Momentum vs Kinetic Energy

[High Tech Redneck]

Last summer I set up an ethafoam target and my chrono.  Using two different bows and 2 similar Carbon Express 200 arrows, one with a yellow (3 grain/in= +82.0 gr) tube insert, and identical 100 grain target points (Carbon Express points made to pull out of foam targets easier because they are larger dia. than arrow shaft). I shot the "light, fast" (378.6 gr) arrows @ 59# and the "slow, heavy" (464.3 gr) arrows @ 50.5# three times each at about 5 feet from the target and compared the penetration to Ke and Momentum.  I attempted to achieve the same momentum with both setups.  

Here are the results:
Slow Heavy: 207fps,207fps,208fps(Avg=207fps).  Penetration 15.25", 16", 15.5"(Avg penetration= 15.58").  Avg Ke=44.2 ftlb, Avg Mom= 0.427#sec.
Fast Light: 245fps,244fps,244fps(Avg=244fps).  Penetration 17.5"(with .25 additional penetration into backup ethafoam target not counted), 18.25",17" (Avg penetration= 17.58").  Avg Ke=50.1 ftlb, Avg Mom=0.410#sec.

Summary:
Fast Light= 12.9% more penetration.
Fast Light= 13.3% higher Ke.
Fast Light= 4.0% less Momentum.

Conclusion: Ke is a better predictor of penetration than Momentum in a uniform medium.

Note: Bow/Arrow combos were not paper tuned so close distance to target may have resulted in less than perfect arrow alignment with target. One would expect the higher poundage bow to have greater penetration as both setups yield essentially the same level of bow "efficiency" (ftlb/bow draw wt). Bottom line is Ke correlated almost perfectly with penetration while momentum actually showed a negative correlation!  Please explain, duplicate, or contradict.

[Todd Hathaway]

Hey, man,
You're like me, you gotta see it to believe it    ...and your conclusions concur with mine.

I actually went so far as to design an air cannon that would ensure the arrows hit exactly straight into the target. I used the exact shaft for all tests, and merely changed the weight of it by adding a cable to the inside.

Speed was varied by changing the amount of air pressure in the cannon.

My results showed clearly that KE is the better predictor of penetration. Note, that many who argue with this will think that I am saying a lighter arrow is better than a heavier one. That is something they are inferring and not anything I am implying. Most trad bows increase their KE with increased arrow weight, so heavier is better.

The only thing I didn't test was the bone cracking ability of momentum vs KE, which a Naval penetration expert told me might favor momentum.

Here is where I posted about it a while ago:
 http://***********.bowsite.com/tf/lw/thread2.cfm?forum=23&threadid=164533&messages=21&CATEGORY=5

[Jeff Strubberg]

I attempted to achieve the same momentum with both setups.

I'm confused.  The only way to keep momentum the same while changing weights is to vary either efficiency or the gross power you are putting behind the projectile.  Either would invalidate the test, as you would effectively be shooting the arrow from two different draw-weight bows....

KE is a better predictor of bow efficiency.  Momentum is a better predictor of penetration.

[Alex.B]

looks like a severe bout with cabin fever. Cold out there, Heh?

[Basic Instinct]

I have wondered about this for sometime myself. I think there is a happy medium in every setup. Where  too light of arrow will deprive you of needed KE and momentum. Too heavy of an arrow does the same thing. I Have found that with all of my setups, Taking deer,elk antelope with 55-60 lb bows at 28" draw, I really like the 515 to 550 gr arrows. They give me good speed yet still have enough weight, I have gotten good pass throughs on various ocassions on all the above animals I listed.

[Lefty]

I think one problem with your test is that it was only done at 5 feet.  The arrow is going to shed speed as the distance increases, but it retains the mass.  So at twenty yards the faster speed that aided in more penetration at close range will be shed, while the heavier slower arrow retained the mass and maintaining more pentration down range.  
  I wold like to see the same test performed at 15, 20, and 25 yards and compared those findings to your original findings.  My opinion is that the heavier arrow will out penentrate the lighter one as the distance increases.  If you really want to check that, set your chrono at 20 yards and shoot both setups through it and see how much speed you lose.

[Lefty]

Which ever camp you are in though, heavy and slow or light and fast, the best way to increase penetration is to have extremely well tune equipment and a very sharp broadhead!

[mmgrode]

Good test. Now test momentum with the same KE in both arrows. I think you will see the increased momentum will then increase your penetration drastically.  In addition, several things need to be taken into consideration here:
- arrow tuning: This could be huge! "Note: Bow/Arrow combos were not paper tuned so close distance to target may have resulted in less than perfect arrow alignment with target." Everything else being equal, poorly tuned arrows penetrate less than properly tuned ones, period.  
- the target media was consistent:  If we want to get great penetration on foam deer KE is great, however, we are hunters and we need to take into account variables; primarily bone structures of the animals we're after and the posibility of a less than perfect shot.
- By adding a weight tube to one you are affecting the FOC. The lighter arrow would then have a higher FOC than the heavier one.  
- Also, as hunters and not target shooters, broadheads are used.  Penetration can be drastically affected by this depending on the design and sharpness.
It would be interesting if you would try the test again with, say, a properly tuned 650 grain arrow out of the same bow as the 378 grain one.  In reality it is difficult to attain the same arrow heavier without affecting something.  Good thread!

[capt eddie]

You set up an unfair test with two differant weight bows. 9 lb is alot of differance.  Both arrows must be shot from the same bow to see the true differance.  This test is not proof of anything.  Switch bows and try again.

[Richie Nell]

Capt Eddie is exactly right.  You haven't proved anything with this experiment.  Shoot each arrow out of the same lb. bow.  

You are not testing the bow. The bow should be  one of the constants in the equation.  Not a variable.  The arrow and the results of the flung arrow is the experiment.

Get back to us.

[Richie Nell]

Shot out of the same bow, the heavy arrow you speak of will out penetrate the lighter arrow, without a doubt.  Especially 10 to 50 yards down range.

Try it.