the same direction (again, I forget which). (head swirl being the direction of the growth of your hair at the top of your head, the terminus of the part, for those who part).
Scientists, you better tighten up. How can you overcome the creationists if you can't get the swirling right?
posted by luser at 8:08 AM on April 23, 2003
Fancy pants Scientific American says that the direction of swirling water going down the drain is not governed by the hemisphere you're in, because local effects (residual currents in the water pre-draining, or imperfections in the shape of the drain) overwhelm the rotational effect of the earth. I spent a slow evening once trying to make the water drain the other way. EVERY drain in my house drains one way (I forget which), no matter how much I push the water around to try and encourage swirling the opposite direction. What's more, everyone I know born in the northern hemisphere has a head swirl going in the same direction (again, I forget which). (head swirl being the direction of the growth of your hair at the top of your head, the terminus of the part, for those who part).
Scientists, you better tighten up. How can you overcome the creationists if you can't get the swirling right?
posted by luser at 8:08 AM on April 23, 2003
I feel it's time to ask:
Why did the mute cat fall off the roof?
posted by twine42 at 8:19 AM on April 23, 2003
Why did the mute cat fall off the roof?
posted by twine42 at 8:19 AM on April 23, 2003
luser I don't remember that article. I do remember two from NS though, one which stated that imperfections in flow caused the spiral, but said nothing about the direction of spin.
The other was about people showing you which way water spinds on either side of the equator, and showing that there is almost no spin there, so it's actually to do with how the water is poured into the bowls in those tests...
posted by twine42 at 8:30 AM on April 23, 2003
The other was about people showing you which way water spinds on either side of the equator, and showing that there is almost no spin there, so it's actually to do with how the water is poured into the bowls in those tests...
posted by twine42 at 8:30 AM on April 23, 2003
Dear concerned toilet watchers, check out Bad Science, especially the page on the Coriolis Effect.
posted by biffa at 9:24 AM on April 23, 2003
posted by biffa at 9:24 AM on April 23, 2003
Sigh. Mark Shegelski. I love him. I may be the world's first ever physicist groupie, but I've been a fan of Shegelski's ever since I read his explanation of why curling stones curl the way they do.
He works at a small University in my home town, and some day, when I'm home for Christmas or something, I'm going to find a way to meet him.
posted by jacquilynne at 9:29 AM on April 23, 2003
He works at a small University in my home town, and some day, when I'm home for Christmas or something, I'm going to find a way to meet him.
posted by jacquilynne at 9:29 AM on April 23, 2003
nah... jacquilynne, lots of chicks dig physicists, 'cuz the physicists know all about the attraction of heavenly bodies.
posted by ph00dz at 10:02 AM on April 23, 2003
posted by ph00dz at 10:02 AM on April 23, 2003
I'd love to take a shit in a hole like this.
posted by SpaceCadet at 11:11 AM on April 23, 2003
posted by SpaceCadet at 11:11 AM on April 23, 2003
The Straight Dope addressed this in 1979. Cecil ducked the time question, though.
posted by kirkaracha at 12:10 PM on April 23, 2003
posted by kirkaracha at 12:10 PM on April 23, 2003
Another assumption in the "42 minutes" calculation is that the density of the earth is uniform. It's not--the core is about three times as dense as the mantle--so the time will be less than 42 mins.
How much less? Unfortunately, since the density varies with distance, the system is now an anharmonic oscillator (ie. the force is not directly proportional to the distance from the center of the earth), it can no longer be solved analytically.
posted by starkeffect at 1:14 PM on April 23, 2003
How much less? Unfortunately, since the density varies with distance, the system is now an anharmonic oscillator (ie. the force is not directly proportional to the distance from the center of the earth), it can no longer be solved analytically.
posted by starkeffect at 1:14 PM on April 23, 2003
stark, if cannot be solved with theory, must dig hole to test theory. could afterward slap a particle accelerator there.
what we really need to find out is how to do this sort of tunneling on black holes. your density-variation will become moot then! v. likely this is how those famous wormholes are actually effected [always suspected a cheat]. how to cut through center of singularity? need a steady hand.
also, what happens if not only is earth completely hollowed out, but all dirt packed into superdense superthin crust? preferably thin grid [hexagons tile nicely]. good testament to buckminster fuller... [or escher, if one gets creative]. then for shuttles, one simply falls in any nearby hole, yes? but as one approaches center [zero g there] if one bumps someone else, both are stuck there.
better, then, to leave certain large lumps in complementary orbit of center. one times one's jump to take advantage of lumps' deflections of trajectory, and can then land anywhere on surface.
also, superdense superthin grid surface ideal for avoiding killer comets - if structure thin enough, they pass through earth none the wiser.
posted by mitchel at 9:58 PM on April 23, 2003
what we really need to find out is how to do this sort of tunneling on black holes. your density-variation will become moot then! v. likely this is how those famous wormholes are actually effected [always suspected a cheat]. how to cut through center of singularity? need a steady hand.
also, what happens if not only is earth completely hollowed out, but all dirt packed into superdense superthin crust? preferably thin grid [hexagons tile nicely]. good testament to buckminster fuller... [or escher, if one gets creative]. then for shuttles, one simply falls in any nearby hole, yes? but as one approaches center [zero g there] if one bumps someone else, both are stuck there.
better, then, to leave certain large lumps in complementary orbit of center. one times one's jump to take advantage of lumps' deflections of trajectory, and can then land anywhere on surface.
also, superdense superthin grid surface ideal for avoiding killer comets - if structure thin enough, they pass through earth none the wiser.
posted by mitchel at 9:58 PM on April 23, 2003
Actually, if the earth were hollow, with all the mass uniformly distributed about the surface, you'd feel weightless everywhere inside, not just at the center. This is a consequence of the inverse-square law of gravitation and a remarkable theorem of vector calculus called Gauss's Law.
posted by starkeffect at 11:44 AM on April 24, 2003
posted by starkeffect at 11:44 AM on April 24, 2003
yes, wasn't thinking clearly - fortunately [if in vacuum] one loses none of one's initial velocity, thus enabling jump to take place at more comfortable speed than 18 megameters per hr. higher one jumps, faster one travels downwards. this speed control helps in avoiding center point collisions.
also, on further reflection, those interested in perpetual motion machines are allowed to become one themselves, if frictionless hole is built. good place to stash those annoying pests.
finally, have reconsidered that concentration of earth's mass into giant superthin ring is best plan. gravity on disk described by ring is zero; gravity within sphere described by rotation of ring pulls objects towards surface of disk; gravity beyond sphere / ring acts as normal [objects pulled towards center]. among many advantages, one can enjoy falling from one end of ring to opposite not in straight line but in pleasant sine curves. also, bonus points if moon passes through hoop of earth.
posted by mitchel at 2:38 PM on April 24, 2003
also, on further reflection, those interested in perpetual motion machines are allowed to become one themselves, if frictionless hole is built. good place to stash those annoying pests.
finally, have reconsidered that concentration of earth's mass into giant superthin ring is best plan. gravity on disk described by ring is zero; gravity within sphere described by rotation of ring pulls objects towards surface of disk; gravity beyond sphere / ring acts as normal [objects pulled towards center]. among many advantages, one can enjoy falling from one end of ring to opposite not in straight line but in pleasant sine curves. also, bonus points if moon passes through hoop of earth.
posted by mitchel at 2:38 PM on April 24, 2003
« Older Cry God for Harry! England and Saint George! | Chandler, release 0.1 Newer »
This thread has been archived and is closed to new comments
posted by riffola at 6:01 AM on April 23, 2003