Penetration Energy

[vidsoutmike]

This may be the dumbest thing you've ever heard but I may be on to something. I know it's hard to convince the average bow hunter to use heavy FOC arrows. Playing with numbers, I've come up with a formula for PE. (Penetration Energy)
For instance, I have 2 600 grain arrows. One has an FOC of 12 and the other has an FOC of 19. Both arrows weigh the same, have the same kinetic energy and same momentum. The only difference is the FOC. I know for learning from you all and DR Ashby that higher FOC has better penetration.
Here you go.
Weight + velocity x FOC = PE
ex: (W)600 + (V)220 x (FOC).12=98.4
ex: (W)600 + (V)220 x (FOC).19=155.8

ex: (W)425 + (V)310 x (FOC).06=44.1
ex: (W)425 + (V)310 x (FOC).09=66.15

Remember, the KE and momentum are the same in each of the 2 examples.

This may be silly but I think it gives me a number to work with when trying to figure "power at my tip" or "Penetration Energy".
What are your thought??
Thanks,

[galamb]

I love formulae - keeps my rather boring existence interesting

I am also an Ashby fan.

The question I would have with your formula, as interesting as it looks is, how do you quantify the result into something that is measurable, in terms of terminal ballistics.

What I mean is, I see your result -

600 + 200 x .12 = 98.4 and
600 + 200 x .19 = 155.8

So while the 19% FOC looks "more/better/stronger/harder" - in "real terms" how much better/stronger/harder etc it it?

50% better (if you simply compare the two numbers) - so if arrow A would penetrate 8", would arrow B penetrate 12" (as the numbers would sorta indicate)

Or is the increase "non-linear" in terminal performance?

You might be onto something, just might need to do a bunch of real world testing to see exactly what it is.

Thanks though, I will make a copy of your work-ups there and do some testing myself - in a couple of months when my range isn't under a few inches of ice

[vidsoutmike]

I don't know how the % can work because when teasing, there is no standard test media. It's just an idea and I enjoyed playing with the numbers and they indicate that there is a difference where FOC is concerned. So many folks look at KE for the answer but I've seen slow, high FOC arrows out penetrate higher KE arrows with lower FOC.

[wabi]

I've tried real life hunting tests with both 150# (Vixen) & 175# Exocet & Phoenix) crossbows.
With a relatively light arrow (350-400gr) and low FOC (7-8%) the tests never seem to give measurable results. The arrow blows right through the test medium (live deer) and buries in the ground where the density varies.

[nchunterkw]

wabi - I see what you did there but understanding this better is not a bad thing. Truth is whitetails are not all that hard to kill - say compared to an Elk or Bison or Moose. In those cases understanding arrow penetration - and how to maximize it becomes more important.

vids - I too am an Ashby fan - and while interesting but I just see your formulas as basically, momentum times a fractional multiplier - which of course will give a larger result for a larger multiplier. But as Ashby writes about, arrow penetration depends on many factors including the resistive forces applied by the target medium on the arrow. My understanding of why he advocates high or extreme FOC is because that reduces flexure of the shaft at impact - thus creating less drag through the animal.

And galamb - I too think it would be great fun to try to put some of this to the test. But we would need more than a couple specially made arrows to do so, and a test range with a very uniform test medium to shoot into - like ballistics gel. I made some homemade stuff once and it worked well, but it was a pain to make a block big enough to get more than 1 or 2 shots into.

maybe a nice summer project

[vidsoutmike]

My idea may be no more than a conversation piece but at least we are in conversation and debate. Awareness starts somewhere and maybe more folks will consider FOC or just become aware.
Thanks for the input and your time. I really appreciate it.

[wabi]

Not discounting the high FOC theory, but I don't believe it is the reason for improved penetration IF an arrow of the same weight/velocity with low FOC is flying perfectly.

If an arrow is not achieving perfect flight (and I doubt any arrow really does) then increasing FOC is highly likely to improve flight. If flight is improved there is less wasted energy and the arrow would be a bit more efficient at delivering that energy to the target.

So increasing FOC might improve penetration, but possibly changing other factors (spine, fletching, etc.) could do the same thing.

[amythntr]

1. Grab Micro and arrows,
2. Drive to hunting spot,
3. Get into blind or climb tree,
4. See deer in my 30-40yd range,
5. Shoot,
6. Watch Lumenok/ignitor go through deer,
7. Get out of blind or climb down tree,
8. Find deer 30-50 yds away taking dirt nap,
9. Repeat...

That's as technical as "I" would like to get with this....Any more for me and it is work...This is just me and not meant to criticize anyone else.

