KE vs Momentum
 

I've heard several memebers say that the momentum that an arrow has plays a bigger role in penetration of an arrow than KE does. So I would like to know what is a good momentum level considered. My bow produces over 80# of KE and depending on which arrow I'm shooting it has momentum of .536 to .555.

Is there a standard of what the acceptable level of momentum should be for a bow?

RE: KE vs Momentum
 

A person can become too scientific to the point that what is normally a simple given, based on historic standards, becomes very confusing.

My simplistic interpretation of KE vs. momentum is:

1. KE is velocity derived from energy transmitted by the bow.
2. Momentum is force derived from the weight of the shaft.

Properly combine the two and you have more than enough to do the job.

A 40# bow, stick or compound, shooting a shaft having recommended minimum of 425-450 grain weight will efficiently do the job on a Whitetail. Therefore, Lower energy (slower) bows are assisted by heavier shafts (momentum = force attained from weight) and cut-on-contact heads.

RE: KE vs Momentum
 

c903,
Actually, KE is the force derived from the weight of the arrow at a given impact velocity. Where in the equation below velocity is actually the impact velocity of the arrow.

KE = (1/2)*mass*velocity*velocity, in (ft*lbs)

Kinetic energy is the work done on an object over a given distance, so in physics terms:

work = Force * distance = KE

As expressed above, KE = (1/2)*mass*velocity*velocity.

In order to make the above equations come out in the units of ft*lbs, which is what we bow hunters like to know, you have to work out the above equations in SI notiation (kg for mass & m/s for velocity) this will give you an aswer in Joules which can then be converted to ft*lbs. Several archery manuals will have a unit conversion built into the equation which allows you to use a modified version of the KE equation above and you can use fps and grains instead of SI units.

Hope this helps...

Redneck

RE: KE vs Momentum
 

KE is useless!

RE: KE vs Momentum
 

I could not agree more. Relying on just one or the other does not give the archer an accurate picture of the entire function and characteristics of the arrow.

That I do not agree with. KE must also be considered when looking at the "entire package". What good is a heavy arrow that travels at a relatively slow speed if the archer is not very good at judging distance? A moderate level of both is usually the best option when applied to the game most commonly hunted with a bow in North America today.

RE: KE vs Momentum
 

PA would you deer hunt with a .22?

RE: KE vs Momentum
 

No. But then the ballistics on a bullet and how it creates damage and death are somewhat different than that of an arrow fired from a modern compound bow.

RE: KE vs Momentum
 

Nobody really answered my question. I'm playing around with some different weight arrows and such and seeing how the speed vs weight debate always comes up, I would just like to know, what is considered an acceptable level of momentum.

RE: KE vs Momentum
 

OHRedneck:

As I said; rocket science is not required to determine the setup necessary to do the job. Of course, you can formula the hell out of physics. However, what great advantage is realized?

Mike from Texas:

Even if you shoot a lighter arrow than necessary, as long as the total shaft weight is not less than recommended for a 70# draw-weight, you will have all of the necessary momentum required.

Keep in mind: light arrows often means more bow shock, more noise, harder on bow, and can be more sensitive to post-shot recovery than a heavier arrow.

RE: KE vs Momentum
 

Mike,

There is a somewhat accepted number but I cannot honestly remember it at this point. I remember a discussion on here awhile back when the Ashby report was reviewed. For some reason I remember the number .57 but that may have been the momentum figure that someone was asking about and not what you are looking for. If only ArthurP would catch wind of this one. ;)

RE: KE vs Momentum
 

I've intentionally been avoiding this one, Frank. ;)

Ashby says an arrow with a momentum figure of .57 is adequate for all game up to the size of zebra. Of course, most KE buffs pooh pooh Ashby's arrow lethality report because they're hunting puny, wimpy little whitetail deer, not that tough African game, and say momentum is meaningless for deer.

