For all you KE people out there...

[JAK]

My curiosity was piqued after reading so many posts about double shafting, 800-900 gr arrows and KE.  I had a suspicion that some people did not appreciate that KE is a result of both Mass,  and  Velocity.  It seems that many people are forgetting the velocity in that equation, and forgetting that for every set of bow setup criteria, there is a happy medium of velocity and mass that will produce the greatest KE.  KE  does  translate directly into penetration power, provided it is the only variable.  For example, with 2 identical arrows (to include broadheads), propelled from different bows (thus different KE, for no two bows will be absolutely identical), the one with greater KE will have better penetration.  Fully realizing that this is a trad bow forum, my virtual test bow was a compound bow, simply because that was how the program was defaulted, which kept me from making user mistakes.  This should not matter, as the physics of external ballistics is fully independent of the firing device.  It only carries the energy imparted by that device, then becomes a function of friction and gravity.

The test bows characteristics are as foollows:

Draw weight, 60#
Draw length, 30"

There were 5 different arrow weights, complete, not just the shaft.  For each weight (WT), I will list the time to target at 30 yards (TTT), speed (FPS), and kinetic energy at 30 yards (KE).  The test broadhead was 3 point for purposes of forward air resistance.

WT: 800, TTT: .502, FPS: 185, KE: 57.29
WT: 724, TTT: .468, FPS: 199, KE: 59.73
WT: 637, TTT: .433, FPS: 216, KE:  61.48
WT: 544, TTT: .402, FPS: 234, KE: 60.96
WT: 438, TTT: .372, FPS: 255, KE: 57.21

Looking at the results, please notice the arrow with the greatest KE was the third, with a weight of 637.  Also notice that the 438 gr arrow possessed fundamentally the same KE as the 800 gr, while reaching the target in about two-thirds of the time, with 50% greater speed.  The 637 grain arrow represents the 'magic' combination of mass and velocity, and clearly beats the heavier and lighter arrows from this bow.  This, of course, ignores the problem of spine, which would take a creative balance to both shaft weight, broadhead weight, and fletching/nock weight.  Once an ideal arrow weight is determined, the spine would have to be worked around that.

Now realizing that many hunters will use heavier bows, the draw weight to get comparable performance from an 800 or 900 grain arrow would be prohibitively strong.  I am guessing somewhere along the lines of 100#.  I am just too lazy to calculate it right now.

As a final note, this is presented as raw information; hunt with what you are comfortable with.  All of us are a tad supersticious, so if that 1000 grain arrow from a 45# bow is what works for you, and you kill game, by all means keep it up.

[LBR]

I'm still running all this through my head as well--I've never had a hunt in the works that required me to do the math to make sure my equipment would do the job.  

On the table you posted, I feel there is one thing missing--energy retained upon impact?  It seems that the heavier arrow will retain more energy longer upon impact, thus improving penetration?

Chad

[Hookus]

Sorry about the double name thing, had some wierd thing going on with my email/password, anyway...

Actually retained energy and kinetic energy would be one in the same.  Penetration relies on an entirely different equation, considering some similar variables such as front cross sectional area, broadhead cutting geometry, and the flesh that the arrow is passing through.  Kinetic energy could be thought of as a representation of inertia.  While an object may possess kinetic energy (continuation of movement), or static energy (resistance to movement), it may only be under one type at a time, for our purposes.  Thus as the static energy is lowered by the release of the arrow, the bow imparts kinetic energy upon the arrow.  Kinetic energy  is  retained energy, they are in fact one in the same.  The only thing that acts upon kinetic energy is friction.  In bowhunting, this comes in the form of air, gravity, and the game when it is hit.  Once the arrow hits the game, the kinetic energy is absorbed by the target.  So, obviously, the higher the kinetic energy, the more is forced to be absorbed by the target.

This is one reason for super skinny-ultra-modern shafts.  By reducing the front cross section, more energy is concentrated in a smaller area.  Same reasons the broadheads with a larger cutting circle do not penetrate as far as a smaller head.  This is why nails tend to work so well...

Anyway, like you said, never had to compute math in a tree stand.  If it kills game, it works fine enough for a hunter.  I guess physics in one reason we shoot trad.

I just think that poeple tend to forget about the "happy medium" of speed and arrow mass, swaying too far in either direction, by both trad, and modern archers.  This stuff is relatively simple physics, I'll try to dig up the formulae if anyone is interested.  Although, I guess I'd be more inclined to shoot instead of do book work.

[LBR]

I've never had a hunt in the works that required me to do the math to make sure my equipment would do the job.
 

In the WORKS--lol.  What I meant by that is I've never been on a hunt where I had to tweak my gear, or change it, to be certain it would do the job.  Now I do--I'm building up to an Austrailian buffalo hunt in the future, and that is why all this stuff is becoming more important to me.

