Cautionary Conversation: Flying on Empty
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Take your business further at T-Mobile.com/now. Pushkin. On the 20th of July 1983, Air Canada Flight 143 was being prepared for its 2,000 mile cross-country flight from Montreal to Edmonton. The ground crew loaded her up with the necessary fuel, 22,600 kilograms, according to their calculations. Those calculations were correct, up to a point,

But unfortunately, they're mixed up kilograms and pounds, and not in a good way. Nobody had any idea of this, but the plane took off for a four-hour flight with only half the fuel it needed to get to Edmonton. The plane was now on course to run out of fuel somewhere over Winnipeg. I'm Tim Harford, and you're listening to Cautionary Tales. MUSIC

This is a new experiment for us here at Cautionary Tales. As usual, you'll hear a story of disaster, but I'll be joined by an expert to help tell the story and reflect on the lessons.

I hope you like it and I'm confident you will because my guest today is Matt Parker. Matt Parker is a phenomenon, a stand-up comedian, mathematician, YouTuber, podcaster and author of the number one bestseller Humble Pie. And Humble Pie is a funny nerdy book about the real-life consequences of mathematical mistakes and it's where I first heard the story of Air Canada Flight 143.

Matt Parker, welcome to Cautionary Tales. Thank you, Tim. It's an absolute honour to be your zeroth guest on the show. Zeroth guest. Matt counts in strange ways. Matt, this story is a bit like an onion. It's got layers. Yeah. On the most superficial level, the sort of papery outer layer of the story, if you like. Why did this plane have too little fuel? The very simple reading is they had a unit conversion error. So the people who were meant to be fuelling the aircraft...

saw a number, they assumed it was pounds of fuel, when in fact it was kilograms of fuel. And the reason they're even doing this in mass, because if you fill up a car, you don't put the fuel in by mass, you do it by volume. Volume changes based on the ambient temperature. As things warm up, they tend to expand. If they cool down, they tend to shrink. And if you're flying an aircraft, it's important you have the amount of fuel you're supposed to have.

And so they made sure instead of using the straightforward volume,

They were going to use mass instead. And sadly, it was that attempt for extra precision that opened up the door for this unit conversion error. Yes, you would think they might just stick in a little bit extra just to be sure, but there's limits to the amount of extra fuel you want on a plane because it's heavy. Yeah, and so they even allowed enough extra. So that 22,600 kilograms you mentioned, that's 22,300 kilograms for the flying bit.

And then they put on the extra 300 kilograms of...

for like taxiing and all the bits that maybe they hadn't factored into the flight. So they were trying to be careful. They were being thorough. They just got the units wrong. What was it about Canada at this particular time that made it particularly vulnerable to a unit conversion error? In Canada, they had just switched. So previously, they were using imperial units, like the old school English style units.

they just swapped over to real units or metric as the

the rest of us. I was about to say that as an Australian you're neutral in this fight, but you're clearly not neutral. Okay, fine. No, not since the 1960s. I love the quirkiness of the imperial system. The metric is nice and straightforward. Yeah, but if there's one thing that's worse than using imperial units, it's using imperial units when you think you're using metric units or vice versa. Exactly. And it was even obscured by one layer.

Because when they were doing the calculations, they weren't actually doing it in terms of the direct mass. They were using something called the specific gravity, which is like a measure of the density of the fuel. And so they used that to get back to the volume that they then had to put into the plane. And because there was this extra one layer of an opaque bit of putting it into a slightly different way of looking at it, they didn't realize that the units behind the specific gravity were based on gravity.

kilograms, and they assumed that they were based the old way on pounds. There's more maths than I had anticipated in filling up a plane. Okay, this is slightly unnerving. But it's not just planes that suffer from unit conversion errors. Your book, Humble Pie, has a whole chapter full of them. Do you have any favourites? Well, this plane is now my favourite. You said you only came across it because you were reading the book. I only came across it researching the book.

