I recently heard someone talk on Facebook about the old "duck and cover" drills that school children used to do in the cold war and how obviously that wouldn't protect you from a nuclear bomb. I've actually heard that same thing several times, so I thought it would be good to chime in in support of the civil defense planners of yesteryear. Duck and cover was actually a pretty reasonable way to reduce one's risk of dying in the event of a nuclear explosion.
To simplify a bit, there are basically four ways an atomic bomb can kill you. When it goes off there's a flash of heat and light that can cause burns and fires. There's a shock wave that can crush you directly, or which can collapse buildings and throw things into you. There's a wave of ionizing radiation that can kill you through radiation poisoning. And then there's any radioactive fallout that might kill you much later.
Someone who is standing directly under a big atomic explosion when it goes off is, obviously, going to be very dead. But only the big ones. Back in the day when Air Force was trying to convince people that nuclear anti-aircraft missiles were a good idea a group of five Air Force officer let them test one of those missiles directly over their heads. It was just a relatively small 2 kiloton nuke, 1/8 the yield of the bomb dropped on Hiroshima, and pretty far above them so they didn't suffer anything worse than tinnitus. According to Nukemap 2 kilotons means that the thermal effects were deadly out to .72 kilometers, the radiation out to .86 kilometers, and the blastwave could knock over buildings out to .89 kilometers, so since it exploded 5.6 kilometers over their heads they were relatively safe (provided nothing went wrong).
You can see that for the nuke those Air Force people survived the radiation killed at about the same distance as the thermals and shockwave did. But that isn't true for all bombs. For big bombs the range at which the immediate radiation is dangerous is tiny compared to the range at which you would be incinerated. You can't really do anything to protect yourself from the radiation, so that's bad. But for larger nukes the range of the shockwave grows much more quickly than the range of the radiation. And unlike radiation, the blastwave only travels at the speed of sound so you have some time to take cover. And there are actually useful ways you can take cover from an explosion.
Now, if you should survive the initial blast you still have to worry about the fallout. Unlike a basic atomic bomb of the sort that was dropped on Japan or a hypothetical pure fusion weapon the Teller-Ulam devices that the US and Soviets were putting on their missiles release a lot of fallout. Back when kids were being taught to duck and cover, however, the nuclear arsenals of the world hadn't risen to civilization destroying quantities yet. Every sort of radioactive substance has a rate at which it decays, a half-life. The shorter the half-life the more able that substance is to kill you by having lots of decay events that deliver lots of ionizing radiation to your body. But the shorter the half-life the faster the radioactive substances go away.
Right after thermonuclear bomb goes off you do Not Want to be outside a fallout shelter. But as the days or weeks pass the really nasty substances will go away, leaving merely the things with long half-lives which will drastically increase your chances of getting cancer but would you rather have a decade knocked off your lifespan or die right now?
So in summary, the idea that you should duck and cover after a nuclear attack wasn't crazy, at least when those videos were being made. Nuclear war? Totally crazy. Duck and cove? Not so much.
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