I built an air cannon out of PVC pipe to do my projectile testing. I thought that since there was no induce paradox, I could get precise entry angles as the bare shaft came out of a long, thin tube.

Unfortunately, even the small space need to put the chronograph between the target and the launcher was enough for the shaft to plane unpredictably, and enter at random angles.

If I could have put the exit tube right up near the target, it might have worked, but then the chronograph would not have worked.

It probably needs to be done with spherical, non-deformable projectiles like marbles into clay.

I am, however, slowly starting to think that KE is more important than Momentum.

Just some other numbers to contemplate: a 40 gram .22 round traveling at 1000 fps has the same MOMENTUM as a 400 grain arrow traveling at only 100 fps, but 10 times more KE.

I think your calculations and tests might correct bro but what you're comparing is apples and oranges.

Momentum and Kinetic energy are not the same and cannot be used in the same fashion to decide the affect an arrow will have on a target.

Momentum is (Mass X Vel.) and is ALWAYS conserved. Which means that if the Masses and velocities are known after a collision then the unknown velocity can be found.

Kinetic energy, on the other hand, is not conserved in collisions if they are inelastic; which simply means a collison in which the two objects don't bounce off each other perfectly! With an arrow the target absorbs the Kinetic Energy of the arrow so it's an inelastic collision.

Kinetic Energy is K=1/2(MV)Sqrd

and momentum is

Mom=(Mass X Vel.)

So, since the two variables are always Mass and Velocity I don't see how one could be more "important" than the other.

if i'm missing your point tell me...

Well, the "point" has been discussed ad-nauseum in other posts, and I didn't really mean for this post to be just another argument about KE vs. Momentum.

I was just trying to show that I was attempting to settle the matter once and for all with experimentation....which would be very easy to do with the proper setup. The proper setup would be easy for someone with a decent workshop, but that is something I lack.

What would be ideal is the pneumatic device with variable pressure (which I made as the air cannon). A consistent target like modeling clay. And spherical projectiles of the exact same dimension, but varying mass. The last being the most difficult component for me to come up with.

Just purely out of curiosity what are you trying to settle? ;-)

HP,

Trying to settle: Which equation is a better predictor of how far a projectile will penetrate.

Many say momentum, and as many or more say KE. A few recent posts discussed the difference at length.

Not important but...that's a 40 GRAIN bullet, not "gram"

doesn't change anything about the discussion. 8-)

Jim

ah ha!! Now that I can bite into! Sorry, thought we were trying to say that one was inconsistent with the other!

As an engineer that works this type of stuff I would have to say that we never use momentum when trying to decide on the affect that a projectile will have on an object. It's all about the Energy released on impact when the kill vehicle strikes the incoming missile of aircraft.

Momentum is not precise enough for this kind of calc.

Asharrow...that's what I meant...lol

Highpockets....the difference between arrows and missles/bullets, etc...is that missles and bullets are usually designed to cause the most damage possible to something, and also suffer damage themselves in the process.

From my understanding of KE, this goes hand in hand with the goal of firearms (stopping power). I could see why maybe few people would care about PENETRATION when dealing with missiles or bullets, so perhaps the science of penetration is often disregarded?

Anyway....much of the controversy stems from the Dr. Ashby reports that claim Momentum is the better predictor of penetration as opposed to KE.

Also, many trad guys look at the recommended KE charts for game and are surprised to see that their gear is barely considered adequate for small game.

Ashby's paper has almost the same example you are proposing (see below) from this link, except he compares bullets and arrows...

http://www.tradgang.com/ashby/Momentum%20Kinetic%20Energy%20and%20Arrow%20Penetration.htm

"If one fills a 5 gallon plastic pail with sand and fires both a .357 magnum and a heavy hunting arrow at it, the bullet will be stopped by the sand, while the arrow will penetrate the pail completely. The .357 magnum handgun has a 158 grain bullet traveling at 1250 fps, for a momentum of 0.83 slug-feet per second, and a kinetic energy of 520 foot-pounds. A 710 grain arrow at 183 fps has only 0.57 slug-feet per second of momentum, and a mere 52 foot-pounds of kinetic energy.

These are actual combinations I have used to demonstrate the penetration power of a heavy hunting arrow. Our baseball, with 96.5 foot pounds of kinetic energy, and 1.39 slug-feet per second of momentum, will simply bounce off. What makes the difference?

A major factor between the bullet and the arrow is the increased resistance force met by the higher velocity bullet. While the bullet has ten times more kinetic energy, and 37.5% more momentum, than the arrow, its almost seven times higher velocity causes the bullet to be met by nearly fifty times as great a resistance force as that encountered by the arrow! Another major factor between the handgun’s bullet and the arrow (yes, we will get to the baseball shortly) is the longer time period of the arrow’s impulse; which results from its higher mass. Though the arrow is traveling much slower than the bullet, and has less momentum than the bullet, it derives a greater percentage of the momentum it does possess from its mass. It is ‘heavier’. The heavier (and lower velocity) arrow “decelerates” more slowly than the bullet or, if one prefers, it has a longer time period over which the force acts. Remember? Force multiplied by the time it acts equals the impulse. The heavier arrow retains a higher percentage of its force for a longer period of time than does the bullet. The bullet’s total net disposable force, though very high relative to the arrow, is entirely dissipated in milliseconds."

In order to make a valid test, it seems that you need to use arrows.

Put a blunt on the arrow in that test and check the penetration.

SteveB, Man, that was so obvious, LMAO.

oops, Missed!

A slower arrow always penetrates more.

Ahh the old sand bucket test. Once again, in my opinion, you're comparing apples and oranges. The explanation of the arrows energy being spread out over a longer time period is correct. As a matter of fact the entire explanation is correct from a physics stand-point.

However, let's stand back from the bucket and take a longer look at what's really happening.

If you were the bucket and the arrow hit you then you would have a nice clean hole right through you.

If you were the bucket and the bullet hit you then your insides would change into jelly, your body would shudder like it was made of rubber and you would fall to the ground in a heap.

Why; because a tremendous amount of energy was just completely spent on your insides. While the arrow merely used it's energy to push through you.

Change the arrow to a blunt or a lead tip. Change the bullet to solid steel! Either of these would change the test results completely.

We're talking about arrows only and we don't want the energy of our arrow to expend itself inside the deer's body. We want the arrow to use its energy to push our arrow through.

So we're right back where we started!

P.S. We actually work for the kill vehicle to remain intact and pass completely through the oncoming target these days. Just like the arrow!

speed 210 weight 200 ENERGY 19.58955224 Momentum 0.185643564

Speed = (D5) Weight = (D6) =((((D5*D5)/7000)*(D6))/(64.32)) =(D5*D6)/(7000*32.32)

For Excel ...