That's just as wrong as saying KE is meaninghless. You don't have momentum without also having KE. You don't have KE without also having momentum. KE simply tells how much impact energy the arrow has. MOMENTUM is what determines how that energy will be used and how deep that energy will drive the arrow.

To get a 400 gn arrow up to .57, you need to move that sucker along at 321 fps. To get a 700 gn arrow to .57, it only has to travel at 183 fps. The 700 gn arrow would carry 52 ft lbs of energy. The 400 gn arrow would be stroking along with 91.5 ft lbs of energy!

You wanna get a dinky little 350 gn arrow up to .57?? Easy! All you gotta do is fire it at 367 fps and 104 ft lbs.

So, we've got a 350 grain difference in arrow weight, a 52 ft lb difference in energy and a 184 fps difference in arrow speed, all to get exactly the same momentum. Or, said differently, the same penetration potential.

Certainly, you don't need anywhere near the levels of energy and momentum these figures represent to blow a broadhead arrow through a deer's ribcage. On the other hand, hopefully you can see why looking only at speed and KE when choosing an arrow weight for hunting is a big mistake. And why those "minimum KE" charts, for hunting this or that animal, are not to be relied on as the absolute last word.

Momentum formula: Arrow weight in grains X speed/225213.8

225213.8 = 7000 grains (per pound) X 32.1734 (gravitational constant)

That formula should be just as well known as the KE formula.

Now, I have never seen a minimum momentum figure for hunting whitetail deer. I'd hazard a guess and say that .33 would be a fair bottom end number. I know there are guys out there hunting with selfbows and 500 gn arrows at 150 fps that are doing quite well on deer.

Oh, by the way, don't forget that arrow speed, energy and momentum are constantly decreasing as the arrow goes downrange. How much you have at the bow is secondary. It's how much oomph your arrow has when it hits the animal that's important.

Here's a link to Ashby's arrow lethality study. It's a very interesting read, whether you agree with him or not. He covers momentum, KE and mechanical advantage very thoroughly in Part IV.

www.tradgang.com/ashby/

RE: KE vs Momentum
 

By the way... .33 pound seconds... That's assuming a cut on contact type head. Use a punch type tip or a mechanical and I'm sure you'll need more.

RE: KE vs Momentum
 

I would think shaft diameter or friction would play an important role also !

RE: KE vs Momentum
 

I think any friction advantage smaller diameter arrows have is a minor advantage at best, and is way overtalked and overblown. IMO, the lubricity of body fats and fluids would minimize any real advantage smaller arrow diameters would have.

Also, when you start talking smaller diameters, that generally means carbon vs aluminum. That also generally means the smaller diameter arrows are significantly lighter arrows. Significantly lighter arrows carry significantly less momentum. So, the friction advantage of smaller diameters is even more offset by their lower momentum values.

Comes pretty close to being a wash, as far as I'm concerned.

Now, if you weight those skinny arrows up to weighing in about the same as a 2216 to get their energy and momentum values up... Then we can start looking at arrow diameter as more of a major player when it comes to penetration.

RE: KE vs Momentum
 

If you want a lot of momentum without a complete pass thru use a 2514 arrow with a 125 grain head on it
if you want less momentum with a complete pass thru use a speed pro max with a 55 grain head on it.

the point I am trying to make is that you Can have an arrow that carries a lot of momentum but if it has a weak spine the arrow will stop dead because of all the flexing it it does and the friction it produces on impact of its target.

while a arrow with less momentum and a stiffer spine and smallet diamiter will penetrate deeper because momentum is lot lost due to flexing of the shaft .
other thing to consider that the cut diamiter the head produces will allow a smaller diamiter arrow to pass thru much more easily opposed to a larger diamiter shaft.

all this momentum and KE equations work good on paper. but the proof is in testing the arrows aginst each other.
doing a side by side compairison of different brands of arrows you will be shocked to find what actually out penetrates another brand.

just because you shoot a heavy arrow does not always mean you are shooting the most energy efficient arrow.

