When they set out in 2011 to build a human-powered helicopter that could fly 10 feet into the air and hover in one place for 60 seconds, Todd Reichert and Cameron Robertson faced one major obstacle: it was supposed to be impossible.

Experts had reached that conclusion after 30 years of failure and crashes, beginning in 1980, when the American Helicopter Society (now AHS International) offered a prize, eventually worth $250,000, for a successful human-powered flight. All evidence suggested that a single pilot simply could not generate enough power to fly that high and for that long. Aeronautical engineer Antonio Filippone of the University of Manchester in England ran through the numbers in a 2007 paper in the Journal of the American Helicopter Society and reported that the idea—and any aircraft based on it—just would not fly: “Overall, all the requirements ... of the American Helicopter Society cannot ... realistically be achieved.”

Reichert, 32, and Robertson, 27, only learned about Filippone's paper after they won the money and the award, known as the AHS Sikorsky Prize, with a record-setting flight in June 2013 by their giant, four-rotor, bicycle-powered machine called Atlas.

Like an awesome toy built with Paul Bunyan's Erector set, Atlas features four skeletal beams, constructed from carbon-fiber tubing and cables made from high-tech line fibers and assembled into an enormous, arching X with a diagonal span of 88 feet. The four rotors, each 67 feet in diameter, with balsa wood ribs and see-through Mylar skin, sit at the end of each arm of the X. Dangling on lines from its center, which arches 12 feet above the ground, is a modified racing bicycle on which Reichert, Atlas's human engine, supplies the pedal power that turns the rotors via an intricate system of spools and lines. That energy lifts the 121-pound craft off the ground.

Their 64-second flight, after so many before them had failed, demonstrates that in an era dominated by large teams of engineers working for huge companies such as Lockheed Martin and Northrop Grumman, a small, nimble group can solve the hardest problems. Benjamin Hein, a senior engineer at Sikorsky Aircraft and chair of the Sikorsky Prize committee in 2013, says the young designers had to figure out the ideal size and weight of an aircraft with a very limited power source, an optimal rotor design and a workable flight-control system. He notes there are important lessons for industry here, chief among them Reichert and Robertson's willingness to fail and make major design changes quickly. “That's the thing that big companies can't do,” Hein says.

In another demonstration of the power of the few, the laptop computer program that Reichert and Robertson wrote to optimize their design is now part of a NASA software tool kit used to configure vehicles intended to fly much farther than Atlas. Next year the two engineers plan to use it themselves to design a human-powered plane to compete for the Kremer Marathon prize, which will go to the first craft to complete a 26-mile course in less than one hour. (The current speed record is 27.5 miles per hour, set during a flight that lasted just over two minutes.)

It is hard to resist invoking another pair of independent tinkerers, Orville and Wilbur Wright, when writing about Reichert and Robertson. Like the Wright brothers, the two men—who met as engineering students at the University of Toronto and now run AeroVelo, their “design and innovation lab”—share a passion for manned flight. Reichert says that they want “to inspire people to see how much more we can do if we really prioritize efficiency.” That is why they mostly use materials that have been around for decades, such as balsa, Styrofoam and Mylar, and why they embrace the limitations of working with human power. It means they cannot go and buy a better engine, Robertson says. “You have to solve your problems without changing your power supply. You can't just increase it.” And surely bicycle shop owners Wilbur and Orville would appreciate the central role of the bicycle in Reichert and Robertson's inventions. In addition to Atlas, the two built a successful bicycle-powered flapping-wing aircraft called an ornithopter.

But the most Wright-like thing about Reichert and Robertson is their method. “The Wright brothers were mechanically inclined,” Reichert says. “They knew how to tweak things and fix things, but they were also scientifically rigorous, which is really the combination that you need.”

The two Canadian engineers are not helicopter designers, which is why they were ignorant of the scientific papers dooming them to futility. What they did know, however, was that the complex computations they had to do would potentially require hours and hours of expensive supercomputer time that they could not afford. And the duo felt their software needed to improve on the conventional approach to aeronautic design, in which the structural and aerodynamic components are developed by separate teams and handed back and forth. That process, Robertson says, results in “a solution that is not perfect from the aerodynamic side and not perfect from the structural side.”

