https://www.caltech.edu/about/news/leonardo-da-vincis-forgotten-experiments-explored-gravity-as-a-form-of-acceleration * DRAFT Skip to main content COVID-19 Information Visit Careers Access Quick Links Click here to open the "Quick Links" submenu Down arrow for Faculty for Students for Staff for Alumni Directory Caltech Today Alumni GIVE Caltech Logo * About + At a Glance Open At a Glance Submenu o University and College Rankings + Leadership Open Leadership Submenu o President o Provost o Board of Trustees o Academic and Administrative Leadership + Values Open Values Submenu o Diversity, Equity, and Inclusion o Freedom of Expression o Honor Code + Legacy Open Legacy Submenu o History & Milestones o Awards & Honors o Caltech Archives o Interactive History Map + News + Publications Open Publications Submenu o This is Caltech o Caltech Magazine o Periodic Table of Caltech o Innovation and Impact o Exploration and Achievement + Visit Open Visit Submenu o Directions o Campus Maps o Parking o Tours + Administrative Offices & Departments * Research + Academic Divisions Open Academic Divisions Submenu o Biology and Biological Engineering o Chemistry and Chemical Engineering o Engineering & Applied Science o Geological & Planetary Sciences o Humanities and Social Sciences o Physics, Mathematics and Astronomy + Jet Propulsion Laboratory + Student Research + Centers & Institutes + Technology Transfer & Corporate Partnerships + Sponsored Research + Research Facilities + Faculty Listing * Academics + Undergraduate Studies + Graduate Studies + Online Education + Executive Education + Teaching, Learning, & Outreach + Resources Open Resources Submenu o Registrar o Catalog o Academic Calendar o Library o International Offices o Career Development * Admissions & Aid + Undergraduate Admissions Open Undergraduate Admissions Submenu o Apply o Cost & Aid + Graduate Admissions Open Graduate Admissions Submenu o Apply o Funding & Aid * Campus Life & Events + Institute Calendar + Caltech Today + Athletics & Recreation + Public Programming / CaltechLive! + Performing & Visual Arts + Housing + Dining + Caltech Y + Wellness Services + Diversity Center + Security + Emergency Information Open search form Search input field[ ]Search Menu Main Menu Close * About Caltech Click here to open the "About Caltech" Submenu * Research Click here to open the "Research" Submenu * Academics Click here to open the "Academics" Submenu * Admissions & Aid Click here to open the "Admissions & Aid" Submenu * Campus Life & Events Click here to open the "Campus Life & Events" Submenu COVID-19 Information Visit Careers Access Quick Links for Faculty for Students for Staff for Alumni Directory Caltech Today Alumni GIVE About Caltech Back * Caltech at a Glance + University and College Rankings * Leadership + President + Provost + Board of Trustees + Academic and Administrative Leadership * Values + Diversity, Equity, and Inclusion + Freedom of Expression + Caltech Honor Code * Legacy + History & Milestones + Awards & Honors + Caltech Archives + Interactive History Map * News * Publications + This is Caltech + Caltech Magazine + Periodic Table of Caltech + Innovation and Impact + Exploration and Achievement * Visit + Directions + Campus Maps + Parking + Tours * Administrative Offices & Departments Research Back * Academic Divisions + Biology and Biological Engineering + Chemistry and Chemical Engineering + Engineering & Applied Science + Geological & Planetary Sciences + Humanities and Social Sciences + Physics, Mathematics and Astronomy * Jet Propulsion Laboratory * Student Research * Research Centers and Institutes * Technology Transfer & Corporate Partnerships * Sponsored Research * Research Facilities * Faculty Listing Academics Back * Undergraduate Studies * Graduate Studies * Online Education * Executive Education * Teaching, Learning, & Outreach * Resources + Registrar + Catalog + Academic Calendar + Library + International Offices + Career Development Admissions & Aid Back * Undergraduate Admissions + Apply + Cost & Aid * Graduate Admissions + Apply + Funding & Aid Campus Life & Events Back * Institute Calendar * Caltech Today * Athletics & Recreation * Campus Public Programming * Performing & Visual Arts * Housing * Dining * Caltech Y * Wellness Services * Center for Diversity * Security * Emergency Information Open search form Search input field[ ]Search Home / About / News / Leonardo da Vinci's Forgotten Experiments Explored Gravity as a Form of Acceleration Da Vinci Leonardo da Vinci's Forgotten Experiments Explored Gravity as a Form of Acceleration February 13, 