Agree or disagree???
 

Hello all :-)
Just looking for an opinion....an article in our latest South African bowhunter refers to KE being rather over rated and heres why. The author reckons that momentum is a lot more important than KE and when you do the calculations with his formulae it looks pretty impressive.
His example of a skateboard flying 100km/h into a brick wall vs a pick-up travelling at 10km/h makes sense. So the deduction is therefore that as long as the sight pins stay in the window, the heavier the arrow the better, thereby reducing the speed. Anyone got opinions on this????

RE: Agree or disagree???
 

With a heavier arrow you will have more KE anyway right.

RE: Agree or disagree???
 

It is a fact (not opinion) that a heavier arrow shot from the same bow will result in both more kinetic energy and more momentum and therefore all things being equal will result in greater penetration. If you want to attribute the increased penetration to the increase in KEthat's fine. If you want to attribute it to the increase in momentumthat's fine too. KE and momentum are merely the result of calculations based onthe measureable quantities of arrow velocity and mass. From a given bow, the facts are quite simple. If you put on a heavier arrow, the veolocity goes down and both the KE and momentum increase thereby resulting in greater penetration.The rest is opinion. Along with reduced velocity as a result of the heavier arrow comes increased trajectory. You have to weigh the gain you achieve in penetration against the negative effect of increased trajectory. Where you decide to draw that line is very much a matter of opinion. Personally I like to lean to the heavy side when picking an arrow.

RE: Agree or disagree???
 

Egg-zactly... I would have said that, but you said it much mo betta. I agree with Sylvan... See bro. Sylvan, I am agreeing with you more and more these days. :D:D

RE: Agree or disagree???
 

Hmmmm./.....I don't buy it. A heavier arrow will ALWAYS produce more KE is just not accurate. I am shooting a 400 gr arrow 290 fps. giving me KE of 75 ft pds. Now, if I increase my arrow weight to 700 gr but the speed slows to 200 fps (which is probably faster than reality) my KE drops to 62 ft. pds.

It's a delicate balance. The trick to KE is to get the heaviest arrow you can flying as fast as you can. There is a happy medium where the optimum for both is achieved. Eventually, the weight of the arrow will slow it down just too much and your KE will drop. Likewise, there is a point where the arrow is just too light and it drops also.

Mementum and KE go hand in hand, but aren't the same thing. I do agree that a heavier arrow will retain more momentum than a light arrow. I mean, which can you throw farther, a light pebble or a heavier rock? But see, I can't throw a boulder at all. Which brings us back to my main point....heavy is not always better. You gotta find the balance.

RE: Agree or disagree???
 

It is possible to go over the arrow weight that will shoot most efficiently from your bow. If you shoot a variety of arrow weights througha chronographand KE keeps climbing, then drops off when you hit a certain weight, then you know you've gone beyond your bow's peak efficiency range. The ol' bell curve in action. I'd stop at the top of the curve.

KE is definitely over emphasized,but I hesitate to say it's overrated. It's important, but it's only part of the story.

The guys who use light arrows say the KE makes their light, fastarrows penetratesatisfactorily when, in reality, it's momentum. They have to pack a lot of extra speed and KE into their light arrows to do the same job someone with a heavy but slow arrow can do with much less KE.

Like I've posted on here, many times, a 700 gn arrow at 150 fps with 35 ft lbs of energy achieves penetration, mostlybecause of it's momentum. A 350 gn arrowat 300 fps and 70 ft lbs of energyalso achieves penetration, but not because it's carrying twice the KE ofthe 700 gn arrow. If it were due to KE alone, then the light arrow should penetrate exactly twice as far as the heavy one, and it doesn't. In reality, it's because it's carrying exactly the same momentum as the heavy arrow.

That's why those minimum KE charts for hunting various sizes of animals are a joke. They focus strictly on KE, totally ignoring momentum, and momentum is at least equally important. Frankly, for somene using heavy arrows, those minimum KE values couldbe substantially reduced.