I understand on the happy medium, and it makes sense.  The devil is finding the time to figure out what it is with your own particular set-up.  I appreciate the information!

Chad

[Hookus]

http://home.att.net/~sajackson/archery.html

This will get you started.  There are a number of ballistic software programs out there as well that are much better, and give mich better information, including sight tapes (actually a printout you could put on your bow), all sorts of stuff.  Most importantly, they will give very detailed ballistic info.

[Ryan Rothhaar]

Hmm, me thinks Rick might have something to say when he gets back on this one.

JAK-one thing you overlook in your calculations is the fact of the major topic of "discussion" (read disagreement) on this issue.  The heavy arrow guys are NOT KE guys, they are MOMENTUM guys.  From physics, the equations used to calculate both KE and momentum take into account both mass and velocity.  The difference is that KE squares the velocity term, therefore over emphasizing it, whereas momentum does not.  The end effect is that a KE based calculation stresses velocity to a great extent over mass and momentum does not.  In other words, KE predicts that a light weight projectile moving very fast will hit harder than a heavy one moving slowly.  My personal take on this includes two things:

1. A person can actually MEASURE momentum-when an object hits something, the force, in ft lbs or whatever you use for units is the actual force exerted.  KE is entirely calculational-there is not a physical method to measure "stored energy".

2. Several people, lately, including Rick, Cory, Monty etc. have taken Australian buffalo with relatively heavy arrows from trad bows, I believe the actual calculated KE of Monty's setup was real low, but he shot thru the animal twice.

I agree that shooting a "900 grain arrow from a 45 lb bow" would be ridiculous, shooting a 900-1000 grainer from a 75-85 lb bow, however, is close to like 12 gr/lb or so-a quite reasonable arrow wt/lb of bow wt.

Ryan

[LBR]

That's the word I was looking for earlier--it seems that is what these discussions usually boil down to is one vs. the other, and/or the significance of each.  I've never paid enough attention to the discussions to know a whole lot about either one--hope Rick and Cory get back into this soon.  Ryan, do you  know the formula for momentum off-hand?

Chad

[O.L. Adcock]

Hookus, I'm not sure where you got your chart but a traditional bow, KE will go up with arrow weight FOREVER. Granted it gets small as arrow weight gets into the unreasonable range but it still goes up. If in testing a drop in KE is seen, it is because of tuning (shelf/rest contact), not arrow weight. In a compound I'd suspect increased frictional loads on the cables and cams could cause a KE drop at heavier arrow weights. Drop me an email, I can send you KE graphs done by Mr. Mulaney on trad bows....O.L.

[erron]

For interesting posts on momentum versus KE etc. try this thread on Ozbow:

  Momentum Theory  

Erron
 www.ozbow.net

[AkDan]

Chad,

Stick to what Woody is telling ya!

Can't wait till he see's this.

[JAK]

Let me work out the momentum, I'll post the results when I get them, I misinterpreted retained energy in that post.

On a seperate note, it is impossible for KE to go up forever on ANY projectile, I would like to see the charts.  [Assuming no other variable changed except for mass, which will have an inverse relationship to velocity for 2 different arrows shot from the same bow] This is because velocity is squared in the equation.  That would mean the effect of velocity change will produce a non-linear result once squared.  Since velocity is squared, and mass is not, this would invalidate the theory that KE would continue to rise.  I would have to see the chart and formulae that were used, but right now, I cannot picture any situation that would be true, without increasing the draw weight accordingly.

KE will be lower from a trad bow, yes, because they will never approach the velocity from a wheel-bow.  But the external ballistic curve would have generally the same curvature, always and forever.  External ballistics is external ballistics, once the object is not longer under power by the bow or launcher, EVERYTHING on earth follows the same laws of physics, from a football, to a bullet, to an airplane; the formulae are fundamentally the same.

Gentlemen, 1000 grains from 45# was a joke.  I also beleive that the hunter should always go with what they are comfortable with, and has worked for them, as I stated in the original post.

[Ryan Rothhaar]

JAK- as was my using in in the reply  

Someone correct me if I'm wrong, but I seem to remember that Monty's calculated KE was somewhere around 40 for his Buff setup?  Worked OK though.

All this math brings back those bad undergraduate memories-year of physics, year of calculus, linear algebra, quantum mechanics, kinetics and thermodynamics---too much math for a pot-boiler!

Ryan

[JAK]

Ryan-

I humbly concede your point.


Momentum basically uses MV, and KE uses M(V^2).  That was a pretty basic point for me to overlook.  Perhaps it is because I see most people talking about KE, and perhaps not realizing that it is different from momentum, which is probably what they are referring to.  I suppose KE would be more valuable to an object such as a bullet, which by having low momentum, and high KE, would most effectively impart its energy to its target.

