Arrow FOC

[TheTone]

F=MA

A 550 gr arrow with 8% FOC will penetrate the exact same as a 550 gr arrow with 22% FOC.

Adding FOC is just a shortcut past properly tuning your arrow/components to your bow.

But some guy shooting pigs and whitetails at close range and another guy shooting dead critters with a recurve say it’s more better…

My top concerns are still a well built arrow that will stay together and a sharp head that penetrates easily. I do like the arrow to have a decent weight to it but I think that’s best achieved for me with one that is a decent grains per inch, not just piling weight at the tip

 

[Mighty Mouse]

I’m just seeing if anyone noticed any forgiveness in fixed blade broadhead flight due to FOC. Fixed blades will show inconsistencies in form, anchor point, trigger punch, etc, especially in the heat of the moment, so if FOC helped to alleviate this and made my bow setup more forgiving, I’d be interested in upping it. However, I have a feeling it won’t make any difference.

One article I found online did say that higher FoC can keep an arrow stabilized and from flying erratically down range, which would help with fixed blade flight, but I’m not noticing it with 8% FoC though.

I'll reiterate my opinion that FOC is way less important than many folks claim and that there's no harm in completely ignoring it.

That said, there is a plausible argument based on aerodynamic principles that higher FOC will improve an arrow's stability in flight. Positive aerodynamic stability—defined as an arrow's tendency to return to its original course when subjected to a disturbance (such as crosswind)—increases the further the arrow's center of gravity (i.e., balance point) lies ahead of its center of pressure (the point through which the resultant force of all pressures exerted on the arrow acts). Center of gravity (CoG) is determined by component weights and arrow length. Center of pressure (CoP) is determined by fletching size/shape, broadhead size/shape, and arrow length/diameter. For two arrows with the same CoP (i.e., same fletching, broadhead, shaft length/diameter), the one with its CoG further forward (i.e., higher FOC) will be more stable in flight. Said another way, you can achieve the same degree of flight stability with less fletching if FOC is higher. Or vice versa, you can compensate for lower FOC by adding more fletching (i.e., increasing vane quantity, height, length, or offset/helical angle).

These aerodynamic concepts are well founded and are true in principle, but I believe the effect of a little more or less FOC on flight stability (aka, forgiveness) will be difficult to notice in practice. 8% is on the low side of what's considered "normal" for a hunting arrow, but if your broadheads are grouping well and hitting alongside field points, I wouldn't make any changes to chase higher FOC.

If you want to delve deeper into CoG/CoP and how they relate to flight stability, here's a good (albeit lengthy) resource in the context of airplanes: https://www.faa.gov/regulations_policies/handbooks_manuals/aviation/phak/media/07_phak_ch5.pdf

 

[Ought Six]

No no I must have mislead you somewhere. I see what you and tone are saying. I added the weight up front, the arrows were 50 grains less beforehand, so I totally see what you’re saying about still having it contribute to overall weight, not necessarily just FOC. Forgive me. As I said, I just observed a greater nosedive after adding them. I wanted deeper penetration, which it provided.

What did you use to test the deeper penetration?

 

[Ought Six]

I'll reiterate my opinion that FOC is way less important than many folks claim and that there's no harm in completely ignoring it.

That said, there is a plausible argument based on aerodynamic principles that higher FOC will improve an arrow's stability in flight. Positive aerodynamic stability—defined as an arrow's tendency to return to its original course when subjected to a disturbance (such as crosswind)—increases the further the arrow's center of gravity (i.e., balance point) lies ahead of its center of pressure (the point through which the resultant force of all pressures exerted on the arrow acts). Center of gravity (CoG) is determined by component weights and arrow length. Center of pressure (CoP) is determined by fletching size/shape, broadhead size/shape, and arrow length/diameter. For two arrows with the same CoP (i.e., same fletching, broadhead, shaft length/diameter), the one with its CoG further forward (i.e., higher FOC) will be more stable in flight. Said another way, you can achieve the same degree of flight stability with less fletching if FOC is higher. Or vice versa, you can compensate for lower FOC by adding more fletching (i.e., increasing vane quantity, height, length, or offset/helical angle).

These aerodynamic concepts are well founded and are true in principle, but I believe the effect of a little more or less FOC on flight stability (aka, forgiveness) will be difficult to notice in practice. 8% is on the low side of what's considered "normal" for a hunting arrow, but if your broadheads are grouping well and hitting alongside field points, I wouldn't make any changes to chase higher FOC.

