Math Is a Rite of Passage for Engineers—But Should It Be?

If you can build and race electric cars, does it matter if you can pass calculus?

Figure 1.David Cullimore with a replica of the car that has won so consistently against other electric cars in Greenpower’s F24+ class that the best competitors can do is fight for 2nd place.

Figure 1.David Cullimore with a replica of the car that has won so consistently against other electric cars in Greenpower’s F24+ class that the best competitors can do is fight for 2nd place.

The keynote speech at Solid Edge University 2016 in Indianapolis—home of America’s most famous auto race—was given by a 23-year-old blue-eyed Brit named David Cullimore, who has been using Solid Edge to make an electric race car he calls Jet, which has been smoking the competition. David Cullimore races in the F24+ class of Greenpower, where the object is to see how far a 45kg car—one that is barely larger than its driver—can go on one standard battery and motor.

The results speak for themselves. Cullimore recites his accomplishments:

  • 24 wins in 32 races entered, including a string of 17 victories in a row
  • In 2016, he has won 12 of the 14 races he entered, and was second in the other two

On the Cullimore Racing site, many more awards and wins are recounted.

What are the critical factors in winning such an event, and what makes Cullimore so successful? He explains the design and engineering in his winning entry. His machines have greater mechanical efficiency, he said. Instead of shifting gears using bicyclederailleurs, the Jet relies on a single gear. With fewer moving parts, there is less energy lost, and the car can go farther.

Aerodynamic considerations include using solid wheels (instead of spokes) that don’t thrash through air as well as enclosing as much of the wheel as possible with wheel covers or the car body. Rolling resistance also plays a part. You’d think the hyperinflated tires would have the least rolling resistance because that is what you learned in engineering school. They will indeed, David explained, until you hit a bump. A bump that isn’t absorbed by the tire will displace the vehicle mass upward as there is almost no suspension in the Jet. That is something you don’t learn in engineering school.

Figure 3.Keynote speaker David Cullimore, 23, speaks to the 500 assembled at Solid Edge University 2016 about his winning ways.

Figure 3.Keynote speaker David Cullimore, 23, speaks to the 500 assembled at Solid Edge University 2016 about his winning ways.

So dominant is David Cullimore in the Greenpower races that the race officials have branded it an unfair competition, and are prone to change the rules to invalidate his innovations, says a Solid Edge executive.

With all this talk of aerodynamics, rolling resistance and energy, it will come as a surprise to learn that Cullimore is not an engineer. Not officially anyway.

It wasn’t for lack of desire. Cullimore knew from an early age that he was chosen to be an engineer. He was always making something in the workshop. For his 13th birthday, he requested a belt sander. In later years, he wanted a milling machine and a lathe. But no UK engineering school would accept Cullimore. Despite his propensity for making things, engineering schools have their admission requirements.

Fundamental to current engineering schools is mathematics. A lot of it. Two solid years of calculus, linear algebra and differential equations form the basis for the engineering courses that follow in the remaining years.

While Cullimore did “okay” in geometry and algebra (“I was never the best student”), he hit the wall with calculus. For him, differentiation and integration remained foreign, unsolvable. A year of trying only earned him a U for unsatisfactory, a failing grade. A lifelong ambition now appeared unattainable.

Calculus as the Gatekeeper

Calculus has been a first year requirement in engineering schools for several generations. Whether you believe it was Isaac Newton who discovered it (also 23 at the time!) or Gottfried Liebniz, neither will be held in reverence by first-year students who are washing out of the program because of their inability to get the arcane notation and weird concepts (“and now as delta x goes to zero….”).

But those who take calculus for granted, and look down upon those who can’t unlock its secret language, would do well to remember that there were engineers before its inventions. Roman engineers, for example, are famous for their aqueducts and roads, which are still around after 2 thousand years.

While calculus does explain a little more about the world—sometimes with grace (the area under a smooth curve)—more often it struggles to explain so much else. Remember squirming or trying to stay interested through lengthy derivations? Think of your professor who took an entire heat transfer class, using derivatives and integral galore, to proudly reveal what everyone who cooks already knows: 20 minutes a pound at 350 degrees Fahrenheit is the formula to cook a roast. A fluid flow graduate class took three hours (maybe it just felt that long) and boardfuls of differential equations to explain why tea leaves collect in the center of your cup when you stir it.

Having taken years to explain what could be considered trivial, the complex mathematical tools are rarely applied directly in typical engineering practice. They are often used, but hidden deep in engineering and design software. Your finite element analysis (FEA) software is wonderfully adept at solving large matrices using linear algebra. Similarly, computational fluid dynamics (CFD)employs Navier-Stokes equations, and relies on partial differentiation. Even 3D CAD solves complex geometrical calculations. But because these applications are performing these tasks, you don’t have to.

So Why Make These Rules?

The wisdom that prevails is to give a graduating engineer every possible mathematical tool to allow him or her to solve any possible problem. It will take all of 4 to 5 years to achieve this.

What’s rarely discussed, as we emerge proudly from our hallowed institutions, is the pride of passing, of enduring, of making it, of feeling superior to those who failed along the way, or who never got in the first place.

How many potentially capable and successful engineers are we not giving a chance due to overly strict math-based admissions standards? People like David Cullimore serve as a case in point.

The ID Work-Around

Cullimore was not to be deterred. He enrolled in “the next best thing,” an industrial design program. But in a field where aesthetics is held in equal regard as engineering, his true colors kept showing through. He was always referred to as “the engineer” in his groups. He worked for a Formula One racing team—shoulder to shoulder with degreed engineers—all of whom were none the wiser.

Did you live in fear that you would have to solve a calculus problem one day? I asked Cullimore.

“I would have had to tell them that it was beyond my learned skills,” he said calmly.

For the record, Cullimore made his employer aware of his lack of an engineering degree when he applied for his position. Only on his last day did he reveal this fact to his coworkers, much to their surprise.