For all you KE people out there...

[O.L. Adcock]

Bogsucker, You are wrong. Trad bows don't work that way. The heavier the arrow the more KE ( MO too) and more efficient the bow is. Look at the graphs on page 1, those are typical for trad bows...O.L.

[Bogsucker]

WT: 800, TTT: .502, FPS: 185, KE: 60.81 MO: 0.66
WT: 724, TTT: .468, FPS: 199, KE: 63.68 MO: 0.64
WT: 637, TTT: .433, FPS: 216, KE: 66.01 MO: 0.61
WT: 544, TTT: .402, FPS: 234, KE: 66.12 MO: 0.56
WT: 438, TTT: .372, FPS: 255, KE: 63.26 MO: 0.50

With corrected KE values using a divisor of 450240 and added Momentum.


The way I read this is as arrow weight goes down, KE goes up, Momentum goes down except for the lighter arrows who's KE values indicate an inefficient transfer of force to the arrow.

As far as page 2 chart goes across the chart momentum more than doubles yet KE increases a mere 25%

I'd like to see more data from trad bows using various arrow weights.

Maybe i should've been saying torque instead of horsepower when talking about my tractor, but not my car.

Either way a heavier arrow has more penentration than a lighter arrow given the same bow, right?

[Bogsucker]

O.L.,
I wouldn't say I was wrong, though, perhaps I've been using an inappropriate example to further the cause of using momentum as an indicator. Though, the correlation between KE and performance is still inconsistent whereas momentum more consitently fits a better relationship with performance.

It would appear now that the use of a heavy arrow is even more important when using traditional equipment.

I think we've both made some good points while debating the issue, but can anyone provide some empirical data that indicates KE is a better unit of measure for terminal(at point of impact) ballistics?

[O.L. Adcock]

Bogsucker, That chart was derived from multiple arrow weights, from 360 grains to 652 grains in aproximatly 50 grain increments.

Compound bows will begin to lose KE as arrow weight goes up because as the load increases there are more loses from friction in the cable/pully system just as you'll have more friction in your axle bearings with a heavy load as opposed to a light load. If they did not have those loses, KE would go up with arrow weight just like they do in trad bows.

As far as I can see, NO ONE here has said KE is a better measure of lethality. But Dr.Ashbey says NEITHER tracks perfectly but MO seems to track more often.

Ke is a good measure of one bows performance over another and that is all! If a person takes a bow with high KE and uses a light arrow and gets poor penetration, that is their fault for not useing the potential of the bow to their best advantage. (if max penetration is the goal) The bow with more KE has the potential for more momentum for a given velocity if the shooter selects a heavier arrow but that doesn't mean they'll get good penetration if they pick a sorry broadhead. The bow with more KE also has the potential for higher speed if they choose to go that direction....O.L.

[Bogsucker]

I agree with you almost 100% except that KE is not stored it is a calclated measure of an object in motion, regardless of design or efficiency.

[Tree man]

JAK, What O.L. meant is that bow efficiency continues to go up with projectile weight. The arrows may get too slow to be useful but the transfer of energy from the bow to the projectile becomes more and more completewith increasing arrow weight. The biggest gains are withing the "normal" range of arrow weights-say 300-700 grains for a 50Lb bow. Heavier arrows still soak up more energy the gains just become slight.Kinetic energy figures fall short in displaying penetrating capacity of an arrow. So does momentum.It isn't because the figures lie-They just don't tell the whole story. Within the range of usable arrow weights momentum seems to reflect things a little more accurately but....

[**DONOTDELETE**]

There are several very interesting points of view here. For what its worth, KE being Ke, there are alot of people that swear by the light arrow/higher, I don't. The KE charts are very accurate up until contact with the critter in mind. In firearms, I think the Taylor Factor gives a more realistic view. Unfortunately, with bows I think there are too many varibles to consider after contact to make any assumptions based on a slide rule.

Its just like Ol Gramma used to say- "If ya go, GO BIG!!"

