# Arrow Speed vs. Kinetic Energy May 04 2017, 0 Comments

For many years now, compound bow manufacturers have been focused on increasing arrow velocity and thus, they have come up with all sorts of radical cams designs while also attempting to reduce the amount of vibration that an archer feels through the bow's riser by also introducing such innovations as pre-loaded and parallel limb designs and integral vibration dampeners. Of course, the reason for such intense focus on increasing arrow velocity is that the greater the velocity at which your arrow leaves the bow's riser, the flatter its trajectory will be and the thus, the better it will compensate for slight misjudgments in the distance to your intended target. However, all of this focus on arrow velocity has lead some archers to also decide to decrease the weight of their arrow/broadhead combination in order to achieve higher arrow speeds. However, provided that a bow's draw weight is not changed, decreasing arrow weight also decreases its kinetic energy and thus, it also decreases its ability to penetrate deeply enough to reach an animal's vital organs; especially on larger game species such as Elk, Moose, and Brown Bear.

**Kinetic Energy -**

So, what is Kinetic Energy? Well, Kinetic Energy is a concept of the field of Physics and is a means by which a person can calculate the amount of inertia an object in motion has based upon Newton's Second of Motion which states:

"In an inertial reference frame, the vector sum of the forces **F** on an object is equal to the mass *m* of that object multiplied by the acceleration **a** of the object: **F** = *m***a**."

** **Therefore, Kinetic Energy is a product of mass and acceleration measured in foot/pounds and thus, provided that the amount of force applied to an arrow to get it moving is held constant (aka draw weight), increasing or decreasing the weight of an arrow also increases or decreases it Kinetic Energy.

**Why is Kinetic Energy Important? -**

However, while it is good to know that Kinetic Energy is a product of mass and acceleration, it does not explain why the amount of kinetic energy any given bow and arrow combination generates is important to bow hunters. Thus, the answer that question is that the more kinetic energy any given bow/arrow/broadhead combination generates, the more deeply the arrow will penetrate a game animal's body and thus, the more likely it is to reach the animals vital organs. Therefore, unlike gun hunters who are looking for a bullet design that dissipates all of its kinetic energy within the animal's body cavity in order to create the greatest amount of hydrostatic shock to the animal's nervous system, the best possible outcome for a bow hunter is that their arrow passes completely through an animal's body in order to cause an immediate drop in blood pressure to quickly and humanely incapacitate the animal.

**How much Kinetic Energy do you need - **

So, how much Kinetic Energy to do you need to hunt various game species? Well, the answer to that question is determined by the physical size of the animals you intend to hunt. For instance, small to medium sized game animals such as Coyotes and Whitetail Deer have much smaller bodies than larger game species such as Elk and Moose and thus, the smaller an animal is the less kinetic energy your arrow needs to penetrate into its vital organs whereas, the larger a game animal is, the more kinetic energy your arrow needs to penetrate its body cavity. Constantly, Easton Archery has conveniently provided the following chart in order to provide bow hunters with some idea of how much kinetic energy they need to humanely harvest various sized game animals.

**Kinetic Energy Recommendations for Bowhunting**

Small Game |
25 ft./lbs. |

Medium Game (Deer, Antelope) |
25-41 ft./lbs. |

Large Game (Elk, Black Bear, Boar) |
42-65 ft./lbs. |

Big Game (Cape Buffalo, Grizzly Bear) |
65 ft./lbs. |

**How to calculate Kinetic Energy -**

So, now that we know what Kinetic Energy is and why it is important to bow hunters, let's more closely examine the formula for calculating it. As stated above, kinetic energy is a product of mass and acceleration and thus, in order to calculate how much kinetic energy any given bow/arrow/broadhead combination generates, you need to use the following formula:

KE = (m x v^{2})/450,800

However, to explain this in terms that those of us who are not math geniuses can understand, you need to multiply the arrow's weight in grains (440 grains = 1 ounce) by the square of its velocity measured in feet-per-second and then, divide that product by 450,800 which will yield an answer measured in foot/pounds. For example, let’s say that we have a compound bow that shoots a 425 grain hunting arrow at 300 feet-per-second. Then, the kinetic energy of this setup would be calculated by taking the arrow's weight of 425 grains and multiplying that by its speed of 300 fps times 300 fps and then, dividing the resulting product by 450,800 which would yield a kinetic energy of 84.85 ft. lbs of kinetic energy.

**Light arrows vs. heavy arrows-**

Last, it should be noted that when a bow is drawn, the bow's limbs store a significant amount of potential energy and the very large majority of this energy is transferred to the arrow/broadhead upon release of the bow's string but, not all of it. Therefore, because some part of this potential energy remains, it causes vibration in the bow which can be both felt and heard by the archer. Therefore, a by shooting a heavier arrow/broadhead combination, more energy will be absorbed by the arrow which leaves less energy to cause vibration and noise in the bow upon release. Also, according to Newton's First Law of Motion, the greater the mass of an object in motion, the more force that is required to slow that object down and/or halt its forward motion. Therefore, it is also important to remember that kinetic energy only remains constant when the mass and velocity of the arrow remain constant. But, because arrow velocity decreases as its distance traveled increases, an arrow's kinetic energy also decreases over distance traveled. Therefore, a heavier arrow will not only absorb more energy from the bow, it will also retain more energy down range because it has more inertia and thus, it is less susceptible to outside forces such as air density and wind resistance. Consequently, while it may seem counter-intuitive, archers with lower draw weights and/or shorter draw lengths should consider shooting a heavier arrow in order to preserve kinetic energy and increase penetration rather than shooting a lighter arrow to increase arrow velocity.

So, even though archery manufacturers seem to be laser focused on increasing arrow velocity due to the fact that the faster an arrow/broadhead combination of any given weight leaves the bow causes it to have a flatter trajectory, it should also be noted that it's still very important to consider shot placement, broadhead design, and a myriad of other factors when determining the effectiveness of a hunting arrow fired from a bow. But, nonetheless, kinetic energy is still a very important part of this equation and thus, it's far better that your arrows have too much kinetic energy than too little!