I would much rather see minimum momentum charts. Then you could make intelligent and informed choices when it comes to balancing speed and trajectory againsthow muchmomentum you need to put an arrow through an animal's vitals. Make the choice then, whatever the KE winds up being, then it's obviously enough KE to do the job.

RE: Agree or disagree???
 

A bow with 125 grains of virtual mass that shootsa 400 grain arrow 290 fpswill shoot a 700 grain arrow 231.3 ft/sec which is an increase in dynamic efficiency from 76% to 85% and an increase in KE from 74.7 ft/lbs to 83.2 ft/lbs. These are straight forward calculations. The only number I assumed was 125 grains virtual mass but the result would be the same regardless of what "reasonable" value you choose. If mass goes up so does KE and its true for all reasonable arrow weights.

The only place I can see where this may break down is if you are at extremes where the limbs of the bow are beginning to fail and Hookes laws nolonger apply.But that certainly wouldn't be a reasonable point tobe made here.

RE: Agree or disagree???
 

The function here is not a bell shapedcurve.Dynamic efficiencyincreases with arrow mass.

Here's the proof.

SE = Stored energy
KE = Kinetic energy
v = velocity
m1 = mass of arrow
m2 = virtual mass

SE = 1/2(m1 + m2) v^2
Therefore:
v=((2SE/(m1+m2))^1/2

and:
KE = 1/2m1v^2
Therefore substituting ((2SE/(m1+m2))^1/2 for v and reducing:
KE=m1SE/(m1+m2)

Now as anyone can see, as m1 is multiplied by SE in the numerator and m1 is only added by m2 in the denominator it isclear that as m1 increases KE increases as well. Now as SE is a constant for a given bow setup as KE increases with arrow mass then so does efficiency.

You can't cheat the physics! Dynamic eff increases linearly with arrow mass. Virtual mass modifies the slope of the function.

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Just like being in algebra all over again LOL

RE: Agree or disagree???
 

I agree 100%.

RE: Agree or disagree???
 

Agreed, it might not always be betterbut a heavier arrow shot from the same bow for all practical arrow weights always means more kinetic energy and momentum. That's just a fact and not opinion. Anyone who claims otherwise is simply incorrect.Don't take my word for it, look it up for yourself. Here's a start http://homepage.ntlworld.com/joetapley/ Go to the section on virtual mass. There are other sights as well or just get a book on archery physics.

RE: Agree or disagree???
 

Well, I did the math and a 400 gr arrow at 290 is 74.71 pounds of KE. A 550 gr arrow flying at 220 is 59.12 pounds of KE. That's not opinion, it's fact.

290x290x400/450,240= 74.71
220x220x550/450,240= 59.12

Now, I am no mathmetician, hell, I may have not even spelled that right, but that's a heavier arrow flying slower and producing LESS kinetic energy. ;)

RE: Agree or disagree???
 

You are absolutely correct with these numbers. However unless you change something else in addition to the increase in arrow weight a bow that shoots a 400 gr arrow at 290 ft/sec will not shoot a 500 gr arrow at 220 ft/sec but rather 255.8 ft/sec using 125 grains virtual mass . That is a KE of 79.9 ft lbs.I don't know where you got the 220 ft/sec but it is incorrect.

RE: Agree or disagree???
 

Well, to be honest, I just made the number up, but I promise you my bow will not shoot a 550 gr arrow 255 fps. It seemed like a fair number to use.This virtual mass you bring up....I have no idea what that is.
Don't misunderstand me....I don't intend for this to sound like I am saying you are wrong, I am just trying to understand.

RE: Agree or disagree???
 

You may well be right about the 255 fpsbut thenof course that would indicate that it wouldn't shoot a400 grain arrow at 290 ft/sec. With regard to virtual mass, try the web site I listed. It gives a pretty good explination. The entire site is interesting too. I think of virtual mass as the equivalent amount of mass the bow has to accelerate in addition to the mass ofthe arrow. For example, if you add a silencer or a peep you increase virtual mass but again the web site or a book on archery physics will explain it better than I can.

