Interesting but short read on KE vs Momentum

[Pac8541]

MattB: Love your comments, both of them. You're absolutely right and while I'd love to be practicing more and hitting the gym, I'm having my left shoulder replaced Wed morning so I'm attempting to settle on these things while I still have time to shoot a bit. I will spend my time off building several dozen arrows in the hopes that come Sept, I can focus solely on practice and conditioning for my Nov bull hunt here in AZ. I appreciate your insight.

 

[moxford]

Thread's been covered pretty well so far, but one last observation.

KE = mv^2 as we all know. So you get big numbers very quickly and that's great on paper.

What's not realized (or at least articulated well) is that once your arrow TOUCHES something it begins to slow down (duh?) but the critical factor is that while it starts with high KE due to the exponent, it bleeds off that KE *exponentially* as well. You slow down very very quickly.

However, slow/heavy high momentum arrows (761@238,70@32") are pretty fun and make my setup super-quiet. When I hit a non-virgin section of bale at 30 yards and think I missed because I don't see the arrow any longer ... well, it's just that it's buried in way deep. I haven't had a full passthrough on a bale, even at 20 yards, but with 30" shafts I've gotten close!

Overkill? For sure!

 

[ozyclint]

But there are anecdotal studies that show that arrows with more mass but with lower momentum can out-penetrate lighter arrows with more momentum.

i believe this can be true and it touches on something i was going to mention.

you have to remember that resistance forces don't increase linearly with velocity, they increase exponentially with velocity. double the velocity doesn't mean double the resistance it means quadruple the resistance! so an arrow shot from a compound at 300fps encounters 4x the resistance of the arrow shot from the trad bow at 150fps.

hence why at times it is possible for a lighter arrow with more momentum to be out penetrated by a heavier arrow with less momentum. the heavier arrow MUST be going slower for this to be the case and therefore encounters less resistance.

now there will be parameters where this won't hold true. i'm not sure where those parameters are for real world comparisons between different arrows.

 

[moxford]

It's not anecdotal, it's what Dr. Ashby et al have been proving for years: the mass of the object plays a more important role in penetration than velocity does. You may get more KE (and even momentum) from a given setup, but the exponential drop as you encounter resistance very very quickly puts the lighter arrow at a disadvantage.

momentum = mass * velocity

To get a lighter arrow with more momentum then you'd need to offset that with higher velocity. As this arrow applies force (KE) to an object it will resist at the same (higher) rate. Remember, this higher rate is due to the higher KE *of the smaller arrow.*

As you begin penetration, your velocity will begin to drop off, but you won't have the inertia (due to lighter mass) to continue carrying the arrow through the substance. With the higher velocity of the lighter arrow you'll have higher starting KE, but it will bleed off exponentially, very quickly dropping you below the momentum-levels of the heavier/slower arrow. As it continues to bleed off exponentially it will finish its penetration before the heavier/slower arrow comes to rest.

A heavier arrow moving slower has has a higher momentum (moment of inertia) and a resistance force will have to counteract that more strongly, usually over time as the arrow penetrates it. The target may be slowing it down but since its mass is a constant then it RETAINS that higher momentum longer.

Where those lines cross is up to the two arrows, the FOC, the target material, air density (due to shaft-diameter drag), humidity (again, drag coefficients), etc.

You could figure it out through empirical testing or computer modeling if you really had time but then you'd hit the field, find out you're shooting in more dense air (or whatever) and be on the wrong side of the equation anyways. =)

 

[Bowhuntr64]

While the value of momentum is undeniable in penetration, I think we should also not understate the value of speed. I don't mean the value of speed in penetration, but the value of speed in hitting an animal in the first place. With greater speed comes a flatter trajectory, which not only affects the need for accurate distance estimation, but also the chance of hitting overhanging branches.

Many people say that with modern day rangefinders, a flat trajectory is not important; I think that is overstated. Even with a rangefinder, animals move, and again, flight arc is increased--both increasing the odds of a miss. You may have a super penetrating arrow, but if you miss the animal, it's not going to help you much...except make it harder to get out of a tree

Finding the balance of momentum and speed is the challenge for each hunter, based on their quarry, terrain, and hunting style.

