Introduction
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Hooke’s law is essential for string tension. The recurve bow and the compound bow have different mechanisms. The compound bow has more advantages than the recurve bow. It depends on several factors. The recurve bow is less efficient and has greater draw weight which makes it difficult for the archer to aim currently. This problem is removed in the compound bow which contains a cam that acts like a pulley.
Discussion
Section 1: Key ideas and principles
Recurve Bow
The recurve bow has limbs that curve away from the archer when it is unstrung which gives the bow more energy and speed than a straight-limb bow. Key features of this type of bow are many. The limbs of the bow can be detached from the riser so the limbs can be easily transported and stored so they can be one-piece or take-down. The bow contains an arrow rest in which an arrow can be placed when it is drawn and an aiding aid, bow sight is attached to the riser. The limbs are the tips of the upper-part curve and lower-part curve away from the archer, the riser is the central part of the bow which connects everything, the string is attached at the tips of the limbs, the grip indicates the hand of the archer that pushes it to shoot (Christmann et al. 2022). The bow's brace height is the distance between the string, grip, and tiller.
Compound Bow
This type of bow uses a system of cams and cables that bend the limbs and store energy The cam has an eccentric shape which changes is mechanical advantages of archers when they draw the bow creating a let-off effect. This bow can achieve higher arrow speeds, easier shooting than the traditional bow, and improved accuracy. The limbs are stiffer and more rigid than that of the recurve bow means more energy. Different radii of different points of the cams affect the leverage of the archer. At large radii, archers exert more force to draw the bow which is the opposite of the case of smaller radii. The let-off effect lower the strain on the archer’s muscle which allows them to aim more accurately and steadily. The effect increases the energy efficiency of the bow. The amount of let-off depends on the shape of the cams which allows the archer to change the let-off percentage (Manca et al. 2022). Draw length is determined by the position of the mod which is a small wheel attached to the side of the cam while draw weight is determined by the limb bolt which is the screw connecting limbs to the riser.
Hook Laws
Hook's Laws state that the force needed for the extension or compression of a spring at some distance is proportional to that distance. The spring constant is denoted by k and is the constant of proportionality (Eren et al. 2022). The constant depends on the stiffness and elasticity of the subject spring. Symbolically, the principle can be written as “F = kx” Here F depicts the amount of force on the bowstring and x depicts the deformation or displacement of bow limbs.
Both recurve bows and compound bows use Hooke’s law for the storage and release of energy. The variables in Hooke’s law are applied to these two types of bows. The amount of force applied by the archer when the archer draws the bowstring back. If the amount of force is increased, the stored energy increases in the bow, and the arrow will fly. The force depends on the length of a draw, which is the distance from the anchor point on the archer’s face to the neck point of the arrow. Spring constant measures the stiffness and the elasticity of the bow limbs. The stiffer the limbs, the more the stored energy and release. Compound bows have a higher spring constant than recurve bow which means that recurve bows are easier to draw but is less efficient while transferring energy to the arrow. Distance is the amount of deformation of bow limbs when it is drawn back (Hook, 2021). It depends on the brace height. The lower brace height, more distance for limbs to bend and can store more energy.
Section 2: Mechanical analysis of deformation of bow
The diagram of Recurve bow is not deformed
Figure 1: Because of an applied force recurve bow’s limbs do not undergo deformation
The limb is not deformed as the force is not enough to make it go through deformation when draw force F is applied. The lower limb and upper limb is the same as the initial position.
Diagram of Recurve bow deformed
Figure 2: Because of an applied force recurve bow’s limbs do not undergo deformation
The limb is deformed and it is moved from its initial position by some amount. It is denoted as the deformation distance of the bow limb in Figure 2. The direction of string tension and limb-defective force is depicted in the diagram.
Diagram of compound cam
-(1)_67dd4bd5ae1d5.jpg "Compound bow one cam which is attached to top limb")
Figure 3: Compound bow one cam which is attached to top limb
E=∫F dx
- d/n= ∫e2 dx
- d/n= 2e2-1 dx
- d/n= 2e +C
- d = 2en+ C
(E: energy, F: Force; C: constant)
The compound cam diagram shows the structure of the bow cam. The way both camps are connected is also shown by the radii of the inner cam and outer cam.