RE: Agree or disagree???
 

Well, I looked over some of it....and it's way over my head. But one thing I just don't understand......how can you have the mass of an arrow and then REMAINING mass....virtual mass. My logical and not mathematical brain tells me that's a made up number. Remaining mass of what?
And my 400 gr arrow is flying 290. Although I haven't chrono'd a 550 gr arrow. Thanks for the explanation. This is actually kinda fun for me.

RE: Agree or disagree???
 

I think what makes this concept a bit confusing is that some of the mass in virtual mass is not mass at all but rather frictional losses or dynamic hysterisis. That's why its called "virtual" mass. It's not all real mass. I'm sure that makes no sense at all does it? But it really all comes down to this equation...

v= (2SE/(m1 + m2))^1/2

where:
SE = Stored energy or Total energy in the system
m1 = arrow mass
m2 = virtual mass
v = velocity

It might not be obvious butm2 is in the denominator so if you increasem2 then you increase how much you divide by and therefore v goes down. If you lower m2 v goes up.

As m1 is only part of the mass that is accelerated, m2 is the "remaining" amount.

Virtual mass is not a "made up" number and it can be measured for your bow if you have a chronograph and and arrow weight scale.

I've probably made it more confusing...

RE: Agree or disagree???
 

I think you might be pleasantly surprised then. I've done this many times where we have chronographed with 1 arrow weight and then used the equations to predicta new velocity with a different arrow weight and it's always within 2 ft/sec of the new chrohographed speed.

RE: Agree or disagree???
 

Gentlemen,

This is n argument that can be settled by no one here with out the quatitative fomulas. All it is is physycs.

Shooting a heavier arrow will NOT neccessarily produce more KE or PE (what some of you refere to as "momentum".)

In theory, yes, a hevier arrow will broduce more PE and KE. However, the arrow will fly slower and have a different trajectory UNLESS the draw weight of the bow is incresed to off set the weight of the arrow.

I have done the math too and a heavier arrow will produce more KE at closer range and less KE than a lighter arrow at longer range. Gravity robs the heavier arrow of KE earlier than the lighter arrow.

RE: Agree or disagree???
 

I respectfully submit that you have done the math incorrectly. Going to a heavier arrow will increase the amount of initial KE and the advantage you gained over the lighter arrow increases the farther down range you go. All flight characteristics being equal, heavier arrows maintainke and momentumbetter then lighter arrows. Go to the web site I listed and then go to vortex shedding.

I gave you the formulas and a web site that will confirm they are the correct formulas. You can also find them in a physics book. And btw there are a lot of people here that are more than capable of solving the equations and understanding the physics.

Absolutely correct, and that's the tradoff. Going to a heavier arrow will give you more PE & KE but also a bigger arch in the trajectory. Whether or not it's worth it is open to opinion. Whether or not it's true isn't.

RE: Agree or disagree???
 

I've pretty much said what Iwanted to say regarding this matter and it has been my experience that this subjectquickly tends towind upin a not so friendlyargument.So I'll say good bye now and "kill em and grill em!"

RE: Agree or disagree???
 

Seemed to be pretty friendly so far.

RE: Agree or disagree???
 

I'm sorry, I think I left the wrong impression. I didn't mean that it wasn't friendly in fact just the opposite. I've just had some not so friendly experiences in the pastnot only here but on other forums when it comes to this kind of a subject so I just thought I'd just say my peace and then politely retreat. I thinkbecause answers to questions of physics and math are often either correct or incorrect, i.e. no room for opinion, as soon as there is a debate by definition, somebody is wrong. With most other types of subject it's easy to say to someone for example "IMO I think you are wrong" whereas in math if someone says 2 + 2 = 5there doesn't seem to be an easy way to say it without compromising what you know to be or at least are totally convinced to be true. People quite naturally, and of course I include myself in this even though I try not to, quickly become defensive. So anyway, sorry if I left the impression that anyone here wasn't friendly but again, I've said my peace and would only be repreating myself from here so like I said "kill em and grill em!"

