6 Small Math Errors That Caused Huge Disasters
If there are any children reading this, there's really only one thing we want to tell you about adulthood: If you make one tiny mistake, people will die.
Don't believe us? Let us share these tales of completely forgivable design mistakes that cost lives.
#6. An Airliner Crashes Due to Square Windows
In the 1950s, companies were making the first foray into jetliners, and leading the pack was the de Havilland Comet. It was a state-of-the-art jet with many never-before-seen features, such as a pressurized cabin that allowed it to fly higher and faster than other aircraft.
Unfortunately, in 1954, two Comets disintegrated midflight for no apparent reason, killing 56 people total. In retrospect, the name "Comet" was a bad choice.
retrothing.com
Although it was superior to de Havilland's first choice, the "Murder Bird."
The Laughably Simple Flaw:
It had square windows.
This is one of those things that is easy to miss (the designers missed it, for instance) but easy to understand once it's explained.
Here's a Kit Kat style candy bar. Where would you say this thing is most likely to break when pressure is applied?
seriouseats
Along the willpower line, probably.
Right there at those sharp notches, obviously. That's why they're there, and it's why no one builds important structures out of Kit Kats.
Well, a square window is made up of four 90-degree notches cut out of your wall, creating four of these weak points. You don't need a diagram -- if you have brick or stucco on your house, go outside and look. You'll find cracks there, protruding right from one of those sharp corners:
Getty
To fix, place head in bucket of sand and hum loudly.
In engineering, that sharp corner (or groove in the Kit Kat) is called a "stress concentration," a spot where the shape of the object makes it more likely to break under stress.
You don't want the red bit.
So if you're an airplane maker, how the hell do you fix that?
Well, have you ever noticed how on every plane you've ever been on, the windows you look out of have rounded corners? Those curves are pretty much the only thing keeping the plane from tearing itself apart in midair like in that scene from Fight Club. It distributes the stress to all of the various points along the rounded curve, rather than on that one sharp corner, which otherwise would (as they found out) tend to pull apart and form a crack over time.
Trust us, this was not easy to figure out. Experts had no idea why the planes weren't holding together until they tested the structure by simulating the repeated pressurization of the cabin. Sure enough, the fuselage eventually burst like a bootleg condom, and the break started with cracks right at those window corners.
Getty / plane-crazy
Top: Safe and enjoyable ride. Bottom: Explosive Caesarean section.
Representatives from competing companies Boeing and Douglas both said that their engineers hadn't thought of it either, and that if the Comet hadn't been first, it would have been one of theirs that crashed. Planes have had windows with rounded corners ever since.
#5. Fighter Jets Crashed Because of the Angle of the Runway
You don't have to be a pilot to guess that landing on an aircraft carrier is really fucking hard. It's a tiny little landing strip crowded with other planes, bobbing up and down in the waves. Keep in mind, this is with a whole host of instruments, computers and signals to help guide planes in. The early planes didn't even have that.
But there was another problem ...
The Laughably Simple Flaw:
Here's what the earlier carriers looked like. Couldn't be simpler, right?
It's a floating runway. How else would you design it?
Well, that design was kind of a suicide factory. As you can see, planes waiting to take off sit at the other end of the runway you're trying to land on. If you don't get stopped in time, you're going to create one hell of a fireball. And getting stopped in time was no small thing -- catching the arresting wire (the thing that stopped the plane) was a tricky business. Eventually carriers went with the cartoon-logic solution and installed barrier nets to stop planes if they missed all the wires. However, it wasn't all that uncommon for aircraft to bounce over the barrier.
militaryvideocom
Like skipping stones over a pond, if the pond had sharks and you had no arms.
So what was the brilliant innovation that allowed them to make landings that much safer?
They angled the landing strip about nine degrees.
Wikipedia
And as the Navy learned from trailer parks, double-wide is always better.
Don't laugh -- it took years to come up with it. While some of the greatest technological advances in history, including space flight and splitting the goddamn atom, came from developments during World War II, we didn't think of angling the flight deck until 1952. Prior to that, every landing was a potential rear-end collision.
By angling the deck, a plane that missed the wires could go to full throttle, take off again and come around for another pass. Planes waiting to take off are near the bow, out of harm's way.
See? Absolutely no planes in the way.
Angling the deck also allowed for the tactical advantage of being able to launch and recover aircraft simultaneously, whereas in WWII, launching had to be postponed while landings were occurring, and vice versa. Who knows how many lives could have been saved if someone had thought of doing this about 10 years sooner.
#4. A Huge Walkway Collapses Due to a (Seemingly) Inconsequential Design Change
When designing their newest hotel to be built in downtown Kansas City, the fine people at Hyatt Regency wanted all the bells and whistles in it. The architectural firm in charge of the building design came up with a series of aerial walkways suspended from the ceiling so that guests could people-watch from a heightened vantage point. All in all, it was a pretty nifty feature. Until it suddenly collapsed and killed more than a hundred people.
Wikipedia
"We can claim these were either terrible walkways or aggressively efficient elevators."
The Laughably Simple Flaw:
One long rod was replaced with two short ones.
