Calculating FOC: question for Dr. Ashby

[David Petersen]

#5025

I’ve recently been in discussion with Fletcher and Dr. Ashby about the best way to measure FOC – from the back of the head, which is the AMO standard and our suggestion for using the FOC calculation chart in the Ashby Library here. But you can also do the calculations including the point length. I knew from reading the Ashby study that FOC is merely a ratio, thus “it really doesn’t matter which method we use, so long as we’re all doing it the same way for comparison’s sake.” OK so far.

Then Fletcher (Rick Stillman of The Feathered Shaft in IL), who’s an aviation guy as well as a top arrow maker, mentioned to me his discomfort with using the back of the head for FOC measurements because—well, I’ll let Rick explain it to you himself when he posts here, but basically he’s talking balance and his argument for including the head length in FOC calcs sounds solid to me. The “problem” I’d like to address here is that including the head length can produce a significantly different FOC value than not including the head length. This is particularly notable with very long heads like the Tuffhead and presents a bit of a snag for those of us who have embraced the Ashby study and view certain FOC numbers as goals we work hard to achieve. Most notable is the 19/20% split between normal and high FOC. While I want the highest FOC I can get while maintaining arrow accuracy out to 20 yards, I always feel OK going for elk if I have “the Ashby minimums” of 650 grains total weight and 20% FOC. But which method to use to know that my FOC calculations are accurate and I in fact do have 20%?

Here’s an example, using some lovely new woods that Fletcher recently built for me. For background, these are Sitka spruce shafts cut to 29.5″ (nock to BOH) with average weight of 410 grains, spined to 85lbs to handle 300-grain Tuffheads through a 53# longbow. In the below figures I calculated FOC for two shafts, one of them wearing a 300-grain field point and using both “with head” and “without head” measurements … then did the same for a second identical arrow mounted with a 300-grain Tuffhead broadhead, which is about 1” longer than the field point. (And to further complicate things with a side issue, the brass field points have the majority of their weight at the front where they’re solid, while the broadheads of course have most of their weight at the back where they’re widest. While I’m not intellectually equipped to deal with this aspect, I’m hoping Ed and others might comment.) Anyhow, here are the results:

23.33 to back of field point

18.75 including field point

15.91 including broadhead

23.73 to back of broadhead

Whoa! While I don’t have my calculator handy, that’s almost 8% difference in field point FOC depending if we include head length or not … while the broadhead figures differ only about 3%. Moreover, the broadhead-equipped arrow delivers high FOC with both measurements … while the field-pointed arrow is well above the 19/20% break point when measured to back of point yet way under with point length included. Hmmm. So, the FOC figures for field point and broadhead when measured to back of head are very close, with less than 1% difference, FOC when measured to include point length differs nearly 6% between field points and broadheads.

While I’ll leave interpretation of these findings it to those with stronger math skills than me (which would be almost anyone), the very close FOC figures between field points and broadheads when measured to back of head are reassuring to me and fit with the fact that both broadhead and field-pointed arrows hit the same place on the target (dead center). But aha! Even though the FOC calcs done to include point length and without point are considerably different … well, they are the selfsame arrows and they all shoot great!

So, do I have enough FOC or not? And either way, how much FOC do I truly have? And the bottom-line question is: “Which measurement method is most meaningful and why? If there’s anyone left who’s read this far and still not confused, I apologize.

[Bruce Smithhammer]

#36325

Dave –

You bring up a question I’ve been wondering about for a while. I’ve never really understood measuring from the back of the head to calculate FOC. After all, I’m obviously not shooting my arrow without a head, and it seems to me that the FOC measurement you’re getting including the head is the more useful and accurate calculation.

But, as you point out, that means overhauling a lot of existing information.

[David Petersen]

#36377

Yep. As the mountain men are said to have said when confused, “It’s too many for me!” Happily, I scrape by either way with the broadhead, but am left to wonder why FOC is so much lower on the field point when measured to include head length … likely because the field point is an inch shorter. We’ll just have to await input from the Big Boys. I think I see one coming now and he looks serious …

[Stephen Graf]

#36920

Dave,

I read your post twice, but maybe I missed it… But in trying to understand the interesting topic you bring up and the apparent difference between the broadhead and the field point… I don’t see any observation about the actual balance point.