RE: Agree or disagree???
 

I aim the bow, release the arrow, deer fall down... Practice with your setup and this will happen again and again. I am not an engineer but I get to eat a lot of backstrap!

RE: Agree or disagree???
 

Both increase and decrease at the same rate relitive to powerstroke , so the question is realy a nonissue when your bow creates more ke it will create more momentum , and visa/versa . Just deferant terms to define how much energy a flying arrow has .

RE: Agree or disagree???
 

Sylvan, you've both confused the hell outta me and inspired me both at the same time. You have made some sense, and I intend to investigate farther just to learn. Thank you for your good attitude with my ignorance. I appreciate you for that very much.

RE: Agree or disagree???
 

You're correct that when you increase energy you also increase momentum. But, when using the same bow and same draw weight, you can only slightly increase energy while really loading up on momentum. Doubling arrow weight will only gain a couple of foot pounds of energy (in theory)but it will double the arrow's momentum.

You're also correct that it's a non issue, but only when your bow is putting out way more energy than you need.A current model, 70 pound compound with hard cams is putting out more energy than the recurve Fred Bear used in the 60's to kill an ELEPHANT.So, yeah. It's probably a non issue for someone using such a bow for hunting puny little deer. (Although... Isn't it absurd that so many folks are shooting enough energy to kill an elephant and then coming on the forum, griping about not getting passthroughs on deer with light carbon arrows?)

If the bow is putting out barely enough to get the job done, it's a huge issue. Bear knew his arrow wouldn't be carrying a whole lot of energy in relation to the size of theanimalon that elephant hunt, so heused a 1200 grain arrow to get penetration into the pachyderm's vitals. He loaded up on momentum.

Sounds like you're saying the terms are interchangeable and they're not. Energy and momentum are interrelated, but not at all the same thing.

RE: Agree or disagree???
 

Arthur, we keep hearing that momentum and KE are related but not the same thing, I even said so in one of my earlier posts on this topic. I think we should define them both and explain the difference.

Kinetic Energy: the mechanical energy that a body has by virtue of its motion

Momentum: a property of a moving body that determines the length of time required to bring it to rest when under the action of a constant force

These are both definitions straight out of webster's dictionary. So, as you can see, KE is the energy it contains, and momentum is how long it will stay in motion by virtue of it's mass. I bring back the rock example. I can throw a pepple not very far at all, but I can throw it fast. But, because it is so light, it has no momentum (nothing behind it to keep it moving). I can throw a rock farther because of it's weight, but I can't throw a boulder at all.
Same is true with arrows. A light arrow may produce more initial KE because of its speed,but by 30 yards it has slowed down so much that the KE drops off quickly; momentum. A heavier arrow may or may not have the same initial KE because of it's slower speed, but it retains its speed longer downrange (momentum) thus retaining it's KE.
Let's say a 300 gr. arrow (I'm making these numbers up, but the concept is actual) is flying at 310 fps producing KE of 64#, but remember, that's at the point of release. By 30 yards let's say it's speed has decelerated to 260 fps, so the KE at 30 yards is 45#, a drastic decrease.
Now let's shoot a 450 gr. arrow. It's launch speed may only be 260 fps, giving a KE of 68#. Now, at 30 yards downrange it's speed is 240 fps (yes, the arrow has dropped more than the lighter one, but that's because of gravity, not speed, it's speed, by virtue of it's momentum has not dropped off so much) giving a KE of 58#.

So, yes, momentum and KE are both measured by velocity and mass, but they are not the same thing.



All numbers here, again, were fictional, (with the exception of the math) but I believe them to be fair and at least close.

RE: Agree or disagree???
 