Section 3: Energy storage and projectile range
Compound bows store more energy in limbs than recurve bows
A compound bow store more potential energy in limbs than a recurve bow with the help of cams and cables that acts like pulleys. Curve limbs of the recurve bow bend away from the archer at the tip increasing the tension on the string and force on the arrow. When a string is drawn back, the angles of the limb reduce and the forward component of tension also decreases stating the bow reaches its peak draw weight and drops off as the string is pulled further back. The compound bow has cams to the ends of limbs and cables that connect the cams and the strings. The shape of the cams enables them to rotate as the string is drawn back while changing the leverage of the system. It reduces the holding weight at full draw which allows the archer to hold the bow steady and aim for a long time without tiring the archer’s muscles (Decheline et al. 2020). The distance of the limbs compressed per inch of draw length by the cams at the end of the draw. The bow reaches its peak draw weight in drawing which is maintained until the release.
The physics of this can be explained by taking energy as force multiplied by distance. The work done by the archer on a bow is equal to the force that is applied on the string times the distance it is pulled back. The work is stored as the potential energy in the limbs that transfers the kinetic energy to the arrow when the arrow is released. The potential energy increases with the increase of work done by the archer increasing the kinetic energy of the arrow. A compound bow can do more work by allowing more work done via increasing force and distance factors (ZANEVSKYY & ZANEVSKA, 2023). The cams increase the force while maintaining the high draw weight in full draw. It can increase the distance by compressing the limbs more per inch of draw length.
In the case of a recurve bow, the limb length is fixed, and the angle and radius of curvature change when the string is drawn back. But for compound bows, the length of limbs changes as the cam rotates and angles and radius of curvature both are fixed by the shape of the cam. The sum of the potential energy stored in each limb is equal to the total potential energy stored in the bow (Leelanoi & Khajornsilp, 2021). For a compound bow, there are two limbs that bend when drawn back so the total potential energy is the same as twice the potential energy of one limb. But for recurve bow, only one limb bends when it is drawn back meaning that the total potential energy is equal to the potential energy of that limb.
The above concept provides the reason why Compound bows store more energy in limbs than recurve bows with a justified explanation.
The range of compound bows is greater than that of recurve bows
The range of recurve bows is lower than compound because of two main factors: arrow speed and draw weight. Draw weight is the force amount required to pull the bowstring back to a specific point. The mechanical system of the compound bow reduces the draw weight at full draw allowing the archer to aim accurately. Recurve bows have a simple curve shape which increases draw weight as the bowstring is pulled back which makes it harder to hold while making the aim. The difference in draw weight is quantified by let-off percentage which is the ratio of peak draw weight to holding weight at full draw (Posess et al. 2020). Compound bows have a let-off percentage of 65% to 85% but recurve bows do not have it. An example is a compound bow with a peak draw weight of 60 pounds and a let-off percentage of 80% has a holding weight of 12 pounds while a recurve bow with the same peak draw weight has a holding weight of 60 pounds.
The arrow speed is the velocity of the arrow when the arrow leaves the bow. Compound bows have higher speed than recurve bows due to the amount of stored energy in the limbs of compound bows and transferring it more efficiently to the arrow. Recurve bow has low energy in limbs and loses from it due to vibration and air resistance. Kinetic energy measures the arrow speed which is the energy of motion. The energy depends on the mass and speed of the object. Draw weight and arrow speed impact the range of the arrow through two concepts: projectile motion and air drag. The range of the projectile depends on initial speed, height and launch angle. Higher initial speed and launch angle increase the range while higher height decreases the range. Streamline shape, lower speed, and smaller size lower the air drug as it opposes the motion of the arrow. Air drag reduces the range of the projectile by slowing it down while changing the trajectory (Zhang et al. 2023). Compound bows launch the arrows with higher initial speed with lower air drag than the arrows launched from recurve bows. This implies why the range of compound bows is greater than that of recurve bows.
