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Hunting Arrows - A Boring In Depth Conversation (Hopefully)

kyler1945

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I started to build out a post to help simplify some of the nonsense surrounding arrow weight, kinetic energy, momentum, FOC, mechanical/fixed and what not. But it's such a broad topic, with so much misinformation, that I figured it would be better to start from a place of reality. I can't really do a better job of clearing these few things up than someone trained in physics. So I'm going to copy/paste a post from user UglyJoe on AT - link here - https://www.archerytalk.com/vb/showthread.php?t=5720701

Someone else has posted a link to this information here before I believe. You can hop on this thread and see 22 pages of why it's so difficult to work through this topic. Lot's of folks knowing lots of things these days... Either way - here it is. I'll post his work directly, then I'll add some information going forward.

UglyJoe:


Let's begin by addressing some common misconceptions that we should eliminate immediately.

Misconception 1.) The one that is going to tick a lot of people of instantaneously—arrow momentum does not determine penetration. This notion is absolutely false. Linear momentum—p, defined in Eqn. 2—is an incredibly useful tool for performing calculations. This stems from momentum being a conserved quantity. In more advanced formulations of classical mechanics momentum is a useful quantity to find the underlying symmetries of nature, so it is a very important quantity—nevertheless, the momentum of an arrow DOES NOT determine its penetration potential.

Now, let's be very precise. An increase in momentum may (and almost assuredly will) correlate with an increase in arrow penetration, but we should be careful about the difference between correlation, when two observations are usually found to occur in tandem, and cause and effect, or causation, where one phenomenon causes another. It is usually the case that an arrow with large momentum will penetrate deeply, but the large momentum does not cause this deep penetration.

In addition, we should be careful about discussing momentum as something the archer actually has control of in their setup. Momentum in a hunting arrow is a dependent parameter. There is no momentum control knob that one may turn on their bow to increase the momentum that their arrow has upon firing. Instead, we must change another independent parameter—also called a control parameter—which will in turn change the momentum of our arrow as it leaves the bow. We will discuss what the appropriate control parameters that we should consider are momentarily.

Misconception 2.) Archery calculators are useful over large ranges of their input parameters, such as arrow mass. To be perfectly honest, most archery calculators are poor, and they tend to give archers very bad information. The most common misconception that archery calculators reinforce is that there is a "sweet spot" of arrow mass that maximizes the kinetic potential obtained from firing the arrow from a particular bow. I have read what seems like countless posts (and shamefully have even posted the same misinformation occasionally myself before actually thinking about the way these calculators work) where the poster thinks that a calculated arrow mass will give the archer the most kinetic energy that they can get out of their bow. This is always incorrect. This will be covered more in misconception 3 and later.

As an example of how archery calculators can give truly horrible predictions, lets take the backcountry bowhunting calculator as an example. I actually like this calculator when used appropriately, but let's see what happens when used incorrectly. Check the default settings on the calculator. The kinetic energy is given as 89.3 ft·lb. Now increase the arrow mass slider to 490 grains; the KE is 96 ft·lb. Above 510 grains the KE begins to decrease again. I assure you, this is NOT correct. This may be demonstrated by going further with the arrow mass slider. An arrow of 800 grains shows a kinetic energy of 74 ft·lb. Take a moment to actually think about this. All of the kinetic energy is transferred to the arrow from the bow, derived from the potential energy stored in the bow at full draw. The calculator is telling us that a 500-grain arrow will absorb 96 ft·lb of energy from the bow. This means that at full draw there must be at least 96 ft·lb of potential energy stored in the bow—in truth, no bow is 100% efficient, so there will actually be more than 96 ft·lb of potential energy stored in the bow. Now shoot an 800-grain arrow out of the same bow—the calculator is telling us that only 74 ft·lbs of kinetic energy will be accounted for in the arrow projection. Energy is a conserved quantity, so that means there is an additional >22 ft·lb of kinetic energy that the bow must be dissipating when it fires the arrow that is not accounted for in the arrow's KE. That much additional energy would result in a sound like a shotgun, and may severely damage the bow itself. We know this is not true in real life—the heavier arrow will result in a quieter bow with less hand shock and generally less energy left over after firing the bow that the bow must dissipate in other ways. The problem with the calculator can be shown in an even more extreme fashion by putting 1500 grains in as the arrow mass. The calculator now predicts the arrow to have 0.1 ft·lb of kinetic energy and to actually leave the bow with negative speed—it predicts that the 1500-grain arrow will be fired backwards. Hopefully this sufficiently demonstrates the pitfalls of using archery calculators to predict the kinetic energy, momentum, etc., of an archery system.

