Trad Gang
Main Boards => Dangerous Game => Topic started by: JAK on February 24, 2004, 02:46:00 PM
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My curiosity was piqued after reading so many posts about double shafting, 800-900 gr arrows and KE. I had a suspicion that some people did not appreciate that KE is a result of both Mass, and Velocity. It seems that many people are forgetting the velocity in that equation, and forgetting that for every set of bow setup criteria, there is a happy medium of velocity and mass that will produce the greatest KE. KE does translate directly into penetration power, provided it is the only variable. For example, with 2 identical arrows (to include broadheads), propelled from different bows (thus different KE, for no two bows will be absolutely identical), the one with greater KE will have better penetration. Fully realizing that this is a trad bow forum, my virtual test bow was a compound bow, simply because that was how the program was defaulted, which kept me from making user mistakes. This should not matter, as the physics of external ballistics is fully independent of the firing device. It only carries the energy imparted by that device, then becomes a function of friction and gravity.
The test bows characteristics are as foollows:
Draw weight, 60#
Draw length, 30"
There were 5 different arrow weights, complete, not just the shaft. For each weight (WT), I will list the time to target at 30 yards (TTT), speed (FPS), and kinetic energy at 30 yards (KE). The test broadhead was 3 point for purposes of forward air resistance.
WT: 800, TTT: .502, FPS: 185, KE: 57.29
WT: 724, TTT: .468, FPS: 199, KE: 59.73
WT: 637, TTT: .433, FPS: 216, KE: 61.48
WT: 544, TTT: .402, FPS: 234, KE: 60.96
WT: 438, TTT: .372, FPS: 255, KE: 57.21
Looking at the results, please notice the arrow with the greatest KE was the third, with a weight of 637. Also notice that the 438 gr arrow possessed fundamentally the same KE as the 800 gr, while reaching the target in about two-thirds of the time, with 50% greater speed. The 637 grain arrow represents the 'magic' combination of mass and velocity, and clearly beats the heavier and lighter arrows from this bow. This, of course, ignores the problem of spine, which would take a creative balance to both shaft weight, broadhead weight, and fletching/nock weight. Once an ideal arrow weight is determined, the spine would have to be worked around that.
Now realizing that many hunters will use heavier bows, the draw weight to get comparable performance from an 800 or 900 grain arrow would be prohibitively strong. I am guessing somewhere along the lines of 100#. I am just too lazy to calculate it right now.
As a final note, this is presented as raw information; hunt with what you are comfortable with. All of us are a tad supersticious, so if that 1000 grain arrow from a 45# bow is what works for you, and you kill game, by all means keep it up.
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I'm still running all this through my head as well--I've never had a hunt in the works that required me to do the math to make sure my equipment would do the job.
On the table you posted, I feel there is one thing missing--energy retained upon impact? It seems that the heavier arrow will retain more energy longer upon impact, thus improving penetration?
Chad
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Sorry about the double name thing, had some wierd thing going on with my email/password, anyway...
Actually retained energy and kinetic energy would be one in the same. Penetration relies on an entirely different equation, considering some similar variables such as front cross sectional area, broadhead cutting geometry, and the flesh that the arrow is passing through. Kinetic energy could be thought of as a representation of inertia. While an object may possess kinetic energy (continuation of movement), or static energy (resistance to movement), it may only be under one type at a time, for our purposes. Thus as the static energy is lowered by the release of the arrow, the bow imparts kinetic energy upon the arrow. Kinetic energy is retained energy, they are in fact one in the same. The only thing that acts upon kinetic energy is friction. In bowhunting, this comes in the form of air, gravity, and the game when it is hit. Once the arrow hits the game, the kinetic energy is absorbed by the target. So, obviously, the higher the kinetic energy, the more is forced to be absorbed by the target.
This is one reason for super skinny-ultra-modern shafts. By reducing the front cross section, more energy is concentrated in a smaller area. Same reasons the broadheads with a larger cutting circle do not penetrate as far as a smaller head. This is why nails tend to work so well...
Anyway, like you said, never had to compute math in a tree stand. If it kills game, it works fine enough for a hunter. I guess physics in one reason we shoot trad.
I just think that poeple tend to forget about the "happy medium" of speed and arrow mass, swaying too far in either direction, by both trad, and modern archers. This stuff is relatively simple physics, I'll try to dig up the formulae if anyone is interested. Although, I guess I'd be more inclined to shoot instead of do book work.
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I've never had a hunt in the works that required me to do the math to make sure my equipment would do the job.
In the WORKS--lol. What I meant by that is I've never been on a hunt where I had to tweak my gear, or change it, to be certain it would do the job. Now I do--I'm building up to an Austrailian buffalo hunt in the future, and that is why all this stuff is becoming more important to me.
I understand on the happy medium, and it makes sense. The devil is finding the time to figure out what it is with your own particular set-up. I appreciate the information!
Chad
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http://home.att.net/~sajackson/archery.html
This will get you started. There are a number of ballistic software programs out there as well that are much better, and give mich better information, including sight tapes (actually a printout you could put on your bow), all sorts of stuff. Most importantly, they will give very detailed ballistic info.
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Hmm, me thinks Rick might have something to say when he gets back on this one.
JAK-one thing you overlook in your calculations is the fact of the major topic of "discussion" (read disagreement) on this issue. The heavy arrow guys are NOT KE guys, they are MOMENTUM guys. From physics, the equations used to calculate both KE and momentum take into account both mass and velocity. The difference is that KE squares the velocity term, therefore over emphasizing it, whereas momentum does not. The end effect is that a KE based calculation stresses velocity to a great extent over mass and momentum does not. In other words, KE predicts that a light weight projectile moving very fast will hit harder than a heavy one moving slowly. My personal take on this includes two things:
1. A person can actually MEASURE momentum-when an object hits something, the force, in ft lbs or whatever you use for units is the actual force exerted. KE is entirely calculational-there is not a physical method to measure "stored energy".
