The Art of Bowfishing

It is not exactly known when the bow was invented, but archeologists suggest that they developed around 15 thousand years ago. Aborigines, Aztecs and Inuits, as well other ancient groups of people, used a device which threw spears known as the atlatl as well as bows that shoot arrows faster for a longer distance with additional force. Along the way bow fishing was invented. Bowfishing is quite difficult because of the physics behind that one must account for. Not only does one have to hit a small moving target but one has to shoot at a small moving target that they cannot see in a straight line. When firing at a target on land you have a straight line of sight to shoot so the main forces acting on the arrow resisting it from its straight path are gravity and air resistance. So based on how far away the target is (the rotation of the earth will not affect the arrow any considerable amount here because the maximum shooting distance is under 100 yards with an initial speed of 300 feet per second (Minister et al. 2016), how fast the arrow is moving, if the target is above, below or level to the shooter and how fast the target is moving are variables that are accounted for that allows the shooter to make adjustments in aiming to hit the target. When bowfishing, the target is in water. Light travels slower in a liquid than air, so, when light travels from the air into the water, it bends and gives a false perception of the fish. If one were observing a fish from a boat or a dock, the fish would actually be located lower than what it is, meaning that if you were to shoot directly at the fish you would more than likely shoot over it. The further away the fish is on a horizontal plane and the deeper or further down the fish is on a vertical plane has a direct relationship to how far below the perception of the fish one must aim. If one is inexperienced with this natural phenomenon it is hard to fathom and much harder to master. However some birds have nearly perfected this type of hunting, birds including: herons, terns, kingfishers, egrets and many other fish-eating birds that have spear-like beaks designed for stabbing fish. These birds encounter this physics problem every day and still sometimes miss their target. One can only imagine how difficult it is for people.

Traditionally, people used wooden bows and arrows to shoot fish in clear water and hoped that the fish was killed instantly or the arrow was stuck in the floor of the body of water to keep the fish from swimming off with the arrow that they probably spent a lot of time making. They would typically hunt in the morning and afternoon to keep the glare of the sun reflecting off the water and hitting them in the eyes to a minimum. This allowed them to better see their prey. They would stay on the bank and softly creep along the shallows, where the fish could easily be seen because of the low water depth, making sure the vibrations didn't scare the fish off. People would scan for dark spots moving among the grass beds and sometimes wading out into the water slowly to get closer to a fish thus decreasing the amount of guessing they would have to do when “loosing” an arrow below the false perception of the fish. In modern times, the most popular form of bowfishing takes place on a flat bottom boat with a trolling motor or an oar to propel the boat around the shallows. Hunting usually takes place at night because more fish are out of the channels or deeper water and in the shallows due to many different reasons including: temperature change, mating and feeding. Also, natural predators are less likely to catch them at night. Lights are mounted to the boat, usually close to the water shining down and out to reduce glare. A platform is built and placed on the boat to help the shooter survey the lit up area and create a better angle to overcome the bending of the light. A mechanical compound bow is used to shoot a fiberglass arrow with prongs protruding out of the sides on the pointed end to keep the fish from escaping once shot. On the other end near the notch, a strong, durable yet lightweight, pliable line is fastened. It is also fastened to a reel that allows the shooter to reel the arrow in after it is fired. As one can see there are several different components of physics.

The first one that will be discussed is buoyancy. Discovered by Archimedes (Holland et al. 2016), this comes into play when hunting from a boat. Buoyancy is described as the tendency to float in water, or the power of a liquid to keep something afloat. An upward force exerted by a fluid opposes the weight of an immersed object. Buoyancy equals the weight of displaced liquid. So the force of gravity applied or weight of the boat, the motor or oar, the shooter(s), the driver, the bow, the lights and any other equipment in the boat is less than the water displaced. Consider an empty boat weighing 400 pounds. That boat will sit at a point where the weight of the boat is equal to 400 pounds of water displaced. If the boat were filled with cement it would weigh more than the water it was displacing making it more dense and causing it to sink like a rock.

The second action mentioned will be a lever system. As Newton’s 3rd Law states, for every action there is an equal and opposite reaction. This is easily seen in the lever system where a lever is classified as a machine consisting of a beam or rigid rod pivoted at a fixed hinge, or fulcrum. As the driver of the vessel pushes or pulls one side of the lever, depending on how far from the fulcrum he is and how far the far end is from the fulcrum. Depends on if the machine is at equilibrium or has a mechanical advantage. If the distance from the drivers grip was shorter to the fulcrum than the distance from the probe end to the fulcrum. Then the ratio would be less than 1 meaning that it would be less than equilibrium meaning a greater force would be needed to be applied to move the boat. For example, if there was a boat weighing 400 pounds with 2 people in the boat weighing 200 pounds a piece with an extra 100 pounds of gear and an oar 9 feet long was used to propel the boat and the fulcrum was 4 feet from the drivers grip and 5 feet from the probe end then the force needed to reach equilibrium would be 1,125 pounds per kilograms. However, if it was at equilibrium then the ratio would equal 1:1 meaning the force applied would be the same to both sides. For example, if that same boat and crew weighing 900 pounds had that same oar that was 9 feet long and the fulcrum was at the center, the amount of force needed would need to equal 900 pounds per kilogram.

