2 arrows of different mass but the same KE = same penetration????

[raideranch]

The two variables that effect KE are mass and velocity.  The heavier arrow will have more mass but less velocity.  The lighter arrow will have less mass but more velocity.  If you plotted the KE for both these arrows at different ranges somewhere on the graph the lines would cross.  At that point (which will relate to a certain range) the KE would be the same for both arrows.  If both the arrows are arriving at that range with the same amount of energy (KE) with everything else being equal (broadhead, arrow diameter, etc...) they will penetrate the same.

[Brook Trout]

well put raideranch

[Jock Whisky]

As the speed of a projectile increases, the resistance the target imparts to the projectile increases exponentially. For example if the speed of your projectile doubled (x2) the resistance of the target would increase by 4 times. It is not a straight line relationship. That is why your gas mileage goes for a crap as your vehicle speed increases.

So the faster your arrow goes, the more the target resistance increases.

The slower heavier arrow penetrates farther than the fast light arrow assuming they have the same KE, momentum, force whatever.


JW

[Richie Nell]

Jock,
"For example if the speed of your projectile doubled (x2) the resistance of the target would increase by 4 times"

If I have an 800 grain arrow going 150 fps and double that speed to 300 fps, are you saying that the penetration would not be as good because the faster arrow's resistance increased by 4 times?

[jrchambers]

now these tests could not be done with a crono right infront of the shooter as a heavyer object slowes slower than a lighter one. so if the ke is the same a foot from the bow at ten yards the heavyer one will have more ke.  and i bet the tests were in some very consistant tofu like blob. no bone or hair hide tendons cartlidge.....

[bowslinger]

I am sorry Don, but swallows are non migratory.

Raiderranch, is it more likley that there may be a point where their momentums are equal, versus where their kinetic energy is equal?

I would assume if the arrows are the same except for mass, if there is a point where their momentums are equal, they will have very similar, if not the same penetration.

[raideranch]

Bowslinger
Yes the two variables of momentum are mass and velocity which are the same two for KE.   Two arrows of different mass and velocity could have very similar momentum through flight at all distances.  The heavy arrow slows down faster but maintains its momentum through its mass while the lighter arrow maintains its momentum because it does not slow down as fast.  The KE for these two arrows will not be paired as well as momentum over a range of distances because velocity has a greater effect on KE than mass does where they have equal effects on momentum.  You can see from the equations that velocity is squared for KE which means it has more effect on KE than does mass.  For momentum they have equal effects.  

KE (kinetic energy) = .5 x mass x velocity²
P (momentum) = mass x velocity

[ozy clint]

raider- i can't see how two arrows of unequal mass but of equal KE can penetrate the same. the lighter, hence faster arrow encounters more resistance. even if their momentum was the same. isn't that right?

or am i confused?

[raideranch]

Ozy
I'm no physicist I just took Physics I and II as an undergrad a couple years ago and understand some of the basic principles.  I assumed they would penetrate the same because regardless of speed if they arrive at the target with the same KE both arrows will be transferring the same amount of energy to the target (so the tissue is absorbing the same amount of energy) unless the arrows pass through in which the rest of the energy is going to be transferred to whatever the arrows hit next.  In this range of velocity the difference in resistance likely insignificant.  Brook Trout is an Engineer he probably has a better answer.

[James Wrenn]

Yeah Richie the fast arrows will bounce off stuff.I am sure you have read that around here before.      

[TheFatboy]

Not sure if I'm just stating the obvious here, but if you have not read Dr. Ashby's study on this, here it is:

http://tradgang.com/ashby/Momentum%20Kinetic%20Energy%20and%20Arrow%20Penetration.htm

I've gotten a lot smarter just by reading this!

[Don Stokes]

Bowslinger, I was referring to African swallows, of course.

A basic flaw in the whole premise- Arrows that are not the same mass are not identical. They may be the same diameter, the same length, the same color, but performance during flight will not be the same by any measurement you choose to use. Heavier arrows leave the bow more slowly than lighter arrows, but at some point the faster arrows will slow to the same speed as the heavier arrows due to air resistance, and beyond that point the heavier arrow will be faster until the target is reached.

The answer to the question is predicated on the variables, and there are too many variables for a realistic evaluation.