2. Several people, lately, including Rick, Cory, Monty etc. have taken Australian buffalo with relatively heavy arrows from trad bows, I believe the actual calculated KE of Monty's setup was real low, but he shot thru the animal twice.
I agree that shooting a "900 grain arrow from a 45 lb bow" would be ridiculous, shooting a 900-1000 grainer from a 75-85 lb bow, however, is close to like 12 gr/lb or so-a quite reasonable arrow wt/lb of bow wt.
Ryan
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That's the word I was looking for earlier--it seems that is what these discussions usually boil down to is one vs. the other, and/or the significance of each. I've never paid enough attention to the discussions to know a whole lot about either one--hope Rick and Cory get back into this soon. Ryan, do you know the formula for momentum off-hand?
Chad
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Hookus, I'm not sure where you got your chart but a traditional bow, KE will go up with arrow weight FOREVER. Granted it gets small as arrow weight gets into the unreasonable range but it still goes up. If in testing a drop in KE is seen, it is because of tuning (shelf/rest contact), not arrow weight. In a compound I'd suspect increased frictional loads on the cables and cams could cause a KE drop at heavier arrow weights. Drop me an email, I can send you KE graphs done by Mr. Mulaney on trad bows....O.L.
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For interesting posts on momentum versus KE etc. try this thread on Ozbow:
Momentum Theory (http://www.ozbow.net/phpbb2/viewtopic.php?t=826)
Erron
www.ozbow.net (http://www.ozbow.net)
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Chad,
Stick to what Woody is telling ya!
Can't wait till he see's this.
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Let me work out the momentum, I'll post the results when I get them, I misinterpreted retained energy in that post.
On a seperate note, it is impossible for KE to go up forever on ANY projectile, I would like to see the charts. [Assuming no other variable changed except for mass, which will have an inverse relationship to velocity for 2 different arrows shot from the same bow] This is because velocity is squared in the equation. That would mean the effect of velocity change will produce a non-linear result once squared. Since velocity is squared, and mass is not, this would invalidate the theory that KE would continue to rise. I would have to see the chart and formulae that were used, but right now, I cannot picture any situation that would be true, without increasing the draw weight accordingly.
KE will be lower from a trad bow, yes, because they will never approach the velocity from a wheel-bow. But the external ballistic curve would have generally the same curvature, always and forever. External ballistics is external ballistics, once the object is not longer under power by the bow or launcher, EVERYTHING on earth follows the same laws of physics, from a football, to a bullet, to an airplane; the formulae are fundamentally the same.
Gentlemen, 1000 grains from 45# was a joke. I also beleive that the hunter should always go with what they are comfortable with, and has worked for them, as I stated in the original post.
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JAK- as was my using in in the reply :)
Someone correct me if I'm wrong, but I seem to remember that Monty's calculated KE was somewhere around 40 for his Buff setup? Worked OK though.
All this math brings back those bad undergraduate memories-year of physics, year of calculus, linear algebra, quantum mechanics, kinetics and thermodynamics---too much math for a pot-boiler!
Ryan
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Ryan-
I humbly concede your point.
Momentum basically uses MV, and KE uses M(V^2). That was a pretty basic point for me to overlook. Perhaps it is because I see most people talking about KE, and perhaps not realizing that it is different from momentum, which is probably what they are referring to. I suppose KE would be more valuable to an object such as a bullet, which by having low momentum, and high KE, would most effectively impart its energy to its target.
You could, I think, say that the amount of energy transferred to the target is a "vector" between KE and momentum. The lower the momentum, and higher the KE, the faster the energy is absorbed by the target. Valuable, I suppose in shooting, but less valuable in bowhunting, which relies on cutting ability of the broadhead. Greater momentum means longer cuts.
Ryan, thanks for correcting me, and I apologize for any confusion.
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I just read Dennis' post on Ozbow. Interesting. The only point I disagree with him on is where he states that 2 different weight arrows travelling at the same speed will have much the same trajectory, since gravity is acting solely and directly upon mass. And perhaps my post agrees with both Stickbow Hunter and Dennis on there, in that they both describe a happy medium of velocity and mass.
Also, I just realized that momentum as well will not indefinitely increase either, since mass will inversely relate to velocity from a given bow. It may level off at very high poundages or unrealistic arrow weights, but it will level off and decline eventually, though perhaps not within the bounds of normal equipment. It is also interesting that Dennis and I use the same bullet reference.
My next thoguht would be this: How much difference does a measure of mementum make? Obviously higher is better, but when would you cease to get gains great eneough to outweigh increases in speed? Again, brings me to my Happy Medium stance. From my first post, the 800 grain arrow had .6448 or so pounds/sec of momentum. The 637 grain arrow had .5978, giving a difference of only .047 lbs/sec, or 7.25% less. How much momentum is this really? To compare it directly to distance of penetration, if the first arrow penetrated 20 inches, the second would penetrate 18.55 in excatly the same medium, provided the only variable that changed was momentum. This is a loss of only 1.45 inches over 20, less than 1 broadhead length.
The 800 grain arrow had a speed of about 185 ft/sec, and the 637 had 216, or 17% greater.
So, you end up with an arrow that has 17% greater speed, and only 7.25% less momentum. When would you make this trade off? This is what I mean by a magic combination.
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JAK-FYI I think Dave Holt was instrumental in introducing KE into "bowtalk" in BH magazine. Dad and I had the same discussion with him a couple of years ago.
Here is another variable to throw in-just in case there arent enough already!