Use this to compare the potential penetration values between arrow setups. For example, the above 210 fps arrow at 200 grains would have kinetic energy of 19.59 fpe and a momentum factor of .185. The higher the momentum factor, the better the penetration probability.

speed 210 weight 200 ENERGY 19.58955224 Momentum 0.185643564

speed 132.7 weight 500 ENERGY 19.55544821 Momentum 0.293272631

Here you have two arrows of equal velocity, but you can see that the heavier arrow has a higher momentum value and would have better penetration.

Aloha....

Well that didn't work....

Aloha...

Highpockets, Do you have the means to create a better test setup similar to mine? All you need is three projectiles of exact dimensions and varying weight, and an ability to fire them into a uniform medium.

Mouse....

What you are trying to do has been done countless times and always with the same end result. If a hands on project with an arrow helps clarify the concept use a medium that is easier to work with. Try a crossbow with an adjustable draw weight so you can maintain speed while varying the weight/spine of the arrow.

The end result will be just what other posters have written above. It always has been.

Scarne, A single crossbow would not work. I need to be able to keep the KE and/or momentum constant while varying the weight of the projectile. If I increase arrow weight, Momentum and KE are also increased.

If there were a way to vary the pull weight of the crossbow or if I had multiple crossbows at varying poundages, then it might indeed be a good experiment.

WHO CARES!!

Both guns and arrows were mentioned. Why not mix the two. Use a muzzleloader to shoot the arrows. The powder charge can be changed easily as well as arrow weight. As far as penetration goes, they will go through the side of a wood barn. My great uncle shot my Dad's cedars that way. Dad didn't get his arrows back!

Scarne, can you show me documentation for any results from any organized testing done by the scientific method? I've been trying to find such a thing and the best I've come up with are the Martin tests and they showed that KE was the best predictor of penetration. http://www.martinarchery.com/faq/facts.php#pene The Ashby FOC chart has results that show KE is a better predictor than momentum, too.

If momentum had any significant bearing on penetration (and it doesn't), then a 1,750 grain fishing arrow going 102 fps would penetrate as far as a 500 grain arrow at 350 fps.

They have the same momentum but the faster of the two possesses much greater kinetic energy and the penetration would, therefore, be much greater.

Why Blindmouse is interested in experimenting for himself is pretty obvious to me. The momentum based theory of penetration is fundamentally flawed. It's never been tested and proven and, frankly, the theory that momentum is more important to preduct penetration than KE will NEVER be proven because it's not so. Actual testing designed to determine whether KE or MO needs to be done because it's important for archers to understand what's really going on.

Please don't any of you take this the wrong way but what Scarne said is ultra-true. I work for the gov. testing missile systems and trust me when I say that if there has ever been a projectile test we took part. I worked at a wind tunnel facility for many years testing star-wars type weapons that relied solely on penetration first and expenditure of kenetic energy second. The projectiles were NEVER made to stop in the target, deform, or otherwise spend all they're oomph in the target. Much like the best tank killer rounds of today they were made to shoot through the target like it was a tin can!

With that said I will re-post something that I have said on here until everyone's tired of hearing it. To find the best projectile for almost any system a room full of too-smart people will first decide what the heaviest projectile the system can shoot is. Then they figure out what the lightest is. The heaviest being stable but slow and the lightest being fast but unstable. And then, we use all of our know-how to just simply find what projectile lies dead between the two. Yes, we sometimes have to tweak one way or the other a tiny bit but never more than a small percentage. That's how we find the best projectile (weight wise); I'm not talking about shape here!

But wait, I think after reading some of the other threads I understand a little better what it is that's being argued and that is if KE or Momentum is the better judge of what arrow is best. I guess from habit I would still go with KE

HighPockets, Maybe it has been done, but the military isn't interested in letting us traditional archers know the results of their testing :)

It should actually be a VERY SIMPLE matter to come up with a PENETRATION FORMULA instead of using KE or momentum as a "predictor".

The reason I say it should be a SIMPLE formula, is that we can assume everything between two projectiles is equal (surface area, angle of impact, drag, gravity, friction, FOC, EVERYTHING) except velocity and mass.

So all those other variables that are needed to predict an actual penetration depth in actual materials could be thrown out, BECAUSE we are only looking for a relative number between two projectiles that differ only in mass and velocity....we are not looking to find an actual penetration depth.

Blindmouse, one other thing that should be assured is that the penetration should be done as close to where the velocity is measured as possible. Testing velocity at the bow and testing the penetration 20 yards downrange is no good because if you use 5.5" feathers on a 300 grain arrow and also on a 1000 grain arrow, the test has been heavily weighted in favor of the 1000 grain arrow because the drag coefficient is grossly lopsided between the two setup like that.

Additionally, all "tuning" issues should be eliminated, which is why shooting the projectile from a bow, particularly with fingers, wouldn't be the best solution. Shooting the arrows (without feathers) out of a tube like a gun barrell would be best for pure penetration testing.

Ideally, the testing should be something like this:

Test #1. Establish a baseline kinetic energy. Modify mass and velocity to maintain that kinetic energy but CHANGE the momentum signficiantly through a range. Record penetration results.

Test #2. Establish a baseline momentum. vary the mass and velocity to mainain that momentum but CHANGE the kinetic energy significantly through a range. Record penetration results.

Analyze results to determine which group saw the greatest variation in penetration.

I assure you that the greatest change in penetration will be from the group where the KE changed but momentum remained constant. (showing penetration is much more closely related to KE than momentum). When the KE remains constant but momentum changes, the change in penetration will change very little, if it's even measurable.

The heavier arrow shot with the same KE will always out penetrate the lighter one period! Assuming both are well tuned and with same head. This is due to the higher momentum value of the heavier arrow.

You sound mighty sure of that, T-bone. Can you back that up with proof or is this one of those facts that is supported by appealing to the authority of "everyone" as in "because everyone knows that"?

Just plug your numbers into any balistics chart and you can see. bowjackson.com

O.L. Adcock,Dr. Ashbey, and Pete Ward to mention

So what we're saying is that two arrows shot with the same KE will penetrate differently according to their weight.

If two arrows have the same KE, and one is lighter than the other, then the velocities of the arrows have to be different to make them equal each other; right?

Ok, i'm a geek so I crunched some numbers of my own and will have to AGREE that if two arrows, one heavier than the other have identical KE then their Momentum will be different, with the heavier arrow having the greater amount. And, according to the related physics the heavier arrow should see greater penetration.

To me that takes us right back to the velocities required and the increase in drop of the heavier arrow.

We have to throw the paper with the math on it in the trash, look around until we see something about 25 yards away and say to ourselves; "can I hit that with this heavy arrow". Because if I can't get it between those ribs an arrow that weighs as much as a cinder block ain't gonna do me a bit of good!

So, I say to myself, "Steve (cause that's my name) what about this somewhat lighter arrow that you can consistently hit a 3" dot with at 20yds."

Heavy arrow in ground or limb because I could not make the arc fit

or

Lighter arrow in deer?

If there is a calculator at Bowjackson.com that supports your statment about the heavier arrow always penetrating farther than the lighter one with the same KE, then by all means post that link because I've never seen it.

