The Importance of Simple Arithmetic

If all of our devices fail, will we still be able to add?

The following story is a twentieth-century tale of progress, computerization and what can go wrong—the proverbial black swan event.

Changing the Parameters—Canada’s conversion to the metric system

Metric conversion in Canada took place incrementally between 1970 and the early 1980s. This was the process of making metric units, such as the metre, litre, kilogram and degree Celsius, the common units of measurement in Canada and, simultaneously, expunging the corresponding British imperial system measurements (yard, gallon, pound weight and degree Fahrenheit). The process was fraught with political interference and public resistance. Today we have a mixed bag of metric and Imperial measurements used by many Canadians. For example, supermarkets may express weight costs in pounds, ounces, kilograms or even units of 100 grams. Temperatures are often indicated in both Fahrenheit and Celsius scales. Tools and construction materials may be calibrated in both metric and Imperial units.

Aerodynamics—the basics of flying

Gliding is an activity whereby pilots fly unpowered aircraft known as gliders or sailplanes using naturally occurring currents of rising air in the atmosphere to remain airborne. The aerodynamic design of the sailplane and the skill of the pilot is what keeps the aircraft afloat.

Gliding began in the 1920s as a recreational sport. The first glider pilots simply sought ways to increase the duration of their flights but soon were attempting to perform cross-country flights away from the place of launch. Improvements in the aerodynamic design of the craft and a better understanding of weather phenomena have resulted in achieving greater distances at higher average speeds. Modern day glider pilots now use any of the main sources of rising air: ridge lift, thermals and lee waves to fly long distances, some even 1000 kilometres in total.

Progress and Computerization—moving from human skills to machine skills and back again

About two decades before gliding became a recreational sport, the Wright brothers, Orville and Wilbur, “made the first controlled, sustained flight of a powered, heavier-than-air aircraft with the Wright Flyer on December 17, 1903, 4 mi (6 km) south of Kitty Hawk, North Carolina. The brothers were also the first to invent aircraft controls that made fixed-wing powered flight possible.” In the following years, 1904–05, the two brothers created a three-axis control system, which enabled the pilot to steer the aircraft effectively and to maintain its equilibrium.

While other individuals and professional organizations were concurrently experimenting with building the first motorized flying machine, their main research objectives often centered around building more powerful engines. By contrast, the Wrights collected data for their experiments. This data, considered to be quite accurate for the time, resulted in their designing more efficient wings and propellers. Interestingly, their first U.S. patent (granted in 1906) did not claim they had been the first to invent a motorized flying machine, but rather a system of aerodynamic controls that manipulated a flying machine's surfaces.

Fast forward to some seven decades later. The Boeing 767, a wide-body airliner developed and manufactured by Boeing Commercial Airplanes, was launched as the 7X7 project on July 14, 1978. Its prototype first flew on September 26, 1981, and it was certified on July 30, 1982. In the design of the Boeing 767, a computer had taken over the tasks once performed by the flight engineer (now called a “fly-by-wire” system^1,2). It was one man down from previous aircraft cockpits. This modern airplane is now known as the Gimli Glider.³

On July 23, 1983, the Boeing 767 (under the flight number Air Canada 143) was flying from Montreal, Quebec to Edmonton, Alberta when, at an altitude of 41,000 feet, halfway through the flight, it ran out of fuel. It subsequently lost the power of both of its engines and the flight control panel. The landing gear under its nose had also malfunctioned. Captain Bob Pearson and First Officer Maurice Quintal, under great duress, used basic manual flying techniques and hand-written calculations to land the disabled aircraft without it exploding. They were forced to touch down prematurely on what used to be an old military base airstrip in a small Manitoba town on which two young boys were playfully cycling without being aware, at first, of the impending approach of the wounded giant.

The Investigation

“...further interviews with the technicians and crew reveal that the events on flight 143 …. were caused by human error involving poor calculations and ultimately inadequate training … The technicians refuelling flight 143 got muddled in their calculations while converting the volume coming out of the fuel trucks to the weight of the fuel in the plane’s tanks. No-one who saw the calculations that day noticed the basic error.

In 1983 Canadian ground crews were used to converting the amount of fuel leaving their trucks into pounds. The 767 was the first plane in Air Canada’s fleet to have metric fuel gauges. Its fuel should have been measured, not in pounds, but in kilograms which requires a different calculation. Flight 143 needed 22, 300 kilograms of fuel for the trip but pilots and technicians let it leave with 22,300 pounds instead. Because a pound is about half a kilogram, the plane only got about half the fuel it required which explains why Pearson’s (the pilot) flight computer told him he had plenty of fuel. He entered the wrong amount of fuel to start with.

In the past the flight engineer calculated the fuel loads. This accident raised an important question: Whose job was it with a two-man crew? Better training is definitely an issue in an incident such as that. If everyone is trained and the lines are drawn as to who’s responsible for what, then there’s no ambiguity on it that people know what they’re responsible for. In this case, it was sort of open-ended. They really weren't aware who was responsible for the final say on this field stuff.

A subsequent inquiry found that none of those involved that day was trained in metric calculations – not the ground technicians, not the pilots. …. The computer that had replaced the 767s flight engineer was broken and no one knew who should be doing its job. Air Canada 143 was essentially down a man and the goal is to prevent a recurrence of this particular event …. It took a string of mechanical and human failures for flight 143 to run out of fuel but another failure that day may have saved some lives...”

(Reference: see the video below (44:00–47:15 mm:ss)

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