Inside the Mind of a Master

I interviewed a physicist once who told me that the kind of “warp speed” space-bending travel made famous by Star Trek wasn’t theoretically impossible. It’s just that we don’t know enough yet how to make it work. Something about requiring more energy than exists on the planet, at our current state of knowledge, or some small obstacle like that.

To many of us, warp-speed travel might sound far-fetched and crazy. But after spending a rainy winter morning immersed in a spectacular exhibit about Leonardo da Vinci at the San Jose Tech Museum, I have a sense that we’ll get there. For advanced space flight is surely no more far-reaching a concept now as human flight was 500 years ago, when Leonardo was trying to crack the code on that seemingly impossible feat. And then, too, one of his biggest problems was the lack of energy. It wasn’t the only issue, but without internal combustion technology to power a machine, even the most brilliant inventor was going to fall short.

And yet, the seeds were there.

In his 1992 book Engineering and the Mind’s Eye, Eugene S. Ferguson talked about how the best engineers were also part artist — able to visualize problems and phenomena in ways that allowed them to come up with innovative and creative solutions. Clearly, the Wright brothers possessed a good dose of this talent. But a close look at some of da Vinci’s sketches, paintings, sculptures, buildings, inventions and studies of animals, architecture and nature reveals a true master of that “visionary engineering” art.

At first pass, the two life-sized models of Leonardo’s flying machines that were displayed as part of the exhibit seem both crude and unworkable. In 1995, two Londoners built a model of da Vinci’s ornithopter, which he designed in the late 1480s but never built himself. Its construction materials included beech, iron, coirrope, leather and tallow. The inclusion of iron, of course, is a dead giveaway that this machine was never going to fly — and that’s without getting into the problems inherent in a flapping-wing design, powered by the pilot’s feet and hands.

A second flying machine, designed about 10 years later, looks even more like a Rube Goldberg contraption. The fuselage is a metal tub, and the four small flapping wings are powered, again, by a pilot sitting upright in the center of the tub. Leonardo’s thought was that by using a head-piece, hand-cranks and pedals, all connected with ropes and pulleys, a pilot could exert 200 lbs of force with his head, another 200 lbs with his arms, and another 200 lbs with his legs — thus creating 600 lbs of lifting force, or enough to lift the device off the ground.

But the genius, and Leonardo’s main contribution to the progress of workable flying machines that followed, lies not in the machines themselves, but the process by which he came to design them. If Leonardo da Vinci was accomplished in so many areas (anatomy, architecture, sculpture, painting, engineering and science) it’s because he applied a relentlessly curious mind to understanding the core forces and elements that connected them all.

As one of the explanatory notes of the exhibit put it, “For Leonardo, understanding the causes of motion by systematically investigating its manifestations was the only way to discover the rigorous laws that govern nature.” The flying machines themselves may be rudimentary and flawed. But da Vinci’s Codex on the Flight of Birds, for example, comprises the first recorded, scientific observations on the subject of flight — and those observations are astounding, both in depth and in insight.

Leonardo studied centers of mass and gravity, and how that influenced the posture and flight paths of various kinds of birds. He noted the disturbed vortices of air that emanated from a bird’s wingtips. He studied the winds and their impact on moving objects — both on the ocean and in the air. He looked at stability, maneuverability, and even postulated about a “compression of air” against the underside of a bird’s wing at a positive angle of attack that might help it to climb. He dissected bat and bird wings to learn more about their structure and function.

And based on those observations, Leonardo developed mathematical analyses of motion and equilibrium that he then applied­­ — not only to his flying machines, but to his sculptures, architectural projects, and even to his paintings. Like the Greeks before him, he also believed, far before anyone knew much about aerodynamics, that there were universal laws of order and proportion — a beauty of harmony in motion and structure — that should be incorporated into any man-made design. Not just for the sake of beauty, but for the sake of efficiency and fluidity of operation and motion.

If we find classical architectural structures like the Parthenon visually pleasing, it’s in part because the proportions follow a universal constant (1:0.618) that repeats over and over in nature and geometry. Likewise, we supposedly find most attractive faces that are symmetrical and proportional. And perhaps the same is true even in airplanes. Just for kicks, I looked up the dimensions of a Cessna 170 — one of the most beautiful-looking airplane designs I know. The wingspan to length proportion was 1:0.66. Not quite the “divine” proportion of Leonardo, but close. A stubby-winged Piper Tri-Pacer comes up with a higher number: 1:0.703. And the ultra-stubby Fokker Triplane? 1:0.801. Could it be that part of the reason we find airplanes — and certain airplanes in particular — such beautiful objects is because they conform to Leonardo’s divine proportion? It’s an intriguing thought.