[T-Bone]

All I know, if I payed more attention to KE instead of momentum's value,  I'd be screwed for hunting with my 48# bow and 600 grain arrow.  Heavy arrows definitely can make up for low poundage bows when it comes to penetration.

[beprepn]

What is funny is that a couple of years ago on the compound bow sites, people were arguing vehemently that KE was the variable to use to predict penetration.

I think momentum, based on the following math.

I can still do a little calculus...if I integrate Newton's second law over time while penetrating a target, the variable which predicts penetration changes with the type of force that is resisting the arrows passage.

If the resisting force is proportional to the arrow velocity, then penetration distance is exactly proportional to momentum.

If the resisting force is constant, independent of velocity, the the penetration distance is exactly proportional to KE. This is the case, by the way, with targets that slow the arrow by squeezing the shaft.

And, oddly enough, if the resisting force is proportional to velocity squared, the arrow never stops! Although after a while it is barely moving - but the force goes to zero faster than the velocity goes to zero such that the penetration continues forver.

In reality, of course, the force that slows an arrow is a complicated function that is a combination of forces that depend on the arrows velocity in different ways.

The other interesting thing is that shooting even the wimpy round wheeled compound that I shoot, if a  bone tries to stop an arrow cold, the force is huge! It can easily reach a thousand pounds, all concentrated at the point of the broadhead. This is again a direct result of Newton's second law, the force times the time that that force is applied just equals the change in momentum. Say I apply 30 pounds (with my bow) over 30 inches to accelerate the arrow. Then if I try to stop that arrow in a quarter inch, the force will be 30 divided by 0.25 times 30 = 3600 pounds (assuming that the distances equate to times)! I.e., the bone has to take away the same momentum that the bow added, but in less than a hundreth of the time which makes the average force a hundred times larger.

[High Tech Redneck]

Beprepn:

I think you almost have it.  From Dr. Ashby's new report #3 He compares penetration in a buff with two set-ups:

70#,756gr,MA2.75,0.477Slug-Ft/Sec,33.84ftlb,15.65"penetration

82#,790gr,MA3.25,0.523Slug-Ft/Sec,38.94ftlb,21.86"penetration(shot thru target)

The 82# setup provided MORE than 39.7% more penetration as it went thru the target. Because the 82# broadhead had a different style head which he reprted to provide 26% greater penetration with "normal FOC" arrows from prior testing due to it's greater mechanical advantage.  Therefore, adding 26% for mechanical advantage plus 9.6% for momentum= 35.6% predicted increase in penetration versus MORE than 39.7% actual increase in penetration.

However, the increase in kinetic energy was 15.1%.  Adding 26% for mechanical advantage and 15.1% for additional momentum= 41.1% predicted increase in penetration.  This fits nicely with the results of AT LEAST 39.7% more penetration because of the pass thru.  Once the arrow breached the far rib there would be little resistance to further penetration but the arrow was probably nearly out of gas by that time so this increase seems entirely reasonable.

From your 1/4/08 post I concur with the middle formula regarding substrates that squeeze the arrow as I have conducted field tests that fit that theory.  

I believe that an arrow that punches thru skin, breaks a rib, then travels thru a lung or two probably encounters all three of the situations you have described because Dr. Ashby's own results correlate better with kinetic energy than momentum from my analysis.  

He may be on to something with extreme front of center arrows not flexing as much when they hit the target so they should penetrate better, but I think he needs to eliminate the other variables better to prove it.  

I also believe that momentum may model penetration a bit better for finger/stick bow shooters because of the archers paradox phenomena as the arrow is apt to still be flexing when it hits the target(is this flexing part of the kinetic energy?).  If an arrow is flexing when it strikes it probably will not penetrate as far as one that is not flexing.  

Note:  Somewhere on the net I saw a video of an arrow striking a target and that thing was whipping all over the place!

[High Tech Redneck]

Dr.  Ashby concludes that momentum is a better predictor of arrow penetration in game than kinetic energy, but his own analyisis of data from the 2004 Broadhead & Arrow Lethality Study Update, Part 2 do not appear to mathmatically support this as presented.  

