Leonardo on the Nature of Water
The currently extant scientific heritage of the greatest universal genius in the human history, Leonardo da Vinci (1452—1519), contains approximately 7,000 pages of manuscripts. Specialists estimate it as only 25—30 percent of the legacy left by the Great Florentine to his pupil, Francesco Melzi. Leonardo planned to publish materials in several research fields; he composed detailed plans for these publications, reconsidered and rewrote them several times. Leonardo’s Codex Hammer (now in Bill Gates collection) includes the plan of the “Book of Water” consisting of 15 parts: water in itself, the nature of the bottoms, things moving in it, canals, machines set in motion by water, etc. Here we will describe only some of Leonardo’s achievements in his basic research on the nature of water and their applications...
“How the clouds are formed...”
“Write how the clouds are formed and how they dissolve, and what it is that causes vapor to rise from water into the air, and the causes of mists and of the air becoming thickened... and the cause of snow and hail, and how water contracts and hard in ice, and write of the new shape that snow forms in the air...”*
The picture taken by Antonio Bandaralli shows a rare phenomenon — the formation of a tremendous cloud above Lake Maggiore in Lombardia. Apparently, the governing role here belongs to the relative motions of large masses of humid air arriving from the Atlantic Ocean, which is captured by the high Alps. Leonardo da Vinci’s observations of a similar process in the same region allowed him to understand the most essential effects that occur during cloud formation:
“When the cloud is created it also generates wind… In the creation of the cloud it attracts to itself the surrounding air, and so becomes condensed, because the damp air was drawn from the warm into the cold region which lies above the clouds; consequently it is necessary for a great quantity of air to rush together in order to create a cloud; and since it cannot make a vacuum, the air rushes in to fill up with itself the space that has been left by the [former] air. It cannot draw the air from the earth, because it would produce a vacuum there: the cloud draws it from its sides... I once had an opportunity of observing this process; and on one occasion above Milan, toward Lake Maggiore, I saw a cloud in the form of a huge mountain, which looked as if it were full of glowing rocks. And this cloud was attracting to itself all the little clouds that were near, itself remaining stationary …”.
Leonardo was the first to explain the process of cloud formation and raining, and his extremely brief and clear explanation was arranged in the form of a fable:
“One day, some water was seized by the wish to leave its usual place in the beautiful sea, and fly up into the sky. So the water turned to the fire begging for help. The fire agreed, and with its heat turned the water into a thin vapor, making it lighter than air. The vapor soared up into the sky, higher and higher, until finally it reached the coldest and most rarified level of the atmosphere. Then the water particles, numb with cold, were forced together and became once more heavier than the air. And they fell — in the form of rain. They did not just fall, they cascaded earthwards! The arrogant water was soaked by the dry soil and, paying for its arrogance, remained imprisoned in the earth”.
It should be noted that the problem of cloud formation had been formulated long before Leonardo da Vinci became interested in it, in “The Book of Job” of The Old Testament, which is assumed to have been written 2,500 years ago by a gifted poet and philosopher. The fragment cited below is an excerpt from Yahweh’s speech with a reference to God’s deeds and wisdom inaccessible to understanding of mortals:
25 Who cuts a channel for the torrents of rain, and a path for the thunderstorm,
26 to water a land where no man lives, a desert with no one in it,
27 to satisfy a desolate wasteland and make it sprout with grass?
28 Does the rain have a father? Who fathers the drops of dew?
29 From whose womb comes the ice? Who gives birth to the frost from the heavens
30 when the waters become hard as stone, when the surface of the deep is frozen?
37 Who has the wisdom to count the clouds? Who can tip over the water jars of the heavens
38 when the dust becomes hard and the clods of earth stick together?
The Book of Job, Chapter 38
The problem formulation in “The Book of Job” allows us to see its origin — the vital importance of elucidating the essence of this phenomenon for the mere existence of human beings in arid climatic zones. The fact that this problem was posed in ancient times emphasizes the cogency of achievements of the Great Florentine.