You'd have to check someone like Norb Mullaney or another bowtester for exact details, but I know, qualitatively, that a recurve bow loses alot of added efficiency per pound as you go higher in overall wt. In other words, a 10% increase to a 50lb bow gives a much larger increase in overall "power" or engergy transfer to the arrow than a 10% increase to an 80lb bow. I dont know the quantitative math behind this, but I've seen several tests to show it. I think I remember seeing that the efficiency per % wt gain tapers off dramatically after 65lbs.
just food for thought
Ryan
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Oh I just love these discussions! ;)
Many of the KE/Momentum discussions folks get into lose sight of the most BASIC physics. Many of the published studies are looking for ways to increase penetration from "A" bow. For all practical purposes, the KE from that bow is a "constant" so from that standpoint, KE is a mute point. Yes, as arrow weight goes up, efficiency does go up as does KE but percentage wise it is small. So, if KE is constant, we can't do a thing about it leaving us only with velocity we can change. The only way we can change that for "A" bow is go up or down in arrow weight.
KE is the basic unit of power available. You can't have velocity without some KE behind it, nor can you have momentum without KE in the first place. So KE is important if your goal is to get the most of either one.
One fellow was on the right track..With KE being constant for practical purposes, our only choice is to decide if I want to use that KE fast, or use it slow. Using the KE available over a longer period of time will allow more work to be done. It takes 4 times the energy to do the same work twice as fast. Want more penetration??....Spread the KE out over time by lowering velocity and the only way you can do that out of "A" bow is go up in arrow weight. Why do 3:1 heads penetrate better then a 2:1 of the same width?? TIME... The 3:1 does the same work in a longer distance. With a constant velocity, cutting over a longer distance is time.. The drag on the arrow goes up or down with the square of the velocity..Again it's TIME. Use the KE over a longer time is the key.
Here are links to a couple of scanned in charts Mr. Mulaney did on a trad bow. One is velocity/arrow weight the other is KE/arrow weight. You'll see all the way to roughly 14gr/lb KE goes up as does efficiency. These were done on a fairly good bow but are typical for all trad bows as the physics does not change....O.L.
(http://www.bowmaker.net/images/n28in10.jpg)
(http://www.bowmaker.net/images/n28in12.jpg)
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Something else to throw into the pot. I was sent some information last night that was very interesting (Woody, jump in any time!). I'm still getting a grasp on all of this (I'm not anywhere near a mathmetician or physicist--I don't even play one on TV!). Anyhow, one very important point that was brought to my attention was that these formulas, as best as I can tell, are based on the arrow's performance approximately 3' in front of the bow--where most folks set the chronograph, not 15+ yds where the impact generally occurs. I don't have any intentions of shoot a water buffalo from 3 feet! I figure the Pucker Factor (whole different scale there) will be off the charts for me at 15 yds! But anyway.......
The charts I was sent show arrow velocity from 15 to 35 yds, in 5 yd increments. Very interesting information to say the least. The arrow weights don't go up to the range I am considering for the hunt, but do show that heavier arrows retain more energy downrange, where it bleeds off the lighter ones faster, with the actual momentum (in slug feet) of the heaviest arrow being much higher than the lightest at 35 yds.
Finally, just for giggles, I did the KE and Slug Feet formulas for my current bow, and (based on the bow I have now) what I expect to get from the bow I have ordered for the hunt. On my current bow:
[email protected], 630 grain arrow, 187 fps: KE= 49, SF=.52
85@30, 850 grain arrow, 180 fps: KE= 61, SF=.68
What does that really mean? Danged if I know. I should know more when I get back with my buff though. lol
Chad
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Chad, EXACTLY! Drag goes up with the square of the velocity..The light/fast bleeds more energy faster. Again doing the same work faster requires more energy. It will do the same in meat too.
Interesting numbers, draw weight to draw weight, Ke to Ke, and slugs to slugs, between the 2 bows, all those are within 20-24% of each other. You can't get slugs without horsepower....O.L.
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I understand the theory behind broadhead cutting geometry, it is basically an inclined plane; the same principles apply, i.e. working over time. I don't understand how that correlates to dispersion of KE, however. Take for example driving a nail. I weigh about 190 lbs, and if I press all my body weight on a nail, it will not drive very far. By using a hammer, however, even though it is lighter, and actually may have less KE than my body, it will drive the nail very fast. I would presume by compressing the KE into a SMALLER time.
I think it has more to do with how you would quantify work. Interestingly, if you take the example of someone diving into water, a dive will go deeper than a belly flop. While the dive is releasing energy slower (upon penetration), than the belly flop, this has more to do with how concentrated the force if across a surface area. The KE is simply being released across many points simultaneously.
I fail to see how a slower object will generate more work by lengthening time, because KE is directly related to time, as is momentum. The time you want to increase is penetration time for a given arrow, not flight time. A slower flight time will NOT increase the work being done. I am pretty sure you were talking about time it takes to penetrate the object, if I read correctly. I think that broadhead geometry is the most crucial "point" in attaining good penetration, and that you can get passthroughs on even thick game without a telephone pole. Again, I think that the advantages of a pefect balance between all elements, cutting surface, speed, and weight, would be best.
Of course, KE and Momentum are both two different types of energy, though closely related. That is KE representing the potential, and momentum measureing how the arrow uses that potential.
Once again, if you are happy with what you shoot, good on you.
I won't even touch bow effeciency, for the intents of this discussion, the arrow has already left the bow, so all we are concerned with is the amount of energy imparted to the arrow, and the physical forces acting upon it. You are right though, I remember reading the same thing about effeciency declining with bow weight. I seem to remember reading somewhere (the where escapes me) that about 60-65# is the highest you go before getting very sharp diminishing returns, that stuck with me.
KE is directly related to momentum though, as is mass (which is an element of both), and you can derive a formula for momentum from using KE as one of the variables.