[Jeremy]

I'll play  

Looking at just one moment, presumably just before impact and assuming that KE1=KE2

If a 500gr arrow is traveling 180fps, a 600gr arrow will need to be traveling at 165fps to have the same KE.

That same 600gr arrow will have 10% more momentum at that point than the lighter, faster arrow.

Going up to a 700gr arrow, it will need to be traveling at 152fps, giving it 18% more momentum than the light arrow.

Read through the Ashby link above, it does a good job of explaining why momentum and not KE is the better penetration indicator.

[Richie Nell]

Yeah Richie the fast arrows will bounce off stuff.I am sure you have read that around here before.

Not if it is also heavy.  But what do I know I haven't shot enough light or heavy arrows to make a post.

[James Wrenn]

Just kidding of course Richie.     I don't but the 4 times resistance for twice the speed thing myself.The bottom line none of this stuff matters much at all.Everything we shoot if it is legal and tuned well will put an arrow out the other side of the critters we hunt if we shoot them in there sides instead of there butts.  

[Richie Nell]

I absolutely agree.

I have always really known that really heavy bows/arrows are not necessary for whitetail. But due to hunters like yourself, I have become more and more a believer in the ability of the lighter weight weapons with the proper educated hunter behind it.

but in the mean time..

Hello...my name is Richie      ...(hi richie)..
I just have this perfectionist sydrome problem
that creates an uncontrollable urge to use a heavy bow, arrow and fist.

WOW...I feel so much better.  It's a new day.

[Jeff Strubberg]

Originally posted by Richie Nell:
Jock,
"For example if the speed of your projectile doubled (x2) the resistance of the target would increase by 4 times"

If I have an 800 grain arrow going 150 fps and double that speed to 300 fps, are you saying that the penetration would not be as good because the faster arrow's resistance increased by 4 times?

Nope.  If you increse that speed and lower the weight to the point that KE was equal, then the lighter arrow would not penetrate as well.

Of course if you apply more energy to accelerate the same weight projectile to a higher speed, it's going to penetrate better.

Heavier arrows equal more momentum.  Assuming a constant amount of energy at launch (i.e. the same bow and draw), more projectile weight is the best way to increase both momentum and penetration.  The longer we can carry a high amount of energy without increasign drag, the more penetration we will get.

[Jock Whisky]

Richie

I'll try to explain a little clearer.

You have two arrows absolutely identical except in weight.
Both arrows are shot so they develop the identical KE, momentum, force, whatever. This means the light one would be moving faster and the heavy one would be moving slower.

The heavy one would penetrate farther, all things other than weight and speed being equal. This is because the target resistance increased as the lighter one went faster.

Does this mean you have to shoot 700 grain arrows to kill an animal??? Absolutely not. However I use heavy arrows for all my hunting because I want the best chance for maximum penetration. That's the choice I made FOR ME after studying Ashby's work. Someone earlier said something about "fast arrows in the hands of an educated archer". Nothing wrong with that. Use the info in Ashby's report to make a decision that works for you.

JW

JW

[jrchambers]

quote from page 2 "The heavy arrow slows down faster but maintains its momentum through its mass while the lighter arrow maintains its momentum because it does not slow down as fast. "

corect me if im wrong but this is wrong,  two arows different weight, same ke right off the bow,  the heavyer one has more momentum, does momentum not equal speed retentoin?
ive done quite a bit of reloading ammo and two slugs with the exact same balistic coeficient, basicly arowdinamics, but different weights fired at the same speed are not equal in trajectory. the heavyer one slowes slower.
so these two arows asuming same diamiter and length will have the same ke only for a given distance, im not saying the heavyer one would ever catch up but if the shot could continue for a imposible lenght before gravity took over completly the heavy one might catch and pass the lighter faster arow.

[raideranch]

jrchambers
No, regardless of KE or momentum, fired at the same angle the faster arrows will have the flatter trajectory and will travel further.  Both arrows are falling at the same speed but the faster one will cover more ground before it hits.  Theoretically, if you shoot a bullet horizontal to the ground and at that exact moment drop a bullet at the same height of the barrel they will both hit the ground at the same time.  They are falling at the same speed (9.8 m/s²) but the bullet shot from the gun is moving in both the horizontal and vertical directions as it is falling.