If you want to delve deeper into CoG/CoP and how they relate to flight stability, here's a good (albeit lengthy) resource in the context of airplanes: https://www.faa.gov/regulations_policies/handbooks_manuals/aviation/phak/media/07_phak_ch5.pdf

That was really well put and makes total sense. You should start a YouTube channel lol. Thanks for the info! Building arrows is probably my next money pit, upgrading from straight blazers to helical, different sizes, different quantities, different shapes, etc is something I really want to play around with.

 

[TheTone]

That was really well put and makes total sense. You should start a YouTube channel lol. Thanks for the info! Building arrows is probably my next money pit, upgrading from straight blazers to helical, different sizes, different quantities, different shapes, etc is something I really want to play around with.

I’ve thought of arrow building as a side hustle or at least offering to build orders for some of my local shops. It’s not exactly hard

 

[sclancy27]

I’ve thought of arrow building as a side hustle or at least offering to build orders for some of my local shops. It’s not exactly hard

No shit, you could prob make 50-100$ to "build" (glue together) these specialty arrows. My mind bends when people start talking all this crap with inserts and outserts and collars and 400 gr upfront.....bro, your arrows are 30$ a piece BEFORE a broadhead....

 

[golfer]

No shit, you could prob make 50-100$ to "build" (glue together) these specialty arrows. My mind bends when people start talking all this crap with inserts and outserts and collars and 400 gr upfront.....bro, your arrows are 30$ a piece BEFORE a broadhead....

Hell thirty bucks is cheap compared to these….

3 HANDCRAFTED COLD VIRGIN GOAT FLF STEEL FOOTED ARROW SHAFTS

bishoparchery.com

 

[Irrelevant]

To the OP, high FOC is great if you can maintain perfect flight. I could not when I went down the RF rabbit hole last year, no matter how I "tuned" or practiced, it just wasn't great. So in the end since it didn't help, I've had to back off a bit down to more like 15%. For whatever reason people get real touchy about arrow builds. RF has a method, it's backed by both science and anecdotal evidence to a degree, but there are real world limitations. Also, F=MA cannot solely explain/model penetration through a variable density fluid (animal).

 

[sclancy27]

Hell thirty bucks is cheap compared to these….

3 HANDCRAFTED COLD VIRGIN GOAT FLF STEEL FOOTED ARROW SHAFTS

bishoparchery.com

Those can't be real

 

[golfer]

Those can't be real

. I’m sure they are why would they have a website if they weren’t?

 

[TheTone]

Those can't be real

The name and description would make you think it’s a total gag. Owner used to post a bunch on bowsite. He seemed to be somewhere between genius and eccentric crazy person. I think he was banned

 

[Flatbrimmer]

What did you use to test the deeper penetration?

The target I was shooting.. lol I had a half dozen without the inserts at the time, and shot them side by side

 

[Redman]

Kind of makes you wonder if it’s a good marketing ploy getting all these hunters who have killed stuff without ever worrying about arrow weight or FoC to buy whole new arrow setups… but I agree if it’s the current rage, I’ll probably tinker with it too! Haha

I was doing it before it was cool. I started out with heavy shaft and broadhead. Then I put a heavy tip on a lighter shaft and shot it out of my long bow. I noticed that it felt different than using the same arrow with a lighter head and it flew remarkably well bare shaft. Owning a archery shop allowed me to test a lot of things out.

 

[ImBillT]

I’m

I’d agree with this, I think @FoodIsMemories might be confusing weight with FOC, although weight can be directly related to FoC by putting it in the front, putting more total weight into your arrow system is going to cause a significant drop down range no matter where you put it. Speed vs weight makes for a flat shooting bow, but then there are the arguments related to weight and penetration. Finding the sweet spot is probably key.

I’m not worried about penetration, I’m shooting a “heavy-ish arrow” (490 grains) at around 295-297 fps. I’m just seeing if anyone noticed any forgiveness in fixed blade broadhead flight due to FOC. Fixed blades will show inconsistencies in form, anchor point, trigger punch, etc, especially in the heat of the moment, so if FOC helped to alleviate this and made my bow setup more forgiving, I’d be interested in upping it. However, I have a feeling it won’t make any difference.

