Submarines are supported by buoyancy as a result of water displacement, so they can be a lot heavier than aircraft which are supported by lift generated by air moving over the wings.

The noise on a modern airplane is due mostly to the 500MPH airflow outside, not the engines. (Edit: a turbofan engine powered by nuclear-heated air would also likely be about as noisy as one powered by burning fuel)

> The noise on a modern airplane is due mostly to the 500MPH airflow outside

Where are you pulling this from? Every interview I've seen with people who have been on planes where the engines had quit talked about how quiet it got.

Nuclear ships are not a trivial matter. Here is an interesting part of the wikipedia page for the Russian nuclear icebreaker Lenin:

"The second accident was a cooling system leak which occurred in 1967, shortly after refueling. Finding the leak required breaking through the concrete and metal biological shield with sledgehammers. Once the leak was found, it became apparent that the sledgehammer damage could not be repaired; subsequently, all three reactors were removed, and replaced by two OK-900 reactors."

Poor bastards had to break into a nuclear reactor with sledgehammers.

Submarines need to be heavy. A major reason they're so cramped on the inside is because they'd float too well if they had more internal space. The weight of reactor shielding is basically free in that context.

Airplanes need to be light. Tons and tons of lead shielding is a harder proposition there, especially where every pound of shielding is one fewer pound of bombs you can carry.

As a thought - time distance and shielding were the 3 features of my education on radiation safety. What if the plane was very large - such that the crew were a long way forward of the reactor? Would some kind of hydraulic movement to shift the cockpit forward once altitude was gained work? This sort of thing happens to wings, why not cockpit?

Distance will help, but I imagine the plane would have to be absurdly large. The reduction in radiation exposure from each additional foot of distance will go down the farther out you go, and at some point, the additional fuselage will weigh more than the equivalent shielding. It wouldn't surprise me if that point was not all that far out.