Kinetic Energy has been promoted as the end all of a bow set up for hunting. We have been told that if you have enough Kinetic Energy then you are good to hunt this or that animal. Kinetic Energy is really the Wrong Focus.
Wikipedia defines Kinetic Energy as “the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes.”
A more Archery oriented definition and description is found on Archery Report and states “The kinetic energy (KE) of an object is the energy of the object due to its speed and mass. In order for the energy of an object to change, work must be done on the object. In the case of an arrow and archery, work is done by the archer’s muscles by pulling back the string and flexing the limbs. The energy is stored in the limbs in the form of potential energy; when the string is released the energy stored into the limbs is released, most of which is absorbed by the arrow.
The energy not absorbed by the arrow becomes friction in the bow parts, noise, vibration and other inefficiencies experienced by the bow. Energy that is absorbed by the arrow is converted into multiple forms, the majority resulting in the forward velocity. The kinetic energy of the arrow that archers care about and calculate is the energy due to its forward motion. As the arrow travels downrange, the total energy diminishes mostly due to air.”
To calculate the Kinetic Energy (KE) of an arrow the following formula is used (also from the same article on Archery Report):
For an arrow, the kinetic energy is calculated by taking the weight in grains, multiplying it by the square of the speed in feet per second, and dividing by the constant 450800.
Then I heard this statement for the first time: If I throw a lead pencil at you at the same speed that I throw an equal size piece of all thread at you, which one will hurt more? Finally something clicked in my brain and made sense to me. I didn’t know it at the time, but this was now an observation of momentum and would forever solidify the light arrow vs. heavy arrow argument. In fact, what it did was cause me to start researching the perfect arrow set up for my bows based upon momentum while not completely ignoring KE, but just placing it in proper perspective.
Momentum is calculated using the following formula:
The second factor and the one we are going to use to determine our set up is also easy to understand. Air resistance is instantly against an arrow. The heavier an arrow is increases the time and force it takes to slow that arrow down. The lighter an arrow is the more impact air resistance has on it and it will slow down more quickly than a like arrow of heavier mass. So if we shoot two arrows of the exact same outside dimensions and one is a 300 and one is 500 (the 300 will be the heavier arrow) the 300 will slow down less until impact than the 500 arrow does. This is all about momentum. These facts started me down a path that I have applied to every bow I have shot since that time. I get on a chart that calculates momentum for me. There are many out there and even some apps, but here is one I found: simple calculator. I plug in my figures and then I play with the weights of the arrow and the speed. You also need a speed calculator. As you put in your factors from your set up it estimates the speed of the arrow based upon your changing numbers of weight. I continually put in other figures until I see that my momentum starts to drop. By doing this I find the set up weight that is most ideal to maximize my momentum. I also have observed that 9 times out of 10, my KE also follows suit closely.
Here is my most recent study. I am trying to set up an arrow for my Arena 30 from Bear Archery that I will be able to hunt all dangerous game in South Africa:
Now that I have thoroughly muddied the waters with this example, let me draw some conclusions. To look only at Kinetic Energy in determining your set up is a crucial mistake that many archers make. The key reason for this is that speed and velocity differ. Speed is used in the calculation of KE. Momentum uses velocity which adds direction to speed and gives a more accurate assessment for the archers down range performance.
I look at momentum first. I then move the numbers around to see the optimal set up to maximize momentum. I then look at Kinetic Energy to just make an observation and FOC for more input and information to make the best decision. The last step for me is to actually shoot the set ups and test with practical penetration at different distances.
I am not an expert in any area of physics, nor am I an expert archer. I am a hunter who takes his art very seriously and wants to be able to maximize my effect to kill any game animal most effectively. That is what drives me to make sure my set ups are in the best position.
For more please go to: Matt Guedes