You could, I think, say that the amount of energy transferred to the target is a "vector" between KE and momentum.  The lower the momentum, and higher the KE, the faster the energy is absorbed by the target.  Valuable, I suppose in shooting, but less valuable in bowhunting, which relies on cutting ability of the broadhead.  Greater momentum means longer cuts.

Ryan, thanks for correcting me, and I apologize for any confusion.

[JAK]

I just read Dennis' post on Ozbow.  Interesting.  The only point I disagree with him on is where he states that 2 different weight arrows travelling at the same speed will have much the same trajectory, since gravity is acting solely and directly upon mass.  And perhaps my post agrees with both Stickbow Hunter and Dennis on there, in that they both describe a happy medium of velocity and mass.

Also, I just realized that momentum as well will not indefinitely increase either, since mass will inversely relate to velocity from a given bow.  It may level off at very high poundages or unrealistic arrow weights, but it will level off and decline eventually, though perhaps not within the bounds of normal equipment.  It is also interesting that Dennis and I use the same bullet reference.

My next thoguht would be this:  How much difference does a measure of mementum make?  Obviously higher is better, but when would you cease to get gains great eneough to outweigh increases in speed?  Again, brings me to my Happy Medium stance.  From my first post, the 800 grain arrow had .6448 or so pounds/sec of momentum. The 637 grain arrow had .5978, giving a difference of only .047 lbs/sec, or 7.25% less.  How much momentum is this really?  To compare it directly to distance of penetration, if the first arrow penetrated 20 inches, the second would penetrate 18.55 in excatly the same medium, provided the only variable that changed was momentum.  This is a loss of only 1.45 inches over 20, less than 1 broadhead length.

The 800 grain arrow had a speed of about 185 ft/sec, and the 637 had 216, or 17% greater.

So, you end up with an arrow that has 17% greater speed, and only 7.25% less momentum.  When would you make this trade off?  This is what I mean by a magic combination.

[Ryan Rothhaar]

JAK-FYI I think Dave Holt was instrumental in introducing KE into "bowtalk" in BH magazine.  Dad and I had the same discussion with him a couple of years ago.

Here is another variable to throw in-just in case there arent enough already!

You'd have to check someone like Norb Mullaney or another bowtester for exact details, but I know, qualitatively, that a recurve bow loses alot of added efficiency per pound as you go higher in overall wt.  In other words, a 10% increase to a 50lb bow gives a much larger increase in overall "power" or engergy transfer to the arrow than a 10% increase to an 80lb bow.  I dont know the quantitative math behind this, but I've seen several tests to show it.  I think I remember seeing that the efficiency per % wt gain tapers off dramatically after 65lbs.  

just food for thought

Ryan

[O.L. Adcock]

Oh I just love these discussions!      

Many of the KE/Momentum discussions folks get into lose sight of the most BASIC physics. Many of the published studies are looking for ways to increase penetration from "A" bow. For all practical purposes, the KE from that bow is a "constant" so from that standpoint, KE is a mute point. Yes, as arrow weight goes up, efficiency does go up as does KE but percentage wise it is small. So, if KE is constant, we can't do a thing about it leaving us only with velocity we can change. The only way we can change that for "A" bow is go up or down in arrow weight.

KE is the basic unit of power available. You can't have velocity without some KE behind it, nor can you have momentum without KE in the first place. So KE is important if your goal is to get the most of either one.

One fellow was on the right track..With KE being constant for practical purposes, our only choice is to decide if I want to use that KE fast, or use it slow. Using the KE available over a longer period of time will allow more work to be done. It takes 4 times the energy to do the same work twice as fast. Want more penetration??....Spread the KE out over time by lowering velocity and the only way you can do that out of "A" bow is go up in arrow weight. Why do 3:1 heads penetrate better then a 2:1 of the same width?? TIME... The 3:1 does the same work in a longer distance. With a constant velocity, cutting over a longer distance is time.. The drag on the arrow goes up or down with the square of the velocity..Again it's TIME. Use the KE over a longer time is the key.

Here are links to a couple of scanned in charts Mr. Mulaney did on a trad bow. One is velocity/arrow weight the other is KE/arrow weight. You'll see all the way to roughly 14gr/lb KE goes up as does efficiency. These were done on a fairly good bow but are typical for all trad bows as the physics does not change....O.L.

 

 

[LBR]

Something else to throw into the pot.  I was sent some information last night that was very interesting (Woody, jump in any time!).  I'm still getting a grasp on all of this (I'm not anywhere near a mathmetician or physicist--I don't even play one on TV!).  Anyhow, one very important point that was brought to my attention was that these formulas, as best as I can tell, are based on the arrow's performance approximately 3' in front of the bow--where most folks set the chronograph, not 15+ yds where the impact generally occurs.  I don't have any intentions of shoot a water buffalo from 3 feet!  I figure the Pucker Factor (whole different scale there) will be off the charts for me at 15 yds!  But anyway.......