If there's one principle consistent across all human nature, it's that we will always prefer the path of least resistance (i.e., "if you can get away with a half-assed job, do it"). The original plan was for two walkways that were directly on top of one another to both be supported by one very long rod that would anchor into the ceiling. Like so:
This is a highly technical diagram.
Looks pretty simple, right? It all hangs off one long rod, which makes it strong, but also makes it a pain in the ass to assemble -- the rod has to extend through both walkways and then alllll the way up into the ceiling. Just in general, big pieces are hard to work with -- what's easier, to carry a whole assembled desk into your house, or a series of small pieces? The rod also has to be threaded all the way along its length so you could screw that nut up to that top platform spot.
Got to be an easier way, right? So, the steel company in charge of making the rods made a design change by replacing the single rod with two shorter ones, shown below.
The guy with the hat is Rodney, a multimillion-dollar investor. The other is Nutter.
Easier to work with, easier to install, works exactly the same. Right?
That little change killed 114 people, injured 216 more and cost $140 million in lawsuits.
Look at the first image again.
Nutter has an idea for an FTL drive, but also a tool that injects bacon with peanut butter.
One rod, two nuts. Each nut only has to carry the weight of its own platform. Which is good, because each nut (and the welded beam it's screwed to) is only rated to carry the weight of one platform.
Now look at the second image. See the nut we've labeled "OH SHIT"?
The twain shall never meet, and civilization is hollower for it.
That one single nut now has to carry the weight of BOTH platforms, and all the doomed tourists standing on them. Look obvious? Congratulations, because none of the professionals at either company caught it.
And so, one night during a dance competition, the stressed "OH SHIT" nut cleaved clean through the beam and the walkways collapsed.
Wikipedia
Considering this was 1981 and something called a tea dance, we're willing to rule it a suicide on the part of the building.
During the ensuing lawsuits, it came out that neither the steel company nor the engineering firm in charge of construction had even bothered to do a back-of-the-envelope calculation that would have shown them this glaring flaw.
The hotel walkway 1/2-donkey job (and the disaster that followed) could've been avoided by one simple device you can buy at any hardware store: the coupling nut. It looks like a nut that's lengthened 4x or 5x along its axis. Screw the coupling nut (and washer) 2/3-way onto the upper rod. That supports the upper walkway. Now, screw the lower rod into the lower 1/3 of said coupling nut. None of that double-loaded beam nonsense. And no need to thread half of a 2-storey-long rod. And I'm no engineer.
ReplyI am a 27 years old doctor,mature and beautiful. and now i am seeking a good man who can give me real love, so i got a sername Andromeda2002 on Agedate.СòM, a nice and free place for younger women and older men,or older women and younger men, to interact with each other.Maybe you wanna check out or tell your friends.
ReplyOoooh interesting. Side scrolling spambot... haven't seen that before!
Every fire door I've ever seen opens outwards and opens by pressing a bar so you can get out just by running at it :) Looks like the UK sometimes gets it right. Also, I heard that the reason the Titanic took on more water than it could hold was because the rivets were weaker than they should have been (something to do with the proportions of the metals used to make them). So there's another one for the list.
ReplyThere were a lot of fuckups on that, but yeah, the rivets were one of them.
I actually finished watching Titanic (again) and for the first time, I noticed that the center propeller had stopped. Funny how these things work out.
ReplyI always thought it was a malfunction because the movie doesnt explain it.
Most of the women in the Triangle Shirtwaist Factory fire died because they were locked in. How does that have to do with the doors swinging inward? They can't even swing if they're locked!
ReplyAh, I just read that a few doors were unlocked, but only opened inward so they were effectively held shut... so the article isn't totally wrong, but as far as I know, the people primarily died because most of the doors were actually locked.
The dummy fourth funnel was actually used to shout expletives at seagulls. Get your facts straight.
ReplyI am hard-pressed to think of a better use of nautical engineering than to shriek obscenities at those dirty flying sea-rats. Well done.
The Tacoma Bridge story is misleading. The problem was not the "holes", but the lack of a chain structure of bracing between the I-beams. A structure without bracing is free to move ("ipostatic", that means "less than static"), while a correct bracing breaks the structure in triangles, a much more solid shape that dissipates forces into the lenght of the beam, that is the direction beams are supposed to work best.
Replyso .. it was pixies?
Essentially right. The bridge didn't need holes for the air to pass through. There was plenty of room for the wind to move around the structure. The main culprit was resonant frequencies.
In a truss structure, the members of different lengths have different resonant frequencies, meaning that the whole structure can't vibrate at the same time. The members that aren't vibrating keep the ones that do vibrate, if any, in check.
The bigger problem is the extremely long length of the beams that made up the bridge. The resonant frequency is inversely proportional to the length of the "string" (in this case, the beam), so the longer the beam, the lower the frequency. The lower the frequency, the slower the speed of the wind that is needed to vibrate the bridge. Had the bridge been built using typical trussed members, it would take wind blowing at thousands of miles per hour to vibrate the beams.
Tell me more about this peanut butter stuffed bacon...
Replynone of these are math errors. they are all logical errors, and things being entirely overlooked.
Reply Hide All See All 3 Repliesstupid misnomer titles.