 

[Colberjs]

So my 458g @ 268fps isn't too bad?

 

[MT_Wyatt]

So my 458g @ 268fps isn't too bad?

That's almost my exact specs, worked fine on a deer and elk this year, I wouldn't worry at all.

 

[Colberjs]

After reading that article and their comments in regards to broadhead performance, has anybody considered a way to establish an industry-wide standard measurable for broadhead penetration? It could be based on a fixed speed, shaft diameter, arrow weight and target density. Doesn't seem like it would be hard to do. Obviously people would still have to experiment with flight performance out of their personal setups but it would be a place to start.

 

[Bowhuntr64]

After reading that article and their comments in regards to broadhead performance, has anybody considered a way to establish an industry-wide standard measurable for broadhead penetration? It could be based on a fixed speed, shaft diameter, arrow weight and target density. Doesn't seem like it would be hard to do. Obviously people would still have to experiment with flight performance out of their personal setups but it would be a place to start.

Well, if the goal is only depth of penetration that would not be difficult at all. Though what constitutes a suitable medium to test it on is always debated...gel, tile, foam, carpet, rubber, steel, wood, etc; each has its advantages and disadvantages. But the bigger debate is the the value of "depth of penetration" vs "cut size." That's where there is not much value to such a test. Some want a wider cut while others want a deeper cut.

Overall, as far as penetration alone is concerned, few debate that a two blade head with a 3:1 mechanical advantage ration of length to width provide the deepest penetration.

 

[BackcountryMT]

"I'm currently stuck on the idea of FOC...."

Honestly, stop it. FOC is the bowhunting equivalent of the latest fad diet. Modern bows with almost any reasonable arrow/point combination will result in ridiculous penetration on any NA game. All the mental masturbation and $ expenditures to bang out that last 4% - or whatever it is - of penetration is frankly a silly exercise.

I'll disagree with this all day. Throwing any penetration ideas out the window, a higher FOC arrow will yield better arrow flight and be more forgiving to errors with form issues (torque). Have you ever looked at a target setup? Those are built around consistency and they use heavier weight heads for a reason.

Yet, a higher FOC will show better penetration. Always.

 

[Bowhuntr64]

I'll disagree with this all day. Throwing any penetration ideas out the window, a higher FOC arrow will yield better arrow flight and be more forgiving to errors with form issues (torque). Have you ever looked at a target setup? Those are built around consistency and they use heavier weight heads for a reason.

Yet, a higher FOC will show better penetration. Always.

Higher FOC can certainly help with penetration, but it's aiding ability in flight is only up to certain point. Why do you think Easton and other manufacturers put a ceiling on their recommendations for maximum FOC?

With old recurves and long bows lobbing arrows at things, it didn't matter, but with compounds and the force you are putting on that arrow, it does.

 

[BackcountryMT]

Higher FOC can certainly help with penetration, but it's aiding ability in flight is only up to certain point. Why do you think Easton and other manufacturers put a ceiling on their recommendations for maximum FOC?

With old recurves and long bows lobbing arrows at things, it didn't matter, but with compounds and the force you are putting on that arrow, it does.

There's a law of diminishing returns to everything, just like TOO heavy of an arrow can be a detriment to bow efficiency. However, considering the normal FOC of your average arrow (8-10%) and a high FOC arrow (12-18%) that are both properly spined there will be a noticeable performance difference in the two.

 

[Pac8541]

And this is why I asked the question of my listed arrows, although I guess it might have helped if I'd provided more info along with each. All 4 of those arrows are within Easton's window with the best one pushing 17%. With my gear and physique I can't hit anything over about 270fps without going below my minimum total arrow weight; I focus on things other than speed as my top priorities anyhow. One of those is FOC because I've seen, with my equipment, how arrows with higher FOC benefit my shooting. The 585gr TAW, >20% FOC FMJs a buddy gave me last year literally stack on top of each other all day long. But they put my speed down around 230, which I find unacceptable. At that point I believe I've exceeded the benefit of FOC and have made the arrow, and me as a hunting system, less efficient. I've passed that point of diminishing returns, or at least I think I have. I don't know how well a 585gr arrow will do against an animal at <230fps. And even if it would do well I'm not sure I want to trade a flatter trajectory and less importance on absolute range finding accuracy for whatever advantages such an arrow might have. Anyway, my question has pretty much been answered in that the ideal arrow is a combination of multiple build facets that matter differently to all of us. And I hope I haven't helped cause a derailment of the original topic.

