A team of engineers studying the 500-year-old, backward writings of Leonardo da Vinci have found evidence that the Italian polymath was working out gravity a century before its foundations were established by Galileo Galilei.
The team’s findings come from a revisit of the Codex Arundel, a compilation of documents written by da Vinci that detail various experiments and personal notes taken down in the latter 40 years of his life. The codex is freely accessible online courtesy of the British Museum. The team’s research is published in the MIT Press journal Leonardo.
Da Vinci was an inventor, artist, engineer, architect, and scientist. He kept busy. It seems unsurprising that someone who in the 15th century designed primeval tanks, flying machines, automatons, and an apparatus for diving (among other contraptions) pondered the nature of gravity. But gravity is no simple thing to demonstrate mathematically, and though he didn’t totally succeed, da Vinci tried, as the researchers recently found.
Mory Gharib, an engineer at Caltech, said he stumbled across the writings in 2017 when looking for some of da Vinci’s work on flow in hearts. Though the codex was written over a long span of da Vinci’s later years, Gharib suspects the gravitational musings were written sometime in the last 15-or-so years of his life.
Gharib recruited co-author Flavio Noca, a researcher at the University of Applied Sciences and Arts Western Switzerland, to translate the Italian’s backward writing on the subject.
Da Vinci understood some fundamentals of objects in motion. He wanted to make an experiment testing how the motion of a cloud would correspond to the hail it produced, if the cloud’s velocity and any changes to it corresponded with the falling hail’s velocity. In lieu of control of the weather, da Vinci substituted a pitcher for the cloud and sand or water for the hail.
Reliable clocks weren’t available until about 140 years after da Vinci’s death in 1519, the researchers note, so the inventor was forced to substitute the constant of time with space: by assuming that the time it took each water/sand particle to fall from the pitcher was constant, he just kept the pitcher at the same height throughout the tests.
Da Vinci’s sketch shows the positions of the falling material over the course of its trajectory toward the ground. By drawing a line through the position of the material at each instance in time, da Vinci realized that a triangle could be formed, with the drawn line being the hypotenuse. By changing the acceleration of the pitcher over the course of the experiment, one would change the shape of the triangle.
Leonardo knew that the falling material would accelerate and that the acceleration is downward. What he wasn’t wholly certain on—hence the experiment—was the relationship between the falling material’s acceleration and the pitcher’s acceleration.
In one particular case, when the pitcher’s motion was accelerated to the same rate as the falling material being affected by gravity, an equilateral triangle was formed. Literally, as Da Vinci noted, an “Equatione di Moti” or an “equalization of motions.”
The researchers modeled da Vinci’s experiment and found that the polymath was wrong in his understanding of the relationship between the falling object and time.
“What we saw is that Leonardo wrestled with this, but he modeled it as the falling object’s distance was proportional to 2 to the t power [with t representing time] instead proportional to t squared,” said Chris Roh, a researcher at Cornell University and a co-author of the researcher, in a Caltech release. “It’s wrong, but we later found out that he used this sort of wrong equation in the correct way.”
The team interpreted tick marks on da Vinci’s sketches as data points the polymath made based on his eyeballing of the experiment in action. In lieu of a timepiece, da Vinci found the gravitational constant to nearly 98% accuracy.
It’s a testament to da Vinci’s accomplishments that this little side project has gone unnoticed for so long. More of the inventor’s secrets undoubtedly remain yet to be highlighted, hidden away in backward writing in the margins of his crammed codices.
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