Misconception 3.) Choosing a particular arrow has any significant effect on the kinetic energy that the archery system will produce. If you are trying to achieve a kinetic energy goal by adjusting your arrow mass, you have already lost the battle. *This misconception has a slight caveat, which I will address shortly.*

With these misconceptions addressed, let's take a look at the real physics behind arrow penetration.

We begin with energy. Energy is the capacity of a system to do work. A system without any energy lacks any ability to change or influence other systems with which it interacts. Energy comes in two general forms: potential and kinetic. Arrows in a hunting situation lack any usable potential energy, so an arrow's entire ability to influence other systems—including the living system that is the game animal—depends entirely on its kinetic energy. As such, the first parameter in determining arrow penetration is—regardless of Dr. Ashby's insistence otherwise—the kinetic energy attained by the arrow in the archer's system. Eqn. 1 gives the usual definition of kinetic energy, 1/2·m·v2. This definition has led to mass confusion in the archery community. Although the equation is, of course, correct, the general interpretation of the equation is incorrect in the case of an archery system. The mistake is in what is taken to be the control parameter and what is the dependent variable. Most on Archery Talk mistakenly take the kinetic energy of their bow to be determined by the mass and velocity of their arrow. In truth, the velocity of the arrow is determined by the arrow mass and the kinetic energy produced by the bow. Like momentum, velocity is a dependent variable and may not be controlled independently of other control parameters.

Let's readdress misconception 3 above. Many archers think (and have been misled by arrow manufacturers to believe) that one may choose their kinetic energy by choosing a particular arrow setup. This is essentially false. The kinetic energy obtained in an archery setup is almost entirely determined by your choice of bow. It is true that bow efficiency will increase when using heavier arrows, but the effect is minor and may essentially be ignored. A recent example that demonstrates this clearly is this video by DIY Sportsman. The data given spans arrow masses from 379.4 grains to 1163.5 grains. That is an increase in arrow mass of 207%—a tripling of arrow mass. The kinetic energy of the arrow leaving the bow increased from 73.3-77.9 ft·lb., a mere 6% increase. A >200% increase in arrow mass yielded a <10% increase in kinetic energy. For all practical purposes, arrow mass does not affect arrow kinetic energy when the two arrows are fired from the same bow. For newer bows (5 years old or less) this effect is pretty general. Bow manufacturers have gotten so good at producing efficient cam systems with even low gpp arrows that there simply isn't much room for bow efficiency to increase with heavier arrows. As another example, an early review of the Realm SR6 showed a 1.7% increase in arrow kinetic energy for a 45% increase in arrow mass. Even with older bows, the above still holds true generally. The same may not be true of trad bows—finding data to check is more difficult, and I've seen reported that increasing arrow mass increases the efficiency of a trad bow more significantly, though I haven't seen data to support or refute that statement. However, even with a trad bow, it will still be true that it takes a huge increase in arrow mass—doubling or tripling—to see a relatively small 10-20% increase in the arrow kinetic energy produced by the bow.

Your choice of arrow has a minimal effect on the kinetic energy produced by your bow.


We have discovered the first control parameter for our archery system—the kinetic energy that the system produces. We control this by our bow choice; what type of bow are we using (trad or compound, etc.), what is the bow's draw weight, how efficient is the bows cam system, etc. Once we have settled on a bow, the kinetic energy we can expect to obtain out of the system is effectively fixed. If you are fiddling with arrow weight in an attempt to "maximize" your kinetic energy, you are doing it wrong. So why then do so many archers feel that kinetic energy is "unimportant" when considering penetration issues? The answer is simple. Any bow that is legal for hunting purposes will produce enough kinetic energy to achieve enough penetration to kill an animal for which that bow is a legal method of taking. That’s why the bow is legal! If the bow did not produce enough KE to kill efficiently and quickly, then the bow would not be legal as a method of take. Furthermore, the amount of KE required to deeply penetrate a large game animal is actually quite small. Dr. Ashby showed that with a low poundage trad bow, producing (if I remember correctly) ≈22 ft·lb of kinetic energy (see the 2008 update, part 1), he could successfully breach the rib cage of a Cape buffalo bull 100% of the time and the arrow still had enough energy to penetrate more than half of the thoracic cavity after smashing through the heavy ribs of the bull. My SR6, pulling 53 lbs, produces well over twice this much kinetic energy. Every bow suitable for hunting produces more than enough kinetic energy to fully penetrate essentially any game animal in North America.