One article I found online did say that higher FoC can keep an arrow stabilized and from flying erratically down range, which would help with fixed blade flight, but I’m not noticing it with 8% FoC though.

In an older bow, completely different setup, speed, poundage, draw length, etc, my FoC was closer to 13%. Only difference I’ve seen between 8% and 13% is when shooting long range and forgetting to set my sight at the range (overly tired dad brain at the range), the 13% was nose diving when it hit the ground and was easy to find either stuck in the spot or a few yards away; the 8% arrow, because it’s flying so much “flatter” (not nose diving as much) skips off the ground and goes another 60-70 yards.

Just keep in mind that “high FOC” when Dr Ashby refers to it, is 19% or more. He chose that number because it was the first point at which he could see penetration improvements. I’m sure that other effects of increasing or decreasing FOC occur at different percentages. The point however is that it’s really easy for someone shooting 8% FOC to consider an arrow setup at 13% FOC to be high, yet not achieve some of the benefits of “high FOC” because you’re not shooting the degree of FOC at which the supposed benefits occurred.

 

[ImBillT]

Physics and FOC lunacy cannot be reconciled...

Actually they can. You just have to understand more than what is taught in a basic physics class, even college physics. In my two college physics classes for engineering majors problems frequently mentioned that we were assuming that an object was rigid and could be represented by a singular point. Neither of those two things is ever reality. It was done for simplicity’s sake. What an arrow does during impact would be covered more by a dynamics class for a mechanical engineer. It was in dynamics that we learned how to figure out what was happening to moving and non-rigid objects under varying loads.

I will do a very poor job of explaining below.

 

[ImBillT]

F=MA

A 550 gr arrow with 8% FOC will penetrate the exact same as a 550 gr arrow with 22% FOC.

Adding FOC is just a shortcut past properly tuning your arrow/components to your bow.

Completely incorrect.

The same amount of force is available, but the force is not equally transmitted between the two arrow setups. The arrow is not rigid. It blows my mind that almost every archer who has tuned a bow/arrow is fully aware that the arrow is not rigid at launch, yet most of them assume the arrow which was flexible at launch has magically become rigid upon impact.

Although nothing is actually rigid, we can sort of consider the broadhead, adapter, and knock as being rigid, but the arrow shaft is absolutely not rigid. Even if we loosely consider some of the components to be rigid, we need to consider them separately from each other because force much be transmitted through them.

On launch, the string applies force to the knock, and the knock, along with every other piece of the arrow applies and equal force to the string. Those forces are equal at the knock/string interface, but they are not equal throughout the bow or throughout the arrow. On launch, the knock is subjected to the highest force. Broken nocks can easily be a result of arrow mass and FOC(FOC matters because it affects bending and bending is related to leverage or torque). Every other piece of the arrow is subjected to less force than the knock. The center of the arrow shaft is being pushed from the piece of arrow shaft immediately rearward if center and the F that piece is subjected to is only equal to M of the arrow forward that point. It is not subjected to the entire arrow’s mass. Anyway, on launch, the knock transmits the force of the string to the arrow shaft, and the arrow shaft transmits it to the insert, and the insert transmits it to the broadhead. And guess what? That force bends the arrow shaft. The shaft bends because the knock is temporarily accelerating faster than the broadhead. Now think of this in reverse. On impact, the broadhead begins to decelerate due to hitting the target. F=MA. But the broadhead and insert and not actually rigid, and there connect must definitely be dealt with when considering strength. The F HERE is generated by the M of the insert, arrow shaft, fletching and knock being decelerated BY THE SLOWING BROAD HEAD. Inserts do not break at impact due to heavy bread heads. Heavy broad heads, all else being equal, decelerate less upon impact. It’s tempting to argue that the broad head is pushed by the rest of the arrow and thus with equal total arrow weight the broad head will decelerate equally regardless of the broad head’s weight. That’s incorrect. The broad head decelerates first before the insert can apply a force to it, then the insert decelerates before the shaft can apply a force, then the shaft must decelerate before the fletching and knock can apply a force. It’s easy to tell yourself this cannot be because it’s all firmly connected, BUT NOTHING IS ACTUALLY RIGID! In fact, the very tip of the broad head slows down before the portion of the broad head just rear of the tip slows down. It all deforms and bends and vibrates to different degrees. This can be easily demonstrated with a long loosely coiled spring slightly stronger than a Slinky. Push the spring along a table into a wall. Does the spring uniformly compress throughout its length when it contacts the wall? NO! First the portion of the spring that hits the wall compresses, and does so more than necessary and a compression wave travels the length of the spring until it achieves equilibrium. A Slinky will demonstrate an identical effect in tension. The arrow does the exact same thing on LAUNCH and on IMPACT! No one argues on launch. There are only two differences between the arrow impacting a target and a long spring impacting a wall. A) the stiffness of the arrow is high enough that the bending and vibration is difficult to see, and B) the arrow is not a single uniform material(broad head, insert, shaft etc. all with different stiffnesses). With all of that in mind, you should now somewhat understand that the F and the A in F=MA are not the total F and A, but must rather be dealt with in pieces. To do it perfectly you would have to break it down into infinitely small pieces. If you took calculus you might remember the first week or two of drawing smaller and smaller bars under a curve, and then solving for the limit as the bars became infinitely smaller. You have to do the same thing for the arrow. You can go grab your high school or college physics text book and find a problem when a whole car gets represented by a dot and think you’ve proven me wrong, but you have not. That’s a simplification for the purpose of teaching concepts. It’s not real life. If it was real life the crumple zones and air bags would not work. Instead, crumple zones allow the driver’s seat to decelerate at a lower rate than the bumper, which decreases the peak force applied to the driver’s back by the seat, and airbags allow the drivers face to decelerate at a lower rate than the dashboard which decrease the peak force applied to the driver’s face. If the car was rigid, these to safety features would not work. Luckily, the safety features do work, and they work because the deceleration of the DRIVER is not solely dependent upon the total mass and velocity of his vehicle. The reason it is not, is because he is not rigidly attached to the car, and the car is not rigid. If the arrow was rigid, then FOC would not matter. BUT THE ARROW IS NOT RIGID, AND NEITHER ARE RHE CONNECTIONS OF ITS COMPONENTS!!!

