| Project Daedalus is a proposal from a British pro-space exploration society. It describes a method for reaching fairly high percentages of c - 'fairly high' meaning high single digits - with mostly existing technology. This is based on an original proposal named Orion, which refers to the propulsion method, specifically.
An Orion powered spaceship accelerates in the following manner. At the back of the craft is a large, armor-plated shield. This shield is (optionally, but highly recommended!) connected to the rest of the vessel with large shock absorbers. A nuclear device, otherwise known as an atomic bomb, is ejected from the rear of the vessel, behind the shield, and detonated. The resulting blast wave will accelerate the spacecraft forward. Since this takes place in a vacuum, the inhabitants of the ship will be fine as long as the shield can stop any prompt radiation from the explosion, since there is no soil or atmosphere to generate secondary radioactive contamination.
Problems include the fact that the major powers have signed treaties banning the use of nuclear weapons in space. I personally believe this will last just until we need to dig extremely large holes in other planets, say, to clean up and live in, cheaply. In any case, a more serious problem is how to get the whole assembly off the Earth in the first place, since no-one in their right mind wants it taking off near them using its main drive! The nature of the shield and the structure means that this vessel will be extremely massive, meaning boosting it off the planet via other technologies will be prohibitively expensive in terms of blood and treasure. We are left with building it in orbit. However, we'd still have to lift the components, unless we mined them elsewhere.
Daedalus is a project proposal from a British group (The British Interplanetary Society - Thanks spiregrain!) which uses micro-sized fusion explosions in the same manner that Orion uses fission blasts. The object of the Daedalus project is to send a probe past Barnard's Star in human-scale time; say, fifty years. The Daedalus probe also gets around the problem of boosting propellant off the Earth by 'scooping' fusion fuel from Jupiter or another outlying solar body.
One graphic example of this technology in fiction can be found in the book Footfall, but Larry Niven and Jerry Pournelle. In this book, a race of elephantine aliens arrives in our Solar System in a massive colony ship and immediately begins to attempt the extermination of the human race. Since they have a technological advantage and the high orbitals as well, Humanity appears doomed - until some clever boffins manage to build an enormous Orion-powered vessel in Texas (Update: Kesper North informs me it was actually built in - and therefore nuked - his hometown of Bellingham, WA). They name it the Archangel Michael, stock it with lots of bombs, the existing space shuttle orbiters, and nuclear-powered steam jets, and
WHAM
(pause)
WHAM
WHAM
WHAM
(etc. etc.)
...off it goes.
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