Testing the da Vinci Codex

Drs. Wilfred T. Tysoe & Nicholas D. Spencer | TLT Cutting Edge February 2015

Repeating Leonardo’s 500-year-old experiments confirm that he was the first to propose the fundamental laws of friction.
 

Leonardo da Vinci: 1452-1519.
ALL TRIBOLOGISTS ARE FAMILIAR WITH AMONTONS' BASIC LAWS OF FRICTION that he propounded at the end of the 18th Century. They underpin our use, both of the term friction coefficient and the notion that it is independent of the apparent contact area. However, the discovery of several caches of Leonardo da Vinci’s notebooks in the 1960s suggest that in fact he discovered the laws first. While he is perhaps best known for his art—his Mona Lisa is one of the world’s most famous paintings—and as an inventor, he was also a remarkably talented scientific experimentalist. Pages from his Codex Arundel (a codex is a manuscript in book form) written in Italian between 1480 and 1518 clearly show what can only be tribological experiments (see Figure 1). He concluded from these experiments that “The friction made by the same weight will be of equal resistance at the beginning of its movement although the contact may be of different breadths and lengths,” and “Friction produces double the amount of effort if the weight be doubled.” These are essentially identical to the laws later published by Amontons—an even more remarkable achievement given that they were proposed two centuries before the concept of force was developed by Isaac Newton! Da Vinci also measured a friction coefficient for wood sliding against wood of about a quarter. Amontons thought that the friction coefficient was about a third.


Figure 1. A page from da Vinci’s Codex Arundel showing the first tribometers. Image courtesy of the British Library.

Professor Greg Sawyer and student Angela Pitenis from the University of Florida collaborated with Professor Duncan Dowson from the University of Leeds in England (a long-time scholar of the history of tribology) to see if they could reproduce da Vinci’s results. They used da Vinci’s drawings and notes to reconstruct his experimental apparatus as faithfully as possible, with the exception being a modern, discretely hidden rolling-element bearing for the pulley. They used a variety of types of wood for the construction but, unlike da Vinci, measured the surface roughness by means of scanning white-light interferometry. They measured the friction force by adding weights to the end of a rope attached via a pulley to the moving block, as shown in Figure 1, and recorded the weight needed to cause sliding. 

In a first series of experiments, Sawyer and Pitenis studied the effect of the nature of the surface. When using clean and sanded surfaces, the friction coefficient increased with the number of times the experiment was repeated, eventually leveling out at a friction coefficient of about 0.7. A clean but unsanded surface reduced it to about 0.43. Adding sawdust reduced it a little further to about 0.3, but using surfaces that had been extensively handled and allowed to accumulate some dust produced a constant and reproducible friction coefficient of 0.25 ± 0.03, just as reported by da Vinci (but without reporting the error). 

In a second experiment, they turned the block on its side to change the apparent contact area and found the same friction force. The last experiment measured the effect of mass by adding a second block on top of the block that was being slid, and showed that the weight needed to cause sliding also doubled, again confirming da Vinci’s findings.

These modern reproductions of 500-year old experiments teach us two important things. First, Leonardo da Vinci indeed discovered the basic laws of friction more than 500 years ago. Second, his workshop was not as clean as it could have been.

FOR FURTHER READING:
1. Dowson, D. (1979), History of tribology, Longman Group Ltd., London.
2. Pitenis, A.A., Dowson, D. and Sawyer, W.G. (2014), “Leonardo da Vinci’s Friction Experiments: An Old Story Acknowledged and Repeated,” Tribology Letters, 56, p. 509.


Eddy Tysoe is a Distinguished Professor of Physical Chemistry at the University of Wisconsin-Milwaukee. You can reach him at wtt@uwm.edu.


Nic Spencer is professor of surface science and technology at the ETH Zurich, Switzerland. Both serve as editors-in-chief of STLE-affiliated Tribology Letters journal. You can reach him at nspencer@ethz.ch.