At least three most important pioneering results have to be noted in this field of research.
Measurement of vapor density
Leonardo was the first to think of a scheme of a setup for measuring the vapor density at the boiling point:
“To experiment and to make a rule about the volume increase of water as it turns into air (into vapor). We shall take a square tank with an open top, ghef, and we shall place inside of it a bag made of a calf’s amniotic sac, which is very thin; set it like a bladder and closed on every side except for the top, on which is placed a straight board the size of the opening of the tank, ab, this bag being half filled with water, the other half remaining empty of water and air; and when the water evaporates, the other half of the bag will come to be filled with vapor; and the cover of the bag will have what takes to lift it, namely the counterweight n, so that the evaporation will make no effort to push it up… And then measure how much water is missing and you will see how much is the evaporated water”.
Leonardo realized the possibility of practical application of vapor energy and designed a vapor gun. When the gun charger is made hot by burning coal, the artilleryman turns the handle, the shutter separating the water tank from the chamber opens, and water
“… immediately is converted to so much smoke that it will seem a miracle; specially at the sight of the fury and at the sound of roar”.
As Leonardo wrote, a small gun made of copper could throw 60-pound shots to distances greater than 2 or 3 miles. He called his roaring toy a sweet name: architronito — the little gun.
Leonardo’s gun is actually a one-shot steam engine. He invented it more than 250 years before the inventions made by I. I. Polzunov (1763) and J. Watt (1784).
Rejection of the Flood
Fossilized shells are frequently found in Italy rather far from the sea. For many centuries, the presence of sea shells in mountains had been considered as a confirmation of the Flood. Leonardo studied various shell types and their biological features in detail, discovering four layers with shells rather than one layer in cross sections in Lombardian river valleys, and concluded that
“The Flood came about as a result of rains which caused rivers together with objects carried by them to rush toward the sea and they did not draw up to mountains the dead things on the seashores. And if you should say that the Flood then rose with its waters above the mountains, the movement of the sea in its journey against the course of rivers would have been so slow that it would not have been able to carry things heavier than itself floating in it. … I do not see therefore in what way the said shells could have come to be so far inland unless they had been born there”.
Leonardo’s final argument that the Flood was impossible from the viewpoint of science on the nature of water was the following:
“A doubt arises, and that is: whether the Flood which came at the time of Noah was universal or not. And it would seem not, for the reasons which will now be given: We have it in the Bible that the said Flood consisted in forty days and forty nights of continuous and universal rain, and that this rain rose ten cubits above the highest mountain in the world. But if it had been the case that the rain was universal it would have formed a covering around the globe spherical in shape. And this spherical surface is in every part equidistant from the centre of its sphere; and the waters of the sphere finding themselves in the aforesaid condition, it is impossible for the water upon the surface to move; because water does not move of its own accord unless to descend. How did the water of so great a flood depart, if it is proved that it had no power of motion? And if it departed, how did it move unless it went upwards? Here, then natural reasons fail us; and therefore to resolve such a doubt we must needs either call in a miracle to aid us, or else say that all this water was evaporated by the heat of the sun”.
Leonardo was the first scientist who introduced the notion of “tenacity and cohesion together” — a property now called “surface tension”:
“That water may have tenacity and cohesion together is quite clearly shown in small quantities of water, where the drop, in the process of separating itself from the rest, before it falls becomes as elongated as possible, until the weight of the drop renders the tenacity by which it is suspended so thin that this tenacity, overcome by the excessive weight, suddenly yields and breaks and becomes separated from the drop, and returns upward contrary to the natural course of its gravity… The part that extends to the break is drawn up by the remainder in the same manner as is iron by magnet”.
He also noted the lifting of liquids in small-diameter tubes and used the capillary effect to analyze the motion of water in the ground:
“Water in the sandy bank of the river moves all by itself, against the force of gravity, and makes the sand wet only because water is attracted by aridity”.
