Study for the design of an overbalanced wheel
This sheet, presumably dating to between the end of the 1490s and the beginning of the following century, is of key importance for the research on perpetual motion carried out by Leonardo. First of all because it dates to a period later than his denial of the possibility of building perpetual motion machines and also because it offers many alternative solutions. During this period Leonardo was engaged in the study of the physics of natural elements and was paying particular attention to upward hydrostatic and aerostatic forces, with their characteristics opposite to the force of gravity, which acts downwards. In light of these considerations, Leonardo sees the hydrostatic thrust as a “force of lightness” antagonistic to that of gravity and tries to apply it in the design of perpetual wheels, which he now designs with the lower part of the axis of rotation immersed in water and the upper part exposed to the air. So taken was Leonardo by this new possibility that, developing the new type of wheel, he felt the need to protect it from prying eyes: “make a model, keep one secretly locked up, and present a similar one to the world.”
Of interest is the note that accompanies the drawing on the bottom right, which states that the structure of the wheel presents sliding rods and that the masses move by gravity through the air and by lightness through the water. Leonardo reasoned about the effects of the differences in density of the elements through which the wheel moves, imagining a mixed air-water region near the surface of the water, with a lower density that somehow allows the rotating masses suspended by the spokes to “break through” the surface of the water without preventing the movement of the wheel. In this area, delimited in the drawing by two lines, in which part of the wheel hub is immersed, according to Leonardo the weights of the b - c - d spokes have no gravity. It seems that he considers this area a mixed space in which air and water mutually cancel out each other’s physical properties, and in which the masses of the immersed bodies have a value of zero. More generally, Leonardo does not seem to notice that, by introducing a symmetrical “lightness force” opposed to gravity, the equilibrium between the forces that determine rotation is maintained. Imagine building the masses at the ends of the radii as if they were ampoules filled with air to try to add aerostatic thrust to the system. His intention is clear: while in previous cases he had only to consider the weight of solid bodies, now—thus reiterating his adherence to the principles of Aristotelian physics that until then he had denied in various ways—he hypothesises a perpetual machine in which the elements come into play with the relations of force specific to them: a hollow mass full of air would have exploited the salient energy intrinsic to it. It was an idea, however, destined, like others, to be abandoned: soon Leonardo would have pointed out as “sophistic” solutions, i.e. not working, this type of perpetual wheel, as he explicitly states in folio 282r of the Codex Atlanticus.