Caltech engineers have found that Leonardo da Vinci’s understanding of gravity was centuries ahead of his time, though not entirely accurate.
In an article published in the magazine LeonardoThe researchers draw on a new look at one of da Vinci’s notebooks to show that the famous polymath had devised experiments to demonstrate that gravity is a form of acceleration – and that he could determine the gravitational constant with an accuracy of about 97 percent further modeled.
Da Vinci, who lived from 1452 to 1519, was way ahead of the curve in exploring these concepts. It was not until 1604 that Galileo Galilei theorized that the distance traveled by a falling object was proportional to the square of the elapsed time, and it was not until the late 17th century that Sir Isaac Newton extended this to develop a law of universal gravitation. describes how objects are attracted to each other. Da Vinci’s biggest hurdle was being limited by the tools at his disposal. For example, he lacked a means of accurately measuring the time as objects fell.
Da Vinci’s experiments were first discovered by Mory Gharib, the Hans W. Liepmann Professor of Aeronautics and Medical Engineering, in the Codex Arundel, a collection of papers authored by da Vinci dealing with science, art, and personal subjects. In early 2017, Gharib was researching da Vinci’s flow visualization techniques to discuss with students he was teaching in a graduate course when, in the newly published Codex Arundel, he noticed a series of sketches showing triangles created by sand-like particles emanating from poured from a jar which can be viewed online courtesy of the British Library.
“What caught my eye was when he wrote ‘Equatione di Moti’ on the hypotenuse of one of his sketched triangles – the one that was an isosceles right triangle,” says Gharib, lead author of the Leonardo Paper. “I was interested in what Leonardo meant by this phrase.”
To analyze the notes, Gharib worked with colleagues Chris Roh, then a postdoctoral fellow at Caltech and now an assistant professor at Cornell University, and Flavio Noca from the Polytechnic of Western Switzerland in Geneva. Noca provided translations of da Vinci’s Italian notes (written in his famous left-handed mirror script, which reads right-to-left) while the trio pored over the manuscript’s diagrams.
In the papers, da Vinci describes an experiment in which a pitcher of water is moved in a straight path parallel to the ground, pouring out either water or a granular material (most likely sand). His notes make it clear that he was aware that the water or sand would not be falling at a constant rate, but would be accelerating—also that the material would no longer accelerate horizontally since it was no longer affected by the pitcher, and that his Acceleration is purely downward due to gravity.
If the pitcher is moving at a constant speed, the line created by falling material will be vertical, so a triangle will not form. As the pitcher accelerates at a constant rate, the line created by the accumulation of falling material forms a straight but sloping line, which then forms a triangle. And, as da Vinci pointed out in a key diagram, if the pitcher’s motion is accelerated at the same rate that gravity accelerates the falling material, an equilateral triangle is formed – which Gharib originally noticed, which da Vinci had emphasized with the note : “Equatione di Moti” or “equality (equivalence) of movements”.
Da Vinci tried to describe this acceleration mathematically. According to the authors of the study, he didn’t quite hit the mark here. To study da Vinci’s process, the team used computer models to conduct their water vase experiment. This led to da Vinci’s mistake.
“What we saw is that Leonardo struggled with that, but he modeled it so that the distance of the falling object was proportional to 2 to the power of t (where t represents time) and not proportional to t squared,” says Raw. “It’s wrong, but we found out later that he used that kind of wrong equation in the right way.” In his notes, da Vinci illustrated an object falling for up to four time intervals—a period in which graphs of both types of equations are closely aligned.
“We don’t know if da Vinci conducted further experiments or investigated this question in more depth,” says Gharib. “But the fact that he tackled this problem in this way – in the early 1500s – shows how far ahead he was in his thinking.”
The paper is entitled “Leonardo da Vinci’s visualization of gravity as a form of acceleration”.
Morteza Gharib et al, Leonardo da Vinci’s visualization of gravity as a form of acceleration, Leonardo (2022). DOI: 10.1162/leon_a_02322