Did the article’s title give you an inkling of what it might be about? Zilch, I guess.
Well, quite recently, I watched a video where a man drew his bow with an arrow and released the bowstring. No big deal! It was a recurve bow, I think. What followed the release led my inquisitiveness to probe into the matter and write this article.
Just after the release, his bow split into three pieces, the gripping part remaining intact in his hand. The arrow, well, didn’t follow its typical parabolic trajectory and fell straight down on the ground ahead of the man.
Basically, he performed the act of “dry firing” the bow, something which archers are very well aware of and is a must not do act, for a fascinating reason.
Strain energy is everywhere! Though beneficial, excess of it is undesirable.
Motorsport racing and archery competitions have one crucial thing in common: the lighter the car/arrow, the faster it will traverse its path. Speed sells in both industries, and the technological focus is always on minimizing the weight of components to make the system more efficient and give it rocket-like speeds. The lighter an arrow is, the flatter its trajectory is, while a heavy arrow has a greater tendency to nose-dive earlier. So a light arrow is less probable to deviate from its target (provided it’s shot towards the target!). This is a general thumb-rule in the archery industry. However, the energy transfer by the bow to a light arrow is less than to a heavier one, thus increasing the penetration ability of the latter. And you can only a make an arrow so much lighter. Strain energy sneaks in every damn time!
Keeping in mind that bows are no toys to be meddled with and should be given as much respect as you’d to a lethal weapon, there are stringent rules on the mass of an arrow that can be used in archery competitions. Typically, a 5 grains per pound of drawing weight is imposed, i.e., for every pound of drawing weight, the minimum mass of an arrow must be 5 grains. Drawing weight is the force required to pull the bowstring to its fullest extent. Grain, unlike gram, is a British system unit and is roughly 1/7000th of a gram. If you use an underweight arrow, you’re more likely to break the bow into smithereens than send the arrow at a rocket-like speed towards the target.
But, why does a light arrow get less energy from the bow than a heavier one? How is energy stored in the bow in the first place? And, why does dry firing make the bow prone to damage?
SOMETHING ABOUT BEAMS
Consider the beam shown below.
If the beam is bent as shown in the picture, it’s obvious that the fibers near the top section compress while those near the bottom stretch. This stretching and compressing increases/decreases the distance between the atoms (i.e., they get strained) and this gives rise to the stored strain energy. Find out more about it here.
This beam can be thought of like a bow with a string attached to its two ends. When the string is pulled, the elastic deformation of the bow lets it store strain energy. Moreover, the pulled string stores a great deal of energy as well, due to tensile loading. Upon releasing the arrow, some of the stored energy in the string gets transferred to the arrow to speed it up, while a major part is used to accelerate the arms of the bow, where it gets stored as kinetic energy. As the string straightens and tautens, the bow arms are brought to rest and its stored energy is transferred to the string which speeds up the arrow furthermore.
Assume two arrows of equal length, made of the same material (hence, same density) but different masses. The heavier arrow, being more voluminous (density is an intensive property!), will consist of more atoms than the lighter one, hence will be able to store more energy given to it by the bow. This is the reason why heavy arrows penetrate more than their lighter counterparts.
THE INTIMATE RELATION BETWEEN STRAIN ENERGY AND FRACTURE
Eventually, when all is said and done, the damage caused to a dry fired bow indicates that it has something to do with the stored strain energy. There’s no smoke without fire! And yes, it does in a way that can be explained with the science of Fracture Mechanics, a fascinating field for one to delve into. In a more elaborate article (in future) that I’ll dedicate to this discipline, I’ll write how this intimate relation came into being and its widespread practical applications. For now, in a simpler way, the relation can be understood by the fact that to break a structure, you simply need to supply energy that will break the atoms apart. If continuously supplied, and in a sufficient quantity, this will eventually fracture the structure. But the atoms in a structure are not so weakly bonded as one might assume. These bond energies are huge but are only easily broken because of the tiny (well, very tiny!) inevitable flaws or cracks present within the structure that act as stress raisers.
When dry fired (i.e., without an arrow), the stored kinetic energy in the bow has to go somewhere when the arms decelerate. It doesn’t just vanish into thin air and only so much can be lost as heat.
As aforementioned, if this strain energy is sufficient, it might start breaking the atomic bonds in the vicinity of a flaw or crack within the bow and sometimes even crack open the entire bow’s cross-section where the flaw was present. This process may occur in multiple areas of the bow, splitting it into pieces. Thus, this excessive strain energy doesn’t spare the bow’s integrity upon dry firing.
While this relation might seem too intimate, science and engineering have seldom been triumphed over. Bows are not simply made entirely of the same material. Taking help of the knowledge of the stress distribution across a beam’s cross-section as discussed earlier, composite bows are made wherein, the core made of wood is only lightly stressed; the tension surface is made of sinew while the compression surface is made of horn, both materials good at sustaining the respective stresses, thus maintaining the structural integrity of the bow and allowing it to flex more without fracture.
So the next time you get a bow and arrow in your hand, make sure to not dry fire it, else the consequences may be deleterious.
AN INTERESTING READ!
In closing, I’ll suggest you read about the great “palintonose” bow of the divine Greek king Odysseus, a cleverly engineered bow to amplify the energy stored in the string and speed up the arrow manifold. Click here to read about it.