Leonardo knew Archimedes’ principle: “A boat displaces as much water from the site where it floats, as is the weight of the boat itself”. He invented water skis.
He correctly wrote the condition of equilibrium of liquids of different densities in communicating vessels.
He invented a device for measuring the pressure on the side wall of the vessel as a function of the water column height.
He studied the dependence of velocity of stream outflow from the side wall of the vessel on the liquid column height.
When considering the interaction of flows and studying turbulence, Leonardo introduced the notion of streamlines and used it in studying the motion of various bodies in water and the water flow around various obstacles.
He was the first to formulate the principle of stream continuity, or of conservation of mass in a tube filled with liquid: VS = const, where V is the stream velocity and S is the cross-sectional area. Based on the principle of conservation of mass, he demonstrated the emergence of a backflow from the shore inward the sea in brakers and explained that this effect was responsible for the formation of clay deposits at large distances from the shore.
Many of Leonardo’s discoveries, when he studied the motion of water and air flows, were obtained with the help of markers. As markers, he used straws, dirt, dust, small seeds, bubbles, smoke, and birds hovering in ascending air flows. The figure (in the center) shows a device for studying the water outflow from an orifice in the vessel’s bottom. The streamlines were observed with the help of small seeds. This picture by Leonardo triggered the development by the author of a device for ensuring the safety of passengers in a car hitting an obstacle. During the impact, the kinetic energy of the car is converted into the energy of a high-velocity stream from a small vessel filled with water and placed behind the bumper. Crash test experiments with a 0.5-liter water vessel validated the effectiveness of the device proposed by Leonardo even for impacts between the car and the obstacle at an angle of 30°. Obviously, Leonardo’s ideas do not become obsolete!
Leonardo was the first to study the generation and evolution of vortices in water. The figure illustrates the processes induced by incidence of a water stream into calm water. Leonardo was able to notice and clearly identify the following important effects: generation of vortices under the surface, failure of vortices of the opposite sign during their meeting, and suppression of vortices owing to their interaction with bubbles (“part of the excited water between the air and the underlying water mass cannot withstand so many revolutions”).
Waves on the water surface
In studying waves on the water surface, Leonardo was impressed by an unusual effect: waves from two stones, though producing clearly visible changes of the amplitude in the interaction region, recovered their initial shapes when moving away from this region:
“…The reason is that despite some evidence of movement water does not leave its location because the openings made by the stones are instantly closed again, and the motion causes certain shaking which one could describe as a tremor rather than a movement”.
Thinking about the effect observed, Leonardo concluded that sound and light had a wave form.
“If you let a stone fall upon water, following a perpendicular line, the water rising from the site of the percussion will likewise rise in a perpendicular line”.
This is Leonardo’s description of one of the beautiful hydrodynamic effects — the formation of a cumulative jet in the region of an oblique impact of the flows. The mechanism of this process was clarified only 450 years later by M. A. Lavrentiev. He conducted an elegant experiment on an oblique impact of a colored water stream and a pure water stream, which was recently repeated at the Institute of Fluid Dynamics in Karlsruhe. This facility displayed two nontrivial effects: the reflection of flows without mixing and formation of waves in the contact zone (p. 58). It should be noted that the hydrodynamic model is successfully used in analyzing high-velocity oblique impacts of metallic plates. A cumulative jet is formed in the contact zone, and explosive welding occurs in a rather wide range of impact angles, usually with typical wave formation. The figure on page 57 shows a thin section of the tungsten-copper bimetal obtained by the method proposed by the author (with a negative impact angle).
Research required by practical needs
“When you put together the science of the movements of water, remember to include in each proposition its applications and use, in order that these sciences may not be useless”.