The above concept provides the reason why the range of compound bows is greater than that of recurve bows with a justified explanation.
Conclusion
The concept has explained the reason for the range of an arrow undergoing projectile in the case of a compound bow is much more than that of a recurve bow. This project shows the structure of two bows and the deformation of the recurve bow is given. Different concepts have explained the reason why compound bows have a greater range in projectiles. Recurve bow does not contain let-off which plays a crucial role in reducing the weight of the bow.
Reference List
Journals
- Christmann, G., Yu-Ren, L., Guerra, R. D. S., & Baltes, J. (2022). Can a Robot Shoot an Olympic Recurve Bow? A preliminary study. arXiv preprint arXiv:2212.11071. [Retrieved from: https://arxiv.org/pdf/2212.11071.pdf] [Retrieved on: 12.11.2023]
- Decheline, G., Widowati, A., Maryani, N. T. S., Ali, M., Aqobah, Q. J., Barikah, A., & Zawawi, H. D. (2020). The Effect of Bow Training on the Endurance of the Arm Muscles of the Beginner Archery at Kobar Club, Jambi City. [Retrieved from: https://easychair.org/publications/preprint_download/X869] [Retrieved on: 12.11.2023]
- Eren, M. I., Bebber, M. R., Wilcox, D., Story, B., & Buchanan, B. (2022). North American Clovis point form and performance II: An experimental assessment of point, haft, and shaft durability. Lithic Technology, 47(1), 38-51. [Retrieved from: https://cris.unibo.it/bitstream/11585/889937/1/postprint.pdf] [Retrieved on: 12.11.2023]
- Hook, P. A. (2021). Litigation Analytics: A Framework For Understanding, Using & Teaching. Peter A. Hook, Litigation Analytics: A Framework For Understanding, Using & Teaching, AALL Spectrum, 20. [Retrieved from: https://scholarship.law.nd.edu/cgi/viewcontent.cgi?article=2479&context=law_faculty_scholarship] [Retrieved on: 12.11.2023]
- Leelanoi, J., & Khajornsilp, J. (2021). THE RESULTS OF ARCHERY BALANCE WITH STABILITY AND ACCURACY ARCHERY RECURVE BOW OF MALE ATHLETES INSTITUTE OF PHYSICAL EDUCATION CHON BURI CAMPUS. Academic Journal of Thailand National Sports University, 13(1), 189-199. [Retrieved from https://he02.tci-thaijo.org/index.php/TNSUJournal/article/download/248392/168825] [Retrieved on: 12.11.2023]
- Manca, G., Fabrizi de Biani, F., Corsini, M., Cesari, C., Femoni, C., Iapalucci, M. C., ... & Ienco, A. (2022). Inverted Ligand Field in a Pentanuclear Bow Tie Au/Fe Carbonyl Cluster. Inorganic Chemistry, 61(8), 3484-3492. [Retrieved from:] [Retrieved on: 12.11.2023]
- Posess, Z. (2020). A shot in the dark: how the Sandy Hook plaintiffs established legal standing against the gun industry. Seton Hall L. Rev., 51, 563. [Retrieved from: https://scholarship.shu.edu/cgi/viewcontent.cgi?article=1766&context=shlr] [Retrieved on: 12.11.2023]
- ZANEVSKYY, I., & ZANEVSKA, L. (2023). Testing and Tuning of the Sport Archery Bow and Arrow System. International Journal of Sport Culture and Science, 11(2), 132-149. [Retrieved from: https://dergipark.org.tr/en/download/article-file/2593112] [Retrieved on: 12.11.2023]
- Zhang, Z., Huang, X., & Zhang, B. (2023, July). On the Curricular Innovation Practice of the Recurve Bow Based on Blended Teaching. In 2023 2nd International Conference on Educational Innovation and Multimedia Technology (EIMT 2023) (pp. 263-275). Atlantis Press. [Retrieved from: https://www.atlantis-press.com/article/125988587.pdf] [Retrieved on: 12.11.2023]
5 Years | MSc
