Abstract:
The bow is perhaps the most revolutionary weapon in mankind’s history. Not only is the bow a pernicious weapon it is additionally an implement for a popular sport. Professional archers practice to control the flight of the arrows they fire so to be precise and consistent with their shots. An arrow is a simple projectile but controlling the flight of an arrow is an arduous thing. Perhaps the authentic adeptness needed in archery is an astronomical understanding in projectile kinetics. This report will explore the effect of components of projectile kinetics on of an arrow.
Aim:
To assess and analyse the effect of surface area and drag on the flight of an arrow.
Hypothesis:
It was hypothesised that if the surface area increases, the final displacement of the arrow will decrease.
Justification of Hypothesis:
Projectile kinetics is influenced by many forces and vectors, each with its own horizontal and vertical component that are independent of each other. The horizontal component of expedition (a_x) would be drag, assuming that there is no drag: the horizontal expedition is 0. The vertical acceleration (a_y) is gravity (9.81m/s/s, G).Assuming that there is no air resistance the horizontal component of velocity (v_x) will remain unchanged as it will not experience any form of expedition (J. Nedic, n.d.). The vertical component of velocity (v_y) will increment in magnitude at a linear rate as it is undergoing the expedition of gravity. The horizontal component of displacement at any given point in the flight of the projectile would depend upon the horizontal velocity and time taken. The same applies for the vertical displacement. These accumulated factors influence the projectile kinetics.
Since vectors depend upon direction as well as magnitude the direction in which the projectile is fired plays a sizably voluminous role in the projectile kinetics. Most projectiles follow a parabolic kinetics when in flight. The trajectory of the projectile affects how steep the flight of the projectile is because of this most archers take in to account the angle at which they fire so that the final displacement of the arrow is controlled.
One vector that greatly influences the flight of an arrow or any projectile is air resistance or ‘drag’ (a_x). Drag is a force and is therefore a vector as it has a magnitude of force and a direction. Typically the direction of drag is antithesis to the flight path of the projectile. Drag force is engendered when a projectile passes through a fluid and is caused by the difference in velocity between the projectile and fluid hence why a static object doesn’t experience drag. Since drag acts as the horizontal deceleration, fletchers and arches minimise the surface area of the arrow to minimise drag and make the arrow peregrinate more expeditious and further. The drag equation is utilized to define how much air resistance is faced by a concrete projectile. The equation is as follows: , where F_D is the drag force, p is the mass density of the fluid( at one atmospheric pressure) that the projectile passes through, v is the velocity of the projectile relative to the fluid, a is the surface area of the projectile and C_D is the drag coefficient of the projectile. Since the direction of drag is antithesis to the flight of the arrow it will have a negative value.
The fluid that the projectile passes through plays a sizably voluminous role in the amount of drag faced by the projectile. This is because different fluids have different densities, the more dense the fluid the more particles that are present to cause skin friction. Drag is engendered by the friction engendered by the projectile passing through the fluid. Skin friction is the direct contact of a solid surface against a liquid or gaseous