Prior to that, it was the Mars Climate Orbiter spacecraft that NASA launched in 1998. That was my favorite unit conversion era. And that's partly because a lot of people know about it. It is this urban legend of when NASA got the maths wrong. And partly, this is something very delightful about NASA, like the mascot of science and precision and achievement coming undone. Because

because of a unit conversion error. It was actually a bit more subtle than that, wasn't it? I think NASA were using metric, but the supplier was using imperial or old school pound. Yeah, Lockheed Martin was the contractor. And like you said, NASA use metric. They're scientists, they're engineers, they're going to use the most efficient, most optimal units. And so everything they were doing was in metric. And in their documentation that they gave to their contractors, it stipulated you

you're going to do this in metric. Now, the kind of common understanding of this is when the Mars Climate Orbiter got to Mars, they had to calculate how far above the surface it was so they could put it into a nice, neat, stable orbit. And people go, oh, isn't that the one where NASA thought it was in feet, but it was actually in meters or vice versa? And then they got the altitude wrong because they were measuring the distance incorrectly. And to be fair...

To this day, if you look at altitude of things like aircraft, it's given in feet, which in one sense is a nice bit of error correction. Because if you hear a number in aviation and its feet, you know it's in the vertical direction. And if you hear a number and its kilometers or meters, you know it's in the horizontal direction. And so it's a bit of redundancy in terms of the directions encoded in the units that are used.

which is maybe the one time I will concede that's an interesting use for Imperial units.

But that's not the case here. First time I've ever heard you defend their use. I know. I know. Well, defend is a strong word, Tim. But actually, that's not what NASA did. They didn't confuse feet and meters and kind of just smash this thing into the surface of Mars because they didn't know how high it was. It is a much more subtle error. It's always more complicated than that. In this case, as they're flying the spacecraft from the Earth to Mars, there's a big flywheel on board because in space, there's nothing to push against if you want to change your direction. But if you have a spinning mass, you get the gyroscopic effect and

and you can push against something spinning to reorientate your spacecraft. The issue with that is sometimes your flywheel is going incredibly fast. And you have to have, what the NASA scientists have deemed, an angular momentum desaturation event, which is just slowing down the flywheel. But to do that, you've got to fire the thrusters, like the little steering rockets on the spacecraft,

to keep it pointing in roughly the same direction as you're slowing down your gyroscope. And those little thruster firings slightly change the trajectory of the spacecraft on its way to Mars. So you want to keep track of those. This was an external system done by Lockheed Martin. And they've got a little program that just logged every single time the thrusters fired, how much force they were firing,

And therefore, later on, NASA could calculate the actual trajectory when it gets to Mars by factoring in all these little thruster flyerings. And NASA said very, very clearly, please write these down using newtons, the proper metric unit for force. And Lockheed Martin wrote them down as pounds force. Pounds force, it's a ratio of 4.4.

four, five-ish. Very similar. It's pounds. Pounds, kilos, all over again, really. And this is the kind of thing that will smash your spacecraft straight into Mars. Oh, yeah. Because they assumed that the firings were in newtons when they've been written down in pounds force, they figured they were going to come in at an altitude of between 150 and 170 kilometers above the surface of Mars. They actually came in at 57 kilometers above the surface of Mars, much, much closer, which

Which means, even though there's not a lot of atmosphere on Mars, there is some. The extra drag of being that much lower slowed the spacecraft down a lot more than they expected.

which meant that it fell out of the sky. It deorbited very ungracefully and billions of US dollars of spacecraft slammed into the surface of Mars because of one unit conversion error. I wanted to ask about a really old conversion error, which pleasingly rhymes with NASA. So it was Vasa. Vasa is this ship? What's the story with that? This was a ship in Sweden that

That was launched in the 1600s, in the year 1628. And it was a magnificent, massive ship. They put a lot of cannons on the top of it, which might have been part of the problem, because almost immediately in its maiden voyage, it toppled over. At the time, they're like, it was top heavy. We put too many cannons on the top. The ship was too tall. And that caused it, almost as soon as it left the harbor, to just fall over on its side and sink. And it wasn't actually found until...

until the 1950s. And in 1961, they dredged it up and they put it in a museum, which if you're ever in Stockholm, I highly recommend you go to the Vasa Museum. The ship was incredibly well-preserved. So well-preserved...

