I have seen quite a few questions about the energy of an arrow at different ranges, so I decided to do a little research this morning with my setup and post the results for a comparison starting point for those of you as interested as I am in the physics of our sport. My bow is a Mathews Switchback, 30" draw, and set at peak draw weight of 69.5 lbs, 80% letoff. The arrows I used were my small game/target arrows: 27.75" Gold Tip XT Hunter, with FOB's (you can see them at www.starrflight.com), ASAT Camo arrow wraps, homemade glow stick lighted nocks, and Magnus Stinger 100 grain 4 blade broadheads, and they weigh in at 391 grains overall; and my elk/larger game arrows: Carbon Express Terminator Hunter, 31", with all the same parts, and these weigh in at 521 grains.

The formulas I used for the calculations are:
Momentum=Weight X Speed / 225218
Kinetic Energy=Weight X Speed X Speed / 450436

I included the KE calculations for the benefit of the bow manufacturers since they seem to love giving us these numbers. However, in the parts of physics that apply to us as bowhunters, the KE number is pretty much useless since it has no direction vector attached to the number. The important numbers for comparison that we should use is the momentum number, since this has a direction and is the force that the flesh and bone ofan animal must stop. The more that an arrow derives its momentum from mass versus speed, the better the arrow will retain its momentum down range as shown by the tables: the light arrow loses 29% of its power while the heavier arrow only loses 23%. (Note that the constants used in the calculations for KE and Momentum may or may not be the same as you have seen in other places, the difference comes from the rounding of the gravitational constant and makes very little difference in the end.)

I used the speed average of three shot groups. If I was unable to get three good readings, then I reshot the entire group. At 90 and 100 yards that became a bit of a challenge since I had no pin set up for that range (my pins are set at 30, 40, 50, 60, 80), but you can see in the photo below that I finally did pull off a good group at 100 yards (about 3.5"). You can also see in the other photo below what happens when you don't follow through at 100 yards...OOPS. At those super-extended ranges your form becomes critical. Amazingly, I pulled the arrow out, took the chrono apart, realigned all of the pieces, put it back together, and it worked just fine. It's a good thing that the circuit boards are all laying on the bottom of the unit and not standing vertically.

This table shows the results from my setup. The % Loss Column is the percentage change in momentum of the arrow from the initial launch. The 10 Yd Loss column is the percentage change in momentum from the previous yardage (i.e., loss between 60 and 70 yds). The Difference column is the percentage of momentum difference between the two arrows at the different ranges.

I use this information to help me choose between arrows for different game species. I look at the difference column and see that the heavier arrow packs 20% more momentum at 70 yards than the light arrow, and I want that extra amount of energy when taking on an elk, but I've decided that I'll take the trajectory advantages of the lighter arrow for smaller game, like deer. What is the magic minimum number or magic maximum yardage that an arrow will harvest an animal...that is purely a personal choice that you'll never be able to get accurate information about due to the myriad of variables.

I can say that these two combinations have harvested many critters for me in the past, so for my hunting, I like the way these perform. But I will always look at the physics of my bow/arrow/broadhead combination before I head out into the woods. The choices I make are ones that I have to live with as a hunter, and I want to do my best to use the most appropriate equipment I have for the animal I am after. Will I ever shoot 100 yards at an animal, NO, but if I shoot at 20 and have the animal stop broadside at 105, you can bet that I can and will put a second one in the boilermaker. The best thing about the long-range practice, 80-100 yards, is that it really does make a 60 yard or less shot a simple little chip shot.

Thebest way to use this information is to perform your own tests, but if you have a bow with an IBO speed that is somewhere around the same as the Switchback that I used to shoot this test (IBO of 315 advertised, but never seen), then you can be reasonably sure that your numbers would come out close to the same. Once the arrow leaves the bow at a set speed physics takes over from there and the type of bow you're holding doesn’t matter.


Gold Tip XT Hunter 391 Grains

YardsSpeedMomentum KE% Loss10 yd Loss

02970.515676.570.00%0.00%
102960.513976.050.34%0.34%
202930.508774.521.35%1.01%
302880.500072.003.03%1.71%
402760.479266.127.07%4.17%
502640.458360.5011.11%4.35%
602530.439255.5614.81%4.17%
702410.418450.4218.86%4.74%
802300.399345.9222.56%4.56%
902190.380241.6326.26%4.78%
1002100.364638.2829.29%4.11%


Carbon Express Terminator Hunter 521 grains

YardsSpeedMomentum KE% Loss10 yd LossDifference

02590.599177.590.00%0.00%16.20%
102560.592275.801.16%1.16%15.24%
202540.587674.621.93%0.78%15.51%
302470.571470.574.63%2.76%14.28%
402390.552966.077.72%3.24%15.39%
502320.536762.2610.42%2.93%17.10%
602250.520558.5613.13%3.02%18.50%
702180.504354.9715.83%3.11%20.53%
802100.485851.0118.92%3.67%21.66%
902040.471948.1421.24%2.86%24.12%
1001990.460345.8023.17%2.45%26.27%