So lets crunch some numbers. A bow that is throwing a 350 grain arrow 300 ft/sec calculates to be 70 ft/lbs KE and 0.47 pound seconds momentum. Now lets double the arrow weight to 700 grains and shoot it. Assuming 100 grains of virtual mass the new result is a 700 grain arrow flying at 225 ft/sec. That's 78.7 ft/lbs ke and 0.70 pound seconds momentum. So the heavier arrow has given us a 12.5% increase in KE and a 50% (not 100% like you said) in momentum. O.K. so what does that mean? Well if you agree that the heavier arrow will penetrate more it means that in this example a 12.5% increase in KE or a 50% increase in momentum (take your pick) resulted in precisely the same increase in penetration.

It's just like I said in my first post...

"If you want to attribute the increased penetration to the increase in KE that's fine. If you want to attribute it to the increase in momentum that's fine too. KE and momentum are merely the result of calculations based on the measureable quantities of arrow velocity and mass. From a given bow, the facts are quite simple. If you put on a heavier arrow, the veolocity goes down and both the KE and momentum increase thereby resulting in greater penetration. "

The relative percentage that each change is irrelevant.

Art, I'm getting a strange de ja vu feeling...

RE: Agree or disagree???
 

Sylvan...... You keep using virtual mass to calculate the heavy arrows FPS...... Not saying you are way off, but your calculations really mean nothing unless you have the exact FPS for the heavy arrow.... Someone needs to get a chrono and run us some numbers..... Then Sylvan's formulas would be alot more useful IMO.....

RE: Agree or disagree???
 

Actually, the subtle but major difference between throwing a pebble and a rock has to do with how efficiently you can transfer the energy from your arm to the object you are throwing. You can transfer more energy to the heavier rock because it takes time to convert the chemical energy stored in your muscles and as you throw the heavier rock slower there is more time for the transfer. You can't move your arm fast enough to transfer the same amount of chemical energy in to the pebble. It's similar with a bow. If 100% of the energy stored in the limbs were always transferred to the arrow, it would make no difference in the amount of ke regarding light or heavy arrows. Lighter arrows would be faster than heavier arrows but the energy level would be exactly the same. If you stored 60 ft/lbs of potential energy in the limbs you would wind up with 60 ft/lbs ke. Problem is bows aren't 100% effiicient and the lighter the arrow the less efficient they are. Virtual mass is the mathmatical value that tells us about how well a given bow transfers the energy. The lower the value the better. Zero virtual mass (though impossible) would mean 100% efficient.

RE: Agree or disagree???
 

You are correct in that I only picked the value for virtual mass out of the air but as the example is only for the pupose of showing relative change, actual measured values are unneccessary. Pick any value for virtual mass you want, the gist of what I'm saying is unaltered. Virtual mass like brace height or peak weight is associated with the bow not the arrow and in this example I am not comparing different bows just different arrows shot from the same bow. So what I am doing is absolutely valid. You can argue over a few ft/sec here and there but it makes no difference realtive to the point of the matter.

BTW, they're not MY formulas. They belong to everybody!

RE: Agree or disagree???
 

The only thing I'm confused about in this thread is.......how the hell did anyone get past mobowhuntr's sig pic?[&:]

I forgot what the question was.

RE: Agree or disagree???
 

Kinetic energy = 1/2 masstimes veolicty squared
momentum = masstimes velocity

As you can see jimmy is correct. They are simply different terms describing exactly the same phenomenon. That isa massin motion. Even the terms foot pounds and pound seconds come about merely because for ke you multiply mass by velocity squared and in momentum only by velocity. IMO in archery it truly is a non issue. I'll say is again. The facts are simple. Put on a heavier arrow and velocity goes down and both ke and momentum go up thereby increasing penetration. KE and momentum are just human inventionsderived from the only measureable quantities of the physical event which are mass and velocity. It makes little sense to me to worry about it. What matters is you put on a heavier arrow and you get more penetration potential. You also get a larger arch in trajectory. So there is the nuts of it. Youmust balance the postitive effect of increased penetration with the negative effect of greater trajectory. IMO the balance point is the fastest arrow you can shoot that still provides adequate ke/momentum for penetration of the game you are hunting and then maybe a little extra just in case... Unfortunately, there is no equation we can solve to give us the answer to this apparent paradox so the debate is destined tocontinue.

