Flight Path of Arrow Shot from Compound Bow

by Nicholas Gaetano

Submitted : Fall 2013

The intentions of this project are to explore and understand the effects of gravity and drag on an arrow in flight in hopes of improving accuracy for hunters. At the beginning of the project an arrow was measured and the velocity of the bow was calculated. From here, the density of air at sea level was researched and the area cross-section of the field tip was found. Next the drag coefficient was determined by relating the shape of the arrows field point to the shape of a bullet. The next step in the project was to determine the distance the arrow would travel after being shot at 5. To do this the project started off with one equation, Newton’s second law.

Newton’s second law was then rearranged into acceleration equations for both the x and the y direction. These equations were then integrated into equations of the arrows velocity in both the x and y directions. These velocity equations were then integrated into position equations in both the x and y directions. Through boundary or initial conditions the constants that came through integration of acceleration and velocity where able to be determined, by simply solving for the equations at t(0). Once the final equations have been determined the distances traveled in both the x and y by the arrow can be found.

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