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How does Elon Musk's Hyperloop work?

By

June 6, 2013

What is Elon Musk's Hyperloop? (Photo: Shutterstock)

What is Elon Musk's Hyperloop? (Photo: Shutterstock)

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Over the past year, Elon Musk, billionaire founder of PayPal, Tesla, and SpaceX, has been floating the notion of a "Hyperloop" as a future replacement for bullet trains; one that would get commuters from San Francisco to Los Angeles in as little as 30 minutes. There has been much speculation over how the Hyperloop works, as Musk has revealed very few details. So what has Musk actually said and what might this translate to in the real world?

What has Musk actually revealed about the Hyperloop? Putting together the bits and pieces from his comments over the past year amounts to something of a performance brief for what the Hyperloop would be capable of. In addition to the killer feature (downtown Los Angeles to downtown San Francisco in 30 minutes), we know that Hyperloop would double the gate-to-gate average speed of an aircraft over that distance, which is 560 km (350 miles). Musk has said Hyperloop is a non-scheduled service which leaves when you arrive, is immune to the weather and never crashes. The only specific technical hints Musk has provided is that it's not a vacuum tunnel, but is a cross between Concorde, a railgun and an air hockey table. This makes quite an impressive list of attributes. Naturally, there is a lot of speculation as to what Musk's Hyperloop must be.

It's clear that he is proposing a system for subsonic transport. Travelling between downtown LA and downtown SF in 30 minutes gives a speed of about Mach 0.91. The same conclusion comes from working out the average speed of an aircraft. Gate-to-gate, the trip between LAX and SFO (337 miles) is listed by the airlines as one hour and 19 minutes, for an average speed of about 255 mph (410 km/h), or about Mach 0.33. Twice this is Mach 0.66.

Business Insider may have been first with its suggestion that the Hyperloop is the old Rand Corporation's Very High Speed Transit System. Unfortunately, this system must run in a vacuum tunnel, which Musk has specifically ruled out. In addition, failure of the control computer would allow cars in the Rand system to collide, which seems to conflict with Musk's claim that the Hyperloop capsules can never crash. The same issue also argues against the popular suggestion that the Hyperloop is essentially a version of the ET3 maglev system.

Another favorite idea is that Musk's Hyperloop may be some version of a Lofstrom Loop, otherwise known as a launch loop. Originally proposed for launching payloads into orbit, a Lofstrom Loop is in essence a vacuum sheath measuring thousands of kilometers long that contains a rotor of iron or other magnetic material. The rotor is magnetically levitated within the sheath, and rotates around the loop at a speed well in excess of the orbital velocity at the Earth's surface (7.9 km/s, or 17,700 mph). The rotor velocity assumed in design studies is usually around 14 km/s (35,000 mph). An external capsule is linked to the loop magnetically, so that it accelerates to the speed of the rotor within the sheath.

A Lofstrom Loop is a much to be desired system for future transporation, but is not a Hype...

Because the rotor is moving faster than orbital velocity, it is pushed away from the Earth's surface by centrifugal force. The maximum altitude of the loop is defined by the length of tethers that attach the sheath to the ground. In the original designs, the top portion of the loop would be around 80 km (50 miles) above the ground, but a loop could be built with an altitude of 100 meters, if there were a reason.

Such a loop could be used for travel between points on the Earth's surface as easily as it can launch payloads. But going by what Musk has said, the Hyperloop does not seem to be a Lofstrom Loop.

The distance from downtown LA to downtown SF is about 560 km (350 miles) as the crow flies. The hypersonic rotor within the loop stretches that distance in both directions, so would be more than twice that length, say around 1,200 km (750 miles). This rotor would have the equivalent energy of about a four-megaton thermonuclear bomb, which some might deem less than ideal in a downtown location. And, use of a Lofstrom loop for subsonic travel between cities is out of proportion to the task. The rotor has to be moving well in excess of escape velocity to suspend the loop in the air. If it is slower, the Lufstrom loop lies on the ground, where it can propel a ground-based bullet train, and encounter all the usual problems.

So if Musk's Hyperloop isn't in a vacuum tunnel, and isn't a Lofstrom Loop, what is it?

