Momentum

[buckskin73]

I have read many post and agrued myself, the point of Kinetic energy being a better numerical representation of penetration than momentum. This last year I did a little experimenting during deer season. I had switched to carbon arrows which gave me almost identical KE and a little less momentum ( I have the number down somewhere if anyone is interested) than my trusty aluminums. I was shooting thunderhead 100, 28 inch CX 3D selects. The first deer I shot was a large doe. She was quartering away at 18 yards. the arrow entered a little to far forward and exited the far shoulder. From the angle of the shot and portion of arrow I found I can only speculate that the arrow must have stopped somewhere in the opposite shoulder. I do not take any pride in loosing a deer and I am embarrassed. It began to rain and the VERY POOR blood trail I had was lost. I returned the next day and look again. I never recovered the deer.

Disgusted with the poor penetration I switched back to my aluminums. Now mind you, identical KE and a more momentum. I had a shot a little buck with 2213' s and the same broadheads ( thunderhead 100). The arrow went through the opposite side shoulder. It passed through the large bone right where it joins the shoulder. While this again was not an ideal shot, the arrow passed completely through and stuck in the ground. The deer went about 50 yards. I thought about this all year and ended up killing another small buck with my bow. Complete pass through with my 2213' s.

While this is not a scientific test and under tight controlls, this was a practical application for me. I have come to the following conclusion.

Momentum and KE depend on the same variables, Mass and Velocity. KE is mass x velocity x velocity x 1/2. Momentum is mass x velocity. Since kenetic energy increases exponentialy as velocity increases, there could be a slight misrepresentation of actual penetration. Momentum is actually a vector. It is not simply a number. It is a number with a direction. As the arrow penetrates the deer, momentum is transfered to the deer. KE is afffected by friction as well as a transfer of energy. Since the friction can vary depending on the shot placement, angle on entry, surface of the arrow, etc, I don' t see how we can correlate KE and penetration. From my experience I think momentum might serve as a better tool to evaluate potential penetration.

I know this is opposite of what I argued last year, but I am big enough to admit, I could possible, sometimes, everyonce in a while, if the planets are aligned corectly, be wrong.

I would like to know if anyone else has some practical applications. Maybe we could come up with a test.

[mez]

Go over to the bowhunting forum and pull up the post " Speed is all you need" there are about 150 responses and some pretty good math and physics.

[Arthur P]

I' d say you' re right. Momentum should be considered more of a factor in penetration than it is. It darn sure shouldn' t be totally dismissed like a lot of people do.

Say someone' s got a rig that shoots a 350 gn arrow, 300 fps. He' s getting 70 ft lbs of energy and .4655 pound-seconds of momentum. Another guy is shooting a 700 gn arrow out of a longbow at 150 fps. He' s also getting .4655 lb-secs momentum, but only 35 ft lbs of energy. Both setups have proven in the field they are capable of poking an arrow clean thru a deer. One arrow carries twice the KE and twice the speed of the other. The only common factor is the momentum.

To get that 700 grain arrow up to 70 ft lbs, it has to be ripping along at 212 fps. A whopping 62 fps more than the longbow is flinging it. At that speed, momentum has increased to .6580 lb-secs. Increasing speed 29% also increased momentum 29%. At the same time, increasing speed by 29% increased KE a full 100%.

KE is the popular number to look at because of the popularity of light, high speed arrows. It' s real easy to get a high KE figure with light arrows, but very hard to get high momentum figures with light arrows. To get that 350 grain arrow up to .6580 lb-secs, you' d have to jack the speed up to 424 fps and KE up to 140 ft lbs. Again, that' s a 29% increase in momentum for a 29% increase in speed and 100% increase in KE.

Since I' m kinda lazy, I like getting my momentum the easy way.

[buckskin73]

Very true Arthur P. LIke you said, it is very popluar to consider KE as the principle factor in penetration. I use to do the same thing. You hit the nail on the head with your observation. Speed affects KE exponential. For example, a increase in speed of only 25% will double the KE. While a 25% increase in speed only affects momentum by 25%.

I think we can all agree that a light fast arrow is not recommended for maximum penetration. If you are going to hunt Cape Buffalo with a bow (psychological evaluation might be need) you will be instructed to shoot a high poundage bow and a HEAVY HEAVY HEAVY arrow. Now, if KE is the only factor governing penentration then speed would be the ultimate factor with a moderately weighted arrow.

Has there ever been a study done with actual numbers. If not I would like some suggestion on how to do a test. Maybe ballistic gelatin could be used. Varying KE and momentum setups and groups of 3 arrows per set up could be used. 3 arrows of each setup could be shot into fresh ballistic gelation. Each new set up would require a new block of ballistic gelatin. The average penetration of the 3 arrows could be compared with KE and momentum. Maybe we could see a trend and answer the question once and for all.

Any ideas?

[bigcountry25]

How do you figure momentum????

[Orions_Bow]

I think both have positives & negatives when it comes to trying to figure out how much penetration we will get. I think a good general rule from my experience has been that arrows that fall within the 400-450 grain range seem to perform better. They are not the fastest nor are they the slowest. just a great mixture of speed & weight. I will say this though - a 2315 with a 125 grain head is a lethal combo out of any bow that it spines correct for!

From my experience I also have noticed that with any given shaft a heavier tip like a 125 grain tip really seems to penetrate a lot better than a 100 grain tip. with all else being equal the amount of speed given up isn' t very much at all but that heavier tip just seems to really hit much harder.

which is more important? heck who really knows! They both have merit & should be considered.

[Trushot_archer]

I' ll be doing the same kind of experiment this season.

Arrow 1. Carbon w/ 100gr. head @415 grains total
Arrow 2. 2512 xx78 w/125gr head @ 525 grains total

I' ve got a feeling I' ll have the same conclusion though.