What I mean is, was there an actual difference in balance point on the arrow between the field point and the broadhead? If you mark the arrow, does the balance point move?

If the balance point doesn’t move, then the FOC including the broadhead should be lower than the FOC not including the Broadhead

My guess is that if you measure the balance points between the broadhead and the field tip that the broadhead balance point is moved toward the end of the arrow as compared to the field tip balance point.

[Stephen Graf]

#36932

Update to my last post – I see that the BOP numbers are about the same. This means that the balance point is about the same on the actual shaft. So I guess my guess was wrong.

So if the balance point doesn’t change, and the length gets longer, then the FOC for the broadhead has to be less than for the field point.

I wonder if something went wrong when you did the field point calculations including the field point length?

[Vintage Archer]

#36943

If one is to compare and correlate your arrow FOC to the Dr Ashby’s finding and theorems then you have to use the same measurement standards that he used to do his test. That is the AMO standard of FOC measurement.

Adding length to the arrow by including the broadhead length or field tip length will always result in a lower FOC.

I would agree with you and Rick it seems that the point should be included in the calculations.

[Vintage Archer]

#36949

“Adding length to the arrow by including the broadhead length or field tip length will always result in a lower FOC.”

I don’t know what I missed in your sample but according what I just wrote your measurement of the FOC with the broadhead on should be less than the FOC with the field tip on.

The balance point of the two arrows should be the same as the tips are basically the same weight…. the broadhead being longer should yield a smaller FOC.

I am a little confused by your findings but that is normal I walk around half confused anyway 😀 I am going back to the drawing board:D

[Fallguy]

#37032

Doesn’t the balance point move due to the length of the lever? The field point has a more concentrated weight versus the broad head.

[David Petersen]

#37165

Responding to your good points and questions: Balance point is almost identical, with field point only 1/8″ forward of broadhead.

More importantly, I ran the measurements and calculations again and apologize for incorrect numbers the first time. The figures in my initial post have been corrected. Turns out the figures for both arrows measured to BoP are correct, but the figures including points were off for both arrows. Don’t know how that happened but I double-checked this time and should have the first time. So now what we see is that FOC for both arrows and both type heads is notably higher when measured to BoP than when including head length. Now, with both field points and broadheads I have much better FoC when measured without heads than with.

So, to bring us back to the beginning: I am using personal examples but this is not about me: The question is for all of us, and it is this: Because we seek a minimum of 20% FoC and the two measuring methods result in “below minimum” when measured with head and “above minimum” when measured to BoP, which is most accurate, reliable, usable, etc.? Would it make any sense to average the two?

[Vintage Archer]

#37219

The answer to your question is they both have the same accuracy and both can be used .If you and your friends use the broadhead on method than you can compare apples to apples.Or arrow FOC to each other’s arrows.

If you want to compare to Dr.AShby’s findings you have to use the AMO method as this is what he used in his testing.

I recommend using AMO so when you tell me you have a 30% FOC and you got certain results like cracked a moose scapula in half I will not only be impressed I can relate it to Ashby’s studies How ever if you were using the broadhead on method you would actually have a higher FOC when reporting 30%:D

[Stephen Graf]

#38081

David Petersen wrote:

So, to bring us back to the beginning: I am using personal examples but this is not about me: The question is for all of us, and it is this: Because we seek a minimum of 20% FoC and the two measuring methods result in “below minimum” when measured with head and “above minimum” when measured to BoP, which is most accurate, reliable, usable, etc.? Would it make any sense to average the two?

As Joe has emphasized, using the BOP is the standard. We all need to use standards (in all subjects), otherwise there is no point of reference, and no progress can be made.

And specifically, in answer to your question in bold, I would humbly suggest that the number 20% only has meaning in respect to the BOP method. If you don’t use that method and that point of reference, than the number 20% has no meaning.

There are no absolutes in the world, so the number 20% is only “magic” in relation to the method used to derive it.