Some people had a good look at it and thought, that looks a little asymmetric. Like the hull is not as symmetric as you would hope a hull would be on a ship. Yeah, I mean, that is a property I tend to associate with ships. Exactly. Everyone likes a good symmetric ship as a rule of thumb. So people looked at it and went, that's not as symmetric as it should be.

As the theory now is, when it was built, it was built slightly asymmetrically because people were using different units. Specifically, people were mixing up Swedish feet with the Amsterdam feet.

feet. And we know this because we've found in all the other bits of paraphernalia that came with the ship, rulers that we assume were used when building the ship. And they found both Swedish feet rulers and Amsterdam feet rulers, which are different lengths. So a foot in Amsterdam is different to a foot in

In Sweden, they've even got different numbers of inches. A Swedish foot is divided up into 12 inches and an Amsterdam foot divided up into 11 inches. And of course, the inches are then different. So the theory now is when this ship was built in the 1600s and people are like, oh, make it to this many inches, this many feet. People are using different rulers at different lengths divided into different numbers of subdivisions and they've got some bits off. And so the ship ended up

A little bit wonky, sadly for them and great for us because it preserved this incredible warship. It toppled over almost as soon as it set sail. So let's get back to Air Canada Flight 143. I flipped over the page in your book and almost the first thing that happens is it lands in Ottawa.

For some reason, they did this before they embarked on the real journey, which is 2,000 miles. So I thought, "Oh, it's a fake out. Matt has faked me out." They landed in Ottawa, they checked the fuel, they figure out there's been a near-miss, nearly fatal error, and they top it up and it's all fine. Not quite. There are layers and layers of mistakes that were occurring. It was a series of very unfortunate mistakes which caused the plane to take off with the wrong amount of fuel.

But then, a stroke of good luck, they had to land early because they were changing passages in Ottawa. And whenever you land, you have to redo the fuel calculations. But as people may have realized, based on the percentage through this podcast we are at the moment, that's not the end of the story. They redid the calculations and made exactly the same unit conversion error. They once again did...

Did the calculations based on pounds instead of doing it based on kilograms. And they're like, yep, that checks out. That's the exact amount of fuel we need. We will carry on with no additional fuel. Well done, whoever fueled this plane in

in the first place. So there we are, Air Canada flight 143 has taken off not once but twice with the wrong amount of fuel, with the calculations all messed up and facing imminently the fate of running out of fuel over the middle of Canada. And after these messages, Matt Parker and I will explain what happened next.

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So we've been following Air Canada Flight 143. It's taken off from Montreal. It has pounds of fuel instead of kilograms of fuel. That is not remotely enough fuel.

has a second chance to fix this because it lands after a short hop, lands in Ottawa. They do the same calculation. They make the same mistake. They say, yep, there's plenty of fuel in there because they're confusing pounds and kilograms. There is not plenty of fuel in there. And the plane takes off again. And now it's really in trouble because now it is going to fly 2,000 miles. People listening to this will be screaming, why didn't they check the fuel gauge? Does a plane not have a fuel gauge? My car has a fuel gauge. Surely a plane has a fuel gauge. So what's going on with the fuel gauge? I mean, a plane does have a fuel gauge.

In fact, it's kind of got a double fuel gauge because redundancy is the motto of aviation. Because, you know, something goes wrong, it goes very wrong. And so they had a gauge that shows the fuel and they've got like a unit that then does the calculations to work out how much fuel. And they've got sensors in the fuel tanks that are measuring how much fuel and they're all joined together.

