In this video on the USSR’s Tsar Bomba H-bomb, they make the impressive claim that they could detect the blast wave on its third trip around earth. Are their any equations I could use to compute this? I tried googling, with limited success.
Compute what?
The pressure wave will be traveling at the speed of sound soon after the explosion. At 760 mph, it would take around 32 hours to circle the Earth. Hard to believe it could be detected 96 hours later.
They detected the Krakatoa 1883 explosion noise going around the world seven times. I would imagine that instruments are much more sensitive now.
Duck! Here is comes again!
The shortest distance that the wave could travel would be around the line of latitude of the site. That length equals
L = πdcos(latitude)
d is the diameter of the earth, 7913 statute mi.
As usual with anything to do with the physical consequencies of setting off a nuclear bomb, the place to start is with Glasstone and Dolan’s The Effects of Nuclear Weapons. (There’s an interesting history of the report/book here.)
In this instance the relevant equations are in “Technical Aspects of Blast Wave Phenomena” at the end of Chapter III. They give formulae for things like how the distance a particular overpressure is felt at scales with the size of the bomb and the like.
There is the snag however that it’s really only concerned with damage from nuclear weapons. That the blast wave from the Tsar Bomba could be detected after it circulated the globe three times is impressive, but this was long after the overpressure from the blast was actually capable of damaging anything. Because damage, even in this case, would happen over much shorter distances, the discussion implicitly assumes that the Earth can be treated as flat. That assumption breaks when one starts to wonder about such small effects very far from the explosion. (In fact this is only one of several assumptions that will break down in the late stages of the evolution of the blast wave, but it’s the easy one to point out.)
So you can’t take Glasstone and Dolan’s equations and directly apply them to this situation. But this is an example of how these sorts of questions can be addressed and what the conclusions look like.
If this is a whoosh, then you got me, but the blast wave would always follow a great-circle route. A blast at the equator takes just as long to travel around the planet and pass the origin as one at the pole.
Here’s a thought experiment: Suppose you light off a large firecracker in Manhattan. Could you hear it in Los Angeles? No. Could it be detected in Los Angeles? I doubt it. Logically, the pressure wave would be swamped by various sounds / pressure fluctuations /wind somewhere in New Jersey.
So for “The Tsar”'s pressure wave to have gone around the world 3 times and be detectible, logically, at an absolute minimum, it should have been audible everywhere on the first go-round.
My guess is that the shockwave being detected 3 times was the ground tremor that was felt directly and then refracting off of various features inside the Earth.
When I took at a globe and imagine a circle spreading out from a point I see the the circle’s circumferance always intersecting the line of lattitude through the point at its center.
Y’know, on further reflection you are right. Before the intersection of the circle and the lattitude line can circle the earth, the circle will have expanded past the lattitude line.