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Introduction
I'm proposing a new formula used for calculating high speed, high yield explosions. The formula is an edit to Taylor's formula, which was a dimensional analysis used to determine the yield of the atom bomb; however, Cook took released government data and extensive lab testing to fix Taylor's, yielding an accuracy of roughly 2% error.
Cook's Formula
You can read all about the derivation of the formula here, but I will also link the relevant formula here. Where gamma is generally 1.4 for standard ground explosions, rho is the density of air, R is the radius of the fireball formed in a time t, and t is the time it took the fireball to get to that radius.
Proposal
A good exert from Cable (found at the bottom of this page) on why it is valid:
“But wait!“, I hear you cry. Isn’t all of this used to determine the power of a nuke anyway? Why yes, yes it is. But it SHOULD apply to any explosion and here’s why: The time factor is what, as I mentioned and showed above, separates nuclear, high, and low explosives. How fast a bomb releases its’ energy can actually change the effects of it. It would be inconvenient, but according to the US government, detonating 500 tons of TNT would be similar (In blast effects only) to detonating a 1 kiloton nuke, and they specifically say it’s all to do with the speed at which that energy is released.
Which leads to my proposal: for blasts that are comparable (or greater) in speed to nukes this formula would apply (the formula proved valid for a fireball with a speed of ~13 km/s). That being because the formula is entirely dependent on the size and speed of the explosion, not the contents of said explosion. The explosion should also be large with a massive shockwave, like the magnitude of high speed explosives this formula was derived from.
I'm proposing a new formula used for calculating high speed, high yield explosions. The formula is an edit to Taylor's formula, which was a dimensional analysis used to determine the yield of the atom bomb; however, Cook took released government data and extensive lab testing to fix Taylor's, yielding an accuracy of roughly 2% error.
Cook's Formula
You can read all about the derivation of the formula here, but I will also link the relevant formula here. Where gamma is generally 1.4 for standard ground explosions, rho is the density of air, R is the radius of the fireball formed in a time t, and t is the time it took the fireball to get to that radius.
Proposal
A good exert from Cable (found at the bottom of this page) on why it is valid:
“But wait!“, I hear you cry. Isn’t all of this used to determine the power of a nuke anyway? Why yes, yes it is. But it SHOULD apply to any explosion and here’s why: The time factor is what, as I mentioned and showed above, separates nuclear, high, and low explosives. How fast a bomb releases its’ energy can actually change the effects of it. It would be inconvenient, but according to the US government, detonating 500 tons of TNT would be similar (In blast effects only) to detonating a 1 kiloton nuke, and they specifically say it’s all to do with the speed at which that energy is released.
Which leads to my proposal: for blasts that are comparable (or greater) in speed to nukes this formula would apply (the formula proved valid for a fireball with a speed of ~13 km/s). That being because the formula is entirely dependent on the size and speed of the explosion, not the contents of said explosion. The explosion should also be large with a massive shockwave, like the magnitude of high speed explosives this formula was derived from.