The hotel walkway collapse was a math error, in that, you originally have nuts made to hold X weight, and now you're using one nut to hold 2X weight. All it would have taken was a person looking at it and seeing that all of the weight was on one nut and to check the weight bearing of that nut. No one noticed the imbalance until it was too late, though.
I actually think a few of these things would be checked mathematically. The bridge and both plane ones, plus the platform one. You can't just say "well this seems logical, so it must be right." Sometimes, things are really better the opposite of the way you think they should be (except the door one, which is just sort of dumb)... Lots of physics, which often translates to math, is used in airplane design, likely runway design too, as well as bridge design. When you're building something so huge and possibly fatal you don't just say "well, that should work," you have to check it BEFORE it's built. And the walkway one was definitely a mathematical error... all they had to do was look at the load bearing capacity of the nut, figure out the weight it would be supporting, do a little adding or subtracting and viola, they'd have seen it couldn't handle it.
i'm not sure why people have thumbs downed this comment. you're mostly right. 6 small misjudgements/oversights would have been more fitting, though that is a little broad. and you're wrong in claiming NONE are mathematical.
fantastic captions and great writing in general! made me actually laugh out loud several times. coque indeed.
Reply"You know what's really safe? No bridge at all!"
ReplyI really liked the article, but I thought the title was a tad misleading. The Titanics flaw was not really mathematical error, was it? Seems more like a logical error to me.
ReplyMath = Logic.
Probably...
"Coquee indeed."
ReplyIt's juvenile but that one little caption made me laugh harder than anything I've read in a long time.
Great article, thank you
The dog on the galloping gerdie died because *the dog* was panicked and wouldn't come out of the car. His owner was the guy escaping the bridge, not the one filming it. The bridge was swinging so hard that it literally threw the guy off his feet more than once.
Reply Hide All See All 6 Repliesword on the street is that the dog didn't die. at least that's what my physics prof told me when my eyes were welling up.
oh yeah, I read about that, they rescued the dog and it went to live on a farm where it still gambols in a field to this very day
Teebie, I SWEAR TO GOD if that is sarcasm...
It was Schrodinger's car on the bridge. Divers have found the car, but they didn't have the heart to check for the dog.
f**k it man, it could have been a god damned Great Dane, I would have carried that mofo by force, or I would have died with him/her.
Teebie, you forgot about the part where the dog was taken behind the birdge and shot after biting everyone in the rescue effort, before it went to the life on the farm.
resonance is a huge problems for structures, that's why soldiers don't march on bridges
Reply Hide All See All 6 RepliesI thought mythbusters proved that was BS...
Mythbusters DID prove it false.
Mythbusters get a lot of things wrong. Sorry.
that's actually a myth, fessier
Mythbusters isn't perfect, and neither the build nor the conclusion in that one was all that robust. Resonance can do damage, but it's something of a coincidence if it occurs.
Check the information on the millenium bridge in London. The wind was causing it to sway, and it was exacerbated by pedestrians naturally falling into synch with the sway while walking.
OK, but for marching soldiers to create damaging resonance, wouldn't there have to be a LOT of them, and have to be marching in PERFECT unison? I doubt that could happen even on purpose.
Triangle shirtwaist wasn't because the door swung the wrong way, it's because the bosses locked the doors so union organizers couldn't get in.
ReplyThey also kept them locked so they could monitor the workers. They'd unlock it and check them before they left to make sure they didn't take anything... but I just read that the only doors that were unlocked opened inward, so that effectively did kill some people too...
The WE you mention in #3 was the British. The invented both the angled flight deck and the arresting cables. It was invented not only to prevent accidents but to allow planes to be launched while planes were being landed.
Reply Hide All See All 5 RepliesPerhaps, but it only counts if done in America. Hence, Edison getting credit for the lightbulb, Linbergh getting credit for flying across the Atlantic, etc...
I assumed by "we" he just meant the human race.
Absolutely correct. But FrankLee, Edison uually gets the credit for having the most practical bulb as well as the system that powered them, even though we then switched to his rival Tesla's AC. Lindbergh gets the credit for being the first to solo the transatlantic crossing, which he totally deserves.
The English also invented blue cheese, which they grew on their teeth until the Dentists' Union threatened to strike, which happens in the UK all the time.
The British also invented blue cheese, which they grew on their teeth and harvested tons annually, until the Dentists' Union threatened to strike.
Very interesting and enjoyable article. In regards to the exit doors opening inwards, they are all required to open outwards as per building codes due to the incident at the nightclub. Also the video of the Tacoma Bridge swaying is mindblowing, watching a huge bridge of solid material sway around like a paper plane!
ReplyI know this much: When you multiply at the wrong time you run a big chance of paying child support. Also, formula comes in to play.
ReplyDid somebody kick the shins of the bastard who ran away from the swinging bridge, leaving his dog trapped in the car?
ReplyThe dog panicked and bit him when he tried to rescue it. So, kinda?
It wasn't the guy's fault. The dog was too panicked to leave the car, and the man wisely chose to leave the bridge before he died as well. He was the last person to walk on the bridge, and he wasn't the one filming its fall.