You know the amazing thing is, American Indians killed buffalo with self bows and flint or bone heads. I don't think the holy man even knew about 3:1, KE, momentum, and ballistics, and I seriously doubt that any of their bows surpassed 45# or so in draw. I think that is amazing, and it is a feat I certainly would not want to try.
All kidding aside, I think that a balance between elements is the best bet rather than swingimg too far to either side (KE or Momentum). You will probably end up with a bow that is easier to tune very well, and a better performing arrow. And remember as well, if there was a perfect solution, we would all be shooting about the exact same thing.
Wow, imagine doing a physics thesis on Arrow Ballistics, too bad I don't go to school
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O.L-I agree with most of your assessment, the difference comes in the fact that KE and MOM, while related, are arrived at differently.
Here is a force/time definition I copied to illustrate my point:
Impulse and Momentum
Momentum
The momentum of a body is equal to its mass multiplied by its velocity.
Momentum is measured in N s. Note that momentum is a vector quantity, in other words the direction is important.
Impulse
The impulse of a force (also measured in N s) is equal to the change in momentum of a body which a force causes. This is also equal to the magnitude of the force multiplied by the length of time the force is applied.
Impulse = change in momentum = force x time
If we assume the "impulse" is the complex factors involved with tissue/bone etc. retarding penetration then momentum, not KE, would be the energy vs. time paramater to use.
As you noted above this is all a moot point anyhow, a good academic discussion at best, the important thing is shooting the arrow through something, and we have precedence for that :)
Ryan
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LBR-
Out of cuiosity run the numbers for the 630 grain arrow from the 85 pound bow, and see what comes up, that would be interesting. My guess would be something that shoots faster than both, but with momentum between the two.
Man, 2 people posted in the time it took me to post once...
Completely understand about light/fast taking more energy to maintain its physical properties, O.L. never doubted that. The amount of energy needed for velocity is exponentially related. Just a tad more speed takes a lot mroe energy.
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Jak, Agreed. Problem is for a given bow, you don't have more energy. You got what you got with out going to a different bow that is either more efficient or more draw weight. To shoot an arrow at 300fps requires 4 times more KE then it does to shoot it at 150 fps....O.L.
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LOL!
The things we can get wound up in between hunting seasons! I've never had an animal complain yet.
Good luck all, and I wish, I wish, I wish I didnt have to wait till Sept to hunt again----Them carps better look out in May!
Ryan
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There was a good article in one bowhunting magazine this month about year round hunting. Of course, most of us can't afford just to jaunt up and hunt black bear, mountain lion, or moose...
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I should clarify, the 85@30 is what I have on order, so I had to make an educated guess at the fps on it, based on the bow I have now (same style and length). By the same token, I can't shoot the 630 grain arrows through it to see how many fps they will get. They wouldn't fly worth squat anyway........
I don't mean to stir the pot over what is right and what is not, I'm more looking to compare what has worked to what I plan on using. Very interesting discussion nontheless.
Chad
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I agree OL, but who has only one bow? YOU of all people.
To make maters more interesting there is often an I-only-have-one-arm-thing going on here where people argue from the fixed point of their strength at any given time, while ilustrating many different outcomes possible from a universe of potential bows traditional or not.
The Momentum/KE thing goes way back past Holt, and eventualy past archery into discusions relative to various external ballistic in firearms. I'm sure it was discussed in earlier archery times also, though I haven't ripped over it. With firearms we had the mamoth black powder age, vs shooting Big Five witht he earliest smokeless military lightweights. Then we hade the Nitros, and after them the magnums, and the beat goes on. It's a complex subject since impact energy is far moreso the killing force with guns than arrows, however at a certain point they become super charged field points dependant for killing power on penetration type drill wounds rather than nock down power.
These arguments got rolled over without reason into archery where the real truth needs to model the cutting power of the whole arrow, at least as much as any KE or Momentum. You can't go to ultimate KE arrows without loosing some column strength also.
The facts are that there isn't any clean comparison between KE or momentum, neither fully encapsulates the event that will take place when whatever arrow impacts whatever structure. It all starts with field testing, from which an engineer, not a Physicist will have to work backwards plunking in whatever values make retrospective sense in whatever situations.
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So my math teacher was right,you do actually find a use for this stuff. :)
I think the important thing to remember is that you match your equipment to the game.Ol is right,by design a particular bow will only produce so much energy.What we do with that is up to us.Bow efficency,how much energy is transferred to the arrow,goes up with arrow weight.If I'm heading out after mule deer or pronghorn out west I would opt for a middle of the road arrow that gives reasonable trajectory and still maintains enough energy down range to do the job.
If I'm like Chad and fixin to shoot a big tough critter,I want a heavy arrow to maximize penetration.I tend to think of momentum as the ability to continue forward when meeting resistance.A heavier arrow with more momentum will retain more energy and bleed that energy off slower than a lighter arrow with less momentum.I think there is a reason some relatively low KE set ups achieve good penetration in game.Heavy arrows with a lot of momentum and a low friction 2 balde broadhead.I think that was the consensus of Ashbys study.
I read the ozbow thread on momemtum.The idea that KE is the total amount of energy in all directions and momentum the linear or straightline energy is interesting.I'm not sure about that idea, it's beyond my depth of physics.