Snell’s Law will be discussed next. Willebrord Snell discovered the law of refraction which we now call Snell's law. This law is applied when trying to compensate for the refraction caused by the water and find the angle between the actual fish and the downward vertical axis, or theta 2. Using the vertical opposite angles rule you can find the perceived fish’s angle from the downward vertical axis (Hecht et al. 2002). If you know the angle of theta 1 which is the angle between the upward vertical axis and the angle at which you are looking at the perceived fish at the top of the water then you can find the angle between the downward vertical axis and the actual fish under the water. So, n1 is the index of refraction of the first medium, and n2 is the index of refraction of the second medium. Theta 2 equals n1 times sin of theta 1 all over n2. So, if n1 = 1, n2 = 1.33 and the angle of theta 1 is 45 degrees then theta 2 is 32 degrees from the downward vertical axis.

The work energy theorem now comes into play. This has to do with the work done on the bow when it is drawn. As the bow is drawn by the shooter and work is being done on the bow the potential energy increases. Once drawn the bow has stored energy that can do work on the arrow. When it is released the kinetic energy equals the potential energy which equals the work originally done. In the other hand of the shooter, the string is released and the bow accelerates towards the string and the string accelerates towards the bow. The bow and the hand connected to the body holding it have a greater mass than the string and arrow causing it to accelerate faster. While this is happening potential energy is decreasing and kinetic energy is increasing as an inversely related proportion.

The arrow is now accelerating and continues accelerating until it leaves the string. From there it starts de accelerating due to air resistance and soon water resistance which is much greater than air since it is more dense, but, unlike firing a bow at a level target on land where gravity is acting against the arrows natural, straight path, gravity is working mostly with the arrow when shooting at a fish because the arrow is fired more downward rather than level. Because of this and the fact that the arrow is not traveling a great distance, one does not need to account for the drop of the arrow due to gravity when bowfishing.

Once the arrow reaches the actual fish, it has one of two options. It may go straight threw the fish continuing to act as a mostly nothing but a wedge where the fish would just be another medium of friction like the air and the water, or it may act as a wedge at first and stop in the fish causing a conservation of momentum. If the fish is not moving at the moment the arrow reaches it the the formula for conservation of momentum is the mass of the arrow times the velocity of the arrow equals the total mass, which is the arrow plus the mass of the fish, times the final velocity of the two stuck together.

Once the fish is stuck, the shooter then uses a reel to bring the fish in. This reel has a small radius where the line actually wraps a round, but the handle that sticks out has a much greater radius and acts a a type of lever system, otherwise known as a compound wheel. Torque, which is classified as a twisting motion that tends to cause rotation, comes into play here. A compound wheel is used in this devise to compensate for the great force the fish is applying to the line which is wrapped around the small radial axis of the reel. The greater radius lever requires a lesser force to be applied to it in the opposite direction to overcome the force applied by the fish. So if the fish were to exert a twice its body weight which is very common, and since the most common freshwater species commonly hunted are common carp, grass carp, bighead carp, alligator gar, and paddlefish, that can be quite some force. Lets say the fish weighed 30 pounds and exerted a continuous 60 pounds of force, thats 267 newtons. The small radius spool that the line is wrapped around will be r2 is 0.02 meters and the larger radius with the handle will be r1 and is 0.05 meters. If both of them are applying a force 90 degrees to the extended radial line and the fish is exerting 5 units of torque (mN) in the counter clockwise direction so the shooter must exert around 100 newtons, or 22 pounds of force, in the clock wise direction to the handle at 90 degrees to successfully reel in the fish.

Once the fish is in the boat and in the bucket or live well, the shooter does it all over again. The species allowed for hunting are management species, meaning their population is higher than it needs to be, so game wardens are grateful for this sport. Some people eat what they catch, but most use their catch as compost. Usually beginning March 1, bowfishing is allowed 24 hours a day on rivers where commercial fishing is allowed (Stonner et al. 2005).

Works Cited

Hecht, E. 2002. Optics. Reading, MA: Addison-Wesley. Print.

Holland, T.J.B. 2016. ”Archimedes and the Tauern Eclogites: The Role of Buoyancy in the Preservation of Exotic Eclogite Blocks." Archimedes and the Tauern Eclogites: The Role of Buoyancy in the Preservation of Exotic Eclogite Blocks. N.p., n.d. Web.

Minister, B. 2016. Story, Read This. "As Bow Velocity Reaches Its Limit, Hunters Must Decide If They'll Continue… CHASING SPEED." Outdoor Life. N.p., n.d. Web. 11 Nov. 2016.

Stonner, R. 2005. "Arkansas Bowhunter Ed Course." Bowfishing Overview. N.p., n.d. Web. 11 Nov. 2016.