Use the following arrow kinetic energy and momentum calculator to estimate Momentum and Kinetic Energy.
Kinetic Energy, Momentum and Arrows
By Bob Robb
When discussing the penetrating ability of a hunting arrow, the two most commonly referred to factors are kinetic energy and momentum. The term kinetic energy is derived from the Greek word for motion, kinesis, and the Greek word for active work, energeia.
Therefore, the term kinetic energy means “through motion, do active work.” Energy can exist in many forms, and each form of energy can often be converted into other forms. When it comes to bows, energy is stored in the limbs and cams when the bow is drawn, then transferred to the arrow shaft at the shot in the form of kinetic energy, or K.E.
Because the speed of the shaft is reduced due to both gravity and air resistance, the K.E. also changes along the flight path. Thus, the K.E. you measure a few feet in front of the bow as the arrow is released is nowhere near the K.E. delivered downrange on the target. That’s why when hunting large animals, such as elk and bears, experienced bowhunters try to “juice up” their bows to deliver more initial K.E., and thus deliver more K.E. on the target.
Kintetic Energy Formula
The formula for K.E. as measured in ft./ lbs. is: Mass x Velocity-squared divided by 450,240, with Mass the total arrow weight and velocity is the arrow speed. So let’s say you have an arrow that weighs 400 grains that flies at a speed of 290 feet per second. Your equation would look like this: 290 x 290 x 400 / 450,240 = 74.72 foot-pounds of K.E.
For years, the following have been the minimum kinetic energy values for hunting game of all sizes: Small game (rabbits, squirrels, etc.), up to 25 ft./lbs.; medium-sized game (deer, pronghorn, sheep, etc.), 25-41 ft./lbs.; large-sized game (elk, black bear, wild boar, etc.), 42-65 ft./lbs.); toughest game (brown bear, grizzly bear, large African game), 66 ft./lbs. or more.
Momentum Formula
Momentum can be defined as “mass in motion.” All objects have mass, so, if an object is moving, then it has momentum or mass in motion. The formula for calculating momentum is: Momentum: p (momentum) = m (mass) x v (velocity).
Using an Arrow Kinetic Energy Calculator for Bowhunting
Because both involve calculations of mass and weight, kinetic energy (K.E.) and momentum (M) are often interchanged, but that’s not right. Simply stated, K.E. can be thought of as a big hammer and the arrow shaft as a nail, with K.E. driving the nail through the animal. K.E. values can be adjusted by altering either arrow speed, arrow weight, or both. On the other hand, think of momentum as downrange energy retention, or penetration potential.
Another way to look at it is that, because velocity is squared, K.E. favors arrow speed, while momentum, which gives both mass and velocity equal bearing, favors weight. And, all things being equal, the heavier arrow will penetrate better than the lighter arrow. The key is finding the sweet spot. You can go to a lighter arrow to increase your speed and flatten trajectory, which might give you a K.E. value increase. But that might actually reduce momentum — and the depth to which your arrow and broadhead will penetrate larger, tougher animals. A good example of the difference – which would hurt you more, being hit in the ribs by an egg traveling at 300 fps, or a golf ball traveling 200 fps?
I’ve never seen a chart showing recommended momentum values for various big game animals. However, when I bowhunted Cape buffalo in South Africa, the minimums required by law were an 80 lb. draw weight on a compound bow, an arrow that weighed a minimum of 750 grains, and with a two-blade, cutting tip broadhead. My bow launched my 810-grain shaft at only about 220 fps – but it penetrated the 1700 lb. buffalo to the fletches. That was all about momentum. At the same time, I shot a bull elk at 15 yards in 2021 with an arrow weighing 410 grains tipped with a 125-grain SEVR mechanical broadhead flying at 285 fps, and it penetrated the entire chest cavity. That was all about a balance between K.E. and momentum – and that’s what you’re striving for.
You can use the arrow kinetic energy calculator to estimate K.E. and M to find the right arrow for any species or hunt.
More on Kinetic Energy and Momentum
Arrow Kinetic Energy Calculator Example
Be aware that when shooting an elk out of a treestand, you will need to aim higher on the chest cavity than if you were shooting on level ground. Because of the downward angle, I try to hit high vitals on the near side and exit out the lower vitals on the opposite side. Because of this angle, I shoot a setup with a higher momentum so I am capable of passing through the opposite side. If I am unable to punch through that opposite side, the chest cavity will need to fill with blood before any significant blood loss will be spilled on the ground. If I get that second hole it is generally lower on the chest cavity giving me an almost immediate blood trail. This can make the tracking job a whole lot easier.
Expert Tips for Shooting a Bull from a Treestand | Tyler Henderson