Of course there is one thing we can all agree on,if that arrow is'nt put in the right place it won't matter. :thumbsup:
CB
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you got it....billy...marco #78 ...lets go shoot
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I have noticed one thing that all of the KE vs Mommentum threads have in common, they give me a headache. I purposely try to avoid thinking about it at all costs, since it is just numbers and dosn't really tell you how well your arrow is going to penetrate. Yes, I know that in theory, two otherwise identical arrows,blah, blah blah. Did you ever try to make two identical arrows that only vary by weight, or spine? Human beings love to have things in black and white in front of them, so they can say, "ah, this is better", but animals are not impressed with numbers. Montys 1500 grain buff arrows, do really well on penetration even though they have a KE of only 43, but he uses long narrow heads and the shafts are very small diameter. The compound guys are very obsessed with the KE numbers and tend to use to light of arrows to get that number up. IMHO 900-1000 grains is a good compromise for most guys going after buffalo, if well tuned, it will give plenty of penetration and the tradjectory is not severe, as long as you get enough experience with it. You won't be taking long range shots at unwounded buffalo anyway. Rick
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Kinetic Energy and Momentum are two distinct and separate units of measure.
KE does not apply to penetration.
It is illogical to use KE as an indicator of bow/arrow performance on an animal.
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Bogsucker, OK, can I film you going after a big buff with a 40 pound bow?? From a distance of course! ;) ....O.L.
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NO. The issue being Momentum vs Kinetic Energy, not 40lb vs 50 lb vs 70 lb bow.
Which would you rather shoot a big buff with, a heavy 70 ft-lb arrow or light 70 ft-lb arrow?
The heavy arrow having much more momentum than the lighter arrow.
KE just doesn't apply to penetration.
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Bogsucker, I guess I've been shoting the wrong bows. I put ft/lbs into mine when I pull them back and get ft/lbs out when I turn it loose. That is all any bow does. What you do with those ft/lb is your choice. KE does matter, no KE, no momentum. More KE you have, the more momentum you can get....O.L.
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No you've just been using the wrong units of measure. Momentum does not come from Kinetic Energy. You cannot store Kinetic Energy in a bow you may store Potential Energy but that is measured in different units (lbs). Kinetic Energy does not correlate with penetration, Momentum does. This is a matter of physics not opinion.
The use of the term KE (Kinetic Energy) to indicate lethality on game is simply not logical.
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70 lb bow 350gr arrow 300+fps 70 ft-lb KE .47 ft-lb-sec Momentum
60lb bow 540 gr arrow 230 fps 63 ft-lb KE .55 ft-lb-sec Momentum
This is very close to IBO and AMO ratings of several popular compound bows.
I haven't seen any IBO and AMO ratings for trad bows lately.
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O.L.,
Actually I'd be honored to have you film me shooting a big buff with a 40lb bow. We'd just have to find someone to sponsor the event as I'm not financially able to hunt the Dark Continent.
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Ya' know, every time I see one of these threads I think about the blind men looking at the elephant and all getting a different idea of what the animal is. You need to see the whole picture. Energy is energy, we give it different names based on where it is and how it is used. We measure it in different ways for the same reasons.
When you draw back your bow the energy in the limbs is called potential energy. When you release the bow, the energy is now used to to move things and it is then called kinetic energy. The amount of kinetic energy is normally measured at the moment the arrow leaves the bow. The amount of kinetic energy remaining in the arrow at any point in time between the bow and the target gets smaller with every second of flight, which brings us to momentum, which I agree is a better number to determine what you can expect for penetration. Momentum is a better way of expressing the remaining energy in the arrow, especially since the light arrow looses energy much faster than a heavy arrow and it also cannot caputre or store as much energy as a heavier arrow. That is why you get more noise with a lighter arrow off the same bow than you do with a heavier arrow.
So, the energy described as KE is still there in the arrow, it is the energy that fuels the Momentum of the arrow, if you will.
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Again, Kinetic Energy (KE) and Momentum are two distinct and separate functions of weight and velocity(speed) and they are not linearly proportional to each other. The energy stored in a bow is not Kinetic Energy. Momentum does not come from Kinetic Energy it is a distinct and separate function. Momentum is a much closer measure of penetration than KE.
I've had enough. Sorry if I've upset anyone but KE don't mean squat.
No, I'm not done (sorry again). Question: Why should I use the unit of measure called Kinetic Energy to indicate performance of a projectile?
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Bogsucker, No one ever said a bow stored KE, PE is measured in ftlb also. Get your momentum from where ever you want. I'll shoot my 12-13 grain/lb and get my MO from the KE......O.L.
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Now your gettin close, however if you were to shoot a 7-8 gr/lb arrow out of that same bow you'd have more kinetic energy but less momentum thereby disproving that momentum comes from the kinetic energy!
May we agree that generally a "heavy" arrow is better for penetration than a "lighter" arrow out of the same bow?
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Bogsucker, You are wrong. Trad bows don't work that way. The heavier the arrow the more KE ( MO too) and more efficient the bow is. Look at the graphs on page 1, those are typical for trad bows...O.L.
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WT: 800, TTT: .502, FPS: 185, KE: 60.81 MO: 0.66
WT: 724, TTT: .468, FPS: 199, KE: 63.68 MO: 0.64
WT: 637, TTT: .433, FPS: 216, KE: 66.01 MO: 0.61
WT: 544, TTT: .402, FPS: 234, KE: 66.12 MO: 0.56
WT: 438, TTT: .372, FPS: 255, KE: 63.26 MO: 0.50
With corrected KE values using a divisor of 450240 and added Momentum.
The way I read this is as arrow weight goes down, KE goes up, Momentum goes down except for the lighter arrows who's KE values indicate an inefficient transfer of force to the arrow.
As far as page 2 chart goes across the chart momentum more than doubles yet KE increases a mere 25%
I'd like to see more data from trad bows using various arrow weights.
Maybe i should've been saying torque instead of horsepower when talking about my tractor, but not my car.
Either way a heavier arrow has more penentration than a lighter arrow given the same bow, right?
