If that is the definition of KE when applied to archery, the formula does not take into account what happens when friction increases dramatically when an arrows path is diverted in the body of an animal - and it always is, at least a little. I'm not an engineer, but I do not believe that KE is a good indicator of pentration potential of broadhead tipped arrow passing through an animal's body. Plain and simple, it's dead last on my list of concerns. However momentum is not dead last. It's a step ahead of KE. The reason is simple. I know that with no more effort on the shot, I can decrease the likelihood of deflection by simply increasing momentum in the easiest manner - using a heavier arrow. Since momentum is increased at a greater rate, it has to have more importance than a factor that is increased by a lesser rate. If it wasn't true, then it wouldn't matter if I just increased KE by drawing more poundage. However, it does matter. Increasing arrow weight has a more significant influence on momentum with no more effort.

Strightarrow: Like I said before I agree: "I have said on several occasions that energy as a result of high mass rather than speed is better for maintaing path and "breaking" through bone. "
Here is what I said about why this is true: "If the force holding the molecules together can not be overcome by the force applied by the penetrating object then the penetrating object either breaks apart or bounces off or some of both. This is where momentum comes in to play. By keeping the energy high as a result of mass rather than speed, the point at which the penetrating object bounces off is increased relative to ke. The time it takes for the molecules to stretch out of the way is increased. " When you draw out the time during collision, the force is lowered. Force = mass x accelleration, Newtons 2nd law.

Now it's fine to come up with theoretical examples like "equalizeing" KE between 2 arrows to make a point but of course you must also accept that by chainging arrow weights it is impossible for this to happen for a given archer. Like I've said many times. The archer can't separate ke and momentum. The archer can't equalize KE between 2 arrows and then make momentum go up or down. When he/she puts on a heavier arrow, both ke and momentum go up and of course the reverse. So although what you are saying is absolutely correct it is irrelevant regarding the options the archer has available to him. The archer simply puts on a heavier arrow and gets more penetration. The argument over how you multiply mass and velocity together is irrelevant.

Straightarrow: This is often the reasoning behind why many attribute far greater importance to momentum but this is absolutely false reasoning. Momentum does indeed increase at a faster rate as you increase arrow weight but as has been shown the result is the same. The 17% increase in KE results in precisely the same increase in penetration as the 52% increase in momentum. It would be just as compelling but equally bad logic to argue that because it only takes a small increase in ke to get the same increase in penetration as a much larger increase in momentum then ke is much more important. I would also point out however that if we hold velocity the same between 2 arrows and only increase mass then both momentum and ke increase at exactly the same rate. In this theoretical example if you doulbe the mass you double both ke and momentum. But for the same reason your theoretical example is irrelevant to the archer, so is this. When changin arrow weight the archer can't equalize the velocity between 2 arrows.

Straightarrow: KE and momentum are only mathmatical tools to aid in understanding the phenomenom of mass in motion. The circumstance or event and the question being asked about that circumstance or event is what determines which tool is more usefull in answering the question. IMO the question of which one is of more importance doesn't even make sense. A wrench is not more or less important than a screw driver. Both are dead last on my list of concerns!

P.S. Straightarrow, I just want to thank you for the way you have been disussing this issue. Though it's clear you don't agree with everyting I've said you have kept your comments tehnical and without a sign of rudeness or sarcasm. I hope I have not offended you in any way as well.

One last point...
These definitions are not just for archery. KE = 1/2mv^2. With regard to it "not taking into account what happens when friction increases"...? Again it depends on what the question is. Friction is "force" that resists the movement of the arrow through the material. Clearly as KE is by definition the capacity to apply force, the more of it you have the more friction you can overcome.

Like I said ELKINMTCWB, very few of us! You must be one of the few! I'm not comfortable even at 60#, 90 isn't even an option for me. Actually I don't even know anybody that pulls 90#.

He’s is a “character” but a likable one. Makes the world enjoyable.

That and your back maybe why you but heads so much with people.

I think the science has advanced a little since the theory of “if it doesn’t move get a bigger hammer” was popular. I believe you that those principles are the rock solid foundation of archery today. The science has helped us become more specialized.

So it would be better to measure peak draw weight on the down stroke. That could be done. I have had some experience with these theories. One was with the term, develops. It had to do with a motors hp. While I do not know if it ever developed the hp. it claimed, I do know that as soon as a load was placed on it, it was gone. The math said it was so, the application proved it to be false. I learned that a motors hp. is determined by it’s windings, plane and simple. It takes a lot (size does count here) to produce 1 hp. I realize it’s harder to pull bows that stay at peak weight longer but I don’t know how that changes the weight. It will send the shaft faster only because of the longer energy/force applied. The motor that developed 2hp. slowed down much quicker than an actual 2hp. because it could not maintain the push. They were both no more than 2hp. If the theory is correct I should be able to push an ash shaft with my 70#/90# bow through at least a 3" thick oak door, yes?

I think you're missing the point. Bows cannot store more energy than the archer's muscles put into them. It doesn't matter so much what the peak weight is as the distance you have to pull that peak weight to get to the breakover. If the limbs have stored 90 pounds of energy on a bow with a 70 pound peak draw weight, you didn't just put 70 pounds of effort into drawing it. Even though the peak draw was 20 pounds less, you did practically the same amount of work as someone shooting a 90 pound longbow.

By the same token, you are correct. When you've drawn that sonuvagun back and released it, the string will power the arrow at peak for the same distance you pulled it - minus however much you lose through inefficiencies in the bow.

If the arrow sticking in that old door was shot from a 90 pound longbow - and research has shown 90 pounds would be on the light end of the scale for an English war bow, so the actual bow that did the deed could've been heavier - then yes, you'd have a good chance to get a 1,000 grain arrow to penetrate a 3" oak plank with a bow that stored upwards of 90 pounds of energy.