2023 Engineers from Caltech have discovered that Leonardo da Vinci's understanding of gravity--though not wholly accurate--was centuries ahead of his time. In an article published in the journal Leonardo, the researchers draw upon a fresh look at one of da Vinci's notebooks to show that the famed polymath had devised experiments to demonstrate that gravity is a form of acceleration--and that he further modeled the gravitational constant to around 97 percent accuracy. Leonardo's journal Image Lightbox Leonardo's journal Download Full Image Da Vinci, who lived from 1452 to 1519, was well ahead of the curve in exploring these concepts. It wasn't until 1604 that Galileo Galilei would theorize that the distance covered by a falling object was proportional to the square of time elapsed and not until the late 17th century that Sir Isaac Newton would expand on that to develop a law of universal gravitation, describing how objects are attracted to one another. Da Vinci's primary hurdle was being limited by the tools at his disposal. For example, he lacked a means of precisely measuring time as objects fell. Da Vinci's experiments were first spotted by Mory Gharib, the Hans W. Liepmann Professor of Aeronautics and Medical Engineering, in the Codex Arundel, a collection of papers written by da Vinci that cover science, art, and personal topics. In early 2017, Gharib was exploring da Vinci's techniques of flow visualization to discuss with students he was teaching in a graduate course when he noticed a series of sketches showing triangles generated by sand-like particles pouring out from a jar in the newly released Codex Arundel, 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 became interested to see what Leonardo meant by that phrase." Leonardo GIF To analyze the notes, Gharib worked with colleagues Chris Roh, at the time a postdoctoral researcher at Caltech and now an assistant professor at Cornell University, as well as Flavio Noca of the University of Applied Sciences and Arts Western Switzerland in Geneva. Noca provided translations of da Vinci's Italian notes (written in his famous left-handed mirror writing that reads from right to left) as the trio pored over the manuscript's diagrams. In the papers, da Vinci describes an experiment in which a water pitcher would be moved along a straight path parallel to the ground, dumping out either water or a granular material (most likely sand) along the way. His notes make it clear that he was aware that the water or sand would not fall at a constant velocity but rather would accelerate--also that the material stops accelerating horizontally, as it is no longer influenced by the pitcher, and that its acceleration is purely downward due to gravity. If the pitcher moves at a constant speed, the line created by falling material is vertical, so no triangle forms. If the pitcher accelerates at a constant rate, the line created by the collection of falling material makes a straight but slanted 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, it creates an isosceles right triangle--which is what Gharib originally noticed that da Vinci had highlighted with the note "Equatione di Moti," or "equalization (equivalence) of motions." Da Vinci sought to mathematically describe that acceleration. It is here, according to the study's authors, that he didn't quite hit the mark. To explore da Vinci's process, the team used computer modeling to run his water vase experiment. Doing so yielded da Vinci's error. "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," Roh says. "It's wrong, but we later found out that he used this sort of wrong equation in the correct way." In his notes, da Vinci illustrated an object falling for up to four intervals of time--a period through which graphs of both types of equations line up closely. Graphs Image Lightbox Graphs Download Full Image "We don't know if da Vinci did further experiments or probed this question more deeply," Gharib says. "But the fact that he was grappling with this problem in this way--in the early 1500s--demonstrates just how far ahead his thinking was." The paper is titled "Leonardo da Vinci's Visualization of Gravity as a Form of Acceleration." Written by Robert Perkins Contact Robert Perkins (626) 395-1862 [email protected] Subscribe The Caltech Weekly Go to The Caltech Weekly Share this Tags engineering See All News > Caltech Torch Caltech Logo California Institute of Technology map marker 1200 East California Boulevard Pasadena, California 91125 Contact Us Claimed Copyright Infringement Privacy Notice Site Content Copyright (c) 2023