 

[BackcountryMT]

One thing to also consider is that a high FOC doesn't necessarily have to be "heavy". My 430grain gold tips come in at around 16% (my arrow length helps this).

In essence, you could replicate that heavy FMJ arrow with a lighter GPI arrow and maintain that accuracy without sacrificing speed.


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[Pac8541]

Yeah, I've substituted a Hexx shaft in place of the FMJ and left everything else the same. What i get is a 425gr arrow w/16% foc @ 264fps. Balance that against the 477gr arrow w/15% foc @ 255fps. What I have to ask myself is:

• Is the additional 10fps worth losing that mass?
• Is losing that mass worth a noisier and less "stable" feeling shot?
• Where is the balance between mass and speed?

The above figures come from Archers Advantage but when I run the same stats through OT2 the Ke and momentum numbers are very close to each other. So which difference is more valuable?

 

[MattB]

I'll disagree with this all day. Throwing any penetration ideas out the window, a higher FOC arrow will yield better arrow flight and be more forgiving to errors with form issues (torque). Have you ever looked at a target setup? Those are built around consistency and they use heavier weight heads for a reason.

Yet, a higher FOC will show better penetration. Always.

Do you have a data set that shows a statistically significant benefit to penetration of high FOC? I am not saying there isn't a benefit, but that IMO the benefit is so marginal at hunting ranges as to be irrelevant - hence the point with which you disagreed. Even Ashby indicated high FOC (12%-19%) was inconclusive in increasing tissue penetration, and only EFOC arrows (19%<) showed significant gains in penetration.

I don't know how to multi-quote, but in regards to your 430 gr./16% FOC arrow, I am going to guess your shaft gpi is in the 8 range in order to achieve that? I had a friend who designed a high FOC arrow very similar to that with a CT Cheetah (7.9 gpi, 100 gr. pt, 50 gr. brass insert), and he had issues with the shafts breaking on game on the sorts of impacts his more durable Whitetails (9.5 gpi) didn't. I cannot recall if I made mention above, but in the context of Ashby's work this sort of exercise trades off the #1 predictor of arrow penetration (arrow integrity) to improve on but come up short on the #5 on the list (extreme FOC).

That goes beyond diminishing returns - that is intentionally degrading the most important criterion of arrow performance in an order to improve a far less important one - and ultimately degrading the performance potential of your arrow. I personally think it is ill-advised. That's why I tell guys to save the time and money and go shoot their bows.

 

[MattB]

Yeah, I've substituted a Hexx shaft in place of the FMJ and left everything else the same. What i get is a 425gr arrow w/16% foc @ 264fps. Balance that against the 477gr arrow w/15% foc @ 255fps. What I have to ask myself is:

• Is the additional 10fps worth losing that mass?
• Is losing that mass worth a noisier and less "stable" feeling shot?
• Where is the balance between mass and speed?

The above figures come from Archers Advantage but when I run the same stats through OT2 the Ke and momentum numbers are very close to each other. So which difference is more valuable?

Go with the heavier/more durable shaft. 425 grs. is plenty for any animal in North America, but I wouldn't go that low and push for increased FOC. 10 fps is almost un-noticeable from a trajectory perspective at reasonable hunting distances, and you won't feel much if any difference in the shot (and you will get used to whichever you chose),

 

[Pac8541]

Gonna build a couple dozen, maybe 3 in the coming months. It will be the heavier arrow because I believe the additional mass will pay more dividends than the few extra feet per second. By playing with different points that vary weight and foc within a certain range, the one that shoots best for me will be the arrow I settle on. I agree with the statements that speed is both still a factor and, that 10fps isn't worth compromising shaft integrity. However, I think the latter is easier to accept when there is a bigger "window" with which to work in. At 248fps, 10fps seems to hold more weight than if my baseline were 268. The axiom that people have been killing critters for centuries with less only goes so far with me; its not a characteristic that I can completely disregard by explaining it that way. Not that anyone here is saying it like that but its cliche' and I feel that some use it to rationalize a decision to chase other characteristics too far. I "chase" foc because it makes me a more accurate shooter and as Backcountry MT stated, "...will yield better arrow flight and be more forgiving to errors in form." That's been my experience and I'll gladly sacrifice a little speed even if it means a lazier trajectory and requires better range est.