RE: KE vs Momentum
 

Mike from texas

what I consider an acceptable level is enough to kill the animal ASAP!

RE: KE vs Momentum
 

I have yet to see any slo-mo video of an arrow penetrating an animal's ribcage. Bigpapascout, if you have the visual proof that arrows flex when passing thru an animal's ribcage, I'd really like to see it. Otherwise, I consider that nothing but a myth.

I have seen so called tests that are set up specifically to 'prove' small diameter, light carbon arrows outpenetrate heavy, large diameter arrows. They've all been conducted on artificial mediums that are designed to stop an arrow by friction. I do not find it shocking in the least to learn that a large diameter arrow with lots of surface area is going to penetrate less in that kind of medium than a skinny arrow with little surface area. In fact, anybody with any sense would EXPECT those results. (That's why they 'tested' in that kinda stuff anyway - to produce 'shocking' results to baffle the unwitting and sell the advertisers' products.)

I'd like to see Ashby's study repeated using one specific brand of broadhead and bow as constants, with the variables being point of impact, arrow diameters, materials and arrow weights. With those results, we would be a long way toward blowing all the theory, mythology and outright BS totally out of arrow selection.

RE: KE vs Momentum
 

Art, I assume you know he's in the process of doing a new study, right? I have no idea what the parameters are this time, but I'm pretty sure he's using a wide variety of modern day heads.

I think it's still a few years from completion, so, keep the faith :)

RE: KE vs Momentum
 

Arthur p

I dont have any slow mo videos
but I have shot animals with large diamiter heavy grain flimsy aluminum arrows with a 70 pound bow and the arrow not completley pass thru the animal
I have NEVER experienced this using Stiff carbon arrows, I have always got a complete pass thru with carbons.

just because you dispute the facts changes nothing.

RE: KE vs Momentum
 

Conversely, sir, just because you said it doesn't make it fact.

Did you use different broadheads? Different bow? Did you simply make better shot selections with better placement at more reasonable distances? You leave out way too many details. Maybe you didn't even consider the details, yourself.

Range... I heard he was preparing to do another study in Australia. Didn't know he was underway with it. The man does his lethality testing the right way though. Several years of in depth work on actual game animals vs an hour in the backyard with a foam target. ;)

RE: KE vs Momentum
 

Check this thread on AT out.

Full frontal shot on African Big Game-

http://www.archerytalk.com/vb/showth...threadid=88679

Wow. Skin on a Giraffe is 1" LESS thick at the front than broadside. That's some seriously thick skin. I can only imagine what a cape buff or rhino have...

RE: KE vs Momentum
 

Thanks for the formula Arthur. I've been playing around on BowJackson's website and I am checking the momentium not only at the bow, but also at 20 & 30 yards. I am not as concerned with the values at ranges farther than that since I have a self imposed limit of 30 yards for a shot on a deer.

RE: KE vs Momentum
 

BPS,

Your ultralight, super duper high speed theory is going to get you no where here.

I am going to side with Arthur. If you didn't get the pass thru's with the heavy set ups, at slower speed, than check your tune, broadhead, or form.

A compromise of KE, and momentum is the key.

RE: KE vs Momentum
 

I really don't want to get into this..but I can't keep my big trap shut..:D But I will keep it short and sweet. :) (yeah..right!)

IMO, Momentum should be emphasized (and is KEY) in 2 set-ups

1) where energy (however you want define it) is low i.e. many traditional set-ups, low poundage, shorter draw lengths softer cams/wheels, etc. In those cases, I believe Momentum is much more critical. You want a pretty heavy shaft and fixed blades of some sort to maximize energy and penetration down-range.

2) BIG and/or "dangerous" Game. i.e. Moose, Buffs, the bigger African/Asian/Australian game species, etc. Where you need every bit of "leverage" you can get.

