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Project Orion was developed in the late 1950's and early 1960's by the US Government.
The idea?
To propel a spacecraft by exploding atomic bombs behind it.
Theodore Tyler and Freeman Dyson were two of the prominent men behind the project when it was brought to the Advanced Research Projects Agency ( ARPA) in 1958.
The most common incarnation called for a battleship-type space vehicle mounted on top of a large, curved metal plate. Bombs would be dropped out of a slot in the plate followed closely by solid-fuel discs. The bombs would then be detonated at roughly 200 feet behind the plate: the discs would vapourise and the resulting plasma pushed against the plate, driving the Orion.
In this way, the craft would operate in a pulsed mode instead of a continuous one. The advantage to this is the same as a car engine: although the peak temperature is far above the melting point of the surrounding chamber or plate, the metal remains intact because the peak temperature is reached only very briefly in the combustion/ignition cycle. Research on the type of metal which could feasibly be used pointed towards either aluminium or steel.

The Orion ships designed by Dyson were massive things compared to the contemporary Apollo craft: capable of carrying a crew of 150, with a lift-off mass of 10,000 tons. On takeoff, they would detonate a 0.1 kiloton bomb every second. The rate of denotation would slow, while the yield would increase as the Orion accelerated, eventually reaching its cruising rate of one 20 kiloton bomb every ten seconds.
Unfortunatly, the signing of the Nuclear Test Ban Treaty in 1963 mostly put an end to Orion, since it would make any flights illegal under the terms of the treaty.
More recent studies into Orion have shown that, surprisingly, it could have worked quite well. For an outlay of roughly the same amount as the entire Apollo project, Orion could have been made feasible.

According to George Dyson's book, the pulse unit for a 30 foot diameter ship was 1 kiloton and weighed a little over 300 pounds. 2,000-3,000 of these would have been needed to get to Mars and back. The Orion team explored a wide range of possible ship sizes and concluded that a 400 meter diameter vessel would be the largest feasible size for lift-off from the Earth's surface. This lift-off would be possible with hydrogen bombs.

There is a quote by Freeman Dyson in the book that mentions a calculated 5 cents per pound of payload (at 1960s era prices) for a 1,000,000 ton ship powered by a few thousand megaton H-bombs.

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