To give you extra redundancy, there's more than one sensor in the tank. There's more than one link between the sensors and the unit. There's the calculation. And then you've got the display on the arm gauge. And one flight prior to this flight, so when the plane was actually in Edmonton, ready to come over to Montreal to start this fateful flight, they realized there was an issue with the sensors because the gauge had stopped working. And a technician realized if you unplug just one of the connections...

if you remove that layer of redundancy, they start working again. And they're like, "Oh, that's interesting." And in theory, that should be fine because they just label, they write, "I've removed this because it wasn't working." You now have to do a manual check as your layer of redundancy because we've removed it from the sensors, you've now got to do it manually. But this is where the chain of mistakes, the layers of this onion really kick off because there'll

there was just one thing after another that went wrong. So that technician poorly labeled what they had done. They just wrote faulty or something to that effect. They then didn't write it very clearly in the logbook. They then didn't explain it very well to the pilot. The pilot understood it as being an ongoing problem. And it was always the case that you had to do the manual fuel check, which is like literally putting a stick in the tank to see how much fuel there is. When they finished the next flight,

The pilot then badly communicated this to the next pilot and the technician handover was equally bad. Like at any point, someone could have realized what was going on, but the communication didn't work. And so the new pilot was

was told, don't panic, as long as you do the manual check, it's fine. Separately, a different technician's popped in, realized it's unconnected, connected it back in again, rediscovered the same issue the previous technician had, left it plugged in, went off to order the new part. The new pilot sees the old label, which is now irrelevant, saying faulty, but it's plugged back in again, which means none of the gauges are working. All of this just

comes together as the pilot is sitting there looking at this label, looking at the blank gauge, and everything they've been told just happens to line up. And they think, oh, it's fine. As long as we do the manual check, we can still fly even though the gauge is completely dead without realizing that is very much not what they should be doing. So I did once run out of fuel

Fortunately, I was on the ground in a car, but I ran out of fuel because there'd been a problem with the pump. The pump kept clicking out as I was refueling in a way that indicated that the tank was full. But the fuel gauge was showing that the tank was nearly empty. I just assumed that the pump was correct and the fuel gauge was wrong. So I thought, "Huh, I've got a broken fuel gauge." Off I drove and I was not full.

So, but yeah, as I say, fortunately, I was on the ground. You're on the ground. But imagine all that happens. And you're like, huh, you know what? I'll just get someone at the fuel station to double check for me. And they put a stick in your fuel tank. They do the calculation. They're like, oh, no, no, no, no. You've got loads of fuel. But they've made a unit conversion error. And that parallel mistake...

has reinforced your series of mistakes and misunderstandings, and then you drive off without enough fuel. And there's actually a theory in accident, well, I guess, mistake mitigation called the Swiss cheese principle of avoiding disasters, where you imagine each check, each bit of redundancy, each fail safe as being like a barrier to stop mistakes from getting through. But no barrier is perfect.

Some of them are operated by humans and we can make mistakes. Some of them are run by code or machines and they make mistakes. And so each barrier has a few holes in it, like a slice of Swiss cheese. But you just hope that if you've got enough slices of cheese, one of them will stop the mistake from getting through. But every now and then, your cheese holes just line up and a mistake will make it through every single layer, every single barrier, every single failsafe, and will make it out the far side and become a disaster.

And that's what happened with flight 143. Just slice of cheese after slice of cheese, had a hole in the wrong spot and the mistake made it through undetected. And so the plane runs out of fuel somewhere over Winnipeg. Yeah. And this can't have been a happy moment for the pilots. It was a startling moment. I mean, the first indication they had that something was up was an error noise in the cockpit.

that no one had heard before. They had to look it up in the manual to see what was going on. Like this came out of nowhere. And suddenly they realize they're out of fuel. And this plane was one of the first aircraft that Air Canada had brought on

which used avionics. And so there's a lot more electronics than normal. And suddenly all of it goes dead. The engines are out and they're coasting. They're coasting a Boeing 767. There were still some very basic rudimentary controls for the aircraft. So they were able to glide it to some extent. And the reason why this isn't a tale of absolute disaster, the reason why there is

a sufficiently happy ending is the pilot before they became like an airliner pilot for Air Canada in their previous career they were a glider pilot so the pilot was

had sufficient gliding experience and they were able to glide this Boeing 767 to a disused military runway in a very small town called Gimli. And they were able to glide this aircraft just over 40 miles and safely, safely, it was abrupt. It's not actually a glider, is it? It's not built to do this. No, no, it's still going to land hard.

and they couldn't bring up like the landing gear and all this like they had so few controls they basically went straight into the tarmac and they just like the nose went into it and they just slid along I guess sparks going everywhere but there was just enough friction to

to bring the aircraft to a halt before the far end of the runway, much to the relief of the 61 passengers and eight crew members on board. And much to the surprise of the people currently using the airfield. And much to the big surprise to the people who were camping at the other end of the runway. So there were people there, they were on a go-karting weekend, and I guess they booked the runway to drive go-karts around?

