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The Physics behind Archery

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Brittney White

on 22 January 2014

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Transcript of The Physics behind Archery

The Physics behind Archery
Dynamics
FBDs
Energy Transformations
Chemical- Muscles in body
Archery can be traced back in history all the way back to around 3500 BC when the Egyptians used longbows as their primary weapon. Prior to that bows and arrows were scarcely mention and/or seen. From there the knowledge of archery slowly migrated. It was used mostly as a weapon in wars and to hunt with until firearms came into play. Bows aren't as effective as firearms so they were used less and less in wars and more for just fun. Archery then became a sport. Still used now but majorly just for sport and hunting.
Bows & Arrows
There is a great variety of different bows currently, ranging for size, material, accuracy, draw weights, purpose etc. The two main types are recurve and compound.
Archer's Paradox
One would assume that in order to hit the target one must aim at the bull eyes, but this is incorrect. In reality you should really aim off of the target. This is because the arrow bends due to the pressure from the accelerating string. The arrow also doesn't initially fly straight when released. When the fingers let go of the string they slightly pull the string to the side.
For every action, there is an equal and opposite reaction. For example the archer is right-handed and the arrow is placed on the left side of the bow, when the string is pulled in the right hand, it is pulled back and slightly to the right. The reaction is when the string is release and propelling forwards. This causes the arrow to release from the notch and to fly forwards and to curve around the bow. When the arrow is in flight it is all wibbily-wobbly because of arrow being force to move sideways to get around its obstacle. Once it starts moving side to side, it wants to stay moving side to side.
The stiffness of the arrow is important because if the arrow is too stiff( has to much spine) then it won't be able to bend around the bow too well. The more force you apply means that the arrow will be pushed more to bend around the bow. One should really know if their arrows and bow are a good match so they can recognize whether they have to aim off target in order to overcome the 'Archer's paradox'.
History of Archery
Recurve Bow
In the picture below you can see the different parts of the bow. The arrow rest gives a stable spot for the arrow to rest on prior to it being shot. The notching point indicates the middle of the string, the placement of the arrow greatly affects the accuracy of the arrow. The two limbs are what stores the energy from pulling the string back. depending on the material the bow is made from affects how much the bow can bend when pulling the string. In order to make the arrow fly further, more force is needed in order to pull the string in order to bend the bow. Sometimes a long stick, called a stabilizer to attached to the bow at a 90 degree angle to the bow. It adds some weight to stablize the bow during and after the shot.
Compound Bow
These bows are more complicated than recurve bows. Compound bows have cams or pulleys to aid the archer to store enough energy in order to create an greater kinetic energy in comparison to the recurve bow. The cams or pulleys also means that the archer doesn't have to put in as much force in order to pull the string to the full draw length. These bows are prominent in hunting because the archer doesn't need to use as much force which allows the archer to hold the string at full draw length for longer in order to wait for the desired opportunity to shoot at the target.
Types of Arrows
Wooden- most basic and oldest type of arrows. They easily break so they aren't used in high power recurve or compound bows. The fletching (fins) are most commonly feathers while the other types of arrows use plastic vanes, these allow the arrow to fly straight.
Carbon- lightest out of all the materials but least stiff. If used improperly they can shatter into little tiny pieces and are dangerous.
Aluminum- heaviest, stiffer, and more durable.

The stiffness and material of the arrow is important because if the wrong arrow used with a bow can damage the bow and/or arrow, as well as affect the accuracy of the shot. The tips of the arrow is also a variable because it could weigh down the arrow more. Stiffness of the arrow is important when taking into consideration the 'Archers Paradox"


