This is what I'm talkin about!

[BT]

Taken from a post on Mathews site
(written by site member - im-ocd )

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Momentum is a factor, but don't ignore KE.
The arrows used in the traditional bow reports were 520 gr.

Let me use two real life examples for momentum:
Traditional 60# bow 540 gr. arrow @ 180 f.p.s. = .431 momentum
Compound 60# bow 340 gr. arrow @ 283 f.p.s. = .427 momentum
Momentum is almost equal, or slightly in favor of the heavy arrow. Think the traditional shooters arrow will penetrate better? Wait....

Lets compare the KE
540 gr. @ 180 f.p.s. = 38.8# KE
340 gr. @ 283 f.p.s. = 60.4# KE
Still think the traditional arrow will penetrate better? I don't.

In my example momentum is basically equal and if momentum was the only valid basis to compare penetration those arrows would have the same penetration. However, there is a huge KE difference and I think the light arrow will penetrate further because of that KE advantage, even though momentum is essentially the same.

[michihunter]

There's a balance, and you can drop mass trying to increase KE to the point where you hurt yourself come killin' time.

OK, I'll offer up one more thought on the KE vs. Momentum discussion. Using an illustration...

You have a 1lb rock moving at 10 ft/sec. You have a 100lb boulder moving at 1 ft/sec. Which would you rather hit the hood of your car? How about the wall of your house?

They both have the same kinetic energy, but the boulder has 10X the momentum of the rock. (OK, all you physics types don't start getting picky about slugs-mass versus Lbs-force-weight! You know what I mean! )

Now change it around to where momentum is equal. Now it's a 10lb rock moving at 10 ft/sec. Boulder is the same. The rock now has 10X the Kinetic Energy of the boulder. Again, which would you rather hit your car/house? Seriously, above a certain point, it's all about the mass.

Bottom line, bowhunter, is you're wanting to get to a speed and _keep_ that speed for as long as possible, right? Keep speed both through the air and _through_ the target, right? When force is applied to any moving object, the object will accellerate in direct proportion to it's Mass. The lighter arrow will be traveling faster, but will have an drag-based accelleration applied to it in proportion to the square of the velocity. To put this in perspective, if a heavier arrow is only doing 250 ft/sec, it's velocity component of KE is 62,500 ft^2/sec^2. A lighter arrow might do 280 ft/sec. The lighter arrows' drag velocity component is 78,400 ft^2/sec^2. Arrows are probably just a fraction of a pound difference in weight, but have approx 15,000 (ft/sec)^2 difference in velocity drag component. That's about 24% higher drag on the faster arrow. And it has less mass for the force to work against. Adds up...

For the plywood test, everything I've talked about previously is assuming the arrow is moving through a fluid-like medium such as air or the liquid guts of an animal. For the case of an arrow breaking a barrier such as skin/bone/plywood/steelplate/etc, we're not talking about penetration/passthrough a medium anymore. We're talking about impact energy applied until yield/fracture, which is where KE comes in. Engineering calls it "Hammer Shock." Get as much energy as possible in as little an area as possible for as short a time as possible, which is why all the broadheads out there have those chisel or cut-on-contact tips. The arrow's KE has to be enough to _break_ the barrier, but even bone requires some measureable Time with force applied before failure. That really short time is counteracted by the highly concentrated Force applied and sometimes, that acceleration robs the arrow of all it's velocity and you don't penetrate. An engineering text would refer to it as an elastic/plastic collision. The "phonebook" test is really just a series of hammershocks one behind the other. Granted, there's _some_ friction as the broadhead moves through the pages, but even that isn't the same as that's a true static/dyanmic surface friction phenomenon, like tires on pavement, and the equations are completely non-transferable to an sort of "Drag" type assumption we were making earlier. Different problem, entirely. And not a true test of a arrow's "passthrough" capability.

[BT]

Good points

On area's that have increased Resistance due to mass , the mass must be elevated as well.
Mass in terms of measurement as opposed to mass in terms of mass is not the same in action.