To address all these issues, what they needed was a program that would simultaneously merge the structural and aerodynamic elements of design parameters that were specific to human-powered helicopters. It also had to be cheap to run. And fast.

So they created one on their laptops in a five-month code-writing marathon that in part drew on earlier work Reichert had done for the ornithopter, which had earned him his Ph.D. To get from an unaffordable supercomputer to a laptop, they decided to forgo high-fidelity modeling capacity in favor of medium-fidelity models of things such as airflow around the rotors. High-fidelity code can provide precise details about what is going on where the aerodynamics are very complex, like at the tip of the rotor. But although that standard is necessary for commercial aircraft design, it was not required for the low, slow, readily modified Atlas. “Medium fidelity will always allow you to get within, say, 2 percent of the correct answer,” Robertson says, “and that's really what we were looking for.”

Their custom program enabled them to test almost any given helicopter design on their laptops. They just plugged in the dozens of variables for a proposed design, such as rotor geometry and the weight, dimensions and failure modes of the construction materials, such as carbon-fiber tubes. The program crunched all those data and, in a matter of minutes, spit out the optimal version of the given aircraft and the minimum amount of power needed to get it airborne. The code is now being used in nasa's software library because the agency liked the way it got very close to the correct answer very quickly.

The first design decision Reichert and Robertson made was to go big: long arms and big rotor blades to maximize lift. Watching the video of Atlas's winning flight, its rotors, turning at just 10 revolutions per minute, may seem too slow to be effective. But it is their huge size, not their speed, which supplies the lift that gets the machine off the ground. The previous failures, the two felt, artificially limited the size of helicopters and rotors to make them fit in places like gymnasiums because wind gusts outdoors would be too much for these delicate aircraft to handle. Staying inside was smart, the engineers agreed, but gyms were too small. That is how a cavernous old barn north of Toronto—and then the Soccer Center near the same city—became the Kitty Hawk of human-powered helicopter flight.

The other major design constraint for Atlas was the weight and power capacity of its engine—Reichert, a shade over five feet, 10 inches, and weighing in at 180 pounds. The aircraft's design, however, limited the pilot's weight to 165 pounds, which meant Reichert would have to drop 15 pounds. He would also have to generate enough power during the flight to raise himself and the 121-pound aircraft—a total of 286 pounds—to the required height of 10 feet and remain aloft for the required time of one minute. The estimated power targets, a function of the total weight of the aircraft and the size of the four rotors, were an initial burst of about 1,000 watts to get up, followed by a steady output of around 600 watts for the remainder of the flight. Basically, it was to be a 100-meter sprint, followed by a slightly slower 400-meter sprint.

Arguably the fittest aeronautical engineer in North America, Reichert is a dedicated athlete who has competed at Canada's highest levels as a speed skater. As part of a machine, Reichert was subject to his own and Robertson's obsession with measurement. “As soon as you can measure something,” Reichert says, “you can improve it.” During his months-long training regimen, he and Robertson used two ergometer systems to measure his power output. Reichert helped the cause when he came in at 160, five pounds below the target weight, reducing the amount of energy required to fly the helicopter with no significant loss of engine power.

To ensure top performance, elite athletes usually time their training so they reach peak levels of fitness just before they compete. Repeated technical delays, however, forced Reichert to maintain his peak level of strength and fitness for more than nine months. Incredibly, during the winning flight, he actually exceeded the targets, generating 1,100 watts (nearly 1.5 horsepower) during the first 12 seconds before dropping back to average 690 watts for Atlas's entire 64 seconds of air time.

Reichert, Robertson and their team of eight students at the University of Toronto built Atlas in the summer of 2012. Although they were constructing a fantastic machine to achieve an “impossible” goal, Reichert and Robertson did not waste time or money on unnecessary efforts or exotic materials. Whenever possible, they went with existing solutions, using proved “plug and play” elements to keep costs down and free them up to focus on the stickier problems. Instead of fabricating a custom, superlight bike, for example, they modified a stock Cervélo R5ca, one of the lightest production road bicycles available. As Robertson likes to tell the high school groups he sometimes speaks to, most of the materials used to build Atlas are available at craft and hobby shops such as Michaels. The newest product they used was Vectran, a liquid-crystal polymer fiber for a high-tech line with exceptional strength and zero creep—once it is loaded, it does not stretch.

