Since KE is a function of velocity, and velocity slows down range due to the drag forces, you'd have to calculate the drag coefficient of your arrow first. Then use the drag coefficient to determine the deceleration of the arrow down range. With that you can calculate the velocity of the arrow at any specific distance down range. Once you know the velocity of the arrow at a specific distance, you can calculate the KE at that distance.
The drag coefficient is the most difficult to calculate. You can do it using fluid dynamics, or you can do it with a wind tunnel and force gauges.
I know there are online calculators that will calculate the KE of an arrow as it leaves the bow, but I've never seen one that calculates the KE down range, probably do to the complicated math involved.
Suffice to say, the KE of any standard weight arrow drops off significantly after about 50 yards. Heavier arrows will retain more KE down range at the expense of trajectory, so yardage estimations becomes more critical for accuracy.
Personally, I think any shot on an elk beyond 60 yards is asking for trouble, regardless of how accurate you are at longer distances.
That is awesome! LOLOLOL
So informative you forkin forgot! LOLOLOL
“ So informative you forkin forgot! LOLOLOL”
Obviously, the conclusion he came to was “Damn! Forget the whole thing!”
So he did.
You probably don’t need to have your angry ex-girlfriend’s phone number memorized to know that she isn’t interested in your companionship….
Lose ten percent of your initial velocity and you've lost 19% of your KE at launch. (90% = .9. ... .9x.9 = .81. ...100%-81% = 19% loss.)
Lose 20% of your initial velocity and you have lost 36%.
If 100% of the energy/momentum stored in the arrow gets pushed through the tip your results will be massively different than even 95%. So while math may or may not exactly explain it, personal experience has been such that I would never worry about penetration at longer distances with a full length arrow. I would worry about the time it takes the arrow to get there, and the other myriad of variables that can change in a long shot, but penetration with a "normal hunting weight arrow" shot out of a reasonably average compound is not one of them.
While it is true that the sample size is much smaller, my experience on penetration at 45-75 yards has been better than 0-45 yards. While I am not arguing that penetration is better at longer distances, it has led me to believe that it is not a worry. I have also only every taken long shots in absolutely perfect conditions. (wind etc.) A small gust of wind pushing the back end of an arrow over or imparting any broadside velocity to the arrow will significantly decrease penetration. That can happen at 20 yards. I've never had it happen on a far shot because I've never taken a far shot with any wind.
Truth, in my experience! It always amazes me at the amount of penetration that I get on longer shots.
If you really want to drive yourself crazy, look into articles that discuss broad head Mechanical Advantage (MA) and Tissue Penetrating Index (TPI) combined with KE and momentum to determine the true penetrating ability of an arrow.
Like some of you, I was obsessed with understanding the physics of arrow flight, energy, and penetration early in my archery career. And also like some, I concluded that arrow flight was the most important factor. I saw this over and over when I competed in archery tournaments. Back then, there was a 280 ft/sec speed limit at the 3D shoots. Many of us were shooting the exact same bows, arrows, draw lengths, and poundage, at the max speed... The only variable was how well tuned each shooter and his bow was. If you watched closely, you could see which guys were shooting darts versus the guys with less than perfect arrow flight. Invariably, the arrows with the best flight out-penetrated the others...sometimes by a considerable amount.
Upon looking at the hole through the lungs of the bull and looking at my arrow fleching floating in the water, I concluded that the first arrow passed through the bull and landed on the other side of the elk in the water. The second arrow of course didn't make contact with anything except a stick and the water and the third arrow punctured the heart and the broadhead was just below the hide on the oppossite side front shoulder. So a 375 grain arrow leaving the bow at 304 fps will pass though an elk at 70 yards no problem. It also will burry itself up to the fletching on a quartering away shot after piercing the heart.
Both momentum and KE are a combination of mass and velocity, but KE depends on the square of velocity, so faster is more impressive.
And as noted above, 'penetration' depends on other factors as well. I've yet to see an equation that takes all factors into account and _predicts_ penetration.
My 56# Habu hybrid triple carbon longbow shoots a 565 grain arrow 190 FPS. I have a 31” draw…. I don’t think anyone would doubt the capability of that setup but in comparison to my compound it’s only producing 45 KE ft/lbs and .45 slug at the bow.
I realize with my draw length my numbers are high but it still makes for a good comparison and highlights the fact that modern compounds way more capable than needed.
This is the first time I’ve looked at these numbers in year and to the point others made I think tuning and working on a torque free grip to ensure perfect arrow flight is way more important than the other numbers.
One more thing I like to do is use the stiffest arrow possible for my compound, while still getting a perfect tune, to reduce arrow flex at impact. Not sure if it helps but it seems like it should. I yet to find an arrow that’s too stiff to tune so it also comes down to a balance between spine and total arrow weight.
Shoot a PSE and welcome to the wild side.
I wonder how far a 500 grain arrow needs to go to scrub from 280 all the way down to 165 feeps???
And I agree that an arrow fully settled in flight will outpenetrate one that’s a lot faster, but still snaking and flying cock-eyed from a poor tune.
Also agree that a stiffer shaft should out-pen a flexier one because arrows flex twice on every shot - at the beginning and the end; flexing can store some energy on launch (still less efficient than zero flex) but flex robs and misdirects “energy” on impact. Bad Juju.
But not as bad as bad Tune….
But even a straight-fletched, 2” vane creates a huge amount of drag compared to a bare shaft; plenty enough that Todd was able to put a relatively large (by modern standards) BH and shoot it through that B&C moose with just 2-inchers… and a #39 recurve…
Think about it…. At 180 fps, my arrows should strike a 60-yard target 1 second off the string… but it feels more like about 3 and is probably closer to 2 than 1.
Only in vacuum ;-)
Arrows slow down way faster than many seem to believe. And the lighter/faster they are, the faster they shed KE.
But I’ll tell ya…. Even though I would be surprised to learn that my #[email protected]“My DL” longbow is generating 175 feeps with a 480 grain arrow right off of the string… I’d sure as hell hate to be standing in the wrong spot when one of those missiles dropped out of the sky from 80 yards out. Even if I was #800 of rutted-up Angry.