Form is often said to follow function … but perhaps, if the laws of proportion hold, function can also follow form. Something that is fluidly and proportionately beautiful may also tend to be functionally efficient and aerodynamic. One might not think that, looking at Leonardo’s cumbersome ornithopter. But that’s by today’s standards of materials and knowledge. In the 1480s, that machine represented a beautifully optimized and efficient combination of available mechanical components and materials — cranks, pulleys, toothed wheels, transmission systems and, yes, even shock absorbers.

Indeed, one of the most astounding realizations I had, going through that exhibit, wasn’t all the ways Leonardo da Vinci got it wrong. It was all the ways in which he got it right. Leonardo lived 200 years before Newton figured out the laws of motion so integral to flight, and 300 years before Sir George Cayley figured out that lift could be separated from thrust in a flying machine design. That’s the equivalent of someone at the Salem witch trials trying to design a workable spacecraft with which to land on the moon.

And yet, while the materials were lacking, some of his ideas were dead-on right. His mind, quite clearly, was hundreds of years ahead of its time. The exhibit showed two different designs he came up with for shock absorbers — including a telescoping model that bears a striking resemblance to the oleo struts on the Piper Warrior in which I learned to fly. He designed a stepless, continuously variable-speed transmission that would be impressive even by today’s standards of efficiency. He was right about the central importance of CG and equilibrium in a workable flying machine.

Recently, a group of skydivers even built and successfully flight tested a parachute Leonardo da Vinci designed in 1483. Landing with it might have been an issue, since it weighed 200 pounds, but the pyramid-shaped cloth-and-wood parachute actually flew. In 2003, another group successfully flew a modern-day version of Leonardo’s “Piuma” glider, having reduced its weight from 220 pounds to 50 pounds through the use of aluminum-alloy tubes and Dacron instead of the original cloth and wood structure. The only thing that kept the original design from working, the Piuma group concluded, was Leonardo’s lack of access to light, modern-day materials.

Looking at Leonardo’s massive collection of drawings and studies, it’s also clear that this was a man who didn’t just study, but learned, because he remained open to the new ideas — even the idea that he might have been wrong. Leonardo’s later flying machine sketches had moved from the flapping wing designs to far more streamlined, fixed-wing gliders. Perhaps he acknowledged that the human body simply couldn’t power a flying machine built with 16th century materials. But his studies of equilibrium allowed him to see that in a glider, control could come from the pilot’s shifting of body and weight.

The line between Leonardo da Vinci’s glider drawings and modern-day hang gliders is straight and direct. And while the Wright brothers used more sophisticated control methods in their glider and Flyer, their work was heavily inspired by Otto Lilienthal and Octave Chanute — both of whom had designed and tested weight-shifting gliders. Not only that, but Leonardo’s studies of a possible helicopter (although he didn’t call it that) was what inspired a Russian immigrant named Igor Sikorsky to investigate this kind of intriguing flying machine, leading to the world’s first successful helicopter.

So what does all this tell us? All sorts of things — and each of us, going through that exhibit, would undoubtedly take away something slightly different. But three thoughts stood out most to me. The first was just how much groundwork Leonardo da Vinci laid for future investigations of flight and the development of flying machines, both in concept and in approach. We laud the Wright Brothers as the fathers of flight. But they were sons, as well … as were the pioneers before them. In the 17th century, Sir Isaac Newton acknowledged as much when he said, “If I have seen a little further, it is by standing on the shoulders of giants.”

The second thought was, as hard as it is to imagine a world 500 years in the future, that day will come. And to those who live then, our frustrated efforts at intransient and seemingly insolvable engineering and physics problems will no doubt seem as fundamental — flawed, perhaps, and limited by available materials and energy sources, but still important as preliminary investigations — as Leonardo da Vinci’s work now seems to us. We, too, are the giants whose shoulders some future generation will stand upon, even if we think we’ve failed.

And the third, and perhaps most important, thought is this: that to be those giants; to push the edges of knowledge and possibility forward and outward … we must remember to nurture art as well as science. For as Einstein said, “Imagination is more important than knowledge.” If Leonardo da Vinci saw so much further into the future than his peers, it’s because he had the eye of an artist as well as the mind of an engineer. He also had an insatiable curiosity, and the strength to keep his mind open to new ideas and changes in thought and opinion. Even if we’re 500 years more modern, with far more technology at our disposal … and even if we’re not inventing the fountain pen, painting famous portraits, building cathedrals or designing fantastical flying machines … we all could benefit from following Leonardo’s lead on that one.