So why is it that we have all seen examples where a hunter drawing 70+ lbs with a 340+ IBO bow producing >80 ft·lb of kinetic energy fails to get more than 4 or 5 inches of penetration on a whitetail doe shot in the rib-cage? The answer lies again in the definition of energy. Energy is a measure of the total amount of influence a system may have on its surroundings; how that energy is used to influence or alter the system's surroundings depends on the details of the system. A gallon of gasoline contains a certain amount of chemical energy. If we simply light the gasoline with a match that energy will be used to heat up its surroundings. If we burn that gasoline in a combustion engine, we will heat its surroundings, but we may also use that energy to accomplish useful work, perhaps transporting a shipment of medicine from one town to the next. The same energy reserve is used for two entirely different purposes.

Our choice of bow determines how much energy we have available to use. Our choice of arrow determines how we budget that energy resource. How we build our arrows determines where our kinetic energy is spent. If we top our arrows with a mechanical broad head, it should be unsurprising that we have chosen to use a significant amount of our energy resources—energy that could be used for arrow penetration—to do the work of opening our mechanical. Additionally, mechanicals generally have very wide cutting diameters; this increased cutting diameter requires more work—energy—to penetrate the animal. This is one reason why use of wide-blade mechanicals is strongly discouraged for those shooting low-energy bows—the energy reserves to open the mechanical and still allow good penetration simply aren't there.

So how do we build an arrow that maximizes our energy use for penetration (I hope we can agree that maximizing penetration is the best way to ensure arrow lethality; if you think other factors are more important than penetration you will chose to build your arrow to maximize energy use with those factors in mind)? Many would argue to turn immediately to Ashby's 12 factors; they may increase FOC, carefully select a particular broadhead, etc. This, however, is the incorrect approach.

There is a well-defined property of a system, called its inertia, that describes the system's resistance to a change in motion. A moving system, such as our arrow, that is very difficult to stop has a large inertia. The inertia of a system is quantified by one measurable parameter and one measurable parameter only: the system's mass. This is why we often refer to mass as inertial mass. When you measure the mass of an arrow, what you are actually measuring is how difficult it is to cause that arrow to start moving, or, conversely, how difficult it is to cause that arrow to slow down. Arrow penetration, which is a direct measure of how difficult it is for the animal's internals to stop the arrow's motion, is a function of the arrow's mass.

This is why it is wrong to state that arrow penetration depends on on arrow momentum. It simply does not. I've seen multiple threads on these forums where one poster shows a system built with a low mass, high velocity arrow and another with a high mass low velocity arrow; both arrows have the same momentum. The poster will inevitably conclude that both have the same penetration potential. A second poster will then—usually following Ashby logic—claim that "not all momentums with the same value are equal" or some such. That somehow momentum "built" from large mass and small velocity is different than momentum "built" from small mass and large velocity, and therefore the penetration potential of the two systems is different. This is nonsense—momentum is momentum, and quantities that truly depend on momentum do not care if the momentum describes a heavy system in slow motion or a light system in fast motion; once the momentum of a system is parameterized it "forgets" what factors went into defining it. The truth is that the heavier arrow penetrates better because it has greater inertia—greater mass—not because it has "mass-derived momentum". I will repeat myself for clarity's sake. Increasing momentum DOES NOT result in an increase in penetration.

