Also look at the power produced by eg a nuke sub plant, vs its weight. Then calculate the power used by a major aircraft. The plane couldnt even get off the ground, and thats not even allowing for all the extra shielding and crash protection youd need. The only way to get the necessary power to weight ratio would be either running your reactor on almost bomb grade fuel or running the reactor at such high temperatures that the reactor can heat outside air as hot as burning het fuel. Which, since the fuel cant touch the air, unlike with jetfuel, means the reactor has to be even hotter yet. So, youre looking at a molten salt reactor, probably.
An MSR would be a good approach - the tech was actually originally developed for the Aircraft Nuclear Propulsion project - but it's not the only one. The historical ANP put most of its resources into a direct-cycle engine with an air-cooled reactor and solid ceramic fuel elements. By 1960 they pretty much knew how to build a nuclear-powered plane, and had tested three nuclear-powered turbojets out in Idaho. The A-Plane would be huge, expensive, and slow, but it would fly.
Later on, in the late 60s/early 70s, NASA-Lewis did some work on civilian nuclear-powered aircraft. They calculated that it could only be economically feasible if it was
extremely large, they were looking at flying wings in the 2-20 million pound range. The reason is that, unlike conventional engines, the mass of a nuclear turbojet scales sublinearly with power - the mass is dominated by the shielding, which is proportional to the system surface area, while the power is proportional to volume. So if your aircraft mass increases by a factor of eight, the mass of the engine - and its cost - increases only by a factor of four. But it's got to be
very big to make it work financially - how big depends on a lot of factors, but certainly the minimum is 2 million pounds, which is in the neighborhood of the biggest planes ever built historically.
Their plan was to use indirect-cycle engines, reactors with solid fuel elements and cooled by liquid sodium or pressurized helium, which would power heat exchangers in the engines. They planned to make the shielding do double-duty as crash padding, and actually tested some mockups using rocket sleds. I've got some pictures somewhere around here.
Needless to say, all versions of this used weapons-grade nuclear fuel.
Anyway, while nuclear-powered aircraft are quite feasible on a technical level, it's very difficult to see being done. I'm not sure if it's possible or not. You'd definitely need a
very different public attitude towards radiation, including widespread acceptance of a linear threshold model of radiation carcinogenesis. And you'd need somebody to be willing to put a
lot of money into airports capable of handling 20-million-pound megajets - for reference's sake, that's big enough to airdrop a Saturn-V rocket.