The most interesting of Musk's statements is that the Hyperloop is a cross between the Concorde, a railgun, and an air hockey table. The Concorde was fast and revolutionary for personal transport, a railgun uses electromagnetic forces to transport objects at high speeds, and an air hockey table reduces sliding friction to next to nothing. These concepts all pull together to make the Hyperloop.

Diagram of a PTS system conceived as a possible modus operendi for the Hyperloop (Image: B...

It could be that the Hyperloop is essentially a pneumatic transport system (PTS) in the form of a closed tube that loops between Los Angeles and San Francisco. People ride in capsules that travel within the tube at around 1,000 km/h (620 mph), but the air in the tube also moves at that speed, so the capsules move with very little air drag. Such a system is simpler to design if the airflow is subsonic, which is in agreement with Musk's claims.

The airflow would lose energy against the inner walls of the tube, so those are perforated with tiny jets that are supplied with high pressure air, which act as do the jets on an air hockey table to dramatically reduce the friction. The separation between capsules makes an air cushion that prevents capsules from colliding in the tube, and the air jets on the inside of the tube levitate the capsules within the tube.

Because the air is moving at the same rate as are the capsules, the air can be kept moving by using the capsules as "paddles" to push the air along faster. The simplest way of doing this is to use the capsules as the armature of sections of the tube equipped to act as linear magnetic drive segments. That is, as railgun projectiles. If the capsules are forced to travel faster, so is the airflow. Power failure? Hook the drive units up backward to pull electric energy out of the PTS.

Another unusual aspect of the Hyperloop is that you leave right when you arrive. This is another role for a railgun. Imagine you arrive at the PTS station, and climb into a waiting capsule. In order to merge your capsule into the tube, it has to be moving at the same speed so it can be directed into the tube with a minimum of fuss. Since the capsules are going to work with electromagnetic drive units in any case, why not speed them up in the same manner? Of course, stopping at your destination is just the inverse of the merging process.

A serious concern in high-speed ground transportation is to keep the g-loads small enough for the general population. A plane taking off can generate about a g of acceleration, so let's take that as our limit. To accelerate a capsule to 1,000 km/h (620 mph) for insertion into the tube at one g of acceleration takes a track about 4.5 km (2.8 mi) in length, which is long, but not a substantial fraction of the tube's length.

When travelling at 1,000 km/h (620 mph), the tightest curve radius keeping accelerations at one g is about 9 km (5.6 mph). This is a more difficult limit to arrange, as it means the track of the tube must be very nearly straight. Building such a PTS on the space between the opposing lanes of a highway system won't work, save perhaps in very flat states. The biggest challenge is likely to be finding a place to put such a PTS.

The air between capsules acts as cushions to prevent two capsules from colliding within the tube. However, what happens in a catastrophic failure, such as total power loss? The first change is that the air hockey levitation of the capsules becomes ineffective. This can be prepared for by placing a series of small wheels on the sides of the capsules. The second change is that the drag force on the walls of the tube increases to its usual level, causing the air and the entrained capsules to come to a rather slow stop.

The PTS system as described above is my candidate for how Elon Musk's Hyperloop will function. Obviously there are numerous technical, practical, and political problems in setting up such a system, but it would work, and might not be terribly expensive, at least compared to the California bullet train project. We should find out his plans in the next month or so.

About the Author
Brian Dodson From an early age Brian wanted to become a scientist. He did, earning a Ph.D. in physics and embarking on an R&D career which has recently broken the 40th anniversary. What he didn't expect was that along the way he would become a patent agent, a rocket scientist, a gourmet cook, a biotech entrepreneur, an opera tenor and a science writer.   All articles by Brian Dodson
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41 Comments

Wow! Great work!

Kris Lee
6th June, 2013 @ 04:27 am PDT

Maybe the capsule can slightly rotate in anticipation of a turn (assuming the capsule is cylindrical in shape). In that case, you won't be pulled to the side during cornering much like banked turn of an aircraft.

onar
6th June, 2013 @ 04:31 am PDT

As soon as I saw Concorde, a railgun and an air hockey table, I thought of Ekranoplans. http://en.wikipedia.org/wiki/Ekranoplan

winslomb
6th June, 2013 @ 05:33 am PDT

So Elon Musk throws some vague ideas out to fuel interest about a futuristic transport system.

Serious engineers and scientists around the world gather to solve the puzzle of the mysterious machine.

The think tank comes up with a few viable solutions to the problem.

