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October 04, 2004

Extra-Super Serious Geek Alert!

WARNING-WARNING-WARNING-WARNING!!!! If you are easily bowled over by technogeeky jargon, just skip on down one. If high school physics broke your spirit, just keep on movin' on - if you think Superman comics are packed full of useful insights into how Newton's Laws and the Laws of Thermodynamics work... just keep on keepin' on!

Still here? You'll like this. The Instapilot will like this. Anybody wanna argue the math? [N.B. - it was sent to me, I didn't work this out]

We know the formula for kinetic energy is KE = ½mass x velocity2 . Now let's check in with the Movie Physics Guys.

So in their example, a small .45 caliber bullet weighing 15 grams and traveling at 288 meters per second yields is 619 joules of energy.

They further explain that if a man weighing 139 lbs (63.2 kg) were to fall off of a bed, it would yield roughly the same energy as being shot by that bullet; the difference being with a fall the energy is disbursed through the entire surface area of the man's body versus a bullet where the focal point is a tiny circle.
KE = ½mass x velocity2
KE = (.015kg / 2) x (288 m/s x 288 m/s)
KE = 619 joules of energy

Potential energy is defined to be PE = (mass) x (g) x (height), where the height is the vertical distance of the object from the ground and g stands for gravitational acceleration or acceleration due to gravity. Near the surface of the earth, g is a constant approximately equal to 9.8 meters per second per second (m/s2). You can use these formulas to calculate the total energy of the system by just adding up the forms.
PE = mass x gravity x height
PE = 63.2kg x 9.81 m/s x 1 meter
PE = 619 joules of energy

So taking this information, let's plug in the numbers of the Apache's M230 automatic gun ammunition. We have each 30mm round weighing 350 grams and traveling at 800 meters per second.
KE = (.3505kg / 2) x (800 m/s x 800 m/s)
KE = .175 x 640,000
KE = 112,160 joules

Now that's a little hard to wrap your army around... I mean just how much energy is 112,000 joules? Well, for starters it's 180 times the energy of the .45 caliber handgun bullet. So imagine 180 people all pointing .45 caliber handguns at this guy's body and everyone pulling the trigger all at the same time. Hmmm, yes...messy.

Furthermore, we can calculate just how high up this guy would have to plunge in order to release the same amount of energy as was released when he caught one of the Apache's 30mm rounds square in the chest...
112,160 = 63.2kg x 9.81 x height
height = 112,160 / (63.2 x 9.81)
height = 112,160 / 619.99
height = 180.9 meters (or 593 feet)

Now, taking our queue (sic) from the evolution of skyscrapers, I found an average 4.26 meters (13.96 feet) per floor. Thus this terrorist you see splattered all over Main Street in downtown Baghdad? He looks the same as if someone tossed his happy ass off a 42 story building.

And the best part? The Apache's 30mm gun is really a popgun compared to the 30mm gun of an A-10 -- same diameter slugs but they're much heavier and travel much faster. So should you be unlucky enough to eat one of the Warthog's tank killing depleted uranium slugs...
KE = (.91kg / 2) x (1500 m/s x 1500 m/s) = 1,023,750 joules of smack down
1,023,750 joules / 619 joules per .45 cal bullet = 1,626 people shooting you at once
1,023,750 joules = 63.2kg x 9.81 x height
height = 1,651 meters or 5,417 feet or a 1.02 mile freefall

But at a fire rate of 3,900 rounds per minute, the A-10's bullets will be more like Lays potato chips -- nobody's gonna eat just one. All you terrorist rats in Iraq and Iran better keep that in mind when you hear the whoop-whoop-whoop of helicopter blades, eh?

Hat tip to Cary!