compound bow kinetic energy help

[inline6power]

ok i am a huge bow hunter and i am have a serious debate on kinetic energy with compound bows. i have a few people that may be right that i am argueing with. here is my question. i am shooting a compound bow at 72 lbs of draw force, the arrow weight is 415 grains and the velocity is 337fps. i am calculating my kinetic energy at 100.4 ke. now here is my question and the debate. i have a few people telling me that now matter what, if i go to a heavier arrow weight, that means that my ke will go up no matter what. i beg to differ unless i am re tarded. if i take a 650 grain arrow and shoot it threw the same bow, same draw force of 72lbs and the arrow is flying at 259.5 fps , my new ke is calculated at 97.2 i know their are alot of varieabls with arrows such as arrow spine, how stiff, carbon or aluminum, and how effecient the bow is. as weight goes up , the more effecient the bow becomes. my next question is there a middle ground where mass will go up, velocity will go down, and ke start to go down? take this for a comparison

 

415 grains at 337fps is 100.4 ke

650 grains at 259fps is 97.2 ke. the real debate is alot of people say ke is king and that the heavier arrow will always have more penetration than the fast lighter arrow and i think they are wrong. can you guys help me out a little?

 

any one?

 

come on someone has to have some answers for me lol. thanks in advance

 

come on lol i know some of you guys must have some answers. i have a big debate going on another forum as we speak lol. just looking for more info on the questions at large.

[Mr Skeptic]

Well, I'm not familiar with your units but that doesn't matter so much. The heavier arrow will probably gain more energy from the bow, not necessarily by much but at least a little due to the bow not having as much kinetic energy if nothing else. All else being equal, the faster arrow will have a lot more air resistance, which goes up rapidly with speed, so the fast arrow will lose more energy to the air. Also, the heavier arrow will have greater momentum even if it had the same kinetic energy.

 

But there's also another aspect to causing damage: how quickly the energy/momentum is transferred to the target. So for example if you have two arrows with the same kinetic energy and one is x times heavier as the other (m for the light one and xm for the heavy one), the speed of the heavy one will be [math]v=\sqrt\frac{2 KE}{xm}[/math] and the lighter one would be faster by [math]\sqrt{x}[/math]. The rate of transfer of kinetic energy would be proportional to KE*v, so that the lighter arrow would transfer energy by the same amount faster as it is moving faster. But the heavier one would have more momentum, by the same amount as the light one is faster. The rate of transfer of momentum will be equal because the more momentum cancels out the moving slower. So the fast arrow transfers the kinetic energy faster, and the momentum just as fast, as the heavy arrow, but the heavy arrow has more total momentum (and should have a very small bit more kinetic energy). I don't know exactly what that means, but my guess is that the light arrow can penetrate a harder target but the heavier arrow penetrate farther into anything it does penetrate. Since you're probably shooting at soft targets, I'd say you should expect the heavier arrow to penetrate farther.

[Ludwik]

You wrote:

"i am shooting a compound bow at 72 lbs of draw force, the arrow weight is 415 grains and the velocity is 337fps. i am calculating my kinetic energy at 100.4 ke."

 

Your calculated energy is 100.4 ke. What is one ke? How many joules is it?

 

Ludwik Kowalski (see Wikipedia)