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O.L.,
I wouldn't say I was wrong, though, perhaps I've been using an inappropriate example to further the cause of using momentum as an indicator. Though, the correlation between KE and performance is still inconsistent whereas momentum more consitently fits a better relationship with performance.
It would appear now that the use of a heavy arrow is even more important when using traditional equipment.
I think we've both made some good points while debating the issue, but can anyone provide some empirical data that indicates KE is a better unit of measure for terminal(at point of impact) ballistics?
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Bogsucker, That chart was derived from multiple arrow weights, from 360 grains to 652 grains in aproximatly 50 grain increments.
Compound bows will begin to lose KE as arrow weight goes up because as the load increases there are more loses from friction in the cable/pully system just as you'll have more friction in your axle bearings with a heavy load as opposed to a light load. If they did not have those loses, KE would go up with arrow weight just like they do in trad bows.
As far as I can see, NO ONE here has said KE is a better measure of lethality. But Dr.Ashbey says NEITHER tracks perfectly but MO seems to track more often.
Ke is a good measure of one bows performance over another and that is all! If a person takes a bow with high KE and uses a light arrow and gets poor penetration, that is their fault for not useing the potential of the bow to their best advantage. (if max penetration is the goal) The bow with more KE has the potential for more momentum for a given velocity if the shooter selects a heavier arrow but that doesn't mean they'll get good penetration if they pick a sorry broadhead. The bow with more KE also has the potential for higher speed if they choose to go that direction....O.L.
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I agree with you almost 100% except that KE is not stored it is a calclated measure of an object in motion, regardless of design or efficiency.
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JAK, What O.L. meant is that bow efficiency continues to go up with projectile weight. The arrows may get too slow to be useful but the transfer of energy from the bow to the projectile becomes more and more completewith increasing arrow weight. The biggest gains are withing the "normal" range of arrow weights-say 300-700 grains for a 50Lb bow. Heavier arrows still soak up more energy the gains just become slight.Kinetic energy figures fall short in displaying penetrating capacity of an arrow. So does momentum.It isn't because the figures lie-They just don't tell the whole story. Within the range of usable arrow weights momentum seems to reflect things a little more accurately but....
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There are several very interesting points of view here. For what its worth, KE being Ke, there are alot of people that swear by the light arrow/higher, I don't. The KE charts are very accurate up until contact with the critter in mind. In firearms, I think the Taylor Factor gives a more realistic view. Unfortunately, with bows I think there are too many varibles to consider after contact to make any assumptions based on a slide rule.
Its just like Ol Gramma used to say- "If ya go, GO BIG!!"
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All I know, if I payed more attention to KE instead of momentum's value, I'd be screwed for hunting with my 48# bow and 600 grain arrow. Heavy arrows definitely can make up for low poundage bows when it comes to penetration.
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What is funny is that a couple of years ago on the compound bow sites, people were arguing vehemently that KE was the variable to use to predict penetration.
I think momentum, based on the following math.
I can still do a little calculus...if I integrate Newton's second law over time while penetrating a target, the variable which predicts penetration changes with the type of force that is resisting the arrows passage.
If the resisting force is proportional to the arrow velocity, then penetration distance is exactly proportional to momentum.
If the resisting force is constant, independent of velocity, the the penetration distance is exactly proportional to KE. This is the case, by the way, with targets that slow the arrow by squeezing the shaft.
And, oddly enough, if the resisting force is proportional to velocity squared, the arrow never stops! Although after a while it is barely moving - but the force goes to zero faster than the velocity goes to zero such that the penetration continues forver.
In reality, of course, the force that slows an arrow is a complicated function that is a combination of forces that depend on the arrows velocity in different ways.
The other interesting thing is that shooting even the wimpy round wheeled compound that I shoot, if a bone tries to stop an arrow cold, the force is huge! It can easily reach a thousand pounds, all concentrated at the point of the broadhead. This is again a direct result of Newton's second law, the force times the time that that force is applied just equals the change in momentum. Say I apply 30 pounds (with my bow) over 30 inches to accelerate the arrow. Then if I try to stop that arrow in a quarter inch, the force will be 30 divided by 0.25 times 30 = 3600 pounds (assuming that the distances equate to times)! I.e., the bone has to take away the same momentum that the bow added, but in less than a hundreth of the time which makes the average force a hundred times larger.
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Beprepn:
I think you almost have it. From Dr. Ashby's new report #3 He compares penetration in a buff with two set-ups:
70#,756gr,MA2.75,0.477Slug-Ft/Sec,33.84ftlb,15.65"penetration
82#,790gr,MA3.25,0.523Slug-Ft/Sec,38.94ftlb,21.86"penetration(shot thru target)
The 82# setup provided MORE than 39.7% more penetration as it went thru the target. Because the 82# broadhead had a different style head which he reprted to provide 26% greater penetration with "normal FOC" arrows from prior testing due to it's greater mechanical advantage. Therefore, adding 26% for mechanical advantage plus 9.6% for momentum= 35.6% predicted increase in penetration versus MORE than 39.7% actual increase in penetration.
However, the increase in kinetic energy was 15.1%. Adding 26% for mechanical advantage and 15.1% for additional momentum= 41.1% predicted increase in penetration. This fits nicely with the results of AT LEAST 39.7% more penetration because of the pass thru. Once the arrow breached the far rib there would be little resistance to further penetration but the arrow was probably nearly out of gas by that time so this increase seems entirely reasonable.
From your 1/4/08 post I concur with the middle formula regarding substrates that squeeze the arrow as I have conducted field tests that fit that theory.
I believe that an arrow that punches thru skin, breaks a rib, then travels thru a lung or two probably encounters all three of the situations you have described because Dr. Ashby's own results correlate better with kinetic energy than momentum from my analysis.
He may be on to something with extreme front of center arrows not flexing as much when they hit the target so they should penetrate better, but I think he needs to eliminate the other variables better to prove it.