Fg
Fa
Fair + Ff
Newton's Laws
1st law- Every object will continue in its state of rest or constant motion in a straight line unless acted upon by an unbalanced force
This can be seen from both the bow string and the arrow. After the string is released it will spring back to its original position but since on release the fingers cause the string to go sideways a bit the string will bounce back an forth in all directions until the air resistance finally slows it to a stop. The arrow will continue in a straight line forwards but it will begin to fall slowly towards the ground due to gravity. If there is a wind the the arrow will be pushed sideways off of its straight line path, which is way archers always have to take into consideration the wind speed.
2nd law- If Fnet=/= 0 then the object will accelerate in the direction of the net force.
The arrow doesn't have a constant motion because it is affected by friction of the arrow across the bow, gravity, mass of arrowhead dragging the front of the arrow down, and air resistance.
3rd law- For every action there is an equal and opposite reaction.
When the bow string is pulled back it bends the bow out of shape and when the string is released the bow will want to go back to its original shape so it pulls back on the string. Also when the arrow hits the target the reason the arrow stops is because the target pushes back on the arrow.
After shot
Fg
Fn
Arrow while on bow rest prior to being shot
Kinetic- Archer getting into shooting stance
Elastic- Pulling the string and in turn bending the bow and storing energy within bow
Kinetic- Release of string and stored elastic energy makes bow go back into original shape. Arrow is flung forwards.
Kinetic+Sound+Gravitational- Arrow in flight and then hits target. 'Twang' sound is made upon release and a 'thud' upon hitting target. Arrow still wobbles a little bit when in target.
The Math
If it takes 30 pounds (13.6 kg) to displace a bow from its original state 0.48m to its stretched state, how much work was done?
W=mgh
W=(13.6kg) X (9.8 m/s) X (0.48m)
W= 63.97J
Work= Elastic potential energy

What is the elastic constant of the bow?
63.97=1/2k(0.48)^2
127.94/0.2304=k
k=555.30 N/m

Et=Et'
Ee= Ek *a little energy is given to sound (twang sound) and thermal energy (friction) but for this one we shall just assume that all the elastic energy is converted to kinetic
Let's try to figure out the max initial velocity of the arrow
Ek=1/2mv^2 Mass of arrow is 0.025kg
63.97=1/2(0.025)v^2
127.94/0.025=v^2
v= 71.53m/s

Archery is projectile motion so we can use kinematic equations to determine how far away the arrow will land (without any wind and launched horizontally).Archer of my height holds bow at 1.5m
dy=1/2(a)(t)^2
2dy/a=t^2
t^2= 2(1.5)/9.8
t=0.55s

V=D/t
71.53 X 0.55=d
d=39.34m

In the video prior to this when I shot my arrow it landed 35.36m away but with the calculations it doesn't include energy lost to friction and sound, as well as air resistance. I would have to practice more because if I were to do archery in a competition the targets are placed 70m away.

By: Brittney White
* Background music
Just for fun-
Reality of the archery seen in movies
Most of the arrows shot in movies are computer generated. Some shots are believable, while others are outright impossible.
Katniss Everdeen- The Hunger Games
The actress who plays Katniss, Jennifer Lawrence was trained by Khatuna Lorig, a five time Olympian. Her stance is correct but for a archery competition and not the Hunger Games, she should be leaning the bow a bit to the right instead of it being completely vertical. As well, you can see in the picture that her finger is acting like a sight for her but when she does that with her silver bow and arrows in Catching Fire, her fingers could of seriously gotten hurt because of the force of the arrow going forwards and the fletching (fins) would of caught her. In Catching Fire, she attaches a cord to her arrow and tried to shot the 'ceiling' of the arena but in order for her to have been able to do that she would have to have a lot of kinetic energy to propel the arrow to the necessary height. The arrow would have been dragged down by the weight of the cord.
Hawkeye- The Avengers
Hawkeye's archery is completely unbelievable if you even know a little bit about the physics of archery. First off, his stance is completely wrong, his hand with the pulled string should be by his cheek and his arm holding the bow is twisting too much, his greatly protruding arm muscle would have gotten in the way of the string when released. He also used a bunch of special arrows in the movie, like one that exploded on impact, but the force needed for each of the different type of arrows would have been different yet he seem to always pull it the same amount. Also if he is supposed to be the 'best' at archery then why is he wearing two arm guards, sometimes children don't even wear one.
Merida- Brave
Despite it being a cartoon, the creators (Disney & Pixar) really seemed to have done their homework. Not only in this competition but for the rest of the movie, all of her archery skills seemed believable. Also they got the correct bow type and materials right. All of the guys who are competing for her hand in marriage are just basically bad at archery, especially the third guy who managed it with just pure luck. Even the part where she hit the arrow with another arrow was believable because her aim is perfect and wood arrow aren't durable, with the sharp arrowhead that she has it is possible for what she did to have happened. Her stance is perfect too
Video
Distance Arrow traveled: 35.36m
Time it took to land: 0.52 seconds
Full transcript