Inside, the carpet running down the aisles is implausibly clean and the seats are unusually wide. They are firmly sprung, more BMW than Jaguar. For 15 or 20 minutes the two-carriage prototype floats around its 31km (19 miles) of track at Lathen, in the Emsland region of western Germany. From a standing start, it accelerates to 382kph (238mph) in less than three minutes - just quickly enough to push you gently back into your seat. Then, seemingly as soon as it began, the ride has ended. Baroque Muzak wafts over the loudspeakers, and the passengers troop obediently off.
The nearest experience I had had to this was a Star Wars ride at Tokyo Disneyland; except there you could join the queue again if you wanted. But this is far from mere entertainment. In five or six years, it could be carrying hundreds of thousands of passengers across Germany at average speeds well above 200mph. According to its developers, a government- sponsored consortium of Germany's most respected heavy engineering companies, the Transrapid could revolutionise the economics that have made short-hop air travel more attractive than trains.
The basic technology inside the Transrapid, a linear motor, has been a scientific dream for most of this century. In 1909, an American called Robert Goddard, who later invented the liquid-fuelled rocket, designed an electric motor that used the standard method of magnetic repulsion and attraction familiar from rotary motors. But there was an important difference. Instead of stringing magnets around to form a cylinder, Goddard stretched them out flat, so that switching on an electric current would produce horizontal motion along a straight line. With magnetic repulsion used to keep an object suspended in mid-air above the track, the linear motor could in theory provide the basis of a railway technology in which the trains never came into contact with the track.
Goddard was not the only one who worked on the idea, however. In 1922, a German engineer, Hermann Kemper, started researching a variant of the idea, in which the train was to be held aloft not by magnetic repulsion from below, but by attraction from above. For years he worked tirelessly at his model, and won a patent for it 15 years later. But the 'magnetically levitated' (maglev) train never became one of the pet projects of the Third Reich. While Adolf Hitler pumped resources into the V-1 and V-2 rockets, and built the autobahns, his regime never took Kemper's ideas seriously.
A great deal of work has been done since. A few short, low-speed maglev railways are already in operation, but it has proved much harder to deliver enough power to move a full-size train at high speed and in reasonable safety. Scientists in Japan have been working on a maglev train that uses superconductivity - the property of certain substances that have almost no electrical resistance at very low temperatures - to provide a powerful magnetic charge aboard a train with only a dribble of electricity.
Room-temperature superconductors, however, remain a Holy Grail; today's have to be kept far below freezing with cumbersome and dangerous refrigerators. Japan's experimental maglev train recently suffered a disastrous fire and crash while undergoing tests at its experimental track.
The German scientists have been working since the early Seventies to make the Transrapid a reality. Their seventh, and latest, model contains a key technical difference from earlier trains. Rather than suspending the train above the track by magnetic repulsion from magnets underneath, it uses Kemper's idea, lifting the train off the track by attraction from magnets above. The new model contains a mechanism that switches off the electric current about 100,000 times a second, in order to prevent the train clamping hard on to the attracting magnets (which would stop it dead in its tracks). This means the train no longer needs to float so high.
With a gap between train and track of only about 1cm, compared with the 10cm used in many earlier maglev trains, much less power is needed to keep it aloft. And to keep the train's weight down, it is the track, rather than the cars, that carry the bulk of the electric current.
The result of all these differences is that the train performs dramatically better than either existing maglev train technology or other experimental systems. It is likely to be able to cruise at well over 400km an hour (250mph) under practical conditions. At such speeds, it can match air travel between two city centres 1,000km (625 miles) apart. More important, the Transrapid performs more like a sports car than a train. It can reach its cruising speed in only a sixth of the distance of existing high-speed trains. That makes it economical for the train to make frequent stops, unlike conventional high- speed trains.
The Transrapid can also climb and turn easily. While France's best TGV (train a grand vitesse) models can manage a gradient of only 3.5 per cent, and the tightest circle that Germany's trains can turn has a radius of 7km, the new train can easily mount a 10 per cent gradient and turn a 1.6km-radius circle. That reduces dramatically the amount of tunnelling and embanking that must be done and allows rail planners to choose curvier but cheaper routes. Finally, the planners say that a double-track line requires less land than conventional railway lines or roads.
These factors combine to make it possible for the train's tracks to be built at about half the cost of traditional high- speed electric train tracks. The technology does have its drawbacks, however. First, the short distance that the train floats above its track means that tremendous accuracy is required in the engineering of both train and track. On the experimental Transrapid track at Lathen, one section of track can never vary by more than 0.6mm sideways or 0.3mm up and down from the next.
So far, there seem to have been no problems in the maintenance of the 31km experimental loop of track. But maintaining thousands of kilometres of track that will have to carry electric power and stay in place to within a fraction of a millimetre for decades to come is an entirely different matter.
Although Green Party politicians complain that the train is too noisy, I found it quite tolerable when I stood less than 100m from the track as it passed at high speed.
The current model of the Transrapid has been hopefully named Europa, reflecting the ambition of its makers to have it accepted as the core of a new trans-European network of super-high-speed trains, capable of carrying vast numbers of passengers as traffic grows in the 21st century. The Bundestag is due to decide later this year on a line between Hamburg and Berlin that will cost DM8.5bn ( pounds 3.5bn).
But there is a one large problem facing the spread of maglev trains. Crumbling though they are, the railway tracks that already exist elsewhere in Western Europe have been built over a period of more than a century. Their cost has been almost entirely paid off. It is likely to be cheaper to make better use of existing capacity, running more and better trains on today's tracks, before building new ones.
This is an example of a disappointing truth: just because a technology is good and efficient, does not mean that it makes sense to use it.