Grace Under Pressure

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The recent failure of a seam in the aluminum skin of a Southwest Boeing 737 jet is cause for reflection on how modern engineering affects our lives.  It has only been about a century that we have had airplanes, or even cars for that matter, and yet roughly a million people fly every day in this country, trusting ourselves to carefully-calculated margins of safety. The fine-tuning of airplane construction is complex, but underlying it are some basic principles that may be helpful in understanding the current flap.  The numbers I use here are rounded and simplified.

An airplane is basically a metal cylinder, as is a submarine.  The airplane skin is designed to hold enough pressure when it reaches cruising altitude that the passengers have a comfortable amount of air to breathe.  The pressure calculations for subs and planes are similar in that they involve cylinders, but whereas the pressure forces on a submarine’s hull are compressive, those on a plane’s skin are in tension, or tensile.  In other words, they stretch the skin, trying to pull it apart.  That’s where the concern over fatigue comes in.  Each time the plane takes off and cruises to, say, 35,000 feet, and then lands again, the skin is stretched and then relaxed.  This constitutes one pressure cycle.  When you do this over and over again, the metal is subjected to stress similar to what you get when you bend a paper clip back and forth repeatedly.  And as everyone knows, when you do that enough times, the paper clip breaks.

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So how much stress can be involved?  After all, the pressure difference is only a few pounds per square inch (psi.) different between ground and cruising altitude, isn’t it?  Yes.  At ground level the air pressure is about 14.7 psi.  At 35,000 feet the air pressure is 3.5 psi and the cabin pressure is typically adjusted to the equivalent of 6,500 feet of altitude, or 11.5 psi.  Therefore, when at altitude the internal pressure that the airplane’s skin has to hold in is 11.5 minus 3.5, or 8 psi.  Doesn’t sound like much, does it? But what is the force then that is trying to pull the thin aluminum skin apart, due to that internal pressure?  The simplistic formula for that tensile stress is:

Stress = [(pressure) (radius)] / (thickness)

where “thickness” refers to the aluminum skin, which, for a Boeing 737 is 0.040″, or forty-thousandths of an inch thick.  This is a little less than 3/64 th’s of an inch.  The internal diameter of a 737 cabin, from the internet, is 11 feet 7 inches, so the radius would be 69.5 inches.  So if you do the calculation you come up with 13,900 psi.  This is the force at 35,000 feet that is trying to tear each square inch of the aluminum skin apart.  Another way to look at it is to think of how much length of aluminum makes up one square inch.  This is 1 inch divided by 0.040″ of thickness.  That equals 25 inches.  So each 25 inches of skin has to contain a tensile force of 13,900 pounds trying to stretch the skin.  Picture suspending 3 SUV’s from a chain connected by clamps on either side of  a 25 inch long strip of aluminum, 0.040 inches thick.

There are good margins of safety built-in to these designs and there is other internal bracing in the cargo hold part of the plane, but here in the real world, nothing is perfect, and that is nowhere more true than in the complex field of metallurgy.  Tiny flaws can grow into cracks that result in failure, as recently happened.

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The good news is that flying is much, much safer than driving, based on simple statistics, and the other good news is that the safety procedures for which crews train worked perfectly. Aviation safety continues to be an outstanding engineering achievement, one that most people take for granted.  It is a triumph of combining entrepreneurial genius with sensible safety regulation by government. We should be grateful.  I just wish hospitals had the same kind of safety record for our skins as the aviation industry does for airplane skins.