O.L. Adcock, Dr. Ashbey and Pete Ward? What about them. They agree with you, but that's not proof, either. Dr. Mark Timney and Martin Archery agree with me, but that's not proof of anything except that "everyone" doesn't agree on this and your "everyone" isn't automatically better than my "everyone".

So where's the proof? How do you really KNOW, T-bone. I know you believe it, but why do you believe it?

PB, That's exactly how I was set up to run my tests....until I realized the entry angle was screwing up my results.

Blindmouse, here's another thing that helps give us a clue about the difference between momentum and KE. When you shoot a rifle, the rifle's recoil has the same momentum as the rifle bullet. For each and every action there is an equal and opposite reaction. The rifle bullet has high KE but the rifle during it's recoil does not. If momentum was the "power" that drives penetration, we wouldn't be able to shoot a rifle without killing ourselves in the process, but instead, we get a tolerable whallop from the butt of the rifle while the bullet going out the other end with the same momentum carries enough KE to destroy it's target.

Good point. As I said, my setup, while flawed, has given me insight that makes me lean toward the importance of KE.

My 1029 grain arrow at 70 fps barely penetrated the foam target. This setup has the same momentum (but far less KE)as a 430 grain shaft going 165 fps which penetrated quite a bit more.....but I don't want to conclude anything until I can assure the shafts are striking at the same angle.

If I can drill holes in the exit tube of my pneumatic launcher, maybe I can place that tube directly over the photo-sensitive "eyes" of the chronograph, so the projectile never needs to leave the launcher. I have a feeling the light gathering ability of the chronograph will be severely degraded with such a setup though.

Blindmouse, If you ran the same penetration test comparing your 430 grain arrow to say a 550 grain arrow, the penetration between the two would likely be noticable. Nobody in their right mind would hunt deer or elk with 1029 grain arrow traveling 70 fps.

I would like to see the results when you get the shafts to impact straight. Eliminating the tuning issue is a huge step in the right direction, IMO. You have to eliminate human inconsistencies as well. I am putting my money down for KE. ;)

Been solo-hunting in the mountains past three days, had a bunch of fun. Everything was on foot going by past memory of a particular north/south ridge. I went in mid day Sunday and it was fairly easy to find bedding areas, scrapes, and a few funnels. I picked out a bench below a part of the ridge that had plenty of fresh sign. Monday and Tuesday I worked that ridge and had little trouble getting in bow range (under 20yds for me) of the buck that was working the ridge, a doe and her two yearlings. The buck was only a six pointer and was not a shooters so I decided to push the envelope and practice my stalking. Lots of fun working into a shooting position when there was no care if the deer made me. Just wish a big bruiser would be such easy pickins. Did a bunch of squirrel hunting as well. Didn't have any trouble nailing a squirrel at 25paces +/- w/ my slow 10gr/# arcing arrow. There was some bear sign higher up. I'll work on that Friday. I had placed one of those high dollar 4x4 blocks up at the cabin to stop my slow heavy arrows. It might work on one of those light carbon arrows but it was worthless on my arrow/BH combo. The dealer was so shocked how my slow takle ate it up that he replaced it free and gave me a heavily compressed Horton block they used to stop high speed crossbow bolt w/ BH. My first arrow on the fresh target sunk past the center core. Just for kicks I shot my lighter/faster arrow into it and as I expected it didn't sink in as far.

Oh that reminds me, so any of you guys hunt and take big animals with basic archery tackle using the lightest arrow you can safely shoot straight? Do you crunch numbers to figure out the combination that maximizes speed and ke? I hope not.

B.T.W.,

Just to throw out another opinion:

- The only validation is empirical data from the field over time when actually used on the intended target. Everything else is only theory and at most only a simulation. Not real and not factual!

- The Martin test was anything but scientific and game animals are not made of foam. But, even thier simulation showed that the arrow with the higher mass and momentum penetrated deeper than the arrow with the higher ke.

- The Ashby report shows nowhere in its findings that ke is a reliable factor to predict penetration. Some, including Papa Bull point at the FOC chart where every arrow has a different %FOC and claim this validates thier position on ke. I'm of the opinion this view is false and misleading to the point of being intentional untruth. I noticed that Papa Bear et al was actually pointed out by Dr. Ashby in his latest 2007 update and clearly Dr. Ashby indicated PB et al are off base. Maybe a lawsuit?

- Deer, Bear, Elk, Squirrel, etc. and arrows ARE NOT planes, rockets, bullets, foam, ballistic jell, boards, clay, air cannons or balls. Anyone who claims they are the same have lost their mind.

- Anyone who claims that a 9-12gr/# arrow is too heavy and too slow to shoot at a deer is from another planet.

I don't know where you guys are from denouncing mass and momentum for arrow penetration but it sure works well in the field.

Daddy Bear

A4C, my thoughts exactly.

T-Bone, the test is designed to test the theories, not necessarily to test any practical shooting or hunting setups. Sometimes things are too close in the results to notice a significant difference....taking it to the extreme (1029 gr arrow) will help highlight any differences in the opposite extreme.

Daddy Bear, I believe you think that I am trying to say something that I am not.

I am in no way denouncing the value of heavy arrows.

Heavier arrows will penetrate more than light arrows when shot from the same bow! I'm not saying that is not the case, but for some reason, that is what you think I'm saying.

I am merely curious as to the performance difference between compounds shooting light and fast arrows and longbows shooting heavy ones.

You keep saying "anyone who claims" such and such is crazy, etc. Well I've never claimed any of those things. You are reading into things and creating your own conclusions which are not anywhere near what I am concluding (in fact, I haven't concluded anything yet!).

My personal hunting setup this season is a 55# longbow shooting 650 gr arrows. Running it through the chronograph and crunching the numbers shows that it has more KE AND more Momentum than shooting lighter arrows from the same bow.

So you are missing the point if you think I am denouncing the value of heavy arrows.

Fair enough, I retract.

I have a friend who shoots a compound with a mid-weight arrow/BH. After one hunting trip where he was exposed to hunting deer with a recurve he went out and picked up an old Ben Pearson to play with. He has a long draw and ordered some 2219s to start with. They are fairly heavy and he noted to me that they were penetrating about as deep into his backstop as his compound. He tried shooting one of the heavier 2219s out of his compound and was stunned that the slower/heavier arrow out penetrated his faster mid-weight combo.

I'm of the opinion that mass and momentum will trump the speed of a lighter arrow on penetration as long as you're within the range the arrows shoots well. I see an advantage to going lighter to flatten trajectory but I do not see this as a way to increase penetration. This is speaking of the same bow.