The charts I was sent show arrow velocity from 15 to 35 yds, in 5 yd increments.  Very interesting information to say the least.  The arrow weights don't go up to the range I am considering for the hunt, but do show that heavier arrows retain more energy downrange, where it bleeds off the lighter ones faster, with the actual momentum (in slug feet) of the heaviest arrow being much higher than the lightest at 35 yds.

Finally, just for giggles, I did the KE and Slug Feet formulas for my current bow, and (based on the bow I have now) what I expect to get from the bow I have ordered for the hunt.  On my current bow:

[email protected], 630 grain arrow, 187 fps:  KE= 49, SF=.52
85@30, 850 grain arrow, 180 fps:  KE= 61, SF=.68

What does that really mean?  Danged if I know.  I should know more when I get back with my buff though.  lol

Chad

[O.L. Adcock]

Chad, EXACTLY! Drag goes up with the square of the velocity..The light/fast bleeds more energy faster. Again doing the same work faster requires more energy. It will do the same in meat too.

 Interesting numbers, draw weight to draw weight, Ke to Ke, and slugs to slugs, between the 2 bows, all those are within 20-24% of each other. You can't get slugs without horsepower....O.L.

[JAK]

I understand the theory behind broadhead cutting geometry, it is basically an inclined plane; the same principles apply, i.e. working over time.  I don't understand how that correlates to dispersion of KE, however.  Take for example driving a nail.  I weigh about 190 lbs, and if I press all my body weight on a nail, it will not drive very far.  By using a hammer, however, even though it is lighter, and actually may have less KE than my body, it will drive the nail very fast.  I would presume by compressing the KE into a SMALLER time.

I think it has more to do with how you would quantify work.  Interestingly, if you take the example of someone diving into water, a dive will go deeper than a belly flop.  While the dive is releasing energy slower (upon penetration), than the belly flop, this has more to do with how concentrated the force if across a surface area.  The KE is simply being released across many points simultaneously.

I fail to see how a slower object will generate more work by lengthening time, because KE is directly related to time, as is momentum.  The time you want to increase is penetration time for a given arrow, not flight time.  A slower flight time will NOT increase the work being done.  I am pretty sure you were talking about time it takes to penetrate the object, if I read correctly.  I think that broadhead geometry is the most crucial "point" in attaining good penetration, and that you can get passthroughs on even thick game without a telephone pole.  Again, I think that the advantages of a pefect balance between all elements, cutting surface, speed, and weight, would be best.

Of course, KE and Momentum are both two different types of energy, though closely related.  That is KE representing the potential, and momentum measureing how the arrow uses that potential.

Once again, if you are happy with what you shoot, good on you.

I won't even touch bow effeciency, for the intents of this discussion, the arrow has already left the bow, so all we are concerned with is the amount of energy imparted to the arrow, and the physical forces acting upon it.  You are right though, I remember reading the same thing about effeciency declining with bow weight.  I seem to remember reading somewhere (the where escapes me) that about 60-65# is the highest you go before getting very sharp diminishing returns, that stuck with me.

KE is directly related to momentum though, as is mass (which is an element of both), and you can derive a formula for momentum from using KE as one of the variables.

You know the amazing thing is, American Indians killed buffalo with self bows and flint or bone heads.  I don't think the holy man even knew about 3:1, KE, momentum, and ballistics, and I seriously doubt that any of their bows surpassed 45# or so in draw.  I think that is amazing, and it is a feat I certainly would not want to try.

All kidding aside, I think that a balance between elements is the best bet rather than swingimg too far to either side (KE or Momentum).  You will probably end up with a bow that is easier to tune very well, and a better performing arrow.  And remember as well, if there was a perfect solution, we would all be shooting about the exact same thing.

Wow, imagine doing a physics thesis on Arrow Ballistics, too bad I don't go to school

[Ryan Rothhaar]

O.L-I agree with most of your assessment, the difference comes in the fact that KE and MOM, while related, are arrived at differently.

Here is a force/time definition I copied to illustrate my point:

Impulse and Momentum
Momentum
    The momentum of a body is equal to its mass multiplied by its velocity.
 
Momentum is measured in N s. Note that momentum is a vector quantity, in other words the direction is important.
Impulse
The impulse of a force (also measured in N s) is equal to the change in momentum of a body which a force causes. This is also equal to the magnitude of the force multiplied by the length of time the force is applied.
 
    Impulse = change in momentum = force x time

If we assume the "impulse" is the complex factors involved with tissue/bone etc. retarding penetration then momentum, not KE, would be the energy vs. time paramater to use.

As you noted above this is all a moot point anyhow, a good academic discussion at best, the important thing is shooting the arrow through something, and we have precedence for that  

Ryan