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Wiki:

The Ford Nucleon was a nuclear-powered concept car developed by Ford Motor Company in 1958. The design did not include an internal-combustion engine, rather, the vehicle was to be powered by a small nuclear reactor in the rear of the vehicle. The vehicle featured a power capsule suspended between twin booms at the rear. The capsule, which would contain a radioactive core for motive power, was designed to be easily interchangeable, according to the performance needs and the distances to be travelled.

The passenger compartment of the Nucleon featured a one-piece, pillar-less windscreen and compound rear window, and was topped by a cantilever roof. There were air intakes at the leading edge of the roof and at the base of its supports. An extreme cab-forward style provided more protection to the driver and passengers from the reactor in the rear. Some pictures show the car with tailfins sweeping up from the rear fenders.

The drive train would be integral to the power module, and electronic torque converters would take the place of the drive-train used at the time. It was said that cars like the Nucleon would be able to travel 8000 km (5,000 miles) or more, depending on the size of the core, without recharging. At the end of the core's life, it would be taken to a charging station, which research designers envisioned as largely replacing gas stations. The car was never built and never went into production, but it remains an icon of the Atomic Age of the 1950s, when concerns and dangers such as radiation poisoning, nuclear waste and the possibility of nuclear meltdown were not completely understood or acknowledged.

The mock-up of the car can be viewed at the Henry Ford Museum in Dearborn, Michigan.

It is very doubtful, if it would be possible to build a vehicle in the size of a standard car with a reactor as propulsion, as it emits neutrons, which require thick absorbers. It is also not possible for physical reasons to build a reactor under a certain size, which depends on the used nuclear fuel. So it is very doubtful, if this car was ever realizeable.