The longbow became a sportsman's device when the musket replaced it during the 1500s.

In 1798 A.D. a record 972-yard longbow shot is performed by Sultan Selim. This record stands to this day.

In 1934, Wisconsin is the first state with an official bow-hunting season.

The Compound Bow is introduced in 1970--this is a bow that uses mechanical aids in the shot.

21st century- increasing knowledge of physics has led to many continuing advances in archery.

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Trajectory

Equations of Trajectory motion:

v = vi + at

v² = vi² + 2ax

x = 1/2(vi+v)t

x = vit + 1/2at²

x = vt - 1/2at²

x = displacement

vi = initial velocity

v = final velocity

a = acceleration

t = time

With these equations, it is possible to determine nearly every aspect of the trajectory of the arrow. We already determined the effect that the bow has on the initial velocity of the arrow.

(Ex: greater brace height=slower initial velocity,

less pliable material=greater initial velocity,

greater draw length=greater initial velocity)

Now we can look at the actual flight of the arrow, and pre-determine the path which it will take at certain angles.

Example 1: Using the given equations, the following diagram and the fact that the arrow being launched weighs 80.0 g, find at what angle the archer should hold the bow to hit the bullseye of the target.

How to solve:

1. Use Newton's second law: F=ma to determine acceleration.

F=ma

100N=(.80kg)a

a=1250 m/s^2

2. Use v² = vi² + 2ax to solve for v.

v² = vi² + 2ax

v^2=0 + 2(1250m/s^2)(.7m)

v=41.83m/s

We now know the initial velocity of the arrow. The next step is the do a vector decomposition and determine the velocities in the x and y directions.

Step 3: According to the following diagram, vyi=vi(sin(theta)). Substitute this is for vyi in the following equation.

Step 4. Once this is substituted in, plug in all of the known numbers for the variables and solve for theta.

With this information, we can determine that this archer will need to hold his bow at a 7.45 degree angle to hit the bulls-eye. For this reason, any person with an understanding of physics has the ability to excel in archery, regardless of physical talent.

Drag:

There are two types of drag: Shear Drag and Force Drag

Terms:

Shear Drag: a result of the arrow's moving through the air. Kinetic Energy is expended to move the air out of the way so that the arrow can pass. As it pushes on the air, so does the air push on it.

Force Drag: a force pushing perpendicular to the direction of flight when applied along side shear drag. A wake is caused by the movement of the arrow through the air, and is created using kinetic energy of the arrow itself. This energy creates a force which pushes the arrow upwards; perpendicular to its path of flight.

P=air density

V=arrow velocity

A=cross sectional area

Cd=drag coefficient

Standard air density: 1.293 kg/m^3

Example: Determine the drag on an arrow with a diameter of .600 cm and a drag coefficient of 0.0026 traveling 41.83 m/s. Assume STP.

Fd=(1/2)*p*v^2*Cd*A

Fd=(1/2)*1.293*(41.83^2)*.0026*(pi*.300^2)

Fd=.6465*1749.7*.0026*.2827

Fd=.831 Pa*m

2

How archers use drag: Arrow Design

Arrow designers add fletchings because of Force Drag. This drag, which pushes perpendicular to the arrow's path of flight and would under normal conditions interfere with the arrow's path, is utilized because of the fletchings. The Force Drag pushes up against the fletchings and stabilizes the arrow, so it does not wobble in midflight and stray from its intended path.

Torque is generated by form drag. Fletchings in the rear of the arrow cause more force to be applied there, resulting in a net counter-clockwise rotation which eventually stabilizes the arrow to a horizontal path.

Larger fletchings will slow the arrow down with more Shear Drag, but will respond better to Form Drag, making the arrow more stable, and increasing accuracy. However, this is compensated for by reducing the amount of distance which an arrow with larger fletchings can travel. Smaller fletchings won't slow the arrow down as much, but it is more likely to wobble in the air.

Fletchings: The stabilizing fins or vanes of an arrow,each individual fin is called a fletch.

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