## Math Mistakes in History: The Gimli Glider

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Pounds, kilograms, what’s the difference? Quite a lot when you’re 41,000 feet in the air and your Boeing 767 runs out of fuel because you used the wrong units to figure out how much fuel to put in.

That’s exactly what happened on July 23, 1983. Captain Bob Pearson and First Officer Maurice Quintal were flying the aircraft, but due to mechanical difficulties the fuel gauges weren’t working. This was realized during a stopover in Montreal and the plane was still allowed to fly, but the amount of fuel had to be calculated manually. Mechanics knew that the plane would need 22,300 kilograms of fuel to fly from Montreal to its destination in Edmonton, and they were also able to determine that there were 7,682 liters of fuel in the tank at that time. The flight crew then [incorrectly] calculated that they needed to add 4,916 liters from the fuel truck.

How did they do this? They multiplied the total of 12,598 liters by the conversion factor 1.77, which gave 22,298. The problem is that 1.77 is the number of pounds per liter, not the number of kilograms per liter: the Boeing 767 was the first Air Canada airplane to use all-metric units, so the standard conversion factor of 1.77 didn’t apply. This incorrect conversion meant that they actually had about 22,300 pounds of fuel on the plane, which is only 10,115 kilograms of fuel. Because the fuel gauges weren’t working, they didn’t discover their error until they got a low-fuel light mid-flight. The plane was near Winnipeg, but not close enough to land; instead they diverted to the small town of Gimli, which had a decommissioned Royal Canadian Air Force Base.

In a stroke of good luck, Quintal had been stationed there when he served in the airforce, so he was familiar with the runways.

In a stroke of bad luck, the runways were currently being used as a dragstrip, and that very day was “Family Day” for the Winnipeg Sports Car Club.

In a stroke of amazing luck, Pearson did some excellent maneuvering and safely landed the plane amid all the people. No one on the ground was hurt, and the only injuries (none life-threatening) occurred when people tried to exit the plane. There was one additional delay, though: the mechanics who came from Winnipeg to Gimli to repair the aircraft got stuck in the back woods because they ran out of fuel.

The Gimli Glider was repaired and flew for another twenty years. Its final flight was on January 24, 2008; Pearson and Quintal (and apparently the rest of the July 23 flight crew) were on that flight.

Most of the information here comes from “The 156-tonne Gimli Glider” by Merran Williams, Flight Safety Australia (July-August 2003), pp. 22-27 and “The Gimli Glider” by Wade H. Nelson. Both articles have a great (copyrighted) picture of what the plane looked like after it landed; Nelson also offers to send teachers Math Lessons using the Gimli Glider. The update comes from “Famous Gimli Glider retired from Air Canada service” in the Vancouver Sun and from Wikipedia.

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### 13 Responses to “Math Mistakes in History: The Gimli Glider”

1. The Trouble with Units « 360 Says:

[…] already been a couple examples of what can go wrong when you mix up Metric and Imperial units on a Boeing 767 or a spacecraft to Mars. But it turns out that even nonstandard units can cause a little bit of […]

2. Decimal or fractional - Page 4 - HomeBuiltAirplanes.com Says:

[…] Decimal or fractional Great discussion about unit confusion! you all probably know about it! Math Mistakes in History: The Gimli Glider 360 remember: Mother nature always […]

3. Decimal or fractional - Page 5 - HomeBuiltAirplanes.com Says:

[…] Posted by Woodenwings Great discussion about unit confusion! you all probably know about it! Math Mistakes in History: The Gimli Glider 360 I’d heard of this one. If I’m not mistaken a small TV documentary was done about this but I don’ […]

4. Wade Fisher Says:

Don’t forget that math also helped save this flight. They calculated their best glide ratio and knew they couldn’t make the first airport. This is why they decided to land at the old Air Force base. They calculated this based on radar tracks and altitude loss.

5. Ξ Says:

Indeed — thanks for bringing that up Wade! And, really, it’s impressive that they could do all those calculations on the fly while running out of fuel and in a stressful situation. I’m totally impressed with how this turned out — it reminds me of the Apollo 13 story.

6. Craig Tatton Says:

date on the article should read 1983 not 1984 – Merry Christmas

7. Daniel Bryant Says:

A great story, and it just goes to show how a simple manual calculation that you could probably do in your head caught them out, but it can happen to anyone.

8. Don House Says:

A great story and a good TV movie, but you should never try and remember the conversion factors. Remember how to do the math, but the conversion you look up every time. I got a reference manual in high school of math tables, formulas and conversion factors for weight ,temp,wire size,inches, metric, mechanical, electrical, and everything else you can think of. I turn 54 this July and I still have it and use regularly.

9. Ξ Says:

Craig — I missed your comment over a year ago (!) but just made the correction — thank you!

My impression is that they did look up the number. From the article by Williams, “With the help of First Officer Quintal, the ground crew used the correct procedure to calculate the weight in kilos. However, they had not been trained in correct conversion, so the figure of 1.76 provided by the refueling company on their refueling document, was taken to be the required multiplier. It was typical of the numbers seen on previous slips and they assumed that the numbers provided over the previous few months had indicated specific gravity in the new metric system.”

[That article uses both 1.76 and 1.77 as the conversion factor.]

10. Freefalling Says:

Hi Guys
I would have thought that fuel, being a critical element to flight and there was a new measure of weight being used by aircraft manufacturers, that there should have been a “double check” safety system in place for a “manual re-fuel”, by the way of driving the re-fuelling truck over a set of scales before take-off to determine the actual amount of fuel that was delivered. Surely this would have found the calculation was wrong and needed to be checked??
Pilots and Crew that day, are hero’s!!

11. bob french Says:

fortunately one or both of the pilots were previously glider pilots.
on subsequent simulator test flights with other pilots, NONE of the flights ended successfully……..

12. dan@blogformen Says:

You really need to be on the ball with things like this. I always try to work in pounds and then do a conversion. But sometimes you will have to work in kilograms. When it comes down to fuel you don’t want to make a mistake.

13. How many grams in an ounce? | 360 Says:

[…] between units can be hard, as seen before (and before and before).  Fortunately, food containers often include both English units and Metric units.  […]