The Optimum Angle To Shoot An Arrow

By Farid Shahid; 7th grade

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Blender Animation - What is the optimum angle to shoot an arrow?
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What is Archery?

Archery is the art or sport of shooting with bows and arrows. During Medieval Times, archery was a major part of war.
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Unfamiliar Vocabulary


  1. Θ (Theta) – An unknown angle of a right triangle
  2. Opposite side of a right triangle – the side opposite of theta
  3. Adjacent side of a right triangle – the side that is next to theta
  4. Hypotenuse of a right triangle – the longest side
  5. Velocity – the speed of an object with respect to direction (vector unit, not scalar unit)
  6. Air Resistance – a force caused by air that produces drag
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Components of Force

If the only factors that are taken into consideration when shooting an arrow are gravity, the horizontal component and vertical component of force, then the following would be true.


When an arrow is shot at a 45° angle, there is an equal amount of the horizontal and vertical components of force.


When an arrow is shot at an angle that is greater than 45°, there is more vertical force than horizontal force so the arrow uses its energy to gain unnecessary elevation and will not go as far as an arrow shot at 45°.


When an arow is shot at an angle less than 45°, then there is more horizontal force than vertical force. This means that gravity will pull the arrow down to the ground faster so it will not travel as great of a distance as an arrow shot at 45°.

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Function To Find Maximum Distance Traveled

v = initial velocity


g = acceleration due to gravity



sin(2θ) X v²/g


sin(2θ) X (68.58m/s)² /9.807 m/s²


sin(2θ) X 4703.216 m² /s² /9.807 m/s²


sin(2θ) X 479.577m

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For the arrow to travel the greatest distance possible, Sin(2θ) must be 1.

Sin(2θ) = 1



1 X 479.6


Distance Traveled = 479.6 meters when launched at ...


2θ = 90° (from the table)


θ = 45°

Okay, so 45° is the optimum angle to shoot an arrow, but that is only true if a lot of other factors are not considered. The optimum angle would actually be lower if you were to include drag, humidity, friction, etc.

Tsukya Asuruk

Fantasy Medieval Music - Dance with Dragons by Tsukya Asuruk

Credits:

A big thank you to the creators of the images that were used.


The video and text were written by Farid Shahid.