Elon Musk appears before the audience, takes the results and picks one to satisfy everyone's desire for an answer. :b

Nairda
6th June, 2013 @ 05:57 am PDT

http://vixra.org/pdf/1301.0043v1.pdf

This is the actual Hyper-loop that Elon has put his own physics in to improve efficiency.

Mino8907
6th June, 2013 @ 06:37 am PDT

Wheels in the tube would cause drag unless they are supposed to magically pop out when needed. High pressure coming in from the side will not create a smooth airflow going forward. The concorde is made for high speed so it could be that a concorde nosed capsule will push air out of the way and magnets will propel it or the magnets will levitate it and wind will push it forward?

Why not just go with a vacuum?

Mitko Ian
6th June, 2013 @ 06:56 am PDT

Northrop-grummman had a concept for a ground based ekronoplane with a launch mechanism.

called TTWIG-TRACK TETHERED WING IN GROUND EFFECT- ANOTHER WAY OUT IMPOSSIBL CONCEPT.

hummer boy
6th June, 2013 @ 09:43 am PDT

My guess is something similar to a maglev train, except that it rides on an air cushion instead of a magnetic field.

This would eliminate the very high cost per mile for maglev track, as the air cushion track could just be plain old concrete with an electrified rail for power.

The issues would be the noise and vibration generated by the air cushion, plus all of the usual right-of-way problems faced by trains.

Jon A.
6th June, 2013 @ 10:37 am PDT

Having perforated walls would allow air flow to bypass a capsule in the event that one stopped ahead of the other. This scenario could allow a crash. Unless you had a significant amount of check valves....

Chris Walker
6th June, 2013 @ 11:00 am PDT

Elon's largest obstacle will not be the physics behind this idea—it will the politics (this coming from experience). He will meet resistance from politically entrenched contractors demanding they be part of the action or else they will stifle his efforts.

Fahrenheit 451
6th June, 2013 @ 11:42 am PDT

Great write-up. If current trains would simply split into two as they approach the station, the front half could enter the station and stop while the back half bypasses the station. A train full of passengers that recently left that station could slow down until the bypassing section caught it, connected to it on the run then continue on. Passengers would then reposition in the train dependent on if they planned to bypass the next station. As such passengers could travel non-stop at 100+ MPH. Simple and inexpensive. mbarbour65@hotmail.com for my 503 other ideas.

JBar
6th June, 2013 @ 12:18 pm PDT

The design is by Alexander Bolonkin and its the Hyper-sonic Ground Electric AB Engine design.

http://beforeitsnews.com/science-and-technology/2013/04/bolonkins-hypersonic-linear-electric-engine-habe-explained-and-why-it-could-enable-cheaper-than-maglev-hypersonic-travel-and-space-launch-2570034.html

http://vixra.org/pdf/1301.0043v1.pdf

This is the design that Elon has been talking about and its just about the only one that fits his description.

Mino8907
6th June, 2013 @ 12:36 pm PDT

http://www.skyscrapercity.com/showthread.php?t=1625067

The above is a very interesting conversation of what the hyper-loop might be.

AnOld BlackMarble
6th June, 2013 @ 02:59 pm PDT

If we didn't worry about speed so much we could probably have a safe, reliable and cheapish form of transport already.

Friction is the problem.

Air mostly.

Either go up really high or seal yourself in a tube.

Both fraught with danger as we can't survive in those conditions should something bad happen.

That's bad mmmkay.

So use the air to our advantage.

Make a track, (like a c channel or a t section or something neat that you can lift off/propel off perhaps too) sit a nice aerodynamic shaped train on it, use ground effect to lift it, go as fast is efficient/safe/practical.

It's all the other little gizmo's/tricks that you can then use on that base vehicle to make it better, I like the air/air cushion idea, i don't know if/how it'd work on a large vehicle in the open air, might be ok if you're going really fast.... or just golf ball dimple the whole thing and don't worry about air jets.

Ask the Russians, they have whole giant aircraft that skim over water, they've probably got some neat maths on it ;)

All in all I'm very glad Elon Musk is making some noise about it, he's an interesting chap, most billionaires only seem interested in... well I don't know, trapeze artists on their superyachts I guess, they don't make much noise or benefit the world much as far as I can tell.

Do something with your money, be interesting, advance something, cure something, just DO SOMETHING.

