Bending Active Systems in Antiquity: What was so special about the bow of Odysseus?

The second Saturday of May is National Archery day (May 14 in 2016).  While today archery is mostly practiced for sport, the bow and arrow have been used by humans in hunting for centuries.  The purpose for bows, regardless of the target, is to propel an arrow using stored elastic energy.  They are one of the most effective ways of storing energy of the human muscle.

The oldest bow in one piece dates back to 800 BC, the same era that scholars believe Homer’s Odyssey was written.  The Odyssey tells the journey of Odysseus, a hero in Greek mythology.  As part of the story, his wife, Penelope, patiently waits for 20 years during and after the Trojan War for her husband to return.  Through this time she challenged her suitors to string the bow of Odysseus.  With the exception of Odysseus himself, none of the suitors possessed the strength needed to string the bow.

Ceramic with depiction of Odysseus holding bow and arrow in The Odyssey

While Odysseus was a Greek hero, there is a limit to human strength when stringing a bow.  The human body allows one to draw their arm back about 60 cm and the maximum force a strong man can withstand holding in a string is about 350 N (Gordon).  Therefore, the available muscular energy is 0.6m*350N= 210 Joules.  Assuming an unstrung bow has zero energy, we can linearly plot the force from the archer’s pull against the maximum extension of the string in Figure 1.  The energy stored in the long bow is equal to the area under this plot (triangle ABC): ½*0.6m*350N=105 Joules.  This stored energy due to deformation is known as strain energy.

Sketches of traditional long bow in unstrung, strung and extended conditions
Figure 1: The archer’s maximum pull on the string plotted against the distance of arm extension.  The area under the curve is equal to the total stored energy in Joules.

Continue reading “Bending Active Systems in Antiquity: What was so special about the bow of Odysseus?”

What to wear to the Oscars?

Do engineered systems play a role in Hollywood style? Engineering is all around us, whether we recognize it or not, from the homes we sleep in, water we drink from, and roads we drive on.  Have you ever thought engineering could play a role on the Silver Screen?  Perhaps you think engineering systems don’t impact Hollywood, but here is an example of the impact of … Continue reading What to wear to the Oscars?

Form Finding Flashback: Basento Viaduct

It is unclear where the unusual shape of the Basento Viaduct (Potenza, Italy) was derived.  Some even say the thin shell concrete pedestrian bridge is shaped like the headdresses of nuns in Federico Fellini’s Italian films [1].  Regardless, the Basento Viaduct is an example of a structure designed using early form finding techniques.

side by side
Similarity in shape between the Basento Viaduct (left) and nun’s headdress (right)      [Photo Credit [1], [2]]
Today, we rely heavily on the use of computational methods for the form finding of thin shell structures. Yet, we see existing shell structures around the world that were designed and realized before engineers had numerical technology.  Who were these extraordinary engineers and how did they generate these unique forms?

Continue reading “Form Finding Flashback: Basento Viaduct”