by Shana Priwer
53
It's all in the circle game
Leonardo first became interested in geometry while he was working for Duke Sforza in the 1480s and 1490s. He first encountered mathematical constructs—geometry in particular—through his study of architecture and perspective painting. In 1496, the well-known mathematician Luca Pacioli was invited to Sforza's court, nominally to teach mathematics there, and Leonardo and Pacioli became friends in Milan, apparently spending much time together discussing the overlap between art and mathematics. During his time in Milan, Pacioli was writing a book, later published as the first of a three-volume set in 1509, called Divina Proportione. Leonardo was so interested in this project that he actually drew the figures for this text.
Leonardo's drawings of three-dimensional shapes called polyhedra (one example is a soccer ball) were the highlight of Pacioli's book. Leonardo came up with a new way of drawing these complicated shapes—he showed them with solid edges and hollow faces that let you see right through them to the structure on the other side. For the book, Leonardo drew about sixty pairs of illustrations. Each pair showed a different three-dimensional shape, in both a solid view and a hollow view. Some of the shapes were new—no one had figured out how to draw them before!
The method of drawing shapes was a breakthrough for the day, and it took a visual artist of Leonardo's talents to come up with it. Leonardo's obsession with geometry continued even after he finished working on Pacioli's book. If you look through his notebooks, you'll find sketches of different geometric shapes in unlikely places, for example, among studies for military fortifications and designs for a fountain.
In addition to his direct work with Pacioli, Leonardo spent some time in Milan conducting his own research into geometry based on that of Euclid and Pacioli. In particular, he was interested in trying to “square a circle,” meaning he wanted to find a way of creating a square with the same area as a particular circle, using only drawing tools such as a ruler and compass.
Beyond his theoretical work in mathematics, Leonardo was also interested in the mechanical methods of automating mathematical work, and he designed a machine that could have been one of the first calculators. A working replica was built in 1968, but whether or not this replica actually represented Leonardo's intention is another story. The sketches on which the calculating machine replica was based are unclear, and it's possible that the machine was not, in fact, a calculating machine, but a ratio machine instead.
54
Before planes, trains, and automobiles
Renaissance inventors were at a crossroads, whether they knew it or not. Europe was slowly emerging from the Dark Ages, and there had already been several significant inventions. At the same time, some of history's greatest achievements were yet to come. Leonardo, living fairly early in the Renaissance period, was on the leading edge of the era's innovation. Against what backdrop can we view his inventions?
One of the most significant inventions of the Renaissance was the mechanical timepiece. Though Casio calculator wristwatches wouldn't come along for a while yet, society was beginning to place more importance on an easy way to tell the time. Clocks were first created in the 1300s, but it was not until the 1580s that Galileo (a scientist and researcher from Florence) developed the idea for a pendulum. It wasn't until the 1600s, long after Leonardo's death, that the concept of the clock was further mechanized with the introduction of gears and screws.
Certainly, Leonardo and his contemporaries didn't have access to most of the modern conveniences we take for granted today. One of the things most noticeably lacking was electricity, which was not discovered until the seventeenth century and not widely used until the late 1800s. The first standardized fuel type was probably fish oil used by ancient Romans and those who came after them, so in the absence of electric lighting, fuel-driven lanterns would have been a possibility for Leonardo. Candles, torches, and lamps were other popular light sources during the Renaissance years.
In terms of weaponry, Leonardo had the advantage of not starting from scratch. Military technology, even in ancient Rome, was years ahead of the general technology available to the rest of the population. Hand-powered weapons such as spears and arrows had been around for generations, and gunpowder was in use by the middle of the eleventh century, though it probably wasn't used in Europe until the 1350s. This invention changed the course of warfare because it became nearly impossible to defend against guns with only hand-powered weapons. Leonardo's designs for cannons, for example, were a response to the new way of waging war.
Eyeglasses were another significant Medieval and Renaissance invention. By the 1300s, guilds in Venice were regulating eyeglass production, which, at the time, were probably considered a luxury item. When Johannes Gutenberg's invention of the printing press (see number 61) made reading into more of a hobby than a luxury, though, eyeglasses came into much higher demand. Everyone wanted to read, and their eyes needed to keep up with them! Readily available books were a major factor for Leonardo because he was able to read the writings of ancient masters and, in the process, create his own interpretations and additions. Plus, if books could be published easily, he could also publish his own writings. In addition to all of these other inventions, Leonardo used the growing worldwide interest in mechanics to utilize and explore water. Naturally, his concepts relied on existing research with water pumps, which were developed in the Middle Ages.
55
War games
When several Florentine forts were attacked in 1479, Leonardo became interested in ladders for scaling walls during an attack as well as methods for defending against those same efforts. Military engineering was just one of Leonardo's many interests, but as with everything else, he dove into it wholeheartedly and came up with several important designs.
