How Many Nukes Would It Take?
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The danger of nuclear winter has actually become worse, and it is not dependent on the size of the bombs. The problem is that urban areas are becoming more and more densely built up, and petroleum products (e.g. plastics) are more frequently being used as building materials. You don't need a truly huge bomb -- just one big enough to set fire to everything, so that it can't be extinguished. The energy released from burning all the plastic and wood and other flammable materials found in a modern city can be even greater than the bomb itself. Further, when plastic burns, it's very dirty, and all that smoke gets carried far into the atmosphere. It's the dust and debris and smoke that gets thrown into the upper atmosphere that does the real damage, blocking the sun and changing the climate.
I guess a couple hundred would be enough to nudge a passing rock into an Earth-crossing trajectory. Better yet would be to use the fuel to power a mighty big NTR attached to a comet and use its own water as propellant. This would be a lot more discrete than a big blast, may provide for a quicker intersection and also add a nice oomph to the comet for when it hits the ground. I would also suggest hitting the Atlantic or Yellowstone as nice strategies for maximizing destruction. Hitting Europe could yield the maximum number of deaths in the first hours, but the other two may provide a larger overall devastation.
And nothing would prevent you from using more than one comet. A string of fragments, like SL9, could rain death from the sky very evenly across all inhabited places.
In the end, it all depends on how long after launch you want to wait until the last human is dead. If you require them to be all vaporized a couple minutes by the end of the afternoon, then, perhaps, we don't have enough nukes. If you are a villain with a little more patience, you could use them far more efficiently to first render useless all emergency services (EMPs or stratospheric detonations), then ruining food supplies (even small nukes could start fires) and only then using the remaining firepower to wipe out whoever is left.
It's doable. In fact, we may even be able to wipe out humanity without using any nukes. Some politicians are much, much more destructive.
If you kill 60% of the industrial, technologically advanced urban centers of humanity, you have essentially destroyed civilization. Who cares if 40% are still scampering around if they have no energy, no infrastructure, no libraries, no communications, no industry, and agriculture spoilt by nuclear fallout and potentially nuclear winter?
I seem to remember that device could take out Belgium with blast but would have killed people way back into Eastern Europe/Russia with its fallout.
There is little limit to how big you make a fusion bomb. If you have enough Deuterium, you can make is as big as you like.
Or, at least, as big as you can carry.
The full 100Mt design would have had the usual 3rd fission stage that would have been incredibly messy. Khrushchev announced they had a full 100Mt bomb even though they could only really test a limited version of the design - not really a weapon as it wasn't practical for a number of reasons.
Who needs a 100Mt device anyway?