Now, if we wanted to calculate penetration, which to my knowledge no one can actually do with a mathematically derived equation(but somewhat can with experimentally derived equations) F=MA where M is total arrow mass would give you a theoretical maximum F to be applied to the target via the broad head in the direction of flight. Forces applied at any other angle only contribute a component to penetrating in the direction we want to penetrate. That theoretical maximum however could never actually be reached. IF an arrow were ever to impact a target perfectly orthogonally to its direction of flight, the arrow would vibrate in a purely compression wave with the arrow shaft rapidly getting larger and smaller in a diameter. In reality however, we can’t ever get things aligned so perfectly. What happens instead is that the arrow shaft vibrates side to side. This side to side vibration causes drag on the target as the arrow penetrates the target, and the force OF THE ARROW SHAFT, FLETCHING, AND KNOCK are what break inserts. Heavy broad heads do not break inserts. Rapid deceleration of the broad head compared to the arrow shaft, and heavy fletching and knocks are what breaks inserts. With equal design, a heavier broad will decelerate more slowly and the forces generated by the arrow shaft against the insert will be lower. However, broad head weight isn’t the only thing effect it’s deceleration upon impact. Dull broad heads, wide broad heads, multi-blades broadheads etc will all increase the deceleration of the broad head upon impact compared to a sharper, single-blade narrow broad head, which will all increase the vibration of the arrow shaft, and will decrease penetration more than would be predicted by the increased force required to simply push a broad head through a target. F=MA ISN’T NEARLY ENOUGH TO INFORM YOU ABOUT PENETRATION!!! How much force was applied by the string ON AVERAGE to the knock? You can easily determine acceleration by from velocity, draw length and brace height, then use total arrow mass, and bingo, you now know your average force applied to the knock by the string. Obviously peak force occurred at full draw. Guess what? It won’t match the average force of your force draw curve! Why? Your bow limbs had to drive themselves forward too! The force applied to the knock during firing is less than the measured force of along your draw length!