Oh, and one more thing… I always tell my kids that no erasers are allowed in science class. Whenever experimental data is recorded, if mistakes are made, the new numbers are written down in addition to the wrong numbers. Even in mistakes things can be learned, and erasing mistakes erases an opportunity to learn something…. I wish you had not erased your original numbers, but had just added the corrections…

[David Petersen]

#38360

Steve — You make good points re relativity. While I fail to see that anything can be learned from faulty data, here are the original numbers you requested:

23.33 = field point, BOP

15.63 = including field point

23.73 = broadhead, BOP

21.21 = BH included

One more, perhaps minor potential for inconsistency: Using the FOC chart we often have to round up or down. I always round up but can’t say why.

[Raymond Coffman]

#38445

I realize I am very new to building and using efoc/uefoc arrows. My tendency would be to stay with the Standard [ bop]

or show both {P-inc } for the individual arrow set up.

My reason is it allows me to compare my arrows and their efficiency to all the others{the standard} recorded in the Ashby studies [ natal on], and everyone else from here on that adds to it—

Scout.

[Ed Ashby]

#38617

Here’s about the best I can explain what we are measuring. I hope it clarifies the question.

No matter which measuring method is used it is imperative to remember one is only getting a relative number. What we measure is not the true FOC. The true FOC depends on the location of the Center of Pressure (CP) on the arrow in flight, in relation to the center of mass (the Gravitational Center). It has nothing at all to do with to do with projectile length. Our main need in measuring “relative FOC” is a method to be able to duplicate an arrow setup.

A good analogy is with the static spine. Why do we measure it at 26” or 28” between centers? Why not measure it at the full length of each shaft? The answer is simply that it doesn’t make any difference what method we measure it by, because it only measures relative stiffness, not the actual dynamic spine the arrow will show when shot. All we need to know to duplicate an arrow is the relative relationship, one shaft to the next. It’s the same for FOC.

We generally do the initial development of our EFOC arrows with something other than a broadhead, then changing over to a broadhead of the same weight. If we measure the FOC using the overall arrow length we are going to have two arrows that shoot the same but have different measured, “relative FOC’s”. Going back to our static spine example it would be like using the traditional 26” or 28” on-center static spine measurement while developing our arrow then, once finished, going back and measuring the static spine using the actual length of the arrow and then stating that as the measured static spine. What actual purpose does it serve? None. All it does is add a layer of confusion.

Similarly, I think measuring the FOC using the overall length merely adds a layer of confusion, where the same arrow setup, with the same point weight shows two different “relative FOC’s” depending on the length of the point. For purposes of duplicating the arrow we don’t really need that information.

It really makes no practical difference which method is used but if one states the FOC of their arrows with broadheads in place, using the overall length, then someone trying to develop an identical arrow, having the same FOC, they will have to ether do the development with a broadhead or periodically take their field point off and stick a broadhead on the shaft to see what the FOC measures. Just seems like unnecessary complication to me.

Though not directly related to how we measure our ‘realative FOC’ I will add (and I HOPE this does not add to any confusion) what MAY help with understanding FOC. The Center of Pressure (CP) is that point along a projectile in flight where the air pressure forward of and posterior to it are equal. The farther the CP is behind the Center of Gravity (GC) the more stable the flight. By moving weight forward on the arrow we are trying to increase the distance between the GC and the CP. The other way we can increase true FOC is by increasing fletching size; but there are downsides to increasing fletching size.

It’s important to realize that the ‘true FOC’ is dynamic; it changes during flight. Our goal is to maintain the highest possible level of true FOC throughout the arrow’s flight; we want the highest ‘AVERAGE TRUE FOC’ from the instant of arrow launch until the arrow stops all forward movement – even during penetration. The big advantage of increasing FOC by moving the weight forward, rather than increasing fletching size, is that the effect remains more of a constant during flight. Fletching’s effect on FOC is nearly nonexistent at the instant of launch, at its maximum at maximum arrow velocity, and diminishes as the arrow slows.

Increasing the size of fletching on an arrow increases it’s stability in flight because it increases the air pressure on the arrow’s rear, which also increases the distance between the GC and CP. The downsides of using increased fletching to get increased ‘true FOC; in flight are: (1) it slows the arrow; (2) the effect is not present at the instant of arrow launch; it comes into effect as the arrow begins to move forward and increases as the arrow accelerates (and decreases as the arrow slows down); (3) it takes longer for it to overcome arrow paradox than does having a higher FOC resulting from increased weight forward and, (4) because the arrow has slowed dramatically it has virtually no beneficial effect on on ‘true FOC’ during tissue penetration.