This was the motto of Leonardo the naturalist. The opposite situation was also possible, when practical needs initiated academic and engineering research. Actually, Leonardo da Vinci was the Court Engineer and Artist at the court of the Milan Duke Lodoviko Sforza for 20 years. Leonardo spent his last years (1517-1519) in France, where he was called “the First Royal Artist, Engineer, Architect, and Official Mechanic.” Thus, his official commitments included the designing of projects and supervising the constructing of fortresses, canals, and bridges, as well as drain marches, and other activities.
Streamlined contour of the ship
“Nature does not break her laws”; hence, Leonardo guessed that the best shape of a ship had to be similar to the shape of a fish:
“These three ships of uniform breadth, length and depth, when propelled by equal powers will have different speed of movement; for the ship ab that presents its widest part in front is swifter, and it resembles the shape of birds and fishes such as the mullet. And this ship opens with its side in front of it a great quantity of water, which afterwards with its revolution presses against the last two-thirds of the ship. The ship dc does the opposite, and fe has the movement midway between the two aforesaid”. It should be noted that the shape of the modern racing yacht below the waterline is consistent with the shape recommended by Leonardo.
We can also add Leonardo’s comment on the influence of the surface quality on the ship velocity: “A certain slimy discharge, which with difficulty becomes separated from the fish, performs that function towards the fish that pitch does to the ship”.
Controlling water flows
Page 15-B of the Hammer Codex contains 38 “propositions of water” with numerous figures and with the final observation: “The science of these objects is of great usefulness, for it teaches how to bend rivers and avoid the ruins of the places percussed by them.” The list of problems contains various issues that had to be studied in detail and formulated as recommendations for practice, including
“3. If the water percusses the obstacle and flows over it, the soil will be removed both in front and in the back of it.
15. Where walls made as banks will collapse toward the river.
25. How navigable canals should be arranged when crossed by some river
31. Where outlets for flood control in canals should be made.
32. How to make the foundation of canal locks permanent”.
Obviously, Leonardo’s works on irrigation affected the invention of a shipping lock consisting of double gates aligned at an angle, where the water pressure itself is used for better contact of the walls; his ideas also led to investigations of exhaust pressure and velocity as functions of the water column height, which are important in design of water mills and drives.
Invention of a centrifugal pump
First, there was an observation:
“If the water in a half-filled vessel is stirred with the hand, a whirling current is produced which will expose the bottom of the vessel to the air.”
Then there followed the search for the reason:
“… and when the force that produces it is no longer applied, the current will continue in motion but will continually diminish in speed until the impetus (actually, the momentum is meant here – M. M.) given by force ceases.”
If such a whirlpool is supported by an external mechanism, a device for pumping water can be created. Leonardo’s notes contain drawings of two types of such a pump: for bog reclamation and for application on ships.
Invention of a turbine
The main drive for machines prior to the invention of vapor-driven and electric machines was a water wheel with blades perpendicular to the axis. Leonardo demonstrated that the effectiveness of using the energy of incident water can be increased by directing the flow through a “water screw” in a tube. This was the prototype of modern water and gas turbines. Using this principle, Leonardo invented the pioneering (the first in the world) automatic device with a feedback: the drive for a roaster from a propeller-screw inside the tube. The more intense the fire, the better the draft in the tube, the faster the propeller moves, the faster the carcass rotates, so the meat does not burn!
