On photo: The School of Athens (detail with Plato and Aristotle in the middle),
Raphael, Public domain, via Wikimedia Commons.

Aristotle (384-322 B.C.) was a man of many professions, no doubt, but was he also a wood scientist? “Nope” would be my first honest answer. However, Aristotle drew a certain attention to wood as it was one of many materials he observed, pondered and used in his explanations of phenomena. Let’s look at two mechanical problems dealing with wood that Aristotle thought about and relate them to our current usage and understanding.

Problem no. 1

Three-point bending of wood

Each of us has done it! I believe that each of us has broken a piece of wood – twig or branch – for a campfire. So, we all did something we call three-point bending of wood until ultimate load – breakage. And because we all have an intuition, we grasped the wood at its ends and broke it over our knee at its middle. Why would we do it differently if it is so easy that way, right? So, we did precisely the same thing Aristotle pondered, as follows:

“Why is it that a piece of wood of the same size is more easily broken against the knee, if one breaks it holding the ends at equal distance from the knee, than if it is held close to the knee? And if one leans a piece of wood upon the ground and places one’s foot on it, why does one break it more easily if one grasps it at a distance from the foot rather than near it? Is it because in the former case the knee, and in the latter the foot is the centre, and the further an object is from the centre the more easily is it always moved, and that which is to be broken must be moved?”

(Mechanics, 14, p. 4443, Barnes 1984)

The problem Aristotle described can be easily displayed (Fig. 1A), and it led him to the correct conclusion that you need the least force to break a piece of material in bending if you load it in the middle. We use this principle – symmetric loading in three-point bending – in testing materials on universal testing machines (UTM) to obtain modulus of elasticity, modulus of rupture, work, yield point and many other pieces of information. The symmetry setup of loading brings the purest information about the material since moments acting on the material are also symmetric. The only extra condition we have to fulfill in the laboratory, in contrast to breaking firewood over our knee, is symmetry of specimen geometry, and that is why our wooden samples most often have a rectangular shape (Fig. 1B).

Fig. 1. Three-point bending test of a branch for (A) campfire and (B) wood in the laboratory.

Another conclusion Aristotle made that is interesting for us is the distance between the knee (aka UTM loading head) and hands (aka UTM supports). This distance is crucial for testing in bending because it allows us to break material at lower forces without including forces needed for compressive imprints of supports and loading head into the material and without major shear stresses. That distance is used in computing the so-called slenderness ratio, which is ratio of distance between supports (2a) and height of the specimen (h) and is prescribed by any national or EU standard for testing any material in three-point bending.

Problem no. 2

Splitting wood

Another thing Aristotle noticed is well known for those who prepared fuel wood for fire by splitting bigger pieces into smaller ones by using an axe. Let’s first look what Aristotle concluded about splitting wood:

“How is it that, if you place a heavy axe on a piece of wood and put a heavy weight on the top of it, it does not cleave the wood to any considerable extent, whereas, if you lift the axe and strike the wood with it, it does split it, although the axe when it strikes the blow has much less weight upon it than when it is placed on the wood and pressing on it? …”

(Mechanics, 19, p. 4448, Barnes 1984)

The problem of wood splitting falls into an area of fracture mechanics, and Aristotle is actually comparing two situations: 1) a heavy wedge placed gently on wood not causing a split (Fig. 2A) versus 2) a much lighter wedge hitting wood with a certain velocity inducing the split (Fig. 2B). The explanation as to why the second scenario leads to splitting is simple: there is a need for a certain energy (critical fracture energy) to onset a crack in the wood that would further propagate through the wood. This critical fracture energy is provided from kinetic energy even though the initial weight of the wedge is much smaller than in the first case. When a wedge with its momentum hits the wood, its kinetic energy is transformed and concentrated into stress at its very tip, and, hence, it easily overcomes the critical fracture energy and opens a crack that further propagates much more easily. Aristotle grasped correctly the difference between the static and dynamic impact of a wedge on a piece of wood, but he could not solve it correctly because Newton’s laws came much later, in the 17^th century.

Fig. 2. Splitting wood with (A) potential energy and (B) kinetic energy.

Conclusions

We can take several lessons from the mentioned Aristotle examples:

• His thoughts about bending and splitting wood represent still-valid principles even after ~2400 years. Several current theories and measurement devices are built on these principles, which further enable us to understand the problems much more in detail.
• The dichotomy between kinetic and potential energy illustrated by the second example is still present in our educational system (taught in all physics classes), and Aristotle is correctly ascribed as its father (not only based on this example).
• Even though Aristotle can be considered a “dead author” in the sense that he is not read much by the common public (it is truly hard to digest his writings), we can recall him when testing materials in the laboratory or preparing firewood.
• Intuition and verbal analysis of phenomena can reveal its principle, but for its deep understanding, development of a theory using the scientific method is necessary.

As often happens in detective stories, the biggest twist comes at the very end. As we know, science is a kind of competition between hypotheses, and evidence then decides which ones are correct. Well, there is a hypothesis that the quotes above from Mechanics might not have been written by Aristotle, but by Archytes of Tarentum (410-350 B.C). Since I am not a professional in ancient Greek, you have to ask someone else for evidence or find it yourself.

Dr Václav Sebera,
researcher at InooRenew CoE

Resources

– Barnes, J (Ed.) The complete works of Aristotle. The Revised Oxford Edition. 1984. Princeton University Press.

– Winter, TN (2007) The Mechanical Problems in the Corpus of Aristotle. Faculty Publications, Classics and Religious Studies Department. 68. https://digitalcommons.unl.edu/classicsfacpub/68