Though we hear tales of the lady pulling 36 pounds who has a 24" draw on an old round wheel bow who shot completey through a Moose with a a 2 inch cut 5 blade mech, I think in those cases, there was a lot of luck invoved and exceedingly good shot placement...neither of which we can always guarantee due to circumstances beyon our control. It's best to plan for the worst..not the best.

On most modern bows shooting fairly light to medium weight arrows at very good speeds, tipped with a stout broadhead of whatever make you prefer, KE is an acceptable benchmark, and momentum becomes less critical unless you are shooting very long bowhunting ranges (i.e. 40-60 yards) for something like Elk, Caribou, big Canadian whitetails, Big muleys, etc where that arrow is coming back into orbit and losing alot of energy.

On deer sized game I feel the point of whether KE or momentum is more important is a moot one. Except in scenario 1 above.

From my experience shaft diameter does provide an advantage in penetration (as well as windrift and less velocity decay) compared to the larger diameter alums with similar (or even lighter in the case of carbon) weights,energy, & broadhead design (many of the old PC style arrows were not exactly light in most cases by the time you glue adapters, older heavier vanes, and a 100-125 grain head on them). And I also agree with BPS regarding shaft flex. While I have no scientific proof, it is only reasonable to assume that carbon will act the same way on game it hits as it does in inanimate targets. Aluminum bends around like a noodle upon impact..while the softer nature of hide, flesh and ribs may not make for as much shaft oscillation as a foam target, It makes no logical sense that the phenomenon is completely suppressed/negated going from one target medium to the next.

Bow tune is another key factor as I'm sure we all know, and a whole 'nother can o' worms.

Regardless...I suspect this topic, like Singles Vs. Duals vs. Hybrids, Mechs vs. Chisel, vs. Cut to the tip, Open Camo vs. Blend camo. and other similar topics are really only topics of argument started years ago to get us from one season to the next on the message boards and are hardly relevant whatsoever!

RE: KE vs Momentum
 

LOL
I dont give a rat who you side with, It aint about sides
It is about you cannot put a mathematical equation on a stiff arrow.

Use what gives you the best results and I will do the same

RE: KE vs Momentum
 

Jeff, it is NOT reasonable to assume an arrow reacts the same way when it hits flesh as it does when it hits an inanimate object, like a target.... unless it hits solid bone, like the ball and socket in the shoulder, and immediately slams to a dead stop.

On a broadside hit where the arrow knicks a couple of ribs, it's not going to have much resistance. An arrow going a mere 200 fps when it hits a deer is going to whip through the deer in about .008 of a second, assuming a 20" wide ribcage. Doesn't give that arrow much time to flex, does it. By the time the arrow could react to the impact, it's already through the deer and gone.

Talk about small diameter and friction. What's the difference in friction between a carbon arrow with stiff plastic vanes and a 2419 wearing feathers? The carbon shaft is smaller and, naturally, has less friction, but those vanes! The 2419 has more surface area and more friction on the shaft, but those feathers slide right through. Prove it to yourself. Grab the shaft of a vane fletched arrow and pull the fletching through your closed fist. Then do the same with a feather fletched arrow.

I agree about momentum/KE being over-argued. Like I said, you don't have one without the other. Like YOU said, with a high performance bow you can stack up a pile of KE and do well. On the other hand, while you're stacking up that KE with speed, you're also stacking up the momentum. That's why a high KE arrow will penetrate. Not so much because of the energy but because it's also carrying a lot of momentum. Don't take my word for it. Do the math!

It's easier and quicker to pile on the momentum with arrow weight than it is to get it with speed, but you do get it with speed. Still, momentum is the key, as far as I'm concerned.

Where I get my dander up is when KE snobs start saying you must have X amount of KE in order to ethically hunt such and such animals. Not only are they operating with a false premise, their BS is dangerous to youth, women, disabled and traditional hunters, who cannot shoot high poundage bows or whose bows cannot churn out gobs of KE. Momentum is a much better indicator and is easily achievable for most people.