I also believe that momentum may model penetration a bit better for finger/stick bow shooters because of the archers paradox phenomena as the arrow is apt to still be flexing when it hits the target(is this flexing part of the kinetic energy?). If an arrow is flexing when it strikes it probably will not penetrate as far as one that is not flexing.
Note: Somewhere on the net I saw a video of an arrow striking a target and that thing was whipping all over the place!
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Dr. Ashby concludes that momentum is a better predictor of arrow penetration in game than kinetic energy, but his own analyisis of data from the 2004 Broadhead & Arrow Lethality Study Update, Part 2 do not appear to mathmatically support this as presented.
I believe the same 82# longbow was used to shoot 820 grain (by my calculation) wood shafted arrows with his modified Grizzley heads, and double shafted aluminum arrows with the same style of head which also had an additional 135 grain rod welded behind the head for a total weight of 1090 grains. Both arrows were within .010” dia. of one another and smaller than the broadhead diameter at the ferrule.
The 36% heavier aluminum penetrated 33% more than the lighter wood arrow even though it only had 13.6% more momentum and 1.6% LESS kinetic energy than the wood arrow.
Discussion:
It is unclear whether the velocity of the arrows was measured at the bow or at the target 20 yards away. This seems important because the reported kinetic energy of the lighter arrow is higher than that of the heavier arrow. This may not be a “statistically significant” amount because a lighter arrow is supposed to absorb less energy from a given bow than a heavier arrow but it lends suspicion to the test data.
An increase of 13.6% more momentum does not compare well to an observed increase of 33% penetration. An increase of 36% more mass compares better to the observed increase in penetration (Note that kinetic energy remained the same), especially if a 3% correction is applied for the ESTIMATED increase in FOC created by the 135 grain rod at the front of the heavier arrow. I would estimate this increase to be three to five percent. Therefore, 36% more mass + 4%for higher FOC – 1.6% for less kinetic energy = 38.4% predicted increase in penetration. This is not a perfect match, even if it is better than the amount predicted using momentum.
Looking at the figures, a better match can be formulated using the sum of the percentage increase in momentum plus the absolute value of the percentage change in velocity. 13.6% more momentum plus 14.9% change in momentum plus 4% for higher FOC = 32.5% predicted increase in penetration. This does compare favorably with the observed 33% increase in penetration. This formula also predicts a 40.5% increase in penetration for the example in my January 17, 2008 post compared to an observed increase of AT LEAST 39.7% (due to arrow penetrating the off side of the carcass ultimate penetration was not measureable). This formula seems to work to compare one setup to another but I am not sure if it can be used to predict penetration.
To me the logic and mathematical formulas presented by Dr. Ashby do seem to indicate that momentum is the key to penetration, and the empirical data seems to suggest that the greater portion of that momentum comes from the mass the greater the penetration will be in game animals. It is interesting to speculate about the effect on penetration of “friction” versus “work” as relates to inclined planes (i.e. the mechanical advantage)and “resistance”, (i.e. the fact that resistance increases at the square of the velocity). I sincerely hope that in his next report the variables of different arrow shaft materials, shaft diameter, broadhead style and weight, and so on are eliminated so a precise formula for determination of arrow penetration can be developed. Hopefully this formula can be correlated to a standard uniform test media so us mere mortals can do our part to take to the field with the proper equipment.
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Looks like this has been beat to death over several years and most clear thinking people "get it"...Just in case someone reading this anew falls into Zaks false assumption that bows have an arrow weight range where optimum KE occures, here is a link that clearly shows how any given bow, the KE will continue to increase as arrow weight goes up:
http://www.archeryevolution.com/pdf/2007Face-OffResultsArcheryTalk.pdf
Here is a couple of graphs derived from real tests by Norb Mullaney, not "theory"..
(http://www.bowmaker.net/images/kevsmo.jpg)
(http://www.bowmaker.net/images/velvsmo.jpg)
These curves would be typical for any bow, only the values would change.
I could show a dozen other examples with trad bows.
Those that try to do bow testing that have little understanding of how bows work can can easily fall into this trap. KE drops seen when arrow weights go up are the result of the testers failure to recognize "other" issues not related to the arrow mass is causing the drop in KE...Mostly tuning issues where arrow contact with the bow and rest, nock fit, ect....
It all boils down to it's not the KE available, it's how "fast" you try to use it.....O.L.
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you are all missing one very important point made by Dr. Ed Ashby, the target(animal body) resists the arrow MORE when the arrow is FASTER. So the resistance of the animal rises with the SPEED the arrow is travelling. It's about penetration and resistance. Jump off a high bridge into water and you might break your legs, get spattered on the surface, or die. Jump into water from the edge of the pool, guess what, you penetrate the surface.
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since I'm terrible at math maybe some here can help me out. If I have a compound launching a 600 gr. arrow at 260 fps versus my recurve (63lb RER) launching a 700 gr. arrow at 170 fps that my recurve will out penetrate the compound bow??? Both would have the same Grizzly broadhead for posterity sake.
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I don't think anyone can truely CALCULATE it. If you read every single ASHBY report and compile the percentage variations you might be able to make a guess. The problem is that the variables are not linear. You would need to come up with a number of equations (non linear) (within a range) to approximate the differences involved. friction coefficients would be required at different speeds, the initial energy to beak through the surface tension of the hide would be required (in a specific location), the rotational rates of the arrow in flight and through the animal would be required, etc., etc.,,,,,,. If you know a math major at a university that is interested in a difficult model to solve, try them.
Rob
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One more observation about Dr Ed.