 

[ImBillT]

^^^^ continued

What does this have to do with FOC? Quite a bit actually. Increasing FOC places more of the mass close to the point of impact. When the arrow starts bending it acts as a lever. Imagine an arrow stuck in a target. Now hang an 8oz weight from the knock 30” from the insert. Look how the arrow shaft is bent!!! That’s going to drag along the target A LOT while being pushed through the target!!! Now move the 8oz weight to the middle of the shaft. Much less deflection!!!(I used to remember how much less. 1/3 maybe? I’m sure I could calculate it or google cantilevers) On impact, your knock is bending your arrow shaft and applying its force to a 30” long lever(I’m imagining a 30” long arrow). The rear 1” and its 10gr of mass are applying their force to a 29” long lever, the next 1” is applying its force to a 28” long lever etc. Back to FOC, in order to have a higher FOC you are moving the weight forward. How do you do that? You can shorten the arrow shaft. Now your knock is applying its bending force to a 28” long lever instead of a 30” long lever! And the arrow lost its two most detrimental inches! 10gr x 30” and 10gr x 29”. How else might you increase FOC? Decrease knock or fletching mass! Now instead of a 12gr knock you have a 9gr knock. 3gr at the knock of a 30” arrow are far more detrimental than 3gr in the middle of the shaft! One could also increase FOC by increasing point weight or insert weight. These actual improve penetration in two ways! First is by decelerating more slowly on impact, and thus directly causing the shaft to vibrate less, BUT the shaft will vibrate less for another reason! In order to tune the arrow to the bow with an increase in point weight you must increase the dynamic spine of the arrow!!!! This comes either through using a stiffer shaft, or a shorter shaft! Both will decrease bending upon impact which will increase penetration!!!! There is one more way(assuming I haven’t missed any) to increase FOC, and that is decrease shaft mass in grains per inch rather than by shortening. Compare a 10gr/inch arrow to a 9gr/inch arrow. On impact the bending force is going to be 10gr x30” + 10gr x29” etc. all the way to the point vs 9gr x 30” + 9gr x 29” all the way to the point. It adds up to a much lower number.(in all of the above examples of forces on shafts I left out A for simplicity’s sake because we were comparing mass and length of arrow shafts, not other factors.)

Test two arrows of otherwise identical construction and the one with a higher FOC will out penetrate the one with the lower FOC, and it ABSOLUTELY DOES NOT VIOLATE PHYSICS.


This is too much and too complicated to type on a cellphone screen. I’m sure I was redundant and missed a lot as well.

 

[ImBillT]

From what I can tell, one of the more difficult things about high FOC arrows is good flight in the wind. I’m not sure whether or not it’s possible to get an arrow with really high FOC to fly straight in high winds, especially at low arrow velocity. Im sure a missile guy could answer that question with very little thought required. Even if it’s possible to get a really high FOC arrow to fly properly in high wind, I’m almost 100% certain that it’s easier to get a more balanced arrow to fly properly in the wind. Remember, there is a difference between wind drift and an arrow shaft that is aligned with the direction of flight. I feel like higher FOC should result in reduced wind drift, but worse shaft alignment to flight path. I may be totally wrong. I don’t remember anything from fluids. That said, I’ve heard a podcast or two involving complaints about high FOC and high wind. An arrow shaft that is misaligned with the arrow’s flight path is going to rob a lot of penetration.

 

[sclancy27]

Completely incorrect.

The same amount of force is available, but the force is not equally transmitted between the two arrow setups. The arrow is not rigid. It blows my mind that almost every archer who has tuned a bow/arrow is fully aware that the arrow is not rigid at launch, yet most of them assume the arrow which was flexible at launch has magically become rigid upon impact.

Given a properly spined arrow, dynamic spine (and there for deformation) at the shot is the same. You get more deformation at the shot with a weak arrow spine. A weak arrow spine is not accurate with fixed broadheads.

Although nothing is actually rigid, we can sort of consider the broadhead, adapter, and knock as being rigid, but the arrow shaft is absolutely not rigid. Even if we loosely consider some of the components to be rigid, we need to consider them separately from each other because force much be transmitted through them.

On launch, the string applies force to the knock, and the knock, along with every other piece of the arrow applies and equal force to the string. Those forces are equal at the knock/string interface, but they are not equal throughout the bow or throughout the arrow. On launch, the knock is subjected to the highest force. Broken nocks can easily be a result of arrow mass and FOC(FOC matters because it affects bending and bending is related to leverage or torque). Every other piece of the arrow is subjected to less force than the knock.

Force per unit area the nock has it, total force is same

The center of the arrow shaft is being pushed from the piece of arrow shaft immediately rearward if center and the F that piece is subjected to is only equal to M of the arrow forward that point. It is not subjected to the entire arrow’s mass. Anyway, on launch, the knock transmits the force of the string to the arrow shaft, and the arrow shaft transmits it to the insert, and the insert transmits it to the broadhead. And guess what? That force bends the arrow shaft. The shaft bends because the knock is temporarily accelerating faster than the broadhead.