Leonardo designed a number of different ladders for wall climbing. Some were stiff, solid ladders, while others were flexible and made from rope. To attach securely to the top of the wall, some of Leonardo's ladders had hooks; others had spikes on the base to keep them immobile on the ground. He also thought about flexible ladders that could hang from a wall as well as the type of chain ladder that's often used for fire escapes today. Ladders were, in a way, a symptom of the problem: war. Leonardo got to the root of the issue and also designed entire defense systems. One of his most clever ideas involved ladders lining a wall, where the tops of the ladders were all attached to a bar. Leonardo's assumption was that attackers would rush to climb the ladders in a sneak attempt to overtake the castle inside. Not so fast! Leonardo's defensive soldiers would push the bar out, and any poor, unsuspecting attackers would fall to the ground along with the row of ladders. It sounds complicated, and it was; perhaps this overdesign was one of the reasons it was never tested.
During his time with Duke Sforza, Leonardo also designed bridges for military applications. Some of these were portable; troops could carry the bridges with them and set them up quickly when needed. Others were designed to be particularly strong and resistant to fire or other means of destruction. Leonardo also considered methods to burn and destroy enemy bridges.
Leonardo's military bridges had a number of different designs. One was arched in such a way as to be particularly strong when assembled. Others used traditional pilings, or were flexible so they could swing without breaking. Leonardo also designed adjustable jacks for opposite sides of a river, to be used if the banks were different heights on each side.
Leonardo designed one particularly massive bridge during his time with Cesare Borgia. In order to connect the Golden Horn and the Bosporus, Leonardo suggested building a huge bridge across the Gulf of Istanbul. This route would have had immense strategic importance, but other engineers vetoed the plan when they saw how large the bridge would have to be. Nevertheless, modern studies show that the structure would have been possible to build with the resources of that era, and the bridge itself would have been solid and well designed.
Vehicles that could serve offensive or defensive purpose
s also piqued Leonardo's design curiosity. Take, for instance, his design for a horse-drawn chariot, which had four large scythe-like blades mounted to the axles. As the horse pulled the chariot, the blades would rotate, slicing off the limbs of enemy soldiers. A similar design placed the four large blades at the front of the machine, in front of the horses even, where a screw-type device turned them, and included a series of smaller scythe blades placed at the back of the chariot. This chariot was designed as a brutal weapon, indeed. Even the initial sketches included images of dead and dying soldiers left in its wake. For the peace-loving Leonardo, this was an incredibly gruesome design!
56
Building a better …cannon?
Leonardo's peaceful, harmonious landscape paintings do not tell the entire story of his career. In addition to his work to support troops with better ladders and bridges, Leonardo also designed or improved weapons. Guns, cannons, and other artillery weapons were on the rise during the Renaissance. Newer was better, especially when it came to national defense. Leonardo appeared to have had a nostalgic side, though, because he still spent time working to perfect or improve older weapons such as catapults, slingshots, and crossbows.
One of his innovations was the rapid-firing crossbow. This was no ordinary crossbow—it actually included four crossbows and got its power from a large treadmill. A number of men walked on steps that were located around the outside of a large wheel, and as they made the machine rotate, an archer would fire each crossbow, reloading them in sequence.
Leonardo also designed a mammoth seventy-six-foot crossbow, which required six wheels to maneuver it. This device, also called a ballista, used a series of gears to draw back the bow; a simple strike of a pin would release the shaft. Leonardo believed that this giant weapon would operate in almost complete silence, but his claim was never tested because the device was too difficult to build given the abilities of the day.
In the interest of defeating more enemies faster, Leonardo designed a rapid-loading catapult system. This machine, which could be mounted on top of a wall, consisted of a rope and winding mechanism used to bend back the arm and, in effect, ease the firing process. Leonardo also designed a row of catapults that could be launched at the same time when hit with hammers. Specially designed missiles, with gunpowder inside, had fins on the tail for extra stability, and when they hit their target, strikers inside ignited the gunpowder and caused an explosion. These sound remarkably similar to modern artillery shells.
While cannons were used as early as 1346, they weren't very advanced by Leonardo's time. They were still simple cylinders that used an explosion of gunpowder at one end to propel a stone ball out the other. One of Leonardo's first improvements to cannon design was to create a model that could be loaded from the back, rather than down the front of the barrel. Since the cannons had to be cooled before they could be reloaded, Leonardo suggested putting them in a vat of water to cool them off quickly. Not a bad idea, but would you want to be the one to lift a hot cannon into a tub?
In his studies of cannon balls, Leonardo was one of the first to explore ballistic trajectories. He studied how changing the angle of the cannon's muzzle could affect the distance the cannonball traveled, and in testing his designs, he supposedly launched a test cannonball 10,000 feet high!
Another invention of Leonardo's was a steam-powered cannon. The end of the cannon was heated to a very high temperature, and then a small amount of water was placed inside. As the water turned to steam, the increased pressure shot out the speeding cannonball. Leonardo's notebooks include information on the size of cannonballs that the device could use, and the distance they could travel. These details suggest that, unlike most of his inventions, this one was actually built and tested.
