Role of resistance forces in Galileo’s experiments

Abstract

Abstract We apply fluid resistance and rolling resistance analysis to the free fall and projectile experiments described in Galileo Galilei’s 1638 Dialogues Concerning Two New Sciences (Discorsi), and his unpublished folio 116v experiment in the Codex 72 collection. Both air resistance and rolling resistance affect the horizontal projection distance in the folio 116v experiment. Newton’s second law and the two combined resistance forces can quantitatively explain Galileo’s observations. The analysis is also applied to replication experiments made by Naylor in 1974. Quantitative agreement is achieved. Resistance forces remove a small discrepancy between observed and theoretical horizontal projectile distances that is present when air resistance and rolling resistance are ignored. The result is significant because it shows that, contrary to prior studies, resistance forces cannot be ignored when one models the folio 116v experiment. Air drag forces due to acceleration (added mass and Basset history) are negligible, but quasi-steady drag and Magnus lift are not. This exercise provides an historical perspective to the description of basic body motion: constant acceleration, uniformly increased velocity, constant inertial motion, and decomposition of two-dimensional motion into orthogonal coordinates. It also serves to give specific examples of significant ‘real-world’ effects, such as steady drag, added mass, Basset history, rolling resistance, spin drag, and Magnus lift that complicate what appears to be a simple experiment. Finally, it shows that a quantitative test of a seemingly obvious assumption can yield new insights.