A team of engineers studying Leonardo da Vinci's 500-year-old archives, found evidence that the Italian polymath was working on gravity a century before its foundations were laid by Galileo. The team's findings come from a re-examination of the Codex Arundel, a collection of documents written by da Vinci detailing various experiments and personal notes taken over the last 40 years of his life.
The code is freely accessible online from the British Museum. The team's research is published in MIT Press magazine on Leonardo. Mory Gharib, an engineer at Caltech, said he came across the archives in 2017 when he was looking for some of da Vinci's works. Although the codex was written in da Vinci's last 40 years, Gharib suspects that the gravitational thoughts were written sometime in the last 15 years or so of his life.
Gharib recruited co-author Flavio Noca, a researcher at the University of Applied Sciences and Arts of Western Switzerland, to translate the Italian's writing.
da Vinci understood some basic principles of objects in motion. He wanted to do an experiment testing how the movement of a cloud would correspond to the hail it produced if the speed of the cloud and any changes in it corresponded to the speed of falling hail.
Instead of controlling the weather, da Vinci replaced the cloud with a pitcher and the hail with sand or water.
Reliable clocks weren't available until about 140 years after da Vinci's death in 1519, the researchers say, so the inventor was forced to replace the constant of time with space: assuming that the time it took each particle of water/sand to to fall from the pitcher, simply keep the pitcher at the same height in all trials.
da Vinci's sketch shows the positions of the falling material during its trajectory towards the ground.
By drawing a line through the location of the material at each point in time, da Vinci realized that a triangle could be formed, with the drawn line being the hypotenuse.
By changing the pitcher's acceleration during the experiment, the shape of the triangle also changed. Leonardo knew that falling material would accelerate and that acceleration is downward. What he wasn't entirely sure about – hence the experiment – was the relationship between the acceleration of the falling material and the acceleration of the pitcher.
When the motion of the pitcher was accelerated at the same rate as the falling material affected by gravity, an equilateral triangle was formed.
Literally, as da Vinci noted, it is an “Equatione di Moti” or an “equation 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 struggled with this, but he modeled it as the distance of the falling object being proportional to the square of the force t [with t representing time] instead of being proportional to t squared," said Chris Roh, a researcher at Cornell University. and co-author of studying.
"It's wrong, but later we found out that he used this kind of wrong equation in the right way." The team interpreted signs in da Vinci's sketches that instead of a clock, da Vinci found the constant of gravity with almost 98% accuracy.