If I find the happy medium with a particular stickbow and a guy compares that to a lighter arrow of a much faster wheel bow, well that may very well work out to out do the slower stickbow. But, I believe the wheelbow will provide even greater penetration by finding its own happy medium with mass and momentum.

later, Daddy Bear

- The Ashby report shows nowhere in its findings that ke is a reliable factor to predict penetration. Some, including Papa Bull point at the FOC chart where every arrow has a different %FOC and claim this validates thier position on ke. I'm of the opinion this view is false and misleading to the point of being intentional untruth. I noticed that Papa Bear et al was actually pointed out by Dr. Ashby in his latest 2007 update and clearly Dr. Ashby indicated PB et al are off base. Maybe a lawsuit?

-----------------------------------------

Daddy Bear, you're making a horrible logical error here. You are assuming the "FOC chart" didn't show a more direct relationship between KE and penetration than MOMENTUM and penetration because DR. ASHBY didn't say so. I took a different track and decided to think about it instead of letting someone tell me what the results mean.

I've already given in this thread proof of concept that momentum has much less, if any, bearing on penetration. Dr. Ashby is wrong about momentum. He made a mistake and whether it was an intentional "mistake" or geared toward proving to South African game officials that Stickbows can generate enough "force" to compete with compound shooters.... that's something that we may never know. But we know it's wrong.

Where you go off the deep end with this, Daddy Bear is that you assume that because 9-12 grains per pound works, anything lighter must not. You also assume that what you've been told by Dr. Ashby must be correct since he's a doctor, after all.

You also assume that a 450 grain arrow out of a 45 pound bow would be just dandy but somehow it would lose all it's penetration ability if you shot it from a 60 pound bow because it would only be 7.5 grains per pound.

It's not that 9-12 grains per pound won't work. It's that they aren't necessarily a better choice than 8 grains per pound, which you argue as "too light".

Following that "heavier is always better" logic, why not shoot 1000 grain arrows? Or 1500 grain arrows?

I'll tell you why. 2 reasons. (1) A 2000 grain arrow wouldn't penetrate any better than our 500 grain arrow or 450 grain arrow in game and (2) velocity makes a difference nad heavier arrows have lower velocities. We all recognize #2 if if we can bicker about #1 forever and a day. The difference between us is that you wnat to abritrarily assign the "right" numbers and defy anyone else to state anything differently.

I won't argue that your "heavy arrows" work. Of course they do. I argue that lighter arrows can be just as effective and advantageous. Think about it. It's not hearsay. Dr. Ashby isn't a divine being and the Ashby reports aren't written in stone and handed down from God.

But let's get thing straight... I'm not saying that lighter arrows will penetrate better, either. I'm saying that KE is KE is KE and the results will be very similar for a very similar KE. Change the KE value and the penetration will change accordingly. Change the momentum value while keeping the KE the same and you'll be hard pressed to point to any "penetration difference" at all.

It's not that momentum and mass are bad. It's that they're overrated, misunderstood and misapplied.

To long to remember who posted what... :)

Heavier arrows will out penetrate light arrows everything else being the same... IE.. Kinetic energy.

300 weight 278 velocity 51.47690941 Energy 0.370469083 Momentum 138.9506217 energy/momentum 19.07060343 Kinetic Pulse 19.07060343 Energy*momentum

550 weight 205 velocity 51.31827265 Energy 0.500843994 Momentum 102.4635879 energy/momentum 25.70244865 Kinetic Pulse 25.70244865 Energy*momentum

I'm hoping this all works here.

A 300 grain weight arrow at 278 fps will have a Kinetic enrgy of 51 foot pounds and a momentum factor adjusted for acceleration of .370 (not much).

A 550 grain arrow with a velocity of 205 will have an energy value of 51 as well, but the momentum factor adjusted for acceleration = .500.. (not much either but better).

Another valuel. brought forth recently was kinetic pulse. This is a bullet thing, arrows cut, bullets "splash", but it is interesting anyway to look at it.

The speedy arrow with 300 grains has a "pulse" of 19, where the heavier arrow going slower has a pulse of 25.

All this is strictly excercise as it doesn't take much to penetrate a deer. What isn't measured is the amount of drag that arrows provide along with the broad head.

A fixed blade will out penetrate a mechanical given the same cutting diameter and size, but in real life, a mechanical will most likely fly faster given the same weight arrow, so it could be moot.

If your arrow can make it to the second lung, you got it...

As a matter of practicality, a 400 grain arrow at 200 fps is way more than adequate, and a 400 grain arrow at 150 still has 19 pounds of Kinetic Energy... Plenty for deer.

I think shot placement and a good sharp broadhead are more important than KE or Momentum, or anything actually.

Aloha...

RAT's...

Aloha...

Rattus... regarding: "Heavier arrows will out penetrate light arrows everything else being the same... IE.. Kinetic energy."

===================================

How do we know that's true aside from "that's what they say?" or "we just know it's true". Without good solid testing, there's no way to really know if it's true or how much difference there is if it is true. I've yet to see any good scientific test with a large enough sampling of arrows, velocities, masses and target media to satisfactorily answer any of the questions and that's what Blindmouse is trying to do - some experiments that can provide measurable results for good analysis.

Right, the point is that the arrow has mass and flies at a speed determined by the power of the bow that launched it. KE and Momentum are formulas we can use to measure certain aspects of what the arrow is doing. We are simply trying to find out which formula is the best predictor of penetration potential. I'd like to know more. The fact that KE exaggerates velocity by squaring it is compelling. If KE is more useful in predicting penetration potential, is it this squaring of V that makes it so? Jim

This is interesting...

"First let us consider penetration. The depth that a projectile will penetrate into a fluid is proportional to its kinetic energy divided by its cross-sectional area."

http://wadcutter.blogspot.com/2005/03/energy-momentum-part-ii.html

Is it to simple to assume? A Volkswagen Bug traveling at 80 miles per hour hits a cinder block wall, versus a semi-truck even empty, hits the same wall (obviously a differnt spot) at 60 miles and hour,, which penetrates ?Farther?

BigCyn, The two vehicles will penetrate according to their KE. The volkswagon will have much less KE than the Truck.

In it's simplest terms, a bow stores energy. It propels the arrow, which then posesses kinetic energy. Regardless of the weight, the bow's "x-amount" of thrust will propel the arrow as fast as it can for that particular mass. What goes up must come down. And what goes in is what the arrow posesses in terms of energy.

The heavier projectile goes slower. The lighter projectile goes faster. They both will posess the same KE adjusted for whatever difference in bow efficiency there may have been. Within 100 grains of arrow weight, that will be less than 5%.

You draw the bow, storing YOUR energy as potential energy in the bow. When you release the string, the bow then releases it's potential energy as kinetic energy, (the energy of motion). Whether heavy and slow or light and fast, it's going to have X-AMOUNT of Kinetic energy. Some will be shed as the arrow travels downrange and loses velocity due to drag. What remains at the point of impact is what energy there is to do the work. Work and energy are always related. Work and momentum are NOT.

