While we're waiting on Fonebone to return and elaborate on his missile theory...can someone help me with some math?
3200 pound missile traveling at 500mph...hits the building with X amount of kinetic energy...then the 1500 lb warhead goes off. How would you calculate the amount of energy released in the explosive?...and can you just add the two together to get the total amount of energy the missile and warhead delivered to the towers?
Kinetic energy is equal to KE = 1/2 m v2, where m is mass and v is velocity.
Using your numbers, a 3200 pound missile has a mass of about 1450 kg. 500 MPH translates into 220 m/s. So the kinetic energy in this case is KE = 0.5 * 1450 kg * (220 m/s)2 = 35,000,000 kg m2/s2, or 35 MJ.
For the explosive, we measure in the laboratory the chemical energy per unit mass. For most explosives it ranges between about 3 to 6 MJ/kg. The benchmark explosive trinitrotoluene, or TNT, measures about 4.184 MJ/kg. Using this, and your mass of about 700 kg, gives us an explosive chemical energy of CE = 700 kg * (4.184 MJ / kg) = 3,000 MJ or 3 GJ.
You could add the energies together, but whether or not that number was meaningful would depend on the problem. In your example, the explosive has about 100 times as much energy as the raw kinetic energy. But then again, in the WTC crashes, we don't typically add the chemical energy of the fuel to the kinetic energy of the aircraft. (That chemical energy is equivalent to a bomb approximately 400 times the size of your hypothetical example). This is partly because the explosives will not be as efficient -- it'll pressurize the atmosphere, make lots of heat which later escapes, and so on, whereas the kinetic impact will be nearly 100% efficient, its major inefficiency being deformation of the missile or aircraft itself.
The kinetic energy alone, both because of its magnitude and its efficiency, can be quite effective in destroying structures. This is why our Air Force has started using concrete bombs -- laser-guided, but not explosive at all -- for some missions, particularly where collateral damage is a risk.
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