And the crazy thing about a Boeing 767, which the engines are turned off, it's pretty quiet. And so they had no idea what was happening until they hear this almighty wham. They all look around. There's a jumbo jet sliding up this, they were told, disused runway towards them, stopping just before it got to the go-karts. So, I mean, oh my goodness. Once again, things could have gone very wrong.

But at the last second, thank goodness everyone was okay. No one, there was no loss of life in the entire situation, which is just amazing. I imagine a few people lost a few hairs. Things were lost. Yeah. There's a note in your book that they recreated this scenario in a simulator for other pilots and it did not always go well. No. So they, obviously there's a big investigation afterwards to work out what went wrong and how and why.

And when I was writing Humble Pie, a lot of my time was spent reading through these old investigations because they make it public to an extent. And so in there, they talk about the fact that they got other pilots and put them in flight simulators in the same situation to see what would happen. And every time they crashed, no other pilot in a simulator was able to glide a powerless 767 that distance and land it safely. So that's...

they were very lucky that they had the pilot they did with the experience the pilot had and was able to land this plane safely. It was, I mean, it very easily could have gone a different way. Yeah. One of the other unit conversion errors in your book is a Celsius Fahrenheit thing.

on a BBC news story. They were trying to figure out what some scientists or somebody had basically said that there might be the following: temperature change because of climate change, and here it is in Celsius or Centigrade, here it is in Fahrenheit. The BBC just kept jumping backwards and forwards with really very radical different answers to this question of how to convert between Celsius and Fahrenheit. They kept changing their mind. People just couldn't settle on the right answer.

Yeah, thankfully, people log changes to news sites. So we can watch as it went backwards and forwards. And you're right, there must have been a shouting match. There must have been Team 3.6 degrees and Team 36 degrees, because those were the two Fahrenheit's that the news story kept flipping between. Two degrees Celsius is 36 degrees Fahrenheit.

And two degrees Celsius is 3.6 degrees Fahrenheit, depending on if that's an absolute temperature or a change in temperature. And it's easy to make this mistake because things like kilograms and pounds, they both start at zero. You've got zero mass and then you have some mass and meters and feet both start at zero. Doesn't make a difference if you're talking about the difference in two people's height or anything. Changes versus absolute, same deal.

Celsius and Fahrenheit start at different points. Their zeros are at different places. And their increments are different. Like if you're outside and it's 2 degrees Celsius, actual temperature, and you look at a thermometer, it would say 2 degrees Celsius, 36 degrees Fahrenheit, absolute temperature. But if it then went up another 2 degrees...

the temperature wouldn't go up another 36 degrees Fahrenheit. It would go up another 3.6 degrees Fahrenheit because that's the relative ratio between the increments. So you've got to factor in where they start and how much they change. And because those numbers look very similar, I can imagine why someone like looked at the news story and went, oh, they've put

They've put 3.6. It should be 36. They've put the decimal point in the wrong place. I'm guessing if you type this into Google or a similar website and ask for the conversion, what is two degrees centigrade in Fahrenheit? The answer to that question is ambiguous, but Google is probably going to return 36 Fahrenheit because that is the most common instance people thinking about the weather.

Yeah, the vast majority of people are looking for the absolute temperature. That's what Google's going to give you back. But this was a percentage change in global warming. Should have been 3.6. Eventually, their solution was just not to give it in Fahrenheit, which is a solution I wholeheartedly agree with. Not just avoiding the problem, but just give it in Celsius and move on. As a journalist, it is surprising how often you can solve a problem by just deleting the sentence you're struggling with, ideally before you hit publish, but...

You know, it doesn't always work out like that. So the story, as we've mentioned, comes from your book, Humble Pie, and it's one of dozens and dozens of stories. Humble Pie is not your first book about fun maths. Why did you turn to the topic of mistakes?