Lets assume for a moment that my suggested minimum of .33 pound seconds of momentum is a good figure. I don't know that it is, but lets assume... That is achieveable with a 500 gn arrow at 149 fps and 25 ft lbs KE. - ie. a 50 pound selfbow. Or a 400 gn arrow at 186 fps, 31 ft lbs - ie. a 12 year old with his youth compound. I don't like the idea of using less than a 400 gn arrow for hunting so I won't figure for a lighter arrow.

Those low KE setups will do the job BUT, you have to have make intelligent choices in arrow selection, broadhead selection and shot selection. You have to have the bow well tuned. You have to execute the shot properly and place the arrow accurately.

Of course, those same choice and performance issues are imperative no matter whether you're shooting a wimpy rig or a mongo rig. It's easy for the hunter to blame the arrow for his failure, even though it's hunter's fault because he chose the wrong arrow to begin with.

RE: KE vs Momentum
 

What I'm saying is that it's relative..While the effect on a softer hit may be reduced..even greatly, it still should react in a similar but less "intense" way..i.e. Aluminum should not have as much oscillation on that soft hit, but do not forget the oscillation will be reduced by a similar % on the carbon arrow. The effect may very well be diminshed by 90%, but the carbon arrow will still have the advantage 'cos it doesn't have nearly as much in the first place.

Actually it has quite a bit of time to flex. I know you've seen all the high speed video camera stuff from Easton before. Arrows go through all kinds of contortions leaving the bow (as does the bow itself) in the matter of a second. At that point of impact, even on a rib or hide where there is a counteracting force (however small), I cannot imagine their not being oscillation whatsoever in any shaft regardless of arrow makeup.

I don't disagree with you on these points. I'm a feather man, and you and I both know why. Vanes are nothing more than a convenience in my book. Convenient for fletching time, and convenient on the wallet. They do nothing for accuracy, and have thier own problems like flutter and pentration impeding drag.

Again I do not disagree. I was just making a point of distinction where the line between KE and momentum blurs..where KE is "just as good" of a factor for determining penetration potential (all other things being equal).

Again, I personally believe there is a "blurry" line where KE and momentum are relative enough to each other that using KE as an indicator is as good an indiactor as momentum (i.e. where momentum is not "key"..though that is not to say it's unimportant, just less so)

Who you callin' a snob??[:@];):D. Agreed, as I laid out in "scenario 1" in my intitial post, momentum indeed should be the determining factor. However the opposite is true as well...when a certain threshold is reached KE is just as viable a means as momentum..the problem is defining where that threshold is. We can argue 'til we are blue in the face, but the game law makers have to make a distinction and go with what they feel is an adequate simple to use indicator. I agree though, it may very well be incorrect.


This is the crux of the matter...all the KE or momentum in the world is not worth a hill of beans unless you adhere to what I just quoted you as saying.



And as you have confirmed here :)

Make no mistake Arthur, I'm not arguing with you. I just that I feel this is one of those cases where the line is blurry, and there are no hard and fast rules for everyone. :) I agree with you on many of your points re: momentum, but I believe the amount of importance of certain factors and under what circumstances is where we will need to just agree to diasgree.

Always fun though.:) Glad to see ya back and in the groove :)

RE: KE vs Momentum
 

I was talking about this with some of my fellow club members at the range last night. Our resident philosopher came up with the quote of the day.

"Archery ain't supposed to be brain surgery!"

:D

RE: KE vs Momentum
 

arthur p
then please explain why those fat flemsy eastons would not penetrate thru the animal not hitting any bone I might add
and the lighter stiffer completley pass thru busting rib bone entering and exiting.

Please do not try to explain that my bow was not properly tuned.

your philosipher is exactley right it is not brain surgery nor is it rocket science.....

even common sence will tell you uncooked spageti will penetrate a potato and a limp noodle will not:D

you can believe what you want to
but you can bring your self to my little Pro shop down here in tennessee and I will proove it to you by shooting the arrows thru any type of medium you want that lighter, faster stiffer arrows will out penetrate
fat, heavy weak slow every time at any distance!