Now all people who went to school know that the perpetuum mobile cannot exist because it contradicts the law of conservation of energy. There were times (not too far off), however, when there was no physical notion of ENERGY, and many people could observe the operation of a reliable natural perpetuum mobile, namely, a water wheel. The inventor who could manufacture the “eternal wheel” would make the humankind happy and would become famous forever and ever. Certainly, Leonardo could not but try to solve this problem. One of the schemes he proposed, a combination of two Archimedean screws, is shown in the figure (in the top right corner of the p.59). Water was assumed to be raised by the first (small-diameter) screw to a certain height and then brought back by the second screw to the initial level. An important feature of the scheme is a larger radius of the screw responsible for the backward motion of water (which would really generate a greater torque than that on the first wheel, but not greater work during one cycle). Leonardo’s comment on the drawing “water returns by the screw bn at the first screw and repeats this process for unlimited long time” indicates that Leonardo did not have any doubts concerning the feasibility of the perpetuum mobile at that time (the record is dated back to 1489). However, the system did not work. He also proposed several other original ideas: a device with compressed air, a structure with asymmetry provided by submerging part of the wheel into water, and a capillary engine. After seven years of experiments and serious consideration, he stopped and studied the situation with only three loads on the wheel. He found that the system simply tends to a state in which the overall center of mass occupies the lowest possible position. The result of these long-time unsuccessful activities was the Principle of Impossibility of the Perpetuum Mobile equivalent to the Principle of Conservation of Energy, which was formulated by Leonardo da Vinci in 1493 (see the paper in the journal Kvant, No. 5, 1999 for more details):
“I came to the conclusion of the impossibility to search for continuous motion, called by some perpetual wheel. Almost all those who worked on hydraulic and military machines, and other subtle engines, dedicated much research and experimentation to this problem, incurring great expense. But with all of them happened the same as with alchemists: always turned up some trifle, which hampered the success... My little work will bring them a favor: they will no longer need to run away as a result of the impossible things that were promised to sovereigns and heads of state.... I remember that many people from different countries, led by their childish credulity, went to the city of Venice, with great expectation of gain, to make mills in dead water /that is still water out of lake or sea/. But after much expense and effort, unable to move the machine, they were obliged to move themselves away with great haste”.
Note that now Leonardo concluded there was always some trifle in all engine schemes which would convert the perpetuum mobile to the perpetuum stabile, he did not even mention the type of the facility tested in Venice.
HOW TO TEACH: abundant knowledge or method?
There may be a long discussion on this topic, but maybe it would be better to give wise men’s opinions on how to develop students’ skills of thinking.
Leonardo da Vinci: “Searching for knowledge is a natural need of a good person.”
Leo Tolstoy: “Knowledge becomes real knowledge only if it is gained by the efforts of your own thought rather than memory.”
Landau: “The method is more important than the discovery proper, because the right research method will inevitably lead to new, more valuable discoveries.”
Dozens of discoveries made by Leonardo da Vinci were 200—300 years ahead of similar discoveries made by other researchers. Leonardo did not get a university education, but he had an insatiable strive for knowledge and developed an effective method for solving scientific problems, “rules that make it possible to readily arrive at good opinions on the basis of good understanding.” Which of Leonardo’s rules are most useful for a scientist, a teacher, or a student?
The scientific fate of Leonardo da Vinci testifies that it is necessary to teach everyone, but it is not possible to teach all in the same manner.
Leonardo says that it is important to teach a student to find and formulate the problem independently in order to develop the ability to think.
Leonardo says that it is necessary to study the process or the phenomenon as a whole: “As a divided kingdom is destroyed, the divided though becomes vague and weak.”
Leonardo says that it is desirable to construct a scientific model of the phenomenon from the very beginning, with accurate evaluation of the role of various governing parameters and possible alternatives of process development.
Based on long-time studying of Leonardo’s manuscripts, the author reconstructed his Research Method. This scheme will be most useful for teachers and pupils of specialized schools and classes, which are abundant in our country after the school reform in the 1960s—1980s.
Unfortunately, the Unified State Examination is aggressively introduced in the country on the initiative of the Ministry of Education. In terms of its organizational structure and financing, the Unified State Examination is a bad copy of tests in the American system of education. It is worth noting that there are many protests in the USA against the orientation of school education to preparing the pupils for testing, where great volumes of information are tested. As a result, teaching thinking skills and solving nontrivial problems is no longer a priority. The most grounded criticism of the American system of school education, which does not provide the required quality of education, was given by the admiral H. G. Rickover, the father of missile-carrying atomic submarines, in his book with a speaking title American Education. National Catastrophe (1963). Still, the situation has not improved.
M. A. Mogilevsky
*All italicized texts belong to Leonardo da Vinci.