It's The End of the World As We Know It...

[ffutures]

I have a vague idea for a doomsday machine for the Harry Potter universe, based on the self-replicating bludgers I used in the last couple of chapters of my story.

I want to work out how long it takes for them to cover the earth given travel at around 60 mph, random paths, and doubling in numbers every few seconds. My feeling is that this ends up working like the destruction of Jupiter in 2010: Odyssey 2 - you get so many that the mass collapses as a black hole - but my maths really isn't good enough; do they spread out and blanket the world first, or does the implosion happen while they're still over the UK? Obviously it depends on things like their mass (20 to 150lb depending on your source), replication rate, etc., and how many times they double before replication errors creep in. Let's assume that it's Voldemort casting the spell and aiming to maximise muggle casualties, so spelled to target cars, trucks, trains, aircraft etc.

Any thoughts?

Comments

[cdybedahl]

Exponential growth is nasty. Starting from a single bludger weighing 1kg, their number doubling every second, and a maximum bludger speed of 60mph (26.8m/s), the mass inside the expanding sphere will exceed the Schwarzschild radius after 101.5 seconds. The only parameter that noticeably affects the time until the black hole forms is the doubling rate, with the time until collapse inversely proportional to the doubling rate. So one doubling every ten seconds gives just over a thousand seconds to collapse, and once every hundred seconds just over ten thousand seconds.

The one doubling every hundred seconds gives a dramatic two hours and 45 minutes before the blob turns Scotland (roughly) into a black hole.

[vicarage]

And the typical distance moved in a random walk is sqrt(n)*step, so most stay really close to base, Most will stay in the area of Glasgow

[ffutures]

Thanks - that's just what I needed!