Why then the confusion? Take a look at the derivation presented below. Most are familiar with the definition of kinetic energy in terms of mass and velocity used earlier. Another definition may be derived in terms of momentum (see Eqn. 3). This definition is actually the better definition and the most commonly used equation for kinetic energy in non-relativistic classical (and even elementary quantum) physics. KE is the momentum squared divided by twice the mass. Rearrangement of this equation gives the magnitude of the momentum (||p||) as a function of kinetic energy and mass. (Momentum is a vector quantity; when we assign a value of "momentum" for an arrow we are actually talking about the magnitude of the momentum vector, properly indicated by the double bars on either side of the vector p.) Momentum is a function of the product of kinetic energy and mass. We have already shown that any legal bow has enough kinetic energy to adequately penetrate a North American game animal. If we increase arrow mass, we will, by the definition given in Eqn. 4, also increase the arrow momentum, since increasing arrow mass has little effect on arrow KE. Increasing arrow momentum does not effect an increase in arrow penetration; increasing arrow mass increases arrow penetration while simultaneously increasing arrow momentum. Momentum increase and arrow penetration increase may be correlated; one, however, does not cause the other!

eq.png

So now we have established our two control parameters; kinetic energy, as determined by our choice of bow, and arrow mass. These are the parameters we are free to change and vary as we wish. Notice that arrow velocity (similar to momentum) is determined by our choice of these two control parameters. Because arrow trajectory is largely determined by arrow velocity, we must carefully choose our bows (KE) and our arrow mass to achieve our minimum acceptable arrow trajectory. Once we have nailed down the values of the two controls that we find acceptable for our personal shooting pleasure, we can begin to talk about the other "factors" of arrow building that come into play: arrow components, broad head selection, front of center, etc. This is the most logical progression for a "archery build" that one can follow when developing a new hunting rig.

That's more than enough for this discussion. If anyone is interested we may start another thread discussing things like heavy bone threshold, FOC, etc. with attention to the real physics at play, not the misconstrued and misinterpreted notions that are often repeated regarding these topics amongst many archers.




 

mattsteg

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That seems like a really wordy way to make a few points, some good, some kinda iffy imo (but more in minor details than conclusions). If we're gonna use that many words, I feel like there's probably a better way to do so. If I have time I'll put some thoughts together.
 
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kyler1945

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That seems like a really wordy way to make a few points, some good, some kinda iffy imo. If we're gonna use that many words, I feel like there's probably a better way to do so. If I have time I'll put some thoughts together.
Normally, I agree. But it is very difficult to unlearn some folks of some of the misconceptions they've developed. Hopefully this thread can whittle down some of it to a form that is easily shared with everyone. I like short/sweet when it comes to this kind of stuff. Sometimes it isn't possible.

You can only say - "shoot heavy arrows, it's better, I promise" enough times. When people say "I shoot light arrows and haven't had a problem", the first statement isn't enough. When people say "momentum is king", saying "no it isn't" isn't effective. There's probably a middle ground for the information, and I look forward to your help in getting there!
 

Bwhana

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Great read, love to see discussions that invoke more thought. I hope folks can get past the verbiage and not just look for a 3 line summary at the end as usual.

Archey is a also a situation where you must overcome the momentum of marketing by the archery industry that is contrary to facts. They hype their latest 4" Meat Saw mechanicals as creating the most damage ever seen so the average hunter has to buy them if you want to have Stevie Wonder blood trails. You need our new Pencil Lead thin and light arrows to achieve more speed and penetration. Bow companies can't sell new bows unless they are touted as much better in some way, even though it is really no more effective in actual use than their three year old model. Most archery shops do not know what they are doing when it comes to the science of killing with arrows. Sure, many can setup bows and tune them, but they are not experts or students in the facts of killing. They usually just recommend to their customers what they are using on their own bows, many times mislead themselves. That is why I stopped using pro shops about 15 years ago and service of my own equipment.
 

DaveT1963

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The problem isn't really the tools we use - that is the "created symptom." The root cause is to many people don't put in the work to become good hunters and archers - they want to use equipment to overcome these deficiencies. Shoot reasonably heavy arrows, with a good COC broadhead at reasonable distances (i.e. learn to be a better hunter and get close) and become accurate with your gear - simple formula that has worked for eons.
 

kyler1945

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The problem isn't really the tools we use - that is the "created symptom." The root cause is to many people don't put in the work to become good hunters and archers - they want to use equipment to overcome these deficiencies. Shoot reasonably heavy arrows, with a good COC broadhead at reasonable distances (i.e. learn to be a better hunter and get close) and become accurate with your gear - simple formula that has worked for eons.
While I agree, sort of, with the bottom line of your message, the problem is that it’s not effective.