Ed

[David Petersen]

#40917

Thanks, Ed and everyone. It seems clear that most here are happy with the AMO method (shaft length measured to BOP) with its higher FOC numbers. So, going with that, and with two measurements coming out the same, I guess I can honestly say that I have 23.73% FOC with wood shafts and 300 Tuffheads, which–given the limits on wood shaft weight vs. spine, and the difficulty Fletcher had in finding just nine shafts (took months of saving them back)that would give 85# spine in a relatively light shaft (average about 410), I don’t think we’re going to do much better with woods. If I don’t break them all in practice, I plan to kill an elk with this set-up this year and predict a full pass-through, though 23/64 shaft diameter is a disadvantage over skinny carbons.

Coincidentally, Fletcher fletched these with 4×2″ feathers, my first experience with four-fletch, and I’m so please I plan to make it my norm henceforth–though it might be tough getting four feathers on a skinny carbon shaft.

[Raymond Coffman]

#41000

David –

Thanks for letting us know the final outcome of your 300gr Tuffhead/wood/efoc quest. It sounds like it would be “very difficult” to accomplish with my shrews [56lb @ 27 ]. I will stick with carbons for same when developing elk arrows. I managed to get a 660gr poc 225th -foc 18.42%, should be a good deer arrow.

Scout.

[Ed Ashby]

#42070

David Petersen wrote: I guess I can honestly say that I have 23.73% FOC with wood shafts and 300 Tuffheads, which–given the limits on wood shaft weight vs. spine, and the difficulty Fletcher had in finding just nine shafts (took months of saving them back)that would give 85# spine in a relatively light shaft (average about 410), I don’t think we’re going to do much better with woods. If I don’t break them all in practice, I plan to kill an elk with this set-up this year and predict a full pass-through, though 23/64 shaft diameter is a disadvantage over skinny carbons.

Coincidentally, Fletcher fletched these with 4×2″ feathers, my first experience with four-fletch, and I’m so please I plan to make it my norm henceforth–though it might be tough getting four feathers on a skinny carbon shaft.

That sounds like an AWSOME wood shaft EFOC setup. I’m anxoius to see the outcome on your next elk. I THINK the large ferrule on the Tuffhead will negate much of the negative effect of the larger shaft diamater. It will be interesting to find out.

Ed

[Troy Breeding]

#42497

My thoughts were the same as Ed’s last statement. The large ferrel on the Tuffheads should take care of the 23/64″ shafts.

Troy

[Fletcher]

#46066

At least some of the question over how we measure FOC has been my fault, as I’m the only guy I know who really has an issue with the AMO standard method. I apologize for taking so long to get here, but I needed to get my thoughts lined out, plus I’ve been busy and my computer died. I’m an aircraft mechanic by trade and have been messing with flying things for about 40 years. FOC in airplanes is called center of gravity and it is measured or calculated for every airplane out there. It is the theoretical point around which a flying object moves. As Dr. Ashby mentioned, the true center is “center of pressure”. However, this can’t be measured without some pretty serious test equipment, starting with a wind tunnel. CG/FOC is very close to center of pressure and for all practical purposes, the same.

When I state an FOC, I generally state whether it is real or AMO, just so others will know what I’m talking about. If all we are looking for is a reference point, then I guess the AMO method is OK, but if we really want to know what the FOC is and its effect on arrow flight and performance, we can’t ignore the length of the point. That is why it is important to me. The whole arrow is what is flying, not just the shaft. Changing from a field point to a broadhead, even though the same weight, can have a noticeable effect on arrow flight and I suspect the change in balance has something to do with it. I also believe that using the AMO standard to determine performance parameters is going to give incorrect numbers simply because the input value is incorrect. The magic 20% we are looking for really isn’t 20%.

I’m gonna go shoot some arrows.

[Ed Ashby]

#47832

Fletcher, with arrows at the lower (AMO measured) FOC’s I think you might be able to notice a flight difference changing from a field point to a