RE: KE vs Momentum
 

For me at least I think it is healthy to discuss KE & Momentum but I wouldn't argue with anybody over it. At a certain level I believe you start splitting hairs. Both have merit and both are tied indelibly to each other.

Bigpapascout back in the mid 90's I was using a setup where I shot a 2514 arrow. Compared to what some of my buddies were using they looked like telephone poles.

At any rate, I went back in my journals and looked at the results; here is what it showed. Using a 2514 arrow there were 11 kills (these were midwest and northern whitetails). Of those eleven deer harvested eight were complete pass throughs. The three where no pass through was acheived hit bone. Two hit the off shoulder and one connected with the spine.

For the last five years I have used carbon arrows. While I do think they penetrate better they also have been stopped at times by an off shoulder or spine.

RE: KE vs Momentum
 

Bigpapascout, curious how your stance changes if the spine on the aluminum thicker heavier arrow is not "weak".

You seem to be comparing a stiff arrow versus one that is underspined. How does your interpretation change when equal spine is compared, with the only variables being diameter, weight and fps?

RE: KE vs Momentum
 

I think I read this in a fortune cookie once...

RE: KE vs Momentum
 

I believe (though am in no way speaking for BPS) he is saying that an overly stiff arrow will yield the same or better penetration with an exceedingly light arrow, compared to a properly spined heavy arrow.

The theory being because the shaft is so stiff, it retains more energy as there is no undue oscillation shedding said energy upon impact..especially compared to an aluminum arrow which has the most shaft oscillation.

The theory makes sense to a certain degree (if I have indeed interpreted it correctly), and I've got to admit, I'd like to grab me a Newberry (since it's warranteed with the light arrows) and some speed-pros' just to prove/disprove it myself. However, finances won't allow for the experiment and IIRC local game laws do not either (arrow weight is under the legal minimum).

RE: KE vs Momentum
 

Philosophy, or just plain 'ol common sense? :D

RE: KE vs Momentum
 

Wife and I had a rare childless evening last night. As we finished our chinese food, I unwrapped my fortune cookie, cracked it open and read "Opportunities exist wherever you look".

I looked over at her, and I'll be danged if it didn't come true...

:D

Since Vic and I'd have to believe that speed freak Kevin (Strother) have shot these things, and given your connections, I'm sure a quick call would get you Bowtech Blessing to do some testing :)

Come on. You know you wanna do it. And I wanna see you do it.

I just visited Speed Pro's site, with their stiffest arrows, I would save 75 grains over my current finished ACCs. Go with a light broadhead, and shave another almost 50 off. That'd put me at at 4.28 grains per # and 3.57 grains per # respectively. Yikes...

Quick math says I'd gain 21-35 fps. Not a ton more, relatively, for a whole lot more potential problems...

RE: KE vs Momentum
 

you have surmised some what correctly however I will add that if you are shooting wuth a release off of a loop and youre bow is properly tuned I dont believe there is any sutch thing as an overly spined arrow,
however if you are still shooting fingers you have a paradox to contend with which makes it nessessiary to have a certan amount of oscelation to overcome the archers paradox IMO this is a handicap however I do commend the guys who still shoot fingers because frankly I cannot hit the broad side of a barn without a using release aid.

but you are right about the spine, the stiffer the spine the more energy it is able to absorb.
most people believe that the heavier the arrow the more energy it can store which is simply not true unless the spine is stiff enough to hold the energy that is being transfered from the bow to the arrow, for each time the arrow flexes energy and momentum is lost.

RE: KE vs Momentum
 

Well, let's see...

