The Trans-Atlantic MagLev VacTrain -- A Magnetically Levitated Vacuum Tube Train

A Maglev train floats about 10mm above the guidway on a magnetic field and is propelled by the guidway itself rather than an onboard engine by changing magnetic fields. An exotic proposal based upon this principle is the Trans Atlantic vactrain: a Maglev train in a long near-vacuum tube with speeds that allow less than one hour travel times between New York and London.
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Maglevs (Magnetically levitated trains)

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The principal of a Magnet train is that floats on a magnetic field and is propelled by a linear induction motor. They follow guidance tracks with magnets. These trains are often refered to as Magnetically Levitated trains which is abbreviated to MagLev.
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From Wikipedia, the free encyclopedia

A vactrain is an exotic, as-yet-unbuilt proposal for future high-speed railroad transportation. This would entail building maglev lines through evacuated (air-less) tunnels.
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Transatlantic tunnel

A transatlantic tunnel is a theoretical tunnel which would span the Atlantic Ocean between North America and Europe and would carry mass transit of some type—trains are envisioned in most proposals. Using advanced technologies, speeds of 300 to 5,000 mph (500 to 8,000 km/h) are envisioned.[1]

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Trans-Atlantic MagLev

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Discovery Channel
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Discovery Channel - Extreme Engineering - Transatlantic Tunnel
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Maglev Trains
Moving Forward with America’s Fastest Eco-friendly Train
Maglev Train Set To Become America’s Fastest Eco-friendly Train - Ecofriend
Vactrain - Wikipedia, the free encyclopedia
Transatlantic tunnel - Wikipedia, the free encyclopedia
Trans-Atlantic MagLev | Popular Science
Discovery Channel :: Extreme Engineering: Transatlantic Tunnel
HowStuffWorks "How Maglev Trains Work"
Maglev (transport) - Wikipedia, the free encyclopedia