Get off my lawn-ing people who are ignorant to the reality underneath a lot of this stuff just gets them digging their heels in more. As does being ‘sort of’ right. When someone can poke holes in any part of what you say, the whole message becomes worthless. The whole point of this thread is to give boring, in depth information on the scientific side of getting an arrow through a deer.
 

DaveT1963

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While I agree, sort of, with the bottom line of your message, the problem is that it’s not effective.

Get off my lawn-ing people who are ignorant to the reality underneath a lot of this stuff just gets them digging their heels in more. As does being ‘sort of’ right. When someone can poke holes in any part of what you say, the whole message becomes worthless. The whole point of this thread is to give boring, in depth information on the scientific side of getting an arrow through a deer.

Most wont care or put in the effort to read it. Heck many "archers" don't even pick up their bow until its a few weeks before season - and hand a stone and a COC broadhead and watch most try to sharpen one....we live in a world that wants instand gratification without doing the work
 

JWP

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The problem isn't really the tools we use - that is the "created symptom." The root cause is to many people don't put in the work to become good hunters and archers - they want to use equipment to overcome these deficiencies. Shoot reasonably heavy arrows, with a good COC broadhead at reasonable distances (i.e. learn to be a better hunter and get close) and become accurate with your gear - simple formula that has worked for eons.
I hunt Whitetails up close and this Is pretty much my philosophy also.
 

DanCrossNYC

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Hmm, just a quick note: there's a small typo in that equation. 'v' on the third line should be squared. Or, $E_k=\frac{1}{2}m\mathbb{v}^2$.

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kyler1945

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Most wont care or put in the effort to read it. Heck many "archers" don't even pick up their bow until its a few weeks before season - and hand a stone and a COC broadhead and watch most try to sharpen one....we live in a world that wants instand gratification without doing the work
I appreciate your cynicism. I share it. But it wouldn’t be the worst thing for people to have a place to get the information, if they want it, without the nonsense. There are plenty of threads for you to go full bore on millennials. Maybe leave us one place to have a somewhat nuanced, thoughtful conversation?
 

DanCrossNYC

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I appreciate your cynicism. I share it. But it wouldn’t be the worst thing for people to have a place to get the information, if they want it, without the nonsense. There are plenty of threads for you to go full bore on millennials. Maybe leave us one place to have a somewhat nuanced, thoughtful conversation?
I for one really dig this thread. Thanks for posting it.

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DaveT1963

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There are plenty of threads for you to go full bore on millennials. Maybe leave us one place to have a somewhat nuanced, thoughtful conversation?
I was not referring to any age structure (nice try though), I gave a very simple formula that like I said has worked for eons. Carry on I will leave this discussion for the masses.
 

DanielB89

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I will start by staying I read through the original post twice and only comprehended about 3 or 4 sentences worth of information. That being said, I've had several people throughout my life say my brain is underdeveloped.
I hate long winded fellers too..

If you want to learn a lot about penetration efficiency, swap to traditional archery and you'll learn what's important really quickly. The only thing I can speak confidently of is my experience. The only times I have ever not had a pass through is when i've hit major bones. I have killed over 20 pigs with my tradbow and it is very rare for one to leave the hit sight carrying the arrow. I have never shot a hog that I didn't have an exit with my tradbows.

It is all about a COC broadhead with enough energy behind it to push it through. I don't shoot excessively heavy arrows, usually around 9-10 gpp.

One thing to remember while discussing this topic is that when the deer is hit in the "good spot"(avoid major bones), it doesn't take much energy at all to penetrate both lungs. But, should you hit a bone first, that's where the extra energy comes in.

It also doesn't take much energy or penetration to actually kill an animal. Go watch a few videos of Tim Wells shooting animals. There are many times when the animal turns and to run and he has(what appears) to be more than 2' of arrow hanging out.
 