My advice is, if you're just interested in archery and hunting, I wouldn't worry about the difference between ke and momentum.Decide on a minimum level be it in ft/lbs or pound seconds or both if you like and then go as fast as you can while still maintaining that/those minimum(s). If you're just curious about the physics get a physics book or take a class. The subject is IMO too complicated to learn properly on an internet forum. But of course in the words of Dennis Miller, "that's just my opinion, I could be wrong".

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Man, you got that right. I spent a little time pondering that subject myself! Ain't no equation going to solve that problem either![8D]

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All the physics classes aside: What difference does it make? For the most part, in my experience, unless you're talking at the extreme end of weight and poundage, all modern arrows penetrate quite well. Most failures of penetration I have heard of are a result of poor shot placement, broadhead failure, or dull blades. I've yet to hear of one arrow bouncing off an animal because of lack of Momentum or KE or whatever unless we're shooting at 1000 yards. I guess if you're shooting a rhino or elephant, which may be the case concidering the magazine in question, does it really make a difference with today's bows? This reminds me of the theological debates of how many angels fit on a pinhead.

RE: Agree or disagree???
 

Well, think of it kind of like making love to your favorite sweetie. Would you want it fast and light or long and heavy. YUP....maybe somewhere in between.[8D] We did this all decades ago. That's where we come up with all these FOC etc etc etc. Heavy was our only real choice before the compound. Now with the blazing speeds we add another factor.....lower trajectory. ME, I kind of like the idea of being able to deliver a leathal blow if I'm off in range estimation a little. I'll give the ole girl a quickie and have a backstrap fried. We found to with this speed we have NEW problems such as finicky tuning and broadheads planing etc. Another vote for something middle of the road. I'm up to it and the ole gal can handle it.[8D][8D]

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If someone could put into words we could all understand......it would be the man in the blue undies...

RE: Agree or disagree???
 

Well, I haven't been on here in a while , but I did want to say something on this thread.
I just wanted to remind everybody about bowhunting in real world situations. I'm glad you guys take an interest in KE , momentum, etc., I do too. However, I just wanted to offer a friendly reminder.

IMO , One of the most important things is stable arrow flight. Many bows, which are built for speed, do not provide a stable forgiving platform for the arrow to launch from. Not talking about the rest, just the bow in general. Many bows shoot so fast , it's hard to get stable arrow flight. Mechanical broadheads allow some guys to cheat on arrow stability. The thing is, An arrow flying with some lateral torque or "wobble" at the speed of sound many times will not penetrate as well as a slightly heavier, slower arrow will that's flying perfectly straight. Not only that, if an arrow hits a deer while in mid-wobble, it may plane through the deer at an undesirable angle. You can often see this on hunting shows and videos on the slo-mo impact scenes.
My dad was killing deer 40 years ago with a 50 lb recurve, fiberglass arrows and a big black diamod broadhead and slicing clean through almost every deer. these shots were always inside of 25 yds, mostly around 15, but still the equipment then was so primitive compared to today.

If you only focus on speed, or KE , you could be asking for trouble. I believe if you are using modern equipment, with your bow, broadheads/arrows,etc. perfectly tuned and flying like darts, and if you and your bow are solid platforms for the launching of the arrow , then you can almost throw the formulas out the window. At that point, the difference is how far it sticks in the ground on the other side.

I guess all i'm saying is although KE etc is important, don't overlook other more important factors in pursuit of KE alone. Chaotic arrow flight, or instability that is hard to see with the eye, can rob your shot of more KE than you gained by making hyperspeed adjustments.

I have never tried to calculate my KE. I ALWAYS have a tuned forgiving bow(ultratec) , stable arrows with fixed blade broadheads, tuned perfectly and spinning straight , and I would put mydead pass through deer up against anyones speed machine!

Good huntin' - cap