In traditional archery this is evidenced by the "archer's paradox"

Now think of this in reverse. On impact, the broadhead begins to decelerate due to hitting the target. F=MA. But the broadhead and insert and not actually rigid, and there connect must definitely be dealt with when considering strength. The F HERE is generated by the M of the insert, arrow shaft, fletching and knock being decelerated BY THE SLOWING BROAD HEAD. Inserts do not break at impact due to heavy bread heads.

They do, but not simply because the heads are heavy. Improperly spined arrows, poor arrow flight and thin-walled arrows (because FOC MUST BE 20%...) are all causes.

Heavy broad heads, all else being equal, decelerate less upon impact. It’s tempting to argue that the broad head is pushed by the rest of the arrow and thus with equal total arrow weight the broad head will decelerate equally regardless of the broad head’s weight. That’s incorrect. The broad head decelerates first before the insert can apply a force to it, then the insert decelerates before the shaft can apply a force, then the shaft must decelerate before the fletching and knock can apply a force. It’s easy to tell yourself this cannot be because it’s all firmly connected, BUT NOTHING IS ACTUALLY RIGID!

All of this assumes a perfectly spined arrow. In an arrow that is spined correctly there would be no discernable difference in penetration of a high FOC setup and an average one

In fact, the very tip of the broad head slows down before the portion of the broad head just rear of the tip slows down. It all deforms and bends and vibrates to different degrees. This can be easily demonstrated with a long loosely coiled spring slightly stronger than a Slinky. Push the spring along a table into a wall. Does the spring uniformly compress throughout its length when it contacts the wall? NO! First the portion of the spring that hits the wall compresses, and does so more than necessary and a compression wave travels the length of the spring until it achieves equilibrium. A Slinky will demonstrate an identical effect in tension. The arrow does the exact same thing on LAUNCH and on IMPACT! No one argues on launch. There are only two differences between the arrow impacting a target and a long spring impacting a wall. A) the stiffness of the arrow is high enough that the bending and vibration is difficult to see, and B) the arrow is not a single uniform material(broad head, insert, shaft etc. all with different stiffnesses). With all of that in mind, you should now somewhat understand that the F and the A in F=MA are not the total F and A, but must rather be dealt with in pieces.

Only in highly elastic systems, or very large, rigid systems (like a bridge, where material deformation is calculated). An arrow is not a highly elastic system or a large rigid system. It is a small, semi-rigid system.

To do it perfectly you would have to break it down into infinitely small pieces. If you took calculus you might remember the first week or two of drawing smaller and smaller bars under a curve, and then solving for the limit as the bars became infinitely smaller. You have to do the same thing for the arrow. You can go grab your high school or college physics text book and find a problem when a whole car gets represented by a dot and think you’ve proven me wrong, but you have not. That’s a simplification for the purpose of teaching concepts. It’s not real life. If it was real life the crumple zones and air bags would not work. Instead, crumple zones allow the driver’s seat to decelerate at a lower rate than the bumper, which decreases the peak force applied to the driver’s back by the seat, and airbags allow the drivers face to decelerate at a lower rate than the dashboard which decrease the peak force applied to the driver’s face. If the car was rigid, these to safety features would not work. Luckily, the safety features do work, and they work because the deceleration of the DRIVER is not solely dependent upon the total mass and velocity of his vehicle. The reason it is not, is because he is not rigidly attached to the car, and the car is not rigid. If the arrow was rigid, then FOC would not matter. BUT THE ARROW IS NOT RIGID, AND NEITHER ARE RHE CONNECTIONS OF ITS COMPONENTS!!!

Now, if we wanted to calculate penetration, which to my knowledge no one can actually do with a mathematically derived equation

you're right, because the number of variables is never the same. It is difficult to study experimentally except in the most rigid experiments due to massive confounding variables

(but somewhat can with experimentally derived equations) F=MA where M is total arrow mass would give you a theoretical maximum F to be applied to the target via the broad head in the direction of flight. Forces applied at any other angle only contribute a component to penetrating in the direction we want to penetrate. That theoretical maximum however could never actually be reached. IF an arrow were ever to impact a target perfectly orthogonally to its direction of flight, the arrow would vibrate in a purely compression wave with the arrow shaft rapidly getting larger and smaller in a diameter. In reality however, we can’t ever get things aligned so perfectly. What happens instead is that the arrow shaft vibrates side to side. This side to side vibration causes drag on the target as the arrow penetrates the target, and the force OF THE ARROW SHAFT, FLETCHING, AND KNOCK are what break inserts. Heavy broad heads do not break inserts. Rapid deceleration of the broad head compared to the arrow shaft, and heavy fletching and knocks are what breaks inserts.