None the less .... if we stay away from mass (heavy bone) it is a moot point.

[stilllearning]

I failed science. ;D ;D ;D

I am kind of lost with all this.

[BT]

;D
Come on stilll....read it a few times .... it'll click sooner or later

[michihunter]

Had to bring this old post up because of a thought I had after reading another post elsewhere. If proponents of KE over Momentum feel that lighter/faster is better than heavier/slower, what can be derived by trad shooters shooting heavier arrows than most? Another question (and this was the thought that came to me) what would you feel is more representative of efficiency? A dart thrown as hard as you can, or a baseball that is thrown as hard as you can? Which will travel further? Which will have greater force of impact at 50 yards? My guess is the baseball. Rememeber, these two things are thrown by the same arm by the same guy (or replicating a bow shooting two different arrows if you will). Do you agree that the baseball would be the winner in impact force?

[BT]

Yes and at a great distance I would take weight over initial speed any day.
But....(damn buts ) the fact is that with the K.E. factors brought about by great speed , the animals in north America couldn't hold either.

It's not until you begin to come back out of the hyper speeds that weight starts showing it's true worth.

[stilllearning]

I think I am begining to understand some of this............

Ok I just scared myself.

[michihunter]

There's actually a pretty good chapter in the link I sent to you on another thread in regards to this topic.

MOMENTUM vs. KINETIC ENERGY:

Should you have an unquenchable interest in ballistic physics, you may find it interesting that a few sporting enthusiasts will even dispute the convention that KE is the best measurement for predicting hunting penetration. A number of enthusiasts will debate that MOMENTUM is the better mathematical model. Of course, KE and Momentum aren't the same thing.....

----> Kinetic Energy = Weight X Velocity Squared /2 X Acceleration of Gravity
----> Momentum = Weight X Velocity / Acceleration of Gravity

Since velocity isn't squared in the momentum formula, arrow MASS plays a much larger role. The kinetic energy of a moving body increases as the square of the velocity whereas the momentum increases directly as velocity increases. So if you recomputed our chart to show momentum, then the graph would look much different. The heavier arrows would show a significant improvement in overall momentum, and you could therefore conclude that heavier arrows would indeed yield better penetration.

Right or wrong, the shooting sports have a number of traditions and conventions regarding technical measurement. And the lethality of a projectile (whether from a firearm or bow) is traditionally expressed as a function of KE (ft-lbs). As such, most sporting enthusiasts have some comprehension of this measurement. Unfortunately, a momentum rating in Slug Feet-per-Second would surely leave many of us scratching our heads. Given the dramatic difference in the two methodologies, it seems unlikely that KE has remained the "standard" for so long if it's entirely incorrect. There are a lot of talented engineers in the archery industry. So either they have ALL missed it, or perhaps the momentum theory has a glitch (not to worry - our team of physicists are working on it now).

Should you have an interest in the debate regarding which mathematical model is best applicable to archery, here's some basic argument on the topic www.booneman.com/_terminalarrow.php For more discussion, Dr. Ed Ashby also has an interesting and exhaustively extensive article on the subject

[BT]

I find it interesting that there is a calculation for momentum at all.
This sprung up very recently and I question it although I will use it from time to time.

The thing about momentum is that it can not be expressed.

That is to say that you can go to a large number of Ivy league schools which have dumped millions of dollars and hours into the K.E. verses Momentum debate and you will find that in each case documentation it is clearly stated each and every time that momentum can not be derived in mathematical form and therefore cannot be expressed to a value that can be used in science.

It is one of the very few things that I have ever heard of that cannot be expressed mathematically.

I used to have a number of links that I would use on other forums while arguing this point.
Since that time my computer has crashed and burned and those links are history but....they are still out there to be found.

I am going to look into this further now that it has been brought up again.
It would be impossible for me to believe that all of these think tanks would say that it cant be done if it could