 

[MattB]

If there is a quantitative characteristic mentioned in this thread to chase, it is momentum. Until somebody presents data to the contrary, I will go with Ashby's assessment that FOC less than 19% cannot be isolated as a positive predictor of penetration. IME the accuracy benefit in hunting situations is even less relevant.

 

[moxford]

High FOC has another overlooked advantage as well: stabilization. Ultra-FOC setups need fletching because it "pulls" the arrow into a straight line (think: a thrown javelin) so you get better arrow flight. You see the same effect while playing dart... very very heavy head compared to the bodies.

High FOC arrows, and Ultra FOC arrows do require stiffer spines. Stiffer spines, along with having the much higher mass at the head both contribute to better penetration.

Easton's FOC recommendations are based on balancing maximum flight and trajectory with penetration in the general case. It's only a recommendation.

High-mass arrows make the bow more efficient as well. More of the energy is transferred INTO the arrow instead of coming out as excess vibration.

High-mass arrows are more wind-resistant (higher inertia resisting the lateral wind forces.)

High-mass arrows have stiffer spines. They don't flex as much and will recover quicker (less paradox that needs to settle out.)

Shooting 200 FPS vs 300 FPS? The speed of sound at sea-level is 1125 fps so you're not really going to have sound issues. In fact, heavier/slower is more efficient and, thus, quieter.

Also, look at it this way ...

At a 20 yard target, call it 60' ...
If your arrow is 300 fps: 0.20 seconds to impact (60/300)
If your arrow is 200 fps: 0.30 seconds to impact (60/200)

At a 50 yard target, call it 150' ...
If your arrow is 300 fps: 0.5 seconds to impact (150/300)
If your arrow is 200 fps: 0.75 seconds to impact (150/200)

So at a 20 yard target you will impact 1/10th of a second slower.
At 50 yards that's up to 1/4th (0.25) of a second.

Does it really matter? Probably not. Maybe if you're hunting something stupid-jumpy where that extra 0.1/0.25 reflex time is important. But probably not. Most of the time ducking the string is going to happen in that 0.5 seconds taken up by a 300 fps arrow and there's not much you can do about that. A quieter shot (solid thrum instead of a sharp twang), though, might prevent the reflex in the first place ...

And if you think 200fps is too slow, go talk to the stickbow guys (they usually cannot break 200fps but still take animals just fine.)

Now, going all the way down to 200 is a bit extreme but, IMHO, 240-260 is a much more reasonable "floor." But that's just me and, as you see from the numbers, isn't really going to make that much of a difference in time-to-target.

I shoot ~240 and 150/240 = 0.625 (0.125 or 1/8 of a second slower than a 300 fps arrow at a 50 yard target.)
The difference? I'm shooting a 22% EFOC 30" 761gr arrow.

In the end, it's all overkill if you make a perfect shot.

But when you don't? When you get a slight gust? Or your range estimation of off a touch? Or if the animal turns just as you let go? That high-mass high-FOC arrow is going to work FAR AND AWAY better than a lighter/faster arrow will.

The only downside to heavier arrows are:
1) Less maximum range. It's hard to get to 100 yard shots with really heavy arrows. Most hunters won't really care about this.
2) More arc. As noted above, heavier slower don't shoot quite as flat and have more arc so they have an increased risk of branches/leaves. You're still substantially faster than a tradbow though, so keep that in mind.

Aron Snyder (Kifaru, Rokslide founder, Gritty Bowman podcast) states that he like to keep it at/above 280fps for compounds.
Tradbow guys are 180-190fps.
Dr. Ashby's studies in Africa were all done with trad gear starting in 2004. The data isn't from from 1600's. =)

It's worth a look if you're at all interested.
Tuffhead has compiled them all together in one place. http://www.tuffhead.com/education/ashby.html