The da Vinci code: notes of the laws of friction uncovered

Scribbled notes and sketches on a page in a notebook by Leonardo da Vinci, previously dismissed as irrelevant, have been identified as the place where he first recorded his understanding of the laws of friction.

The research was undertaken by Professor Ian Hutchings of the University of Cambridge as part of the first detailed chronological study of da Vinci’s work on friction. It has been published in the journal Wear.

It is widely known that da Vinci conducted the first systematic study of friction, but exactly when and how he developed these ideas has been uncertain until now. Professor Hutchings has discovered that da Vinci’s first statement of the laws of friction was in a tiny notebook, measuring just 92 x 63 mm, which dates from 1493 and is now held in the Victoria and Albert Museum (V&A) in London.

The page of the book in question had already attracted interest because it also carries a sketch of an old woman in black pencil with a line below reading “cosa bella mortal passa e non dura”, which can be translated as ‘mortal beauty passes and does not last’. However, the director of the V&A in the 1920s referred to the text below the quote, scribbled quickly in da Vinci’s characteristic ‘mirror writing’ from right to left, as “irrelevant notes and diagrams in red chalk”.

Now, Professor Hutchings’ study has revealed that the rough geometrical figures sketched by da Vinci show rows of blocks being pulled by a weight hanging over a pulley — in exactly the same kind of experiment students might do today to demonstrate the laws of friction. Above these figures is the statement “la confregazione si fa di duplicata fatica in duplicato peso”, translated as “friction is of double the effort for double the weight”.

“The sketches and text show Leonardo understood the fundamentals of friction in 1493,” said Professor Hutchings. “He knew that the force of friction acting between two sliding surfaces is proportional to the load pressing the surfaces together and that friction is independent of the apparent area of contact between the two surfaces. These are the laws of friction that we nowadays usually credit to a French scientist, Guillaume Amontons, working 200 years later.”

Professor Hutchings’ research traces a clear path of development in da Vinci’s studies of friction and demonstrates that he realised that friction, while sometimes useful and even essential, also played a key role in limiting the efficiency of machines. Sketches of machine elements and mechanisms are pervasive in his notebooks and he used his understanding of friction to analyse the behaviour of wheels and axles, screw threads and pulleys, all important components of the machines he sketched.

“Leonardo’s sketches and notes were undoubtedly based on experiments, probably with lubricated contacts,” said Hutchings. “He appreciated that friction depends on the nature of surfaces and the state of lubrication and his use and understanding of the ratios between frictional force and weight was much more nuanced than many have suggested.”

Despite his apparent discovery of the laws of friction, da Vinci’s work had no influence on the development of the subject over the following centuries. According to Professor Hutchings, however, da Vinci holds “a unique position as a pioneer in tribology”.

Image caption: Leonardo da Vinci’s first note and sketches relating to the laws of friction, probably written in 1493 and certainly before September 1494 (Codex Forster III folio 72r). Image credit: V&A Museum, London.

This article is a modified version of a news item published by the University of Cambridge under CC BY 4.0