Kurt

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I think it's good that a logical based conversation show the science behind what most folks should know to be true. That way the doubters need not only refute the individual but the science as well. I Have been shooting deer with a 70# bow for 28 years. I go to the shop get the arrow shaft that they tell me is spined properly for the shaft length I'm shooting, the head weight I'm using, and I pick out the scariest looking, in budget broadhead I can afford. I keep my shots close. I am considered by those who know me to be a consistent killer. I'm not the best shot in the world, but I am a closer, and as we've seen on other threads my bow isn't perfectly tuned, and my form could use some work. I ran into trouble this year because I made changes to my arrows that were uninformed and untested by me. I didn't use the necessary components recommended by the manufacturer to build a proper arrow and I had two deer pay the consequences for that. I learned a lot of important lessons this year. I don't know as much as I need to know, and I rely on others to do for me what I need to be able to do for myself. Some times you need to go through some pain, in order to "see". If a thread like this can help just one person, whether it be a new hunter, or someone who wants to do it better, and it helps us better understand that we need to tool up for the inevitable "oh ****" moment that WILL come, then it will be worth it. No one needs to be shooting arrows that dwell in the margins of performance, there's to much information out there for that. There are many ways to skin the cat, I for one want to utilize all the information I can to build the arrow that's going to cover me not only through the best of times, but also through the worst of times. That being said, individuals will determine for themselves, in the face of all this information, what parameters they will deem most important to satisfy what they believe to be the best mix of properties to go into the arrow they will shoot.
 

Art_Vandelay

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It’s definitely true that most wont care, or put in the effort to read it, but I think that’s completely irrelevant to the purpose of your post.

I took the time to read it. There isn’t anything “iffy” about physics, and understanding the physics of your arrow can only help you as a hunter/archer. To simply say someone just needs to be more accurate with their gear or be a better hunter doesn’t help to promote any real discussion. I found your post to be interesting and helpful, as will the many others researching this topic in the future. Thank you for taking the time to share it.
 

Gamover06

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Tell ya what I have gone down the rabbit hole of arrows. I have built ALOT. Light (Speed arrow) with 10%, 13% and 17% FOC I have used shop arrows 400 grains 12% FOC and then I have gone to the heavy side 500, 556 and 587 with average FOC to 19% FOC.

Findings I LOVE my 587 grain with 19% FOC. Why. Quietest set up, tuned the easiest (for me), grouped amazing and I loved the thump when it hit the target. This arrow is for giving , flies like a dart, and packs a punch. Before the season I had bare shaft hitting within 2 inches out to 40 yards. I also shot filed point (125), mechanical (125), and buzzcut fixed (150) out to 40 and was grouping well also.

To be honest nothing really matters with your arrow if your bow is not properly tuned and you have terrible form. I think a lot of people get hung up on FOC and Weight and for get to tune there bow to the arrow and fix their form. Well if your bow is out of tune or your form is terrible nothing will shot well or be forgiving.

I have also done 4 different vanes with 3 and 4 configuration and found I prefer 4 fletched with my current set up. In the end what I have found is I will never shoot an arrow sub 500 grains and sub 17% FOC.
 

slonstdy

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Put me in the same group as most who are or should be chiming in. For years I've racked up my share of bow kills without putting a thought into bow tuning, paper tuning or proper arrow building. In my ignorant mind I thought "if I'm hitting my target where I'm aiming then everything must be good and I'll leave that tuning crap to those afflicted with a more serious bout of OCD than me!"

Well right before the season opened this year I became curious why my arrows were sorta porpoising during flight and were hitting the target at different angles (like they've done for years) so I mentioned it here and was told it's my form, tune related or both. YIKES!! Long story short paper tuning squared things away to my surprise. Never in a million years would I"d have thought it would make such a difference to arrow flight.

My arrow weight and % FOC were also brought into question. So deeper down the tuning rabbit hole I went, a place I was never interested in going but found myself enjoying the experience. Turns out my arrows are on the light side and have a low % FOC, now add the fact I shoot mechanicals (again, bad experience with fixed blade erratic flight so naturally I jump to mechs and problem goes away...NOT!) which completes my recipe for poor arrow terminal performance.

Seeing first hand the difference paper tuning made has opened my mind to accept new ideas and question the "misconceptions" that I always took as facts. My one and only goal for next season is to build a proper hunting arrow coupled with cut on contact fixed blades so I am able to bring the most effective and efficient weapon on my hunts.

Here's something to reflect on...
As a community here this year we have seen posts of "...gotta good hit but..."," ...broad head failed to open...", and " ...must have deflected off bone..." and in every instance arrow build was brought into question and what I have noticed with all of them is the fact that not a single post like that was started by a hunter shooting heavy, high % FOC arrows with COC broadheads...

@kyler1945, I've watched you preach the benefits of a heavy high % FOC all season long. Your message has sunk in with me!
Thanks brother :cool:
 
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