Thursday, March 30, 2017

Bullets, Bikes and Rotor Blades: Random Motion, Perfectly Predictable



Bullets rip from the barrel of modern rifles at more than 3000 feet per second.  Tanks fire armor-piercing shells that travel nearly twice that speed, just over a mile a second.  Rotor blades on helicopters sweep the air at a constant speed, but a small  change in the pitch (tilt) of the blades causes the ‘copter to rise, drop, hover or hurtle through the air at more than 100 knots.



Each of these complex motions is almost perfectly predictable moving through an utterly random medium: air.  The atmosphere, from sea level to stratosphere, is nothing but randomly moving molecules.  The molecules of air are vanishingly small,  so each cubic foot of air has about 30 sextillion molecules (3 with 22 zeroes) of air in it at any moment.

Since air is mostly nitrogen and oxygen, most air molecules are just under a millionth of a millimeter long. These tiny particles move in random directions: up, down, left, right and everything in between at speeds around 1000 miles per hour at room temperature and normal atmospheric pressure. 



And yet.

The collective motion of hundreds of trillions of individual molecules is so predictable that a 95-pound artillery shell fired from a 155mm cannon can hit within meters of a target ten miles away.  A 105mm tank cannon firing a practice SABOT round can make  will punch a perfect 40mm hole within inches of the middle of a one-meter circle a full kilometer away. In 1976, my gunner made a smiley-face triangle with three rounds while we were zeroing our main gun. 

If random motion meant changes in wind resistance, gunners would never be able to fire with inch-perfect accuracy.

Every week I coast down a ¾-mile-long hill. At the top of the hill are two big wind-power generators.  A mile away from the hill I check the direction the blades are facing and their speed. I know before I get to the hill what my speed will be at the bottom within less than 5mph. The difference comes from how much draft I get from other cyclists.  In the distance down that hill, my bicycle and I pass through 15 cubic feet of air for every foot we move down the hill.  So from top to bottom the bike and I pass through 50,000 cubic feet of randomly move molecules of air, billions of sextillions of molecules of air.



And yet.

The motion is perfectly predictable.  Any single molecule of air might be racing ahead of my bicycle at 1000mph or it might get passed by a bullet or a cannon shell. But the collective motion of all those molecules is wind resistance. And wind resistance is as predictable as electrical resistance in a wire fluid resistance in a pool of water. 

The world is full of randomness at every level from atoms to stars and yet the universe is so stable that the greatest theories of science are based on permanency across millennia of time and light years of space. 

This is beauty we are immersed in every day. 

If we could see air molecules move, it would look like the tracers from a hundred monkeys firing a hundred machine guns while swinging through trees. 

Nature is often this way. A surprise. Not at all what we expect and somewhere beyond amazing. 


SPQR and America

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