Understanding the Momentum and Kinetic Energy of Arrows
Does Knowing the Kinetic Energy of Hunting Arrows Help?
Bow hunting is one of those interesting passions/hobbies that takes a blend of science and art to do it well. You need to have a well-functioning and properly tuned bow setup to shoot consistently. But you also need to have the practice and time afield (we’ll call that the ‘art’ component) to shoot well. When most bow hunters think about improving an arrow’s “punch,” they usually focus solely on the speed of their bows. But there’s a lot more to it than just that. Did you know that the momentum and kinetic energy of arrows actually also influence the knockdown power they have? Have you even heard those terms before? And if you have, do you know how to influence them so your arrows can be as deadly as possible? In this post, we’ll walk you through how you can change your setup for any wild game species you want to pursue.
Basic Concepts of Momentum and Kinetic Energy of Arrows
As we mentioned, most people are obsessed with arrow speed for deer hunting – the never-ending pursuit for more feet per second (fps) – or adjusting the weight (in grains) of their arrows, which includes their broadheads and nocks. Some people also go beyond that to focus on their arrow FOC (front of center), which is essentially a measure of how much of the weight of an arrow is located in the front (i.e., broadhead). This affects the arrow trajectory and penetration power. But if you want to really dial in your arrows, you need to grapple with two new concepts: arrow momentum and kinetic energy. Though they are often confused, they are separate things.
Momentum of Arrows
The basic definition of momentum is the force required to stop an object. In the case of arrows, it’s the amount of force that is needed to stop the arrow. Momentum is important to consider because it directly influences the penetration power of your arrow (or bullet, or anything else). The more momentum your arrow has, the more force or resistance it will take to stop it, which means it will penetrate deeper through an animal’s chest cavity. You can find an arrow momentum calculator online, but it’s very easy to do yourself (see the arrow momentum formula below).
Momentum (arrow) = mass of arrow (grains) x arrow speed (fps) / 225,400
As an example:
400 grain arrow x 300 fps bow / 225,400 = 0.53 pound seconds (momentum)
As you can see from the formula, an increase in your arrow weight or bow speed both mean an increase in momentum. That’s true only to a certain point though, since significantly heavier objects will start to give into gravity before lighter things do.
Kinetic Energy of Arrows
Kinetic energy is defined as a type of energy possessed by moving objects (in this case, hunting arrows). When you draw your bow back, there is potential energy stored in the bow limbs. When you squeeze the release trigger, that energy is transferred to the arrow as it speeds away. When the arrow strikes a target or game animal, the energy is transferred again to it. Therefore, hunters can think of kinetic energy as the knockdown power of a projectile. When you shoot a heavy bullet at an animal, it usually possesses a lot of kinetic energy, which is why the transfer of energy can literally knock them down or cause such trauma and devastation to the wound site. With bows, however, the kinetic energy is nowhere near as devastating, which is why the arrow vs. bullet kinetic energy topic is so interesting. Again, you can find a kinetic energy calculator online, but this kinetic energy formula is also simple:
Kinetic energy (arrow) = mass of arrow (grains) x arrow speed (fps)2 / 450,240
As an example (remember to square the fps first):
400 grain arrow x (300 fps bow)2 / 450,240 = 79.95 foot pounds (kinetic energy)
As with momentum, increasing the hunting arrow speed or arrow weight will increase the kinetic energy of arrows. But when it comes to arrows and quickly killing a game animal, speed and kinetic energy don’t improve penetration like momentum does.
Consider the Other Factors
There are plenty of other factors and variables that affect how an arrow hits a target or game animal. Though momentum and kinetic energy are important, the other items listed below are also worth noting.
The species you’re going after is a large part of this equation too. The minimum arrow momentum for deer will be a lot less than the minimum momentum for larger animals (and similar for kinetic energy). For example, thicker-skinned moose or bear will offer more resistance than white-tailed deer and turkeys. Their tough hides, meaty shoulders, and thick shoulder blades can all quickly shuffle your momentum and kinetic energy thoughts into the garbage. So you need to have a higher FOC, higher momentum, and higher kinetic energy as the animal you pursue increases in size and toughness. Here are a few general measurements to consider for kinetic energy required for different game animals. However, always consider that a heavier, slower arrow will likely have less kinetic energy, but will have more momentum to punch through a tough exterior. In most cases, momentum will trump kinetic energy requirements.
Additionally, the type of broadhead you use will make a big difference in the penetration equation. Lightweight broadheads don’t have the same momentum as heavier broadheads (all other things being equal) and so won’t penetrate as deeply. Also, broadheads with large cutting diameters have more resistance than broadheads with smaller diameters. But the increased cutting surface may be a good tradeoff for the reduction in penetration if you only hunt deer or turkeys. For larger game animals, a heavier and narrower broadhead will be better suited to punch through the tough hide and bone.
The arrow flight path (influenced by the arrow FOC and balance) can also cause inefficiencies that reduce its momentum or kinetic energy. For example, if an arrow takes a nosedive soon after leaving the bow, the kinetic energy won’t be delivered with the broadhead straight on, and the momentum can also suffer.
How You Can Change Them (and Why You Might)
As you can see, the arrow weight and the speed of the arrow are both things you can control to play with the momentum and kinetic energy of arrows. The more momentum and kinetic energy you have, the more likely you are to penetrate and quickly dispatch an animal. One way to do that is to get a faster bow. But using a heavier arrow (to increase your momentum) is a better bet in most cases. If you want to use a heavier broadhead and increase your arrow FOC for better penetration, there is a great way.
Nock Out® offers Lock-n-Load® inserts, which essentially add weight (grains) to the front end of your arrow while providing an easy and glueless method to insert a field tip or broadhead. This is not only an easy way to quickly index the blades to your vanes, but it will help improve your trajectory and increase the momentum and kinetic energy of arrows at the same time. Ultimately, you need to experiment with your own situation to see how the two measurements affect your shooting.