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xkcd #2929: Good and Bad Ideas
(imgs.xkcd.com)
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It would probably work just fine, but it needs a huge ship. It could get up to a few percent of the speed of light.
FWIW, nuclear test ban treaties are considered to outlaw it. I think we're more likely to solve the technical difficulties of antimatter propulsion than we are to get over the political difficulties of nuclear bomb propulsion.
So could a person sticking their head out and blowing, but it's still a terrible idea.
Just as an observation, there was a time when everyone on the Internet was gaga over the idea of Project Orion, and you didn't dare speak out against it lest you get a hail of downvotes.
It'd work fine in deep space. It's not a good idea to launch from Earth this way. But again, we'll probably find something better once we're at the stage of needing it.
But then how would you launch nukes on orbit without the risk of accudental nuclear explosion?
Implosion-type nukes are all but impossible to make go off that way. They need a whole bunch of small explosives to go off very precisely to squeeze the core in just the right way. A short circuit or a crash won't have the necessary precision. This isn't entirely safe, either--it can still cause a small explosion with a flash of fallout and radiation--but it's a manageable problem.
Gun-types (Little Boy was one) are easier to go off on accident, but the US retired its last gun-type design decades ago. I don't think Russia used them much, either. They're only good for smaller bombs, and their safety issues make them questionable for any use. Smaller nuclear powers aren't bothering with them.