
Arrow Speed and Kinetic Energy 
How Much KE Do I Need?
If you have a hotrod modern compound bow producing 70+ ftlbs of KE, and you only hunt Whitetail Deer, the speed vs. KE debate is just academic. No matter what arrow you shoot, you'll have practically twice the energy required to harvest your deer. In fact, at 70+ ftlbs, you would have plenty of power for even the largest North American game species. But if your bow isn't such a hotrod, or if you shoot low poundage and/or a short draw length, the KE issue may be a hair worth splitting.
According to Easton's field chart, the amount of KE you'll need varies by the species you intend to hunt. Obviously, the larger the game, the more KE you'll need. And regardless of the power of your bow, you'll still need to land your shots in the boilermaker. If you hit an animal in the shoulder, all bets are off. But assuming you do your part, Easton's recommendations gives us a place to start. Of course, these recommendations aren't absolutes, nor are they guarantees of success.
To give this some perspective, refer back to our Bowtech Patriot test. Would our bow be capable of harvesting a Whitetail Deer? According to the chart, yes. A properly placed arrow  impacting with 50+ ftlbs of KE  has a very good chance of generating a clean passthru on a Whitetail Deer. So with respect to kinetic energy and Whitetail hunting, there may be no practical difference between the 300 grain arrow impacting with 49.66 ftlbs of KE and a 600 grain arrow impacting with 54.16 ftlbs (as in our experiment above). Assuming favorable conditions and a good shot, either arrow would provide sufficient energy to make a clean harvest on a deer. But if we decided to take our Bowtech Patriot out for some Minnesota Black Bear or Rocky Mountain Elk ... we just might come up short on power. So in that case, the extra KE might come in handy.
How Do I Compute Kinetic Energy?
Kinetic energy of an arrow can be found by using the formula KE=(mv²)/450,240 where m is the mass of the arrow in grains and v is the velocity of the arrow in fps. The 450,240 just sorts out all the units and converts things from fps & grains to ftlbs. So if your new bow setup ultimately shoots a 400 grain arrow at a respectable 250 fps, your actual kinetic energy or "knock down power" will be:
Before we move on, we should mention that KE and Momentum aren't the same thing. We received an email several seasons ago from a gentleman who emphatically insisted that Kinetic Energy was NOT the best mathematical predictor of hunting penetration with a bow and arrow. He said that the industry standard expression of Kinetic Energy was "shortsighted" since the benefit of speed is exaggerated by squaring velocity in the equation (we didn't make up the equation BTW) and that the KE model applies better to highspeed projectiles like bullets. He explained (at some length) that Momentum was the better model for archery. With over 10 years in the archery industry, we have yet to see an archery product rated for slug/fps. But in the interest of leaving no stone unturned ...
MOMENTUM vs. KINETIC ENERGY:
Should you have an unquenchable interest in ballistic physics, you may find it interesting that a few sporting enthusiasts will even dispute the convention that KE is the best measurement for predicting hunting penetration with a bow and arrow. A number of enthusiasts will debate that MOMENTUM is the better mathematical model. Of course, KE and Momentum aren't the same thing.....
> Kinetic Energy = Weight X Velocity Squared / 2 X Acceleration of Gravity
> Momentum = Weight X Velocity / Acceleration of Gravity
Since velocity isn't squared in the momentum formula, arrow mass and velocity play more equivalent roles. The kinetic energy of a moving body increases as the square of the velocity whereas the momentum increases directly as velocity increases. So if you recomputed our chart to show momentum, then the graph would look much different. The heavier arrows would show a significant improvement in overall momentum, and you could therefore conclude that heavier arrows would indeed yield dramatically better penetration.
Right or wrong, the shooting sports have a number of traditions and conventions regarding technical measurement. And the lethality of a projectile (whether from a firearm or bow) is traditionally expressed as a function of KE (ftlbs). As such, most sporting enthusiasts have some comprehension of this measurement. Unfortunately, a momentum rating in Slug FeetperSecond would surely leave many of us scratching our heads. Given the dramatic difference in the two methodologies, it seems unlikely that KE has remained the "standard" for so long if it's entirely incorrect. There are a lot of talented engineers in the archery industry. So either they have ALL missed it, or perhaps the momentum theory has a glitch (not to worry  our team of physicists are working on it now).
Should you have an interest in the debate regarding which mathematical model is best applicable to archery, here's some basic argument on the topic: (http://www.alaskafrontierarchery.com/Articles.html). For more discussion, Dr. Ed Ashby also has an interesting and exhaustively extensive article on the subject (http://tradgang.com/ashby/Momentum Kinetic Energy and Arrow Penetration.htm) you might want to check out (have your scientific calculator handy).
Perspective On Hunting Math
Regardless of how you crunch your numbers during preseason, you can't avoid the elements of chance during the actual hunt. Shooting a live animal in the woods is quite different than shooting a block of ballistics gel in a laboratory. In the field you'll encounter unpredictable and complex variables that limit any mathematical model to just a "best guess." If you consider that your arrow must arrive on target then pass through layers of hair, hide, muscles, bones (perhaps), and a host of other tissues.....AND that all of this is happening in an uncontrolled outdoor environment, it's pretty clear that the issue of hunting penetration cannot truly be distilled into a mathematical puzzle. As many experienced bow hunters can attest, just as it's possible to make mistakes and get lucky, it's also possible to do everything right and comeup empty handed. That's just part of the sport. However, with good equipment, good technique, smart planning, and some goodold common sense, you can surely tip the scales in your favor and maximize your chances of success in the field.
Jon Henry is an avid outdoorsman who enjoys both hunting and fishing. He has been shooting and competing in archery for almost 40 years, and began competitive archery in the NFAA at age 12 as a youth. He was a sponsored PAA pro archer for several years, and before that competed for 15 years in both the NFAA and NAA. Jon retired from competition about 8 years ago, due to a series of shoulder injuries that impacted my ability to sustain competitive performance.
Jon is in his mid 50's, and still very much enjoys shooting his bow and now crossbows as well. He is taking a great deal of his experience gained from building and tuning archery equipment and applying it to crossbow shooting, since they are very similar in many respects.
Jon's goal is to help as many new shooters gain a solid knowledge of their equipment as possible, so that we can continue to grow the sport of target shooting and hunting with a crossbow, until it becomes as popular as the other traditional forms of archery.
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