When he needs more penetration, what does he do? It appears that he goes to 1000+ grain arrows from a 80-90# longbow.He does not stay with a 700 grain arrow and shoot it faster.This is a guy (there are others)that has killed many different dangerous animals (the big 5 i think). I think for north america, you should use 650-700 grains for moose and elk, (650 being the "threshold" Ed defines) but not necessarily required for deer. Some deer are no bigger than dogs while others are as big as elk.
you decide.
Rob
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Babaloo, "since I'm terrible at math maybe some here can help me out. If I have a compound launching a 600 gr. arrow at 260 fps versus my recurve (63lb RER) launching a 700 gr. arrow at 170 fps that my recurve will out penetrate the compound bow???"
The "resistance" Tradwannabe speaks of goes up by the square of the velocity. Increase velocity 10% and the resistance to penetration goes up 40%. It's difficult to "cross" from one example to another the way you are looking at it since you are not only changing velocity you are changing KE at the same time. One has 45ft/lbs and the other 90, in the real world they'd be close to the same penetration. Are you sure of those numbers? 45ft/lb is about what one would expect out of a decent 55# bow......O.L.
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OL,
If you see this please explain the comment, "45ft/lb is about what one would expect out of a decent 55# bow......O.L."
I've got one of the new A&H ACS CX, which I consider more than decent bow, that I draw to 31" at 47# and with a 460 grain arrow I get 200 FPS and 41# KE. I consider the 200 FPS at nearly 10 gr/# very good, even at my draw length, so either my KE calc is off or I've got a slow version of the ACS CX... With a release I get about 205 FPS and both speeds are with musk ox wool silencers and a tied in nock point. To get to 45ft/lb KE I'd have to shoot the same arrow 210 FPS, by my calculation, which is smokin' fast by trad bow standards! Is my calculation wrong, is there a faster bow out there or is my testing fouled up???....Scott
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Scott, Your draw length is a blessing many would die for! :) Say a bow has a 1:1 se/pdf (most don't) at 47# you'd store 47ft/lbs, if you were getting 41ft/lbs in your arrow it's 87.2% efficient. Since it probly isn't storing an se/pdf of 1.0, it's even higher then that.
My example of 55# with an se/pfd of 1.0 and 45ft/lbs in the arrow is an efficiency of 81.8% which is close to what the better recurves spit out and they do typically have an se/pdf higher then 1.0. So, no, your numbers are better then the example I used, not worse....O.L.
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O.L. This old Navy BB stacker is missing something. Let's say your shooting a 55# recurve.
your arrow weights 550gr with an arrow speed of 180fps gives you 39.58 ft.lbs of KE. If arrow weights goes up, speed goes down. If I'm using the right chart, KE starts to drop off at a certin combo. I'm I just missing something? I don't understand how KE can go up forever.....
The Red Shirt......
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Oh you BB stackers! :) Thanks for your service by the way. Only 20 years? I had to be quiter too thanks to slick Willie after 25!
Works like this: Stored energy = limb energy + string energy + arrow energy
That equation must remain ballanced cause you can neither create nor destroy energy. If I increase the mass of say the string, the numbers for the other two MUST go down, and they do. So no matter how heavy the arrow goes, the energy wasted by the limbs/string continue to go down. Now you can get the arrow so heavy we no longer have the ability to measure the tiny changes in arrow velocity, but that's way over 20gr/lb and over practical usage.
Those are not graphs based on theory, actual measurements by Norb Mullaney but it also matches the theory which is nice. Remember that in KE velocity is squared, it's also squared for the wasted energy in the string and limbs. The limbs only move about 1/5th as far as the arrow so they only have about 1/5th the velocity. If anyone ever sees a situation where the KE does drop in the heavier arrows, that's a clue something else is wrong like nock fit or severe riser contact due to poor tuning. You red shirts, even drawing pictures don't help! :) Good on you bud....O.L.
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To put arrow weight and velocity into further perspective, if our bows were 100% efficient and you went from a 250gr arrow to a 500, you'd lose 25% of your velocity. Go from 500 to 1000 and you lose another 25%. So going from a 250gr and increase your arrow weight 400%, you'd only lose 50% of your velocity. Because they aren't 100% they don't follow those numbers exactly but close. Keep in mind arrow velocity is like RPM to an engine, it depends on the load and doesn't cross directly to horsepower without knowing the load....O.L.
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Or ... note that the increase in arrow FORCE (the momentum) has a near-linear relationship with the increase in arrow mass. It's more analogous to the 'break horsepower'; the force output 'where the rubber meets the road'. :)
Ed
TGMM Family of the Bow
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My, my we've gone into a deep, scientific discussion that requires way more concentration than I can muster late on a Friday night after a week of the same at work. OL and Dr. Ed are on a roll and I've got to read this when I get up tomorrow morning and I'm fresh so I can comprehend what they're writing since it's very interesting!
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hmmmmmmmmmmmmmmmmm didn't this get discussed by a guy named newton? and if i'm not mistaken you can pretty well take his word as LAW on this point
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sure but was he an archer? This is why I loved science and then going out and finding that it actually does describe the world.
chrisg
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I have to agree that Newton nailed it down firmly. A body in motion tends to stay in motion. A heavy bond in motion tends to stay in motion longer than a light body when they meet equal resistance, even if the light body is moving faster.
I have to say DR Ashby and O.L. Adcock have this one pretty well figured out.
If you are planning to hunt buffalo, give up the whole fast arrow idea. Get your arrow weight up above 650 grains. Optimize all the other factors and crank your FOC above 20% and preferably closer to 30%. This usually means keeping your shots at 30 yards and less due to arrow drop past 30 yards.
Shoot a really high KE arrow out of a compound into a buffallo and you will often find your arrow broken and a pissed buffallo looking for the cause of his pain. Shoot a high momentum of impulse arrow into the same buffallo and your going to have meat on the ground.