I mean, because I've previously written about kind of enjoying maths, doing it, having some fun with it. I thought, you know what? Maths, it's wonderful. It's lovely. We play with it. I think it's great. But we do use it in a lot of critical situations and we use it like it's behind the scenes in our modern society and we never really notice it. And so I thought, you know what? If I write a book about maths mistakes, I can tick two boxes.

Partly, it means people want to read it. I mean, people love things going wrong, as this podcast is a testament to, right? And we can learn from these terrible situations. And so I was like, okay, that'd be a good hook to get people reading a book about mathematics. And because I'm telling stories of maths going wrong, it's an excellent excuse for

to first of all have to set up what the maths is and why we're using it. So it justifies me writing about all these fantastic situations where maths makes our modern society possible, which I found deeply pleasing. One more thought, Matt. Air Canada have made this mistake.

twice. NASA have made this mistake. 16th century Swedish shipwrights have made this mistake. The BBC have made this mistake. I mean, this sort of problem seems to be absolutely all around us. And it's the kind of thing that does bring planes out of the sky and causes bridges to collapse. Does it make you nervous knowing that we're trusting all of these people all around us to get these things right? And they sometimes don't.

It does and it doesn't. So the underlying issue is, as humans, we're not naturally good at mathematics. And that's kind of reassuring because everyone has ever struggled with maths or found it difficult. We all do. Everyone finds maths difficult. The human brain doesn't do maths like...

natively, it's going to learn it. But thankfully... Yeah, that's not reassuring at all. I'm not reassured by the thought that the people refueling planes can't do maths. That's a valid point. Allow me to continue. But what I do like is, and I'll try and land this with a nice, happy conclusion, that because we have maths, we can do so much more than our brains can do intuitively. We don't have to design, like we have to make a building by...

by eyeballing it and like super over-engineering it, we can actually do the mathematics and work out exactly what we need and how it's going to work. And using maths, we can do far more than the human brain was ever designed to do. The cost, however, is that we are beyond our intuition and we have to do the maths and do it very carefully and double check everything. And so I like the fact we can achieve so much more because we can use maths. I accept that this is the cost it comes with. And I'm also reassured

All the stories I found, obviously they're very spectacular. They're very interesting. There's a lot to learn. I love the fact now students at school are told, pay attention to units, otherwise these things can happen. They are the exception. The vast majority of the time, we've got all these redundancies and checks in place and they work. And so these stories are interesting because they are such freak occurrences they managed to slip through. And thankfully, with a very statistic-minded approach,

head, I can still happily fly knowing that the vast majority of the time it works fine. Matt, what else are you working on at the moment and where else can people find your stuff? Oh my goodness. Well, I'm still writing away on a new book, which will be out at some point in the distant future.

You know what? I don't think it's been announced, but it'll be a book about trigonometry. So there you are. That's a Cautionary Tales exclusive trigonometry book coming up at some point when I finish writing it. If you'd like to know when, you sound a lot like my editor. Around that, I'm still doing a lot of work, obviously, on YouTube and live works picking up again. Actually, I just filmed the stand-up special version of Humble Pie.

So I was on tour with the show that goes with the book in 2019 into 2020. We obviously had to delay and cancel a lot of those shows. And we only just filmed the stand-up special a month or two ago. And that will be out at some point around September. So if people want to see the live stage version of all of these, if you head over to standupmaths.com, that's my website where everything happens. And if you go onto YouTube.com,

dot com slash stand up maths you'll see all of my videos as and when they come out Matt Parker thank you very much for joining us on Cautionary Tales Tim it's been my absolute pleasure Cautionary Tales is written by me Tim Harford with Andrew Wright

It's produced by Ryan Dilley, with support from Courtney Guarino and Emily Vaughan. The sound design and original music is the work of Pascal Wise. It features the voice talents of Ben Crow, Melanie Gutteridge, Stella Harford and Rufus Wright. The show also wouldn't have been possible without the work of Mia LaBelle, Jacob Weisberg, Heather Fane...

And Maya Koenig.

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