And to complicate things, muscle tissue is elastic and stretches. The quicker the cutting motion, the less stretch there is before the fibers are severed and the less energy is wasted stretching and pushing the fibers. Think of a meat cleaver that you press really really hard into a piece of meat and one that you "chop" with. The fast movement is more efficient than hard pushing.

This stuff isn't as simple as golf balls and ping pong balls or Volkswagon Beetles and 18-wheelers or Buffalos and baseballs. But neither is it so complicated that we shouldn't be able to understand that a small marble out of our slingshot will break the window just as well as a big rock - and it will be easier to hit the window with it because it will fly fairly straight instead of looping like slow pitch softball.

speaking of which.... would you rather get hit with a big, heavy slow-pitch softball or a small, light hardball hurling toward you at 95 mph.

The only testing I have ever done was very unscientific but did show me something. It went like this: When I bought my first serious bow (55# Bear Montana) several years ago, I didnt even know you could buy a chrono "off the shelf" so to speak. I learned about tuning and did as well as I could. My first set of arrows were carbon that I bareshafted as best I could and weighed about 505gr. After shooting them for a couple of months I became obsessed with POC so I called Tim at KustomKing and he set me up with a dozen tapered POC that I managed to tune up as best I could and weighed 660gr. At this point I had never heard of KE or momentum as it related to archery, I just shot. Long story a little longer, I had a layered foam target that was backed up to a big ole oak tree in my yard which I shot both the carbon and POC shafts into side by side for a pretty good while. I dont remember ever pulling a 505gr carbon out of anything but foam. Conversely there are still a few fieldpoints that were on my cedars that were driven far enough into the tree that I have never retrieved them. Like I said, unscientific to be sure, but it makes a point. I think under normal circumstances within normally accepted parameters for bows and arrows, a well tuned heavy arrow will out penetrate a well tuned light arrow out of the same bow. I think a lot of this KE/momentum stuff if splitting hairs.

Ok, I've sent an email to one expert who should know the answer. His name is Nathan Okun, and he is a terminal effects engineer for the Navy and is "the foremost expert of armor penetration of our time." according to one website. If anyone can answer a question about penetration, it is he.

LOL, Blindmouse. I just posted questions about this and asked for critical analysis of the Ashby report on a couple of physics forums. I hope some people in the scientific community consider it worth their time to take a look.

The funny thing is....a couple weeks ago I emailed 2 different "Ballistics Experts" who actually provide expert testimony in court cases.

One sided with momentum, the other admitted he wasn't sure, but was betting on KE and wanted me to let him know the results of my experiments. He did have some good advice for setting up the experiment though. Unfortunately I don't care to purchase a large quantity of modeling clay for the target medium.

It is funny that the "experts" disagree on this and I think that's mostly because there aren't any "experts" on this as much as there are a bunch of different guys with small views of a big puzzle and pet theories about how it all fits together. I'm one of those guys and, of course, my theory is that KE is more significant (by far) than momentum.

Like I've said several times now... the momentum based theory of penetration MUST be discarded if a number of different projectiles with the SAME momentum penetrate to different depths based on varying KE. They would all have to penetrate the same distance if momentum really told us anything at all about penetration capacity.

For that to work, a fishing arrow from a 55 pound bow would have to be able to penetrate as far as a 500 grain arrow from a 120 pound compound. They both have 0.78 momentum, but widely different KE. And, of course, the penetration from these two projectiles would also be widely different.

So much for the momentum theory. That's proof positive that it's absolutely and completely wrong.

Wrap your brains around this (ugh). I contacted Nathan Okun who is an expert at Armor Penetration, and probably one of the most knowledgeable people on the planet when it comes to such things. Here is what he wrote....unfortunately, much of it deals with face-hardened armor penetration that isn't something we can really relate to, but the homogeneous armor parts may be more applicable. What is clear is that the material being penetrated is far more important to any "predictor" equations than I thought. One thing he does say that caught my attention is that if the mass of the plug being pushed out by being penetrated is greater than, or the same as, the projectile, then no amount of velocity will allow the projectile to penetrate...but again that applies to hardened armor....but it was still interesting. Here is the full email he wrote:

If you study my penetration formulae, you will see that there are several methods of plate failure, each one having its own rule concerning the relationship between momentum, energy, projectile nose design, projectile damage, projectile weight, projectile velocity, obliquity, and plate thickness (both absolute and relative to the projectile diameter). This is NOT a simple subject, unfortunately. Here are some examples: (1) Let us say that you have an indestructible, non-deformable, flat-nose projectile of mass M hitting a hard, rigid plate at right angles (normal obliquity = 0 degrees) at some velocity V that barely allows the projectile through by punching out a roughly cylindrical plug of plate material and the projectile falling to the ground just at the back of the plate. What happens if you double the plate thickness, keeping all else constant? Well, the projectile cannot penetrate at all until the double-thick plug has completely sheared out from front to back (or back to front, depending on where the plate fails first) and then is pushed out the back against the resistive forces around the side of the plug (assume that the projectile has no friction and slides through the hole with almost no velocity afterward and again falls to the ground just beyond the plate. If we make the simple approximation that the resistance force to shearing out (R) and to being pushed out afterwards (r) depend directly on the plate thickness T, we have total resistance = (R + r) x T = K x T, where K = R + r = "Constant resistance/unit plate thickness". The energy (work) required to push out the plug = T x Resistance force = T x K x T = K x T^2. The energy of the projectile is (1/2) x M x V^2. Let us assume that the forces take so long to work that the total M of the projectile is required (not usually true in this case, as I will explain in a moment, but we will pretend it is to simplify this for now). When the projectile barely penetrates, its energy and the work match exactly, so (1/2) x M x V^2 = K x T^2. Rearranging things, we get T = V x SQRT{M /[(2 x K)]} or penetration is directly proportional to the velocity or to the momentum, since the square-root term is a constant here. So if you double the plate thickness, you need to double the striking velocity. Note that you also need some additional energy to accelerate the plug mass m, which is also directly proportional to T, to at least the speed of the projectile at any instant, though much of this may be lumped into resistance r, so I am ignoring it as a separate factor at the moment. In this example, penetration only goes up with the square-root of the projectile mass M, so increasing the mass only slowly increases the penetration ability. In reality it is even worse than that. To shear out this plug, the impact has to hit so hard that it will generate a shockwave in the plate and, because of action-reaction, also in the projectile, that radiates out from the impact site and that moves much faster than the projectile does (in steel we are talking about circa 16,000 feet/second, so the projectile is almost standing still during the shockwave travel effects). Once the shockwave has caused the plug to shear out by directly shearing it out along its entire side front to back -- or, more likely, reflecting off of the plate back so that the shearing starts at the plate back and moves forward toward the face -- the plug can now move toward the plate back under the force of the projectile nose until it is ejected out the plate back, followed shortly by the projectile. Two things cause problems here: (A) If the plug mass m equals or exceeds the projectile mass M, penetration of the projectile is IMPOSSIBLE (repeat, IMPOSSIBLE). The projectile can hit at almost the speed of light and it will merely turn into an incandescent gas and stop, while the plug will be ejected as a gas out the hole in the plate back, moving at a high speed, depending on the ratio of m to M (that toy with the row of steel balls hanging from strings that goes click-click-click as the balls swing back and forth when you pull one or more of them out at one end and let them swing back and hit the stationary balls, ejecting one or more balls on the far end of the row, which then swing back and hit the original end, making the original balls swing backward, etc., etc., shows the effect). (B) Even if m is smaller than M, so complete penetration is possible, remember that the shockwave is shearing out the plug in the plate. If the projectile and plate are of the same material (but the plate is not indestructible, of course!!), then the shockwave in the plate that does the shearing only moves a total of twice the thickness of the plate before the plug is completely free to move (resistance R ends and r begins). This distance is also the distance from the flat nose that the shockwave reaches into the projectile body when the plug is finally sheared out and note that only half of the projectile mass within that distance is actually applied to adding its force to the plug shearing effect (that is, only the material near the projectile nose that the shockwave has "told" about the impact -- material farther toward the projectile base does not even know an impact has happened yet!!) and then this "informed" material's inertia has to move forward (assuming this force application is at the speed of the shockwave, too, but in reality it is possibly slower than that) to the flat nose tip to exert its effect on this shearing action, so only the half of that informed material nearest the flat nose actually has an effect during the plate plug shearing process. Indeed, the projectile can be sliced off behind this length (in this case roughly equal to the plate thickness T) and the shearing action against R will be identical!!!! The projectile only has to be longer than this to provide the added energy to overcome resistance r, which is obviously going to be much less than R, so only a rather small added length of projectile is needed to finish the penetration process. What does this mean? It means that increasing M has very little effect, if any, to reducing the velocity V to barely penetrate -- any more M at a given V and the plug will be ejected faster and the projectile remaining velocity of the shell after eliminating r will go up, but this is rather small compared to the energy needed to overcome R and thus the total projectile mass (weight) M has rather little effect on the penetration minimum velocity V(limit), once a minimum M (due to projectile useable length T plus the small length (momentum) increment to overcome r) is achieved. The combination of A and B, above, make penetrating thick plate more and more difficult for a given projectile mass M until when m equals M, no direct complete penetration is possible at any V, just spalling of the plate (ejecting the plate mass as a replacement projectile out the plate back). (2) Against moderately-thick homogeneous, ductile armor, the material resisting the projectile is only the material surrounding the nose and any farther-away material that must be displaced toward the plate back and/or sideways to allow the projectile to "bore" its way through like a nail pushing through a piece of wood. Each increment of penetration into the plate is roughly independent of the material already penetrated or not yet reached. There is less resistance near the plate face and near the plate back as the armor can bulge upward -- either back toward the projectile base to form a crater ("coronet") or forward making a deep bulge at the plate back that eventually tears open ("petals") -- to get out of the way, while in the center of the plate it can only be forced sideways into the surrounding plate material, which is VERY difficult to do in a strong armor ("plastic deformation" or "wedging"). With thick plates, the material is mostly this central region and the resistance per unit depth can be considered a constant. This central region, to a first approximation, does allow penetration to go up directly with the energy available to push through it (like swimming where each stroke is the same as every other stroke, only different at the initial jump into the pool and when you have to reverse direction at the far end of the pool). So with thick homogeneous armor, if the projectile were on the end of a hydraulic ram, the energy that the ram would need to penetrate would go up directly with the added thickness of the central area (the near and far face bulging/tearing effects reduce the needed energy to go through those areas, but they become less and less important as the plate gets thicker). It turns out that the near and far face effects are similar to plugging in their energy requirements until they max out in the plate thickness that they occur in -- that is, the sides of the crater in the face and the bulge at the back resist as a unit, so the energy needed to penetrate these plate face/back zones goes up with the square of their thickness, meaning in turn that the penetration of these edge regions, T(crater) and T(petal), is linear with V (that is, with momentum), eventually each becoming a constant as they no longer get bigger and the rest of the penetration is through the central region increasing in thickness. The complete penetration curve using a bluntly-pointed cylindrical non-deforming, indestructible projectile of a fixed weight at normal obliquity giving kinetic energy needed/unit plate thickness in the vertical axis (increasing upward linearly) versus plate thickness in the horizontal axis (increasing linearly to the right) looks much like a nearly straight sloped line from very near sheet-metal thickness through about 0.75-projectile diameters ("calibers") of plate thickness for WWII armor steel (this is the penetration going up with momentum region where the sum of the crater and petal thickness is still getting thicker and there is little central region yet). Above the 0.75-caliber region, the central region is now getting thicker and thicker and the penetration curve gets flatter and flatter, since a horizontal line means a constant amount of energy needed to penetrate each increment of plate thickness. Note that it never quite gets horizontal because energy is lost due to shockwave formation (including the "wham!!" noise on impact, for example) and the cratering+petalling region still makes up a noticeable part of the plate even when the total plate thickness is 2-3 calibers. These high thicknesses require impacts at near muzzle velocity in WWII guns to get such deep penetrations -- anything more requires such high striking velocities that the projectile and plate metal starts to break apart and/or melt and the projectiles start to erode from the nose back even if they stay in one piece otherwise; this gets you into the region of today's APDS and APFSDS super-high-velocity anti-tank rounds, which are another thing altogether!! (3) Note also that at the very thin end, where the plates get down to paper thickness, they act more and more like trampolines, so thinner armor actually takes MORE energy to penetrate per unit thickness than near the 0.05-caliber sheet-metal thickness (a trampoline spreads the energy around over a wide area like a spider's web). However, projectiles are rarely ever going so very slow that this thin material will stop them unless they hit it at a very high obliquity or have punched through a lot of plate material already, so it is interesting, but not usually of consequence with non-deforming gun projectiles. All of this makes the penetration curve for homogeneous armor with a medium-length-point projectile at normal have a "check mark" or "square-root symbol" appearance with that zig upward at the very thin end of the curve as plates get even thinner and the straight increasing edge-zone portion just above this out to about 0.75-caliber thickness, and finally flattening out toward a horizontal shape (but not quite getting there) for thicker and thicker plates. The curve ends somewhere about 2-3 calibers of plate thickness, since above this the projectile usually always are severely damaged and the super-high-velocity region, with its own different laws of penetration, begins. As you see, things are not so simple. For example, face-hardened armor has both a hard rigid face region and the soft, ductile back region, so it is a compromise with some effects depending on the ratio of the hard to soft regions, while other effects do not care. My program FACEHARD is so complicated due to this and due to the fact that this armor is SUPPOSED to damage projectiles to stop them from penetrating and it does so differently with different projectile and plate characteristics, which must be matched one to the other to get any reasonably accurate results. A real mess. Projectile damage is a mess with homogeneous ductile armor, too, and things are even worse with this armor type, since nose shape has a big effect, which is not true with hard-faced armors (the latter either break open or they don't, with simple adjustments to projectile nose shape that are usually absorbed into the projectile's overall damage resistance effects, anyway). Also, homogeneous armor, depending on its hardness (strength) and toughness (crack resistance) and the projectile nose design, can partially fail by different causes as the projectile goes through the plate (this always happens due to cratering and petalling even with a known pointed nose shape, but those can be handled as linear constants for the most part) -- for example, some plates will fail by plugging of the face layer (no crater due to a very flat projectile nose) and then tearing open by petals at the back, ejecting part of a plug. This kind of thing makes this armor a total mess to do anything with under even slightly non-standard conditions, but get very crude average effects as plate and projectile characteristics change from the known evaluated designs. I hope this gives you some idea of the problems involved. And notice that I did not get into oblique impact, which is yet another BIG "can of worms"!!! Nathan

Wow, that is hard enough to read when formatted.....sorry it didn't post like it was in the email when I pasted it.

