Sunday, February 17, 2013

Calculating megaton blast radius

So, I'm no physicist, but I'm writing a story that involves a large explosion.  I couldn't find a good calculator to just do the calculation, but I also can't create one yet.  However, I can put all of the information together for anyone who's interested.

Let's say you're using a story that involves some sort of relativistic kill vehicle. Say, the object weights 100 kgs and is traveling at 0.1c (c being the speed of light).  Now, Einstein's famous equation is E=mc2 but this is only true when the object is traveling very close to the speed of light.  Normally, the energy equation is E=(1/2)mvand this is still true even at 0.1c. In this equation, m is mass in kilograms, and v is velocity in meters/second.  So, in this case, the energy is ((100/2)((0.l*300,000,000 m/s)(0.1*300,000,000 m/s) which equals (50)*(9x10^14).  This equals 4.5 x 10^16 joules. The amount of energy released by one megaton of TNT is 4.2 x 10^15. So, to figure out the megatons of damage take your energy divided by 4.2 x 10^15 joules.

In this case, it's essentially 45/4.2 (you can subtract the scientific notations: (10^16)-(10^15)=10^1=10. So, there are 10.7 megatons of damage that occur in this case.

Now, let's say something like this hits Earth.  What kind of damage would it cause? To figure out a rough estimate of damage, square root the megatons (sqrt(10.7))=3.27. Then, multiply it by 4 to get the rough blast radius in miles (4 x 3.27=13.08) which is a 13.08 mile blast radius.  This is pretty amazing damage, and the blast radius includes moderate damage.  On the edge of the blast radius, the wind power is still 2 psi which can completely destroy most buildings.  It important to note that this calculation is just a rough estimate, but it's an interesting idea. If someone knows of a calculator, please let me know.

So, things you need to know:  E=(1/2)mv^2; one megaton of TNT releases 4.2 x 10^15 joules; and the speed of light is 300,000,000 m/s (roughly).




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