First off, you decide to set up your hunting rig with 2514 arrows. Big, fat, weak and fragile arrows designed to cut lines on a target rather than punch through ribs. An arrow that's far better suited for 20 yard indoor spot shooting than hunting. I assume you chose the 2514 because it is the lightest aluminum arrow that would spine correctly for your bow? I mean, you have to have flat trajectory for sniping at elk 50-60 yards downrange. I believe I remember you saying on another thread that's a commonplace tactic for you? That you MUST shoot 50-60 yards at elk where you hunt or you don't get one?

So... You made a conscious arrow selection that placed highest priority on speed and trajectory and little priority on strength and durability for hunting a relatively tough critter. You got unsatisfactory results. My-O-My! Who'da thunk it!

You'd have been served far better by living with a tiny bit more trajectory and a heavier, stronger, tougher arrow like the 2317. That's a hunting arrow.

Using the arrow weight calculator at Jacksons, assuming you use a 31" arrow, the difference in weight between the 2514 and 2317 would have been a mere 44 grains or thereabouts. With weights and trajectories being that close, I would definitely have gone with the stronger 2317 myself.

You are like every other guy I've ever run across who champions carbon arrows and pontificates on their 'superiority' over aluminum. TO A MAN you guys invariably choose to use weak, thin walled aluminum arrows to compare to carbons. Do your comparison to a sturdy aluminum arrow like the 2216, 2219, 2317 or 2419. At the end of that comparison, all you'll have to talk about is speed and trajectory.

Anyway, to answer your question, you made a terribly rotten choice using a 2514 for a hunting arrow, but it's not entirely your fault. IMO, Easton should have left 2514's on their target chart and never have put the blasted things on their hunting arrow chart

By the way, when it comes to lightweight hunting arrows, I ALWAYS recommend carbon - even with all their straightness and consistency problems - over puny, thin walled aluminums. I've detested thin wall aluminums ever since the ONLY dozen 2213's I ever bought. Shooting into excelsior bales over a week's time and every single one of them looked like they'd been in a wreck. Collapsed like an accordian. Not to mention that their speed bled off so bad downrange that my 50 and 60 yard pin gaps opened up considerably and my 80 yard stack was closer to what I'd have to shoot 90 for, when using my normal 2216's.

If there's a type of arrow I dislike more than carbon, it's thin walled aluminums. I'd rather shoot cedar than either of them.;)

But ACC's now... I have a high comfort level with them. Too bad my wallet doesn't. [&:]

RE: KE vs Momentum
 

Bigpapascout, in case you missed this, have you tested this way?

RE: KE vs Momentum
 

Range ball

first let me say that I test arrows that are by the charts suitable for the poundage that I am shooting.

I would imagine if you could get an aluminim 9/32 shaft the same stiffness as the arrows I shoot a heavier arrow would have good penetration values.
but larger diamiter shafts even if the spine is as stiff will not penetrate as deep as a smaller dia shaft because of friction.

speed is another factor that seems to be over looked concerning the lighter arrows

what you should keep in mind is that my current hunting arrow is traveling 350+ FPS off the string
and is traveling over 340 at 20 yards, speed does equal deeper penetration.

what I fail to understand why so many people are so bent to discredit this phenomenon without really examining it.

I have been a bow hunter over 30 years and trust me if I did not get such good results from shooting these arrows I certanly would not be using them!

I am not here to try to get people to change over to light weight arrows

i just want people not to be so quick to criticize something that they dont fully understand, I get so sick of the nay sayers who are totally ignorant to the concept, when I say ignorant I am not calling any one stupid but un willing to study the concept for them selves or un learned.
see what I am trying to say?

I remember when the 65precent let off bows were introduced, every one said it will never work now we have 80percent let off bows
if it was not for people thinking outside of the box we would all be shooting with flint broadheads tied to a stick and hand carved long bows.
people want more speed and the only way to achieve this is to shoot lighter arrows and like it or not that is the direction the industry is headed.

RE: KE vs Momentum
 

Don't really know the correct answer to your question, but I'm sure that out of your setup, they'll be adequate momentum remaining after the arrow has gone through the deer.:D