Here are his formulas that he uses for each type of armor.

http://www.navweaps.com/index_tech/tech-033.htm

The homogeneous armor seems like it's more applicable to us. And if you take away all the variables that would be equal between two arrows, you are basically left with mV^2!

Well don’t that beat all, I think he says that up to .75 x caliber (diameter) that penetration is governed by momentum, and beyond that (0.75 x caliber) penetration is governed by KE.

Just as I was thinking (most) my deer fall under the .75x caliber line; Nathan throws in the trampoline effects of thinner armor and it’s non-linear energy requirements.

Now, I just don’t now?

canopy

lol

That right there is why I hate what I do sometimes. The people I work with talk about stuff like this at LUNCH!!!

The way you spot an extravert where I work is they stare at YOUR shoes while they talk instead of their own!

"The homogeneous armor seems like it's more applicable to us. And if you take away all the variables that would be equal between two arrows, you are basically left with mV^2!"

LOL

I need a large bottle of Tylenol !!! Did It pass Through? LOL on "king of the hill"

I see now, we're gonna have to classify the deer hide thickness from Florida to Sasketchewan before we can get this right!

Different strokes for different folks?

Check out the thread entitled "PHOTOS OF TEST ON DEAD COW," and see which arrow penetrated best into the cow from that 45# recurve. I'd bet the KE was around 26 or less, and the momentum value was very, very high.

Dead cow tests and the like are random at best. Angle of entry is not the same for each arrow. What it strikes or misses while going through is different for each arrow. Broadhead rotation and sharpness are different for each arrow. But if you see that as proof positive, so be it. I, on the other hand, see too many variables, and prefer to be convinced by less random testing.

I doubt to see that same result with a 400 grain arrow and a sixty lb bow putting out twice the KE.

I am actually pretty darn sure you would get better penetration with that setup T-bone. BlindMouse1 is correct, too many variables and not enough shots. Not to bash the thread, cuz I think it was a cool test, but its author stated "the arrows were tuned pretty good to the bow." In order to perform an accurate test you must eliminate tuning variances from arrow to arrow and inconsistent test mediums. Also, only one shot was taken with each arrow if I'm not mistaken. If you must use an animal carcass, you're going to have to do a whole lot of shooting into a bunch of different fresh carcasses to prove your point to me, again, with no tuning variance and smaller fletching for the lighter arrow. You've also got to use the same arrow point, resharpened each time if it is a broadhead, on all the arrows.

"Check out the thread entitled "PHOTOS OF TEST ON DEAD COW," and see which arrow penetrated best into the cow from that 45# recurve. I'd bet the KE was around 26 or less, and the momentum value was very, very high." - T-bone

This pretty much duplicates every test I've seen, including Ashby, the homebrews into foam and boards and everything I've arrowed during the last three plus decades. Note how the mass and momentum consistently outpenetrates the lighter/faster arrow without any great worry about pristine/perfect flight. This has been repeatedly duplicated over hundreds of years in the field in game and on the battlefield in humans. Also note how most in favor of less mass and momentum in favor of lighter and faster will always express concern over how the lighter/faster arrow was never in perfect tune, the broadhead was never sharp enough, or it always struck something harder.

It seems at times we have short memories and have a tendancy to discard generations of real data from the field. This is why someone, whose only experienced is what they've read about the worlds fastest IBO compound, would discard a 45# recurve or longbow as being incapable of producing enough speed and energy to kill big game animals. The reality is as anyone with experience using such light basic archery tackle is that with mass and momentum of a heavier (not lighter) arrow, a 40-45# bow is devistating. KE neither explains this nor discards this. No matter how you wish to crunch numbers, this is what is and this is what will be.

Daddy Bear

"It seems at times we have short memories and have a tendancy to discard generations of real data from the field. This is why someone, whose only experienced is what they've read about the worlds fastest IBO compound, would discard a 45# recurve or longbow as being incapable of producing enough speed and energy to kill big game animals. The reality is as anyone with experience using such light basic archery tackle is that with mass and momentum of a heavier (not lighter) arrow, a 40-45# bow is devistating. KE neither explains this nor discards this. No matter how you wish to crunch numbers, this is what is and this is what will be"

That is pretty much it in a nutshell. :)The slower the bow the heavier the arrow to overcome it.Any bow shooting as heavy of an arrow that will give you a trajectory you can live with will always be best.Some folks just can't live with a little arch in there archery and others can. ;) jmo

PapaBull,

Yup ;) I love that show.

Daddy Bear,

I've seen tests go either way, and all the ones I can currently think of that say that momentum is the predictor of penetration are trad guys who largely disregaurd the need for optimum arrow tune, ESPECIALLY in such a test. One of them, Ashby's, seems to have been biased against KE in the first place! It seems Ashby wanted KE rules to be dumped in Africa so stickbow guys, who can acheive high momentum much easier, could hunt over there. JMO

Craig

That settles it. Iam going to get a 10lb bow and a one-hundred lb arrow! LOL!

What would be the difference from Africa and Ashby with some blanket rule here? What if some legislative body with no experience whatsoever hunting with bows and arrows decide to listen to a college professor (who also has no experience hunting with bows and arrows) and they decide to place into law a minimum energy requirement for archery tackle based on KE theory for penetration. Well, wouldn't that be dandy. You will then have persons without a clue of reality outlaw that 45# recurve for use on big game because cruching the numbers will show it cannot produce enough speed and energy to kill big game. Discard the fact that it actually works well in the field and discard any concept of proving or disproving theory by reality with empirical data from the field. This is why it is wrong and this is why I'm of the opinion that lab coat theories are of no value unless such theories are supported by empirical data from the field.

If this becomes reality in your state you better hope you have an Ashby collecting real world data to show what works and what doesn't.

Daddy Bear

I'm not saying that their KE rules are on target. I think a 45# bow is a very effective hunting tool for deer, and I think with good tune, it'd do great with 350-400 grain arrows, or possibly lighter.

