How Feathered and Plastic Fletchings Affect the Control Of Arrows By Lucy Kiefer 7B 12-10-17
Archery has had a resurgence in popular culture with prominent roles in movies like Brave or the Hunger Games and even a TV series based on a superhero called Arrow. Archery can come in many forms like compound (common for hunters) and recurve (seen in the Olympics). Recurve archery will be the focus of this science experiment. A recurve archer has many pieces of equipment including limbs, risers, and stabilizers. All archery equipment has undergone advances in technology. For example, limbs are made with naval foam and arrows are made from different types of carbon fiber (Hurst NP). Yet, the goals of archery have remained consistent since the invention of the bow - shoot an arrow and hit a target. It seems simple, but shooting an arrow is a complicated process including wacky laminar-turbulent transitions for the arrow as well as the physical and mental training of the archer. It starts with the Archer s Paradox -- the curious observation that arrows bend in flight. A Bending Arrow Resulting from the Archer s Paradox Figure courtesy of The Traditional Archer's Handbook NP To discuss the paradox, a simplification is required: the equipment, the arrow, and the fletchings ("wings" added to an arrow in a common radial pattern of three or four) will be
analyzed. A shot arrow is acted upon by two equal and opposite forces which causes it to bend. The result is an oscillating arrow, which can alter a shot severely. Archers have adjusted to the archer s paradox with equipment like the plunger and more importantly with attention to their arrows. Dealing with the aerodynamics of an arrow in flight is about gaining stability over the arrow and overcoming the archer s paradox. While in flight, the arrow is affected by resistance. Air resistance along the arrow pushes down on the fletchings, causing the arrow to spin. A spinning arrow has more stability than an arrow with no fletchings. It is proposed that if feathered fletchings cause more stability than plastic fletchings, then the feather fletched arrows should score more. This paper will discuss the bow, arrows, physics, and aerodynamics of archery. The recurve bow is familiar to anyone that has watched archery in the Olympics. They have one string, and require more force to draw. To shoot seventy meters on a recurve bow takes about fifty-three pounds of drawing weight. Most of the power in a recurve bow comes from the stiffness in the limbs. Limbs can be made of wood, bamboo, or carbon fiber which is woven in different directions in order not to twist or flex. Inside of the outer skin, there is incompressible foam made of glass microballoons. The foam makes sure that the bow will not bend or deflect when drawn. Grips are where the archer s hand connects with the riser. (Hurst NP). Sights are simple aiming devices that help an archer concentrate on the shot and shoot a range of distances. Plungers are tiny, spring loaded pads screwed into the riser. The plunger cushions the arrow and pushes it away from the riser during release. This makes a consistent flight because it softens the first bend of the arrow caused by the archer s paradox (Reilly Olympic Archery Explained... NP). With all
of the equipment in place, an archer is ready to launch arrows that will interact with many forces and aerodynamics. Aerodynamics and fletchings are the central interaction being studied in this paper. To understand fletchings, it is easier to look at arrows without fletchings. A bare arrow will wobble and almost tumble in flight towards the target ( Is it Safe NP). Fletchings stabilize the arrow by pushing the center of pressure towards the nock (back of the arrow) and the center of gravity towards the point ( Blazer NP). Air pushes on the fletchings as the arrows fly causing the arrow to rotate. The spinning arrow is more stable in flight and the stability will produce a straighter and more consistent shot. A launched arrow that starts spinning can bring accuracy to a shot, even while the arrow is flexing due to the archer s paradox. To figure out why this happens, focusing on the physics step by step is easiest. The first force on the arrow is being applied by the released string which is transferring the stored energy of the flexed limbs. Figure courtesy of (Allain NP) Excluding any equipment failures or archer errors, the arrow can only speed up or accelerate as the string pushes on it. Over short distances, like 18 meters, gravitational