No, Thank you Sylvan.

I haven’t read much archery history, but history that included archery. Most of what I've read is from a man who lived in the late 1800’s. He wrote history books for boys.

There is one story he told, that I tell to kids today involving the hugh packs of wolves in northern Africa during the time of Hannibal. A real archers story that’s bound to send even grown men to bed dreaming of being involved in a hunt like that. The author was G.A. Henty. The title of the book is “The Young Carthaginian”.

I don't know why that would be impossible. I alway shoot at a draw weight that is well below my maximum draw capacity. I have many dozen of arrows, that are of different weights. If I wanted to shoot an arrow with higher K.E., but with less momentum than my typical medium to heavy arrow, it would be very easy to do. This may not be a solution for the average archer, but it does not seem impossible. It's not a choice I see myself making, because I believe that weight should be as high as you can get without trajectory being affected to a great degree. Anyway, this discussion hasn't been limited to what the average archer should do, but has had a lot of theory and science injected.

All I'm really saying is, in a situation where a person wants more penetration and they have already paid attention to factors like blade design & sharpness, FOC and arrow stiffness, they would be better off concentrating on improving factors (weight) that are favorable to higher momentum measurements, rather than things (speed) that are favorable to higher K.E. measurements.

I have never been offended by a disagreement on a subject. I am bothered by personal statements that are intended to demean me, rather than argue their point on the subject, but you never did that - at least to me.

The context of my statement is that you are established with your draw weight. Like I said before, an archer should shoot as much weight as he/she is physically able to handle accurately. IMO it makes no sense to shoot less than that. Arbitrarilly lowering your draw weight simply gives away energy for no good reason. Thats what I meant when I said a given archer. So in this context, the only influence the archer has over KE and momentum is by changing arrow weight. When changing arrow weight, both KE and momentum move up and down together so it is therefore impossible to "equalize" KE and make momentum move simply by changing arrows. Of course it would be possible to put on a heavier arrow thereby increaseing both momentum and KE and then lower your draw weight which would lower both ke and momentum and because KE, unlike changes in arrow weight, changes at a faster rate than momentum with draw weight you could find the point where you have held KE equal and raised momentum relative to your prior conditions. This is what I would call a theorectical example. If you are comfortable shooting the weight you are at, it would make absolutely no sense to back it off and loose on energy and momentum too.

All I'm really saying is that for all practical purposes the archer can not favor momentum over ke or ke over momentum. He can only change the weight of his arrow which makes them both go up and down with the results being increasing or decreasing penetration potential. It really doesn't make any difference to the archer if he puts on a heavier arrow, penetration goes up say 5%, ke goes up 1% and momentum goes up 5000%. The result was some increase in penetration. If he puts on a lighter arrow he looses penetration potential. The rate a which 2 numbers that he has basically no independent control over is of no importance.

BTW, did you agree regarding the % differences between ke and momentum when changing arrow weight or do you still maintain that...

Sorry, I don't believe that just because both change, that they are equal in importance when determining which is the best measurement of penetration potential.

Once again, this is clearly not impossible. I gave you myself as an example. Arguing why or why someone should not shoot lower than their maximum is not relevant to this discussion. I do for a couple reasons. I want to be able to draw at odd angles, with no movement anywhere but my release arm. I want to be able to do this, no matter how cold or how stiff I may be that day. I gladly give up some penetration potential to get advantages in other areas. Hunting is not simply about pulling the most I can comfortably. It is about getting close and trying to gather advantages in many areas. Hunters do differ in what they consider important and that is why they put emphasis on other areas. Many hunters clearly choose to draw far closer to their maximum than they have to. I could choose the same, but I don't, and for reasons that I consider good ones. However, I'm absolutely positive that I could if I wanted to. It is not impossible and I could make the choice to key on increasing KE with speed or momentum with weight. It's all a matter of choices.

A better example would be my brother. He is a very strong person that can easily pull a 100 lb bow, and I mean easily. Does that mean that he should? Of course not. It's not necessary. He can choose to if he wants to. He chooses to shoot at 75 lbs with a very heavy arrow. If he wanted more speed and a higher KE and less momentum, it would be simple for him to accomplish this.

Actually I was trying to leave draw weight out of it. I said it was irrelevant after you brought it up. That was my point. It doesn't matter what you decide for a draw weight but after you have established it and the only thing you change is arrow weight, it is without question impossible to raise or lower momentum without rasing and lowering KE. It is impossible to equalize KE and raise momentum simply by changing the weight of your arrow. The only possible way to accomplish this is as I explained earlier is to take 2 steps. The first is to put on a heavier arrow, thus raising both ke and momentum. The second is to lower your draw weight therby lowering ke at a faster rate than momentum. So in other words, lets say you have established your draw weight at 55#, for all the good reasons you mentioned. Knowing full well that you could pull more weight. Now at this point if you decide you want to increase your momentum and either hold your ke the same or lower it, it is not possible to do it unless you lower your draw weight. It is impossible to do it by changing arrows alone. But if you have decided that 55# is a good weight for you for all those good reasons, why would you want to lower it and give away both ke and momentum. The only reason it is even possible to do what you are suggesting is that you will give up ke at a faster rate than momentum but if you are comfortable with the 55# why give up either? It makes no sense to me. Of course you could do it, but to me that's why this is a theoretical. IMO it's simply not a realistic ooption.

But what we are discussing is your conclusion that because momentum changes at a faster rate with arrow weight than KE then momentum must be more important with regard to penetration. I'm simply arguing that because the resulting increase in penetration is exactly the same you can not logically conclude by this reasoning that either is more important. It would be just as logical to conclude that KE is more important because it only takes a small increase in ke to achieve the same increase in penetration as a much larger increase in momentum.