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.
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.
However, in the Odyssey Penelope does not have just any bow. Homer describes the bow as being “palintonos” which is translated as “bent or stretched backwards”. Unlike the bow in Figure 1, which has zero energy when initially strung and straight, this bow requires significant energy to be strained from backward to forward curve. From there, additional stored energy is added as the archer draws back the string. In Figure 2 a plot has been made for a palintonos bow. While the archer’s force on the string and maximum extension is the same as the first case, there is already a large amount strain energy stored in the bow before the archer begins drawing his arm back. This is displayed in Figure 2 which shows the linear plot including the initial extension to strain the bow from backward to forward, prior to the archer’s extension loading the arrow. Now, the energy available for arrow propulsion is equal to the area of ABCD, about 170 Joules (Gordon) compared to 105 Joules in the first case. This higher energy stored in the bow, allowed Odysseus, a skilled archer, to eliminate Penelope suitors with well-aimed shots.
Historic records shows the incredible engineering detailing of these palintonos bows. Figure 3 shows that the core was made out of wood and was surrounded by horn and sinew. The sinew, or dried animal tendon, experience tensile stresses while the horn withstands compressive stresses.
Although archery may not directly relate to structures, the bow of Odysseus demonstrates how flexible rods can be curved and released to achieve great shape changes. Today we see similar examples of strain energy being used to create structural forms such as in pop up tents or Volvo’s deployable solar-powered pavilion.
Author: Kendall Schmidt
Sources: Gordon, J. E. (2009). Structures-Or Why Things Don’t Fall Down, p. 70-75.