On the evening of 23 July 1983, Air Canada Flight 143 was cruising over northern Ontario at 41,000 feet.

It was a Boeing 767, one of the newest and most advanced airliners in the world. There were 61 passengers and 8 crew on board, flying from Montreal to Edmonton with a stop in Ottawa. Everything was normal.

Then a warning sounded in the cockpit. Low fuel pressure in the left engine.

The captain, Robert Pearson, assumed a faulty fuel pump. A few moments later a second warning sounded, for the right engine. He decided to divert to Winnipeg.

Then the left engine stopped.

Then, as they were preparing for a one-engine landing, the cockpit filled with a sound that nobody on the flight deck had ever heard before: a long "bong" that meant all engines have failed.

And then most of the screens in front of them went dark.

How do you run out of fuel in a brand-new jet?

The answer lies in a mixture of bad luck, unfamiliar technology and one of the most famous arithmetic errors in history.

The gauges didn't work. The 767's fuel quantity system had a faulty processor, so the fuel gauges in the cockpit were blank. The plane was cleared to fly with the gauges inoperative, as long as the fuel was checked manually.

Canada was going metric. The country was in the middle of converting from imperial to metric units, and the 767 was among the first aircraft in Air Canada's fleet to measure fuel in kilograms rather than pounds.

The conversion went wrong. To fuel the plane, the crew and ground staff measured the fuel already in the tanks with a dipstick, in litres, and had to convert that into a weight. The right factor was about 0.8 kilograms per litre. They used 1.77 — the figure for pounds per litre.

Everyone checked the maths. Everyone made the same assumption.

The plane needed 22,300 kilograms of fuel for the trip. It took off with about 22,300 pounds — less than half as much.

A very large glider

When the engines stopped, the 767 became, in effect, an enormous glider.

Most of the cockpit instruments went dark, because they drew power from the engines. A small propeller called a ram air turbine dropped out of the plane's belly and spun in the wind, providing just enough hydraulic power to move the controls — heavily.

Pearson and his first officer, Maurice Quintal, had one crucial piece of luck. Pearson was an experienced glider pilot. He knew how to fly an aircraft with no engine. But the 767 manual didn't have a section on what to do if both engines failed, because it wasn't supposed to happen.

They calculated they couldn't reach Winnipeg. Quintal had a suggestion. He had been stationed at RCAF Station Gimli, a former air force base not far away.

They turned towards it.

Gimli was not empty

What neither pilot knew was that the Gimli base had been decommissioned. One of its runways had been converted into a drag-racing strip.

And that evening, it was hosting a "family day" for the local sports car club. There were cars, go-karts, campers and families with children near the runway.

The landing

As they approached, Pearson realised they were too high and too fast. There was no engine power to go around and try again.

So he did something you would almost never see in an airliner: a forward slip. He crossed the controls — turning the plane slightly sideways to the airflow, so that the body of the aircraft acted as a giant air brake. It's a manoeuvre glider pilots know well. In a 767, it was extraordinary.

The plane dropped rapidly. Pearson straightened it at the last moment.

The landing gear had been lowered by gravity, but the nose gear didn't lock. When the jet touched down, the main wheels held — and the nose collapsed onto the runway, scraping along the concrete in a shower of sparks.

That turned out to be lucky too. The friction helped the plane stop. It came to a halt short of the people on the runway.

What happened next

An investigation identified a chain of failures: the faulty fuel gauge processor, confusion about whether the plane could legally fly without working gauges, unclear responsibilities for fuel calculations, and inadequate training for the new metric system.

Pearson and Quintal were initially disciplined. But they were later honoured, receiving the first Fédération Aéronautique Internationale Diploma for Outstanding Airmanship in 1985.

Saved by the strangest coincidences

Look at everything that had to line up for Flight 143 to survive.

The captain happened to be a glider pilot. The first officer happened to know about an old air base. The base happened to be in range. The nose gear happened to fail in a way that helped them stop.

A modern airliner, packed with the latest technology, was brought down by a units error and saved by a weekend hobby.

That's aviation in one sentence: incredibly sophisticated machines, flown by humans, in a world where small things matter enormously.