forces are not substantial. But what causes the wobble seen in the archer's paradox? Why would the seemingly rigid arrow start to bend? To understand the bend, there needs to be a second force -- a so called fake force. Fake forces are not forces, but they feel real. An example of this is when someone goes up an elevator. The elevator is accelerating, but the person feels heavier. The mass and weight do not change, but interacting with a force of acceleration makes the person feel like another force is pressing against them. The fake force can be placed at the center of mass of the arrow. Figure courtesy of (Allain NP) The force of the string pushes in one direction and the fake force opposes creating two equal forces on the arrow. If these forces were to act on a perfect arrow, with no deflections, the arrow would simply fold up on itself. However, because the arrow is not perfect, it bends. Once the string stops accelerating the arrow, there are no forces still acting upon it. A bent arrow with no forces acting upon it will try to return to the original shape. The arrow will get to its original point, but not stay there. The momentum carrying the arrow will also cause it to overshoot its equilibrium, and begin bending again (Allain
NP). This bending arrow is hard to control. The archer needs some way to control this projected arrow and looks to fletchings. Two types of fletchings are going to be tested: plastic and feather. Plastic fletchings are made using extrusion, in which hot plastic is put through a mold ( Quadel Acquires NP). Most plastic fletchings are quiet in flight and somewhat flexible. They are very durable because they are heavier and they can survive being shot through hay bales. In contrast, feather fletchings are very light and are usually made from turkey feathers (Reilly Feathers vs. Vanes NP). The turkey feathers are processed in factories and get washed, dyed, dried, and the keratin gets removed. They then get cut into different shapes, much like badminton feathers. Feathers are either left or right orientated and it is best to use only one orientation ( Why Choose NP). Their natural curve causes more spinning (Carbon Arrow NP) (Reilly, Feathers vs. Vanes NP) and they create a smaller loss of trajectory ( Carbon Arrow NP). Which fletching is the best choice? To answer this question, an experiment needs to be designed. Two groups of arrows will be created. A group with plastic fletchings and a group with feather fletchings. All arrows will be the Easton Aluminum model XX75 Platinum Plus. The arrow shaft is manufactured with very tight tolerances. Easton says that this model of aluminum arrow will vary in straightness by only +/-.002 inches (Lancaster Archery 75). The nocks and tips are the same on each arrow as well. Every part of the bow will be kept the same. The only complications are the fletchings and the archer. Many arrows will be shot over several sessions to minimize the effect of the archer. All arrows will be shot indoors at the same distance. The arrow data will be measured by
placement, score, and grouping. Arrow placement will be measured in four sections: top left, top right, bottom left, and bottom right. Placement will help qualify the differences between the arrows. Score will be measured by the concentric rings of the target. Arrows that frequently land in the yellow (center) are more stable than arrows that land in the white (outer). Grouping may show the effect of the archer. Arrows should group together. In addition to the two types of fletching, an additional control will be the use of bare arrows (no fletchings at all). Many researchers have already looked at the effect of plastic and feathered fletchings on the stability of an arrow. K. Owaka and other scientists studied plastic fletchings and spin fletchings (mylar) in a wind tunnel (Owaka et al. 67). Spin fletchings are thought to be more aerodynamic because of their curved nature. This holds true by the experiment, which says that with spin fletchings the transition from orderly to turbulent air flow along the body of an arrow occurs at a certain Reynolds number. This transition, however, does not happen with plastic fletchings (Owaka et al. 72.) K. Mukaiyama of the University of Electro-Communications researched if the shape of the point of the arrow affects aerodynamics (Mukaiyama et al. 265). They discovered that streamlined points have a laminar effect on the shaft and broadheads are more turbulent. Broadheads increase the drag on the arrow and slow it down (Mukaiyama et al. 270). Ìpek Eroglu Koyalis and other researchers assessed the number of arrows in the yellow ring of a target shot by male and female archers (Kolayis et al. 453). They split the targets in fourths and studied which arrows hit in which section. They identified that in all four corners, blue was least commonly hit and yellow was hit the most. The upper part of the
target got shot 63.5% of the time. However, there was no difference between left and right placement (Kolayis et al. 456). The importance of the experiment in this paper is to be able to identify which fletchings are good for shooting short distances indoors. Understanding how the archer s paradox, aerodynamics, and fletchings affect the flight of an arrow will make shooting less mysterious. Armed with more knowledge and more data, archers can make better choices when it comes to the choice of fletchings. It is proposed that if feathered fletchings cause more stability than plastic fletchings, then the feather fletched arrows should score more.