In the barn north of Toronto, Reichert says, the complex math and cool algorithms gave way to intuition and to trial and error. One early victim of the process was Atlas's control system, a complicated arrangement of levers and wires connected to small L-shaped airfoils (called canards) on the tips of the rotors. It was supposed to prevent the helicopter from drifting outside the 10-meter-square (33-feet-square) box stipulated by the Sikorsky Prize rules by changing the pitch of the rotors.

But with too much lag time between pilot action and result, the fancy control system simply did not work. “It was really cool mechanically,” Robertson says, but it could not counter drift. So they replaced it with a simpler system, rerouting a few cables to connect the bottom of the bike to the axles of the four rotors. The pilot controlled drift by leaning forward to move forward, left to move left, and so on. “I still can't believe it worked,” says Reichert, who can be seen leaning hard right most of the time in a video of the winning flight. Not only did it make Atlas easier to fly, it reduced the total weight of the aircraft by 10 percent. Combined with a reduction in drag, this lowered the power requirement by a whopping 20 percent.

Parts of the fragile aircraft broke all the time during testing, including two spectacular crashes just a few weeks before the successful flight. Both were the result of an aerodynamic phenomenon called a vortex ring state, in which the turning rotors dip into air they have already pushed down and lose lift. The two engineers took a close look at the rotors and saw the leading edges were not smooth enough: the Mylar skin, applied in a rush as they raced to finish the aircraft, had rough spots, creating excess drag. So the duo carefully smoothed out the skin.They also shortened the carbon-fiber struts and stiffened the wire bracing system on the rotor arms.

The fixes worked. Eight weeks after the second crash, they won the Sikorsky Prize. The video showing that flight, in which Reichert appears to be flying some kind of crazy sideways construction crane outfitted with huge propellers, has been viewed more than 3.1 million times on YouTube. The competition was intended to inspire the next generation of engineers and capture the public imagination, and by YouTube measures, the Atlas flight succeeded.

After Reichert's winning flight, every member of the team got a chance to fly Atlas, each lifting off at least a foot or two from the ground. “Before that day,” Robertson says, “more people had walked on the surface of the moon than had flown a human-powered helicopter. We doubled that number.”

When Reichert talks about the reasons for his and Robertson's success, he goes beyond technology. He talks about their commitment to doing the impossible or at least trying to. “You have to set crazy goals,” he says, “because that's what motivates people.”

There is plenty of uninspired goal setting to go around, Robertson complains. Fuel-efficiency standards are his prime example. He says admirable government efforts to increase overall automobile fleet fuel efficiency, such as the current U.S. goal of 54.5 miles per gallon by 2025, an 88 percent boost over current standards, are not ambitious enough. “But if all of a sudden the government mandated a 1,000 percent increase in fuel economy,” he says, “then you've forced everyone to stop and think totally differently about the problem.” And that, he argues, could help launch a new era in superefficient transportation.

It is also a complete nonstarter in political and policy circles, for obvious reasons. Reichert and Robertson know that. What they hope such lofty goals will do is foster a new way of looking at seemingly intractable problems. “Taking on the impossible is not necessarily easier,” Reichert says, “but it's more satisfying, it's more motivating and, in the end, it's more important.”

This fall the men tried to break the cycling world speed record of 83.127 miles per hour in competition at Battle Mountain, Nev., and failed by about four and a half miles per hour. Next year they will return to the air to pursue yet another human-powered challenge that has gone unmet for decades—the Kremer prize, which carries a £50,000 award for a flight that covers 26.2 miles in one hour or less. They are already identifying constraints and assumptions and are confident they can rack up another unlikely win.

Because the only human-powered aircraft to reach that speed came down after about two minutes, well before it covered a marathon distance, one might conclude that the requirements for the prize “cannot realistically be reached.” One might also conclude, correctly, this is exactly what Reichert and Robertson want to hear.