Craig

Can't we just go hunting and have fun? If what we shoot penentrates two lungs and makes a quick, clean kill can't we all just know in our minds that our set up is perfect? If everybody here is focused on maximizing penetration I'll share a secret I learned years ago; a seventy pound compound with a 2219 and a 125 gr. Thunderhead, properly tuned, will blow through shoulders, leg bones, and anything else in it's way. It just isn't any fun, but neither is novel length threads debating the merits of kenetic energy vs. momentum.

Robo- whats the FOC on that?

Steve

"Most guys shoot light to medium arrows, because that's whats offered down at Sporty Warehouse, and that's what they learned to shoot. Heavy arrows pretty much disappeared with wood arrows in general."

And damned if "most guys" have no problem whatsoever getting all the penetration they need to take deer all they want. Go figure!?!

I hear you, Robo. Light, medium and heavy arrows all kill deer but the heavy arrows kill them even deader. You just got to deal with that rainbow trajectory and they'll make deer more dead than anything else you can kill them with. :) I know that my lighter arrows shoot much flatter and that I'm much better at putting them where they belong, so I've settled for just regular dead, but extra dead wouldn't be such a bad thing, I guess. I suppose that's what they call "overkill". LOL.

OK so we seem to have expressed a desire to keep this thread oriented in a practical way. I've found that with my selfbows performance is enhanced when I shoot 9- 11 grains per lb. which somewhere around 500 grains per lb for a 52# bow. Not too heavy. Not too light. Moderation is pretty good for deer sized game. PB, you are right. That 520 grain arrow killed that deer deader than dead. :) Jawge

The deader they are, the easier they are to field dress, George. Next time I kill one with a 420 grain arrow out of my 55# DAS, I may have to try killing it again when I get up to it to see if it speeds up the field dressing process.

By the way, Jawge.... Patriots 42, Colts 24

LOL, PB. BTW I think I'll be watching the Pats and Colts Sunday. The Pats are playing with a vengeance. Jawge

For those who are following this thread (I've contemplated starting a new one) I will add my further correspondences with the Armor Penetration expert, Nathan Okun.

After his first reply I responded with my thanks, and the following:

Since much of what you explained is beyond my comprehension (despite having read it 3 or 4 times now), maybe I can pose the question in the form of a specific example and you could tell me what you think:

Say I have 2 arrows of exactly equal dimensions. Arrow 1 is 400 grains and impacts a uniform, foam block at 300 fps.

Arrow 2 is 1000 grains and impacts the same block at only 190 fps.

Can you predict which one will penetrate further, and if so, how? I purposely made the two arrows have roughly the same kinetic energy. All the variables (including target material) are equal except for mass and velocity.

He responded, in part, thusly:

"Against soft foam, the penetration would, I assume, be about the same. The material gradually slows the arrow at each point independent of any other point, so it follows a more-or-less strict KE (0.5xMxV^2) Penetration Depth formula.

The Momentum (MxV) Penetration Depth formula applies when the entire block of target material from front to back has to be completely "cracked" prior to the projectile penetrating at all and it is also subject to the speed of the failure limiting the effective mass of the penetrator (the material near the rear end of the penetrator may not ever get involved in defeating the target and thus is a dead weight, regardless of striking velocity)."

End quote. He went on to explain how there is a "scaling" effect when dealing with targets that crack, etc.

It seems that momentum would be more pertinent than KE when it comes to breaking bones, if I understood his reply.

I replied again and mentioned the Dr. Ashby reports, and gave him a link. I don't know if he read it all, but he did respond thusly:

"I wholly agree with Dr. Ashby as to the fact that you go from actual test results (or "battle results" -- actual shooting in the field) backward to find out why. That is how I did all of my face-hardened armor evaluations, once I determined that the formulae sets used more-or-less successfully for homogeneous, ductile armor were "falling on their faces" when attempts were made to apply them to face-hardened armor. This method is "semi-empirical" in that I had a very generic format for a penetration formula based on the DeMarre Nickel-Steel Homogeneous Armor Penetration Formula (French, 1890) and then "let the chips fall where they may" as I changed that formula in numerous ways to fit the actual test data that I had.

"These changes were considerable and I tried to understand why I had to do them at every point in my analysis. Hence, my discussions concerning scaling effects and the lack of the importance of projectile weight compared to striking velocity in its penetration and so forth. I later found out that I had reproduced almost verbatim test results and evaluations done in the 1870-1895 time frame by a pair of experimenters (father and son) in England on how iron rods failed under impact loading that pulled them abruptly until they snapped in two!! While the laws of physics always apply, just HOW they apply in a given situation is not always obvious (shockwaves in hard materials breaking them prior to much of the impacting projectile even knowing that the projectile has hit the material in the first place being one of these less-than-obvious factors, at least to the people back then testing the armor, in this topic)."

"Note something else: Short projectiles passing entirely through an object act somewhat differently than long projectile merely digging in a certain distance. There is drag along the side of the projectile, as well as the edge effects (cratering and petalling/plugging/spalling), that make it act different than it would if merely moving in the interior of the plate hit.

"Also, if you are talking about a deer or some large animal, even if you miss bone and only pass through the muscle (constant resistance assumed during the entire penetration attempt), then this side drag can exert a decided effect on penetration. I am not sure what the rule would be for side drag as to velocity, though it would seem to me to follow a total-kinetic-energy-based formula (KE to some exponent power) than momentum. If the friction varies much with projectile speed even in the range of speeds we are dealing with here, then that exponent may actually not be a constant, but be a function of instantaneous speed at each point in the penetration)."

"My experience is with armor that is rather thin compared to the length of the projectile (up to two calibers thick, usually less, for projectiles that are 3-5 calibers long), not long arrows into targets that can be considered "semi-infinite" in thickness (no far side unless the projectile hits at a very high speed and can punch entirely through the animal). This can alter things, I would think, but we shall see, won't we?"

End Quote.

I like the fact that he admits that he is not familiar with longer projectiles going through thicker materials and is not sure how the velocity component will come into play. He understands the value of actual testing over theory.

Some more from Nathan:

Regarding Ashby's report: "The statement the mass is MORE important than velocity in penetration is NOT true from my experience!!"

"All things considered, I would say penetration is probably much more a total-KE effect than one that is a total-momentum effect, barring the transitory effects of hard bones where momentum of the nose region of the arrow may be more important, making velocity more important than weight in these portions of the target. BUT, I cannot see ANY case where total projectile mass is MORE important than projectile velocity, if you adjust M versus V^2 in a fixed KE balance."

Nathan's opinion lines up with mine pretty well. That's why you need a heavy arrow for water buffalo; a heavy bone hit is inevitable, and the heavier arrow with a high momentum will more efficiently break the heavy barrier protecting its vitals. This higher level of heavy bone efficiency, however, IMO, is not needed on most game. I'd rather just avoid the bone that will stop me (the small, yet very thick, ridge of the scapula). An arrow traveling in excess of 200 fps helps me personally do that best.

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