I believe the same 82# longbow was used to shoot  820 grain (by my calculation) wood shafted arrows with his modified Grizzley heads, and double shafted aluminum arrows with the same style of head which also had an additional 135 grain rod welded behind the head for a total weight of 1090 grains.  Both arrows were within .010” dia. of one another and smaller than the broadhead diameter at the ferrule.
The 36% heavier aluminum penetrated 33% more than the lighter wood arrow even though it only had 13.6% more momentum and 1.6% LESS kinetic energy than the wood arrow.

Discussion:
It is unclear whether the velocity of the arrows was measured at the bow or at the target 20 yards away.  This seems important because the reported kinetic energy of the lighter arrow is higher than that of the heavier arrow.  This may not be a “statistically significant” amount because a lighter arrow is supposed to absorb less energy from a given bow than a heavier arrow but it lends suspicion to the test data.  

An increase of 13.6% more momentum does not compare well to an observed increase of 33% penetration. An increase of 36% more mass compares better to the observed increase in penetration (Note that kinetic energy remained the same), especially if a 3% correction is applied for the ESTIMATED increase in FOC created by the 135 grain rod at the front of the heavier arrow.  I would estimate this increase to be three to five percent.  Therefore, 36% more mass + 4%for higher FOC – 1.6% for less kinetic energy = 38.4% predicted increase in penetration.  This is not a perfect match, even if it is better than the amount predicted using momentum.

Looking at the figures, a better match can be formulated using the sum of the percentage increase in momentum plus the absolute value of the percentage change in velocity.  13.6% more momentum plus 14.9% change in momentum plus 4% for higher FOC = 32.5% predicted increase in penetration.  This does compare favorably with the observed 33% increase in penetration.   This formula  also predicts a 40.5% increase in penetration for the example in my January 17, 2008 post compared to an observed increase of AT LEAST 39.7% (due to arrow penetrating the off side of the carcass ultimate penetration was not measureable).  This formula seems to work to compare one setup to another but I am not sure if it can be used to predict penetration.

To me the logic and mathematical formulas presented by Dr. Ashby do seem to indicate that momentum is the key to penetration, and the empirical data seems to suggest that the greater portion of that momentum comes from the mass the greater the penetration will be in game animals.  It is interesting to speculate about the effect on penetration of “friction” versus “work” as relates to inclined planes (i.e. the mechanical advantage)and “resistance”, (i.e. the fact that resistance increases at the square of the velocity).   I sincerely hope that in his next report the variables of different arrow shaft materials, shaft diameter, broadhead style and weight, and so on are eliminated so a precise formula for determination of arrow penetration can be developed.  Hopefully this formula can be correlated to a standard uniform test media so us mere mortals can do our part to take to the field with the proper equipment.

[O.L. Adcock]

Looks like this has been beat to death over several years and most clear thinking people "get it"...Just in case someone reading this anew falls into Zaks false assumption that bows have an arrow weight range where optimum KE occures, here is a link that clearly shows how any given bow, the KE will continue to increase as arrow weight goes up:

  http://www.archeryevolution.com/pdf/2007Face-OffResultsArcheryTalk.pdf

Here is a couple of graphs derived from real tests by Norb Mullaney, not "theory"..

 

 

These curves would be typical for any bow, only the values would change.


I could show a dozen other examples with trad bows.

Those that try to do bow testing that have little understanding of how bows work can can easily fall into this trap. KE drops seen when arrow weights go up are the result of the testers failure to recognize "other" issues not related to the arrow mass is causing the drop in KE...Mostly tuning issues where arrow contact with the bow and rest, nock fit, ect....

It all boils down to it's not the KE available, it's how "fast" you try to use it.....O.L.

[tradwannabe]

you are all missing one very important point made by Dr. Ed Ashby, the target(animal body) resists the arrow MORE when the arrow is FASTER. So the resistance of the animal rises with the SPEED the arrow is travelling. It's about penetration and resistance. Jump off a high bridge into water and you might break your legs, get spattered on the surface, or die. Jump into water from the edge of the pool, guess what, you penetrate the surface.