If you cannot, I'll happily do it in anonymity in your most exalted name.

Craig Jennings
6th June, 2013 @ 03:48 pm PDT

Calculate the kinetic energy of the air in the tube and have a laugh.

kwarks
6th June, 2013 @ 04:10 pm PDT

Oh Dear God !! PLEASE NOT ANOTHER 'BULLET TRAIN' FOR CALIFORNIA !!! The one propsed now is contoversial, Some farmers don't want it on their land,some counties don't want it at all. It is supposed to reach 200 mph, however if a train from Sacramento tops out at 200 mph, it will have to hit its brake fast or wind up in Bakersfield instead of Stockton, Merced or Fresno. From S.F to L.A. would take about 2-1/2 hours. Okay for through traffic, but local traffic would extend that time by hours. Take a plane.

Being located on a major earthquake fault doesn't thrill me much either.

Also the system proposed is to be built by the Chinese, who can't seem to keep their own 'bullet train' system working right.

Starper
6th June, 2013 @ 04:50 pm PDT

Hey ! I just thought of another great idea.

A giant circus cannon in San Francisco (maybe Treasure Island) and a gigantic net over Griffith Park.

Survivors can pop in to a Dodgers game.

(On my t-shirt = 'Sanity is Overrated')

Starper
6th June, 2013 @ 04:57 pm PDT

A simple tracked hovercraft without a linear motor assist would work up to 400 km/h. About half the target speed. If the air were already moving at a high speed the speeds would multiply not just add. A linear motor could double it again. If the tracks were banked around corners then curvature under 9 km (5.6 mile) are possible.

http://en.wikipedia.org/wiki/A%C3%A9rotrain

Wesley Bruce
6th June, 2013 @ 11:55 pm PDT

Nice article! It has to be a track or tube system in order to achieve that kind of door to door timing. Beyond that, in order to remove the massive aerodynamic costs at sea level, you need reduced air pressure or no air pressure. Either that or minimal friction and super efficient propulsion. How that is achieved via cost effective infrastructure is the question I guess.

After watching those space x grass hopper videos, I'm taking this guy much more seriously. He has runs on the board and the money to put ideas into practise.

Hogey74
7th June, 2013 @ 12:13 am PDT

Space will be conquered by private industry, because pure research, as noble as it sounds, doesn't pay the bills.

He's succeeded when others have said he won't, Tesla is outselling some luxury cars and Space X speaks for itself. I'm sure this will succeed also

Tom Phoghat Sobieski
7th June, 2013 @ 02:25 am PDT

Seems like vacuum tube since it uses pneumatic like those old message tubes in banks etc.

Same idea only scale up.

Stephen N Russell
7th June, 2013 @ 09:16 am PDT

In order not to become a high speed ball of compost, should one of several systems fail, the design will have to be in the form of a central tube (rail), on which the passenger vehicle rides; all enclosed in a second (larger) tube which can be used to manage air resistance and interface with stops and stations.

If the passengers are carried beneath the horizontal center line, the passenger compartment will naturally tip in the direction of corners, without having to worry about banked corners (and their coffee won't spill).

In order to synchronize passengers senses with physical forces acting on the capsules, a set of LED screens will need to act as the "windows"; providing visual clues (possibly a representation of the actual cityscape or countryside) and a feeling of familiarity. That will result in less clean-up of "ejected" stomach contents.

Mirmillion
7th June, 2013 @ 09:31 am PDT

Or maybe, he's throwing out requirements for what it must do and getting ideas from everyone else's speculation.

bimccarthy
7th June, 2013 @ 09:46 am PDT

The model you propose is very much a machine that moves air and suffers from very high frictional losses at these speeds.

The Concorde at altitude operated in a partial vacuum with significant reductions in frictional losses.

It would seem that you did not include the need for differential support air jet pressures in order to compensate for operational loading.

It's a tube system which inventors from Goddard (his last patent was a maglev vacuum train) to Terraspan's rocket scientist all agree is the best performing and most environmentally friendly (very low energy- lower then Ocean freight costs) is the safest, most beneficial long range travel method.

Of course when you really do the math on the need for personal road transport in SF and L.A., add in the very high energy cost of the Musk guesstimate proposal you are better off or at least nearly the same by driving Highway 5 (if you are lucky in a Tesla).