One problem that plagued Leonardo was that cannons had a large delay between repeated firings. Leonardo's answer was, in retrospect, pretty obvious: He proposed a system with multiple cannons that could either be fired all at once, or one after another. His designs included eleven or fourteen guns in three rows: While the top row was being fired, the middle row could be reloaded, and the bottom row cooled off. These systems are considered to be the predecessors of today's machine guns. Just think about how dangerous Leonardo would be today if he were making improvements to modern military technology!
57
Leonardo's robot
Compared to, say, the history of architecture, the field of robotics is relatively new. Most development in this area has happened in the twentieth century. However, leave it to Leonardo to be at the front of the pack! He was one of the first to have an impact on robotics design.
In 1495, Leonardo sketched out an idea for a mechanical robot that may have been the first such design in history. It was a mechanical, humanlike figure whose purpose was somewhat unclear—maybe Leonardo designed it just for fun! Leonardo's robot could turn its head via a bendable neck, open and close its jaw (which was close to being anatomically correct), move its arms, and sit up and down. In the drawing, the robot looks like a knight, since it appears to be wearing a suit of armor. It was designed with at least two gear systems that operated separately from each other: one to control the lower body (legs, feet, hips) and one for the upper body (arms, shoulders, hands).
You could call this robot design a culmination of Leonardo's research into anatomy and geometry. What better way to combine mechanical science and human form? He took the proportions and relationships inherent in Roman architecture and applied them to the movement and life inherent in all living beings. In a way, the robot was Vitruvian Man brought to life.
Historians are not certain that a physical model of Leonardo's robot was ever constructed. This design was misplaced for many years and was only discovered in the 1950s. Computer models of Leonardo's design have since been constructed, attempting to show how his robot might have been realized in sixteenth-century Italy.
58
Chutes (we already covered ladders)
Leonardo was a flyboy from day one. As a child, he spent hours watching birds. He drew every kind he saw, and this fascination stayed with him throughout his life. He was particularly interested in wings, and they occupy page after page of his notebooks. He did more than draw, though—he actually set out to make himself a pair of wings. The design matured into something resembling a modern parachute. Probably the first of its kind, this design depicted a fabric-based device that a person could use to float from the sky onto the ground.
His first parachute, seen in one of his early notebooks, probably dates to 1485. This design looks a lot like a modern kite, with a person dangling from an airborne fabric structure that was held together by rigid poles. The parachute itself would probably have been made of linen, sealed at the edges so it wouldn't unravel or fray during flight. The poles would have been arranged in a pyramidal shape, with a maximum length of about twenty feet. (In contrast, modern parachutes all use flexible structures and fabric.)
Unlike the parachutes of today, most of Leonardo's designs made no real provisions for personal safety. His notes suggest that the parachute could be used from any tall outcropping, and the user would be perfectly safe upon arrival back to earth:
“If a man had a tent made of linen, of which all the apertures have been stopped up, and it be twelve braccia [twenty-one feet] across and twelve feet in depth, he will be able to throw himself down from any great height without sustaining any injury.”
However, the rigid structure probably could have caused serious injury if it crumpled on top of the passenger inside. Like most of his other inventions, however, Leonardo's parachute was never built and tested during his lifetime. One of the biggest hurdles was probably finding something high enough to jump from!
Leonardo's design was finally tested in June of 2000 by a skydiver and camera flyer named Adrian Nicholas. After constructing a version of Leonardo's design using canvas, wooden poles, and ropes, Nicholas landed safely after jumping from a hot air balloon at 10,000 feet (for safety reasons, he broke out a modern fra
meless parachute 2,000 feet from the ground). Leonardo's parachute actually floated to the ground more slowly than a traditional parachute would have. While most people thought that Leonardo's design wouldn't work or would spin too much to keep the occupant from excessive nausea, Nicholas proved that the master's design was flight worthy. A model of Leonardo's parachute currently hangs in the British Library in London.
59
It's a bird, it's a plane, it's a flying machine!
Leonardo's first memory, as he tells it in his notebooks, was of himself as a small baby, lying in a cradle outside, minding his own business, when a hawklike bird called a kite landed on him and poked its tail feathers in his mouth. While it would have been extremely unusual for an infant to retain such a memory (as well as unlikely that such a bird would even land on a baby), it might explain Leonardo's later obsession with flight!
Leonardo started with the assumption that people could eventually fly using their own strength, and he tried to design a device to help them do just that. He also wrote up his ideas about flight into a treatise now called the Codex on the Flight of Birds. In these notes, he summarized his scientific theories about how birds were actually able to fly, including his idea that the wing's movement created circular areas of wind thrust. Not so shabby for a fifteenth-century scientist!
In the course of his studies, Leonardo determined that human-powered aircraft would be difficult to build and use. In the late 1480s, he repeatedly studied an ornithopter, an aircraft that was almost completely powered by flapping wings. He wanted to create a machine that would mimic the flight of a bird as much as possible. Other designers after Leonardo continued research in this area, although it was never very popular once aircrafts with other means of propulsion came along.