Improper arrow flight is what breaks inserts

With equal design, a heavier broad will decelerate more slowly and the forces generated by the arrow shaft against the insert will be lower. However, broad head weight isn’t the only thing effect it’s deceleration upon impact. Dull broad heads, wide broad heads, multi-blades broadheads etc will all increase the deceleration of the broad head upon impact compared to a sharper, single-blade narrow broad head, which will all increase the vibration of the arrow shaft, and will decrease penetration more than would be predicted by the increased force required to simply push a broad head through a target. F=MA ISN’T NEARLY ENOUGH TO INFORM YOU ABOUT PENETRATION!!! How much force was applied by the string ON AVERAGE to the knock? You can easily determine acceleration by from velocity, draw length and brace height, then use total arrow mass, and bingo, you now know your average force applied to the knock by the string. Obviously peak force occurred at full draw. Guess what? It won’t match the average force of your force draw curve! Why? Your bow limbs had to drive themselves forward too! The force applied to the knock during firing is less than the measured force of along your draw length!

 

[sclancy27]

^^^^ continued

What does this have to do with FOC? Quite a bit actually. Increasing FOC places more of the mass close to the point of impact. When the arrow starts bending it acts as a lever. Imagine an arrow stuck in a target. Now hang an 8oz weight from the knock 30” from the insert. Look how the arrow shaft is bent!!! That’s going to drag along the target A LOT while being pushed through the target!!!

Dude, you this is a vast oversimplification. Arrow deformation at impact pales in comparison to putting half a pound of weight at the end of a 30" arrow shaft. Deformation at impact is easy to show with low-speed video. Hint, there ain't much, even when hitting a very, very hard target.

Now move the 8oz weight to the middle of the shaft. Much less deflection!!!(I used to remember how much less. 1/3 maybe? I’m sure I could calculate it or google cantilevers) On impact, your knock is bending your arrow shaft and applying its force to a 30” long lever(I’m imagining a 30” long arrow). The rear 1” and its 10gr of mass are applying their force to a 29” long lever, the next 1” is applying its force to a 28” long lever etc. Back to FOC, in order to have a higher FOC you are moving the weight forward. How do you do that? You can shorten the arrow shaft. Now your knock is applying its bending force to a 28” long lever instead of a 30” long lever! And the arrow lost its two most detrimental inches! 10gr x 30” and 10gr x 29”. How else might you increase FOC? Decrease knock or fletching mass! Now instead of a 12gr knock you have a 9gr knock. 3gr at the knock of a 30” arrow are far more detrimental than 3gr in the middle of the shaft! One could also increase FOC by increasing point weight or insert weight. These actual improve penetration in two ways! First is by decelerating more slowly on impact, and thus directly causing the shaft to vibrate less, BUT the shaft will vibrate less for another reason! In order to tune the arrow to the bow with an increase in point weight you must increase the dynamic spine of the arrow!!!! This comes either through using a stiffer shaft, or a shorter shaft! Both will decrease bending upon impact which will increase penetration!!!! There is one more way(assuming I haven’t missed any) to increase FOC, and that is decrease shaft mass in grains per inch rather than by shortening. Compare a 10gr/inch arrow to a 9gr/inch arrow. On impact the bending force is going to be 10gr x30” + 10gr x29” etc. all the way to the point vs 9gr x 30” + 9gr x 29” all the way to the point. It adds up to a much lower number.(in all of the above examples of forces on shafts I left out A for simplicity’s sake because we were comparing mass and length of arrow shafts, not other factors.)

Test two arrows of otherwise identical construction and the one with a higher FOC will out penetrate the one with the lower FOC, and it ABSOLUTELY DOES NOT VIOLATE PHYSICS.


This is too much and too complicated to type on a cellphone screen. I’m sure I was redundant and missed a lot as well.

This is like picking fly shit out of the ocean.