Anthony

[paulaboutform]

1. Grab Micro and arrows,
2. Drive to hunting spot,
3. Get into blind or climb tree,
4. See deer in my 30-40yd range,
5. Shoot,
6. Watch Lumenok/ignitor go through deer,
7. Get out of blind or climb down tree,
8. Find deer 30-50 yds away taking dirt nap,
9. Repeat...

That's as technical as "I" would like to get with this....Any more for me and it is work...This is just me and not meant to criticize anyone else.


Anthony

Anthony, I'm guessing that after crunching numbers all day that's the last thing you want to bring into your hunting world.

[amythntr]

1. Grab Micro and arrows,
2. Drive to hunting spot,
3. Get into blind or climb tree,
4. See deer in my 30-40yd range,
5. Shoot,
6. Watch Lumenok/ignitor go through deer,
7. Get out of blind or climb down tree,
8. Find deer 30-50 yds away taking dirt nap,
9. Repeat...

That's as technical as "I" would like to get with this....Any more for me and it is work...This is just me and not meant to criticize anyone else.




Anthony

Anthony, I'm guessing that after crunching numbers all day that's the last thing you want to bring into your hunting world.

....ya think?

[nchunterkw]

wabi - according to Ashby, as I understand it, ... and arrow flexes about the center of the shaft when shot, but about the center of balance when it hits a target. So an arrow with 0% FOC would flex at the midpoint when it hits a target, and one with 25% FOC would flex somewhere like 5" forward of the mid point upon impact. Now if you take an arrow in your hand and try to flex it at the mid point it takes XX amount of force. But if you try to flex it the same amount 5" further towards the front it will take much more force. So on the low FOC arrow, the amount of flex is greater because the moment arm between the front of the arrow and the flexure pt. is longer, than on the arrow with high FOC. So if you had two arrows that looked identical outside, and weighed the same but had different FOCs the one with higher FOC should flex less when it hits the target. Less flex would translate to less "drag" as it goes into the target.

You are making a very good pt. about good flying arrows as well, and it is also similar to the argument above. If and arrow flies well, it spins very tightly and all the energy is focused behind the pt. (once it is stabilized and stops flexing) when it hits rather than the arrow flying in a spiral fashion where energy is wasted. And you are also right in saying that higher FOC usually helps arrow flight. So IMO higher FOC arrows are a win-win. Better flight and less drag upon impact.

Now I will concede that perhaps most of this is moot when it comes to something like the Zombie Slayer or Executioner shafts. Their increased stiffness, I think has improved things immensely as far as crossbow arrows go.

[galamb]

I have read Ashby's work many times and still confused in a lot of places

Ultimately, I tried a number of higher FOC combinations because he said they were "good/better" (paraphrasing there of course).

What I found was (regardless of all his studies), that with my bow, which shoots slow compared to what most of you guys/gals are shooting, I can get the most "consistent" groups by shooting an "extreme" FOC (somewhat over 20%).

So for me it boiled down to "knowing" how my arrow was likely to react and where it would impact whether the air was still or there was a 10 mph crosswind etc.

If I get better penetration shooting 22.5% FOC that is just an added "bonus" that resulted from my best grouping arrow set-up's.

Because if the impact points looked like a shot-gun blast, I wouldn't be shooting extreme FOC whether or not it penetrated better..

[racking up points]

Now I will concede that perhaps most of this is moot when it comes to something like the Zombie Slayer or Executioner shafts. Their increased stiffness, I think has improved things immensely as far as crossbow arrows go.

Ashby probably wrote with compound shooters in mind with arrows from 25"-32", yeah I could see there being a slight amount of drag at entry from flexing. But some of us are shooting 15"-18" BEEs or Zombies . . . I can't imagine the same effect.

[Jerod B.]

Now I will concede that perhaps most of this is moot when it comes to something like the Zombie Slayer or Executioner shafts. Their increased stiffness, I think has improved things immensely as far as crossbow arrows go.

Ashby probably wrote with compound shooters in mind with arrows from 25"-32", yeah I could see there being a slight amount of drag at entry from flexing. But some of us are shooting 15"-18" BEEs or Zombies . . . I can't imagine the same effect.

I agree on the short shafts producing less flex upon entry.

However, Ashby showed in a video these little short bolts, I mean very short, and how the 30% FOC'er out shot two lighter bolts, with less FOC. I mean that 30% sucker FLEW of that miniature bow.

[SEW]

Some FOC findings. With 380 & 405, Zombies.
Increasing FOC beyond 15-16% didn't help(field point) groups but increased FOC(up to 30%) didn't hurt accuracy but greatly increased drop, especially from 70-100 yds. So, increasing FOC beyond that needed for optimum accuracy will give the effect of a slower velocity. Penetration - ?