[BMG]

since I'm terrible at math maybe some here can help me out.  If I have a compound launching a 600 gr. arrow at 260 fps versus my recurve (63lb RER) launching a 700 gr. arrow at 170 fps  that my recurve will out penetrate the compound bow???  Both would have the same Grizzly broadhead for posterity sake.

[tradwannabe]

I don't think anyone can truely CALCULATE it. If you read every single ASHBY report and compile the percentage variations you might be able to make a guess. The problem is that the variables are not linear. You would need to come up with a number of equations (non linear) (within a range) to approximate the differences involved. friction coefficients would be required at different speeds, the initial energy to beak through the surface tension of the hide would be required (in a specific location), the rotational rates of the arrow in flight and through the animal would be required, etc., etc.,,,,,,. If you know a math major at a university that is interested in a difficult model to solve, try them.
Rob

[tradwannabe]

One more observation about Dr Ed.
When he needs more penetration, what does he do? It appears that he goes to 1000+ grain arrows from a 80-90# longbow.He does not stay with a 700 grain arrow and shoot it faster.This is a guy (there are others)that has killed many different dangerous animals (the big 5 i think). I think for north america, you should use 650-700 grains for moose and elk, (650 being the "threshold" Ed defines) but not necessarily required for deer. Some deer are no bigger than dogs while others are as big as elk.
you decide.
Rob

[O.L. Adcock]

Babaloo, "since I'm terrible at math maybe some here can help me out. If I have a compound launching a 600 gr. arrow at 260 fps versus my recurve (63lb RER) launching a 700 gr. arrow at 170 fps that my recurve will out penetrate the compound bow???"

The "resistance" Tradwannabe speaks of goes up by the square of the velocity. Increase velocity 10% and the resistance to penetration goes up 40%. It's difficult to "cross" from one example to another the way you are looking at it since you are not only changing velocity you are changing KE at the same time. One has 45ft/lbs and the other 90, in the real world they'd be close to the same penetration. Are you sure of those numbers? 45ft/lb is about what one would expect out of a decent 55# bow......O.L.

[Tilzbow]

OL,

If you see this please explain the comment, "45ft/lb is about what one would expect out of a decent 55# bow......O.L."

I've got one of the new A&H ACS CX, which I consider more than decent bow, that I draw to 31" at 47# and with a 460 grain arrow I get 200 FPS and 41# KE. I consider the 200 FPS at nearly 10 gr/# very good, even at my draw length, so either my KE calc is off or I've got a slow version of the ACS CX... With a release I get about 205 FPS and both speeds are with musk ox wool silencers and a tied in nock point. To get to 45ft/lb KE I'd have to shoot the same arrow 210 FPS, by my calculation, which is smokin' fast by trad bow standards! Is my calculation wrong, is there a faster bow out there or is my testing fouled up???....Scott

[O.L. Adcock]

Scott, Your draw length is a blessing many would die for!    Say a bow has a 1:1 se/pdf (most don't) at 47# you'd store 47ft/lbs, if you were getting 41ft/lbs in your arrow it's 87.2% efficient. Since it probly isn't storing an se/pdf of 1.0, it's even higher then that.

My example of 55# with an se/pfd of 1.0 and 45ft/lbs in the arrow is an efficiency of 81.8% which is close to what the better recurves spit out and they do typically have an se/pdf higher then 1.0. So, no, your numbers are better then the example I used, not worse....O.L.

[DesertDude]

O.L.  This old Navy BB stacker is missing something.  Let's say your shooting a 55# recurve.
your arrow weights 550gr with an arrow speed of 180fps gives you 39.58 ft.lbs of KE. If arrow weights goes up, speed goes down. If I'm using the right chart, KE starts to drop off at a certin combo. I'm I just missing something? I don't understand how KE can go up forever.....

The Red Shirt......