Let's not forget Musk has never proposed or executed on any new technology. Be careful.

attoman
7th June, 2013 @ 10:57 am PDT

What's the big hurry?? How can one enjoy the scenery at 350 mph? This is fine for carrying cargo, but people should conduct business online and travel for pleasure.

ezeflyer
7th June, 2013 @ 11:14 am PDT

Keith Lofstrom here. It's launch loop, not Lofstrom Loop, which is what my intestines do after a great Mexican dinner. If Musk plans a launch loop segment, I'll be out front of his house with a picket sign - loop tech is great for space launch, but lousy for near-city safety.

Brian Dodson's speculations are interesting, but miss three important points - drag, maintaining track alignment in Seismofornia, and twisty topograpy like the grapevine north of LA. Land surface tracks can't go very fast.

But in fawning appreciation of Brian sticking his neck out, I will stick out mine, embellishing a clever idea from my buddies at stratosolar.com . Here's my (literal) trial balloon:

Imagine a an aerostat (balloon) track floating at 12km altitude, above most commercial aircraft, tethered to the ground with well marked power cables. Assume (we'll be doing a lot of that) a track mass of 50 tonnes per kilometer, including a 5 meter wide strip of sun-tracking solar cells (I'm a solar skeptic, but we're having fun here). We are above the clouds and most scattering, in the 1300W/m² insolation zone, so a 15% efficient array generates a megawatt per kilometer, most of which feeds the grid in daytime.

Assume our small passenger vehicle weighs m = 1000kg, moves at v = 300m/s, has a drag coefficient Cd = 0.4, and a frontal area of A = 1m². Air density rho is 0.3kg/m³. Drag power is ½rhoCdAv³, or 1.6 megawatts (on the ground it would be 6.5MW and make a hell of a lot of noise). We can draw that from the track before and aft, and turn it into hand-waving motor power.

Vehicle passage deflects the track downwards, about 0.7 m/s trailing. That can be restored by temporarily releasing tension in the tether anchor motors.

Vertical and horizontal alignment is critical. A 10cm sinusoidal variation over 100meters (0.1%) results in tooth-loosening 0.4 gee 3 Hz shaking. We will need to damp out all perturbations before another vehicle passes, and that may limit passenger rates to less than airline rates.

OTOH, if we skip the silly "no vacuum" claim, an evacuated steel tube running below the surface of the ocean from Daly City, past Pt. Arguello, to El Segundo makes more sense. ½mv² = 45MJ, 12.5 kilowatt-hours, most of which you can recover when you stop. With other vehicles behind you, don't stop too soon!

P.S. My first posting. I assume UTF-8 characters work. If not, (½) = 1/2, (²) = exponent 2, (³) = exponent 3. Where's the preview button? Why does the edit page time out? What are you kids doing on my lawn? Grumble, grumble.

keithl
7th June, 2013 @ 02:04 pm PDT

Assuming this is how it works and that it is built, the efficiency will never even pay the interest on the loans to finance the construction of the track.

Slowburn
7th June, 2013 @ 06:42 pm PDT

What is commendable about Musk is that he is using his money to do something that we are already doing ,.. better and creating excitement. So when others call him a genius or revolutionary it is just the Americans boasting about there own, a self projection. There are ideas but likely one that will work is the one imagined by someone unknown today and if Musk finds it and takes it of - hats of to him.

anmufti
8th June, 2013 @ 01:16 am PDT

You have heard that "everything works on paper" - now you can add - everything works in the minds of Billionaires! There is nothing like money to cloud one's judgement and there is little hope for progress when there is NO money.

donwine
8th June, 2013 @ 04:26 am PDT

Sigh...he's a cutting edge type of guy w/ a PHD in physics...try this:

Quantum locking:

Chastad
8th June, 2013 @ 11:41 am PDT

The author describes an air tube delivery system with air moving past its enclosing tube at 600 odd MPH that has the friction made acceptably low by pumping air into the tube through perforations.

Has he done any back of the envelope calculations to see whether that make the energy requirements any less that powering, say, all of Metro LA? Obviously not.

Bruce A. McHenry
8th June, 2013 @ 01:36 pm PDT

Elon Musk may just merely try to divert public attention from forthcoming air transport solutions -- much in line with DOT and other government-sponsored anti-GA policies.

There's indeed a pending opportunity out there for GA ultra-light aircraft builders, when mass-produced EVs will make electric power units (motor & battery) available at an affordable cost -- remember the similar opportunity that had occurred decades ago with VWs air-cooled flat four-cylinder boxer engine? And since noise is currently the main practical obstacle to mass-use of personal aircraft, electric GA aircraft will definitely change the game.

If Elon Musk were really a visionary, he would anticipate the sole survivor of the automobile era in the longer run, i.e. the urban mini-EV embodied by the detachable cockpit of an ultra-light electric VTOL aircraft, to drive downtown with after landing at the urban periphery...

euroflycars
8th June, 2013 @ 02:23 pm PDT

A man from the Isle of Wight,

Could travel much faster than light.

He departed one day - in a conventional way,

And returned on the previous night.

There once was a man named Musk

Who spoke in a manner most brusque:

"Give your problems to me - I'll solve them for free,

And have you there and back home before dusk".

OuldBill
9th June, 2013 @ 08:39 am PDT

Keith Lofstrom has it right, vacuum or near vacuum is the way to go.

In all fairness to Elon Musk we must not judge his proposal until we actually hear the details from Musk himself.

Brian Dodson took a good shot at second guessing Musk's proposal but I'm sure he would be first to call for the details from Elon. After all Brian ends by telling us the actual plans will come to the public in late July or August.

attoman
10th June, 2013 @ 08:39 am PDT

ET3 patents (the first one is US 5,950,543 from 1999) disclose a system that exceeds Musk's claims for 'hyperloop'. PTT (pneumatic tube transport) has extremely high drag at high speed and /or long distance (unless helium or hydrogen is used as the working fluid -- and then the drag is still much greater than ET3). see www.et3.com

Daryl Oster
17th June, 2013 @ 06:03 pm PDT

Under the heading "there's nothing new under the sun", here's your Hyperloop... it's been done before not quite 150 years ago in NYC and London. Here's some interesting links:

http://gajitz.com/blown-opportunity-new-york-citys-failed-pneumatic-trains/

and a five part article about the London pneumatic train, starting with part 1 here: http://www.ianvisits.co.uk/blog/2012/11/26/londons-lost-pneumatic-railways/

Of special note is the sevice concept for the London train which was show up / on demand (like Hyperloop) rather than strictly scheduled.

CaZ
18th June, 2013 @ 09:51 am PDT

Pneumatic tube - high velocity air moving through low friction metal tube. Cars are un-powered most of the time - pushed by moving air.

(Conventional so far. But next...)

Cars are made to travel somewhat slower than the air around them, via permanent magnets inducing a current in the tube walls to create a bit of drag. This causes air to move past and around the car at high pressure and velocity. Small wings in that airstream carry the weight of the car - with the magnets at their outer tips.

However, with such close tolerances between the walls and potential for air turbulence shaking, a second mechanism is needed for control. The same magnets that induce drag are run in metal channels so that induced magnetic repulsion keeps them centered in the channel, keeping the car from oscillating up/down/left/right or rolling - and also providing banking control for curves.

Near stations, the tube will be wider, reducing the air pressure and velocity. Coming into a station, the car will brake enough (magnetically) to stay slower than the airflow, maintaining the necessary lift until the car is moving slow enough to roll on a track - probably a direct extension of the channels the magnets ride in.

Leaving a station, the car is simply rolled into the narrowing tube, where it is accelerated by the air and soon lifts off the track again.

TomC
26th June, 2013 @ 04:47 pm PDT

if the high pressure air is injected into the tube to levitate the 'carriages', wouldn't there be an ever increasing pressure inside the tube? you would need some sort of blow off valve to relieve pressure, can't see that working.

Anna Pepar
21st July, 2013 @ 04:03 am PDT

Here's a chance for all the really smart kids to shine!

Shawn Jenkins
28th August, 2013 @ 11:59 am PDT

The Hyperloop looks to be an exciting option for fast distance traveling, but similar to current public transportation options like San Jose’s light rail system or Caltrain, it relies on the public to travel to and from specific destinations. Our BiModal Glideway would be a better solution as it would provide the same high speed distance travel, but allow drivers the freedom to go from door to door during their commute.

Tony Alvarado
24th September, 2013 @ 11:32 am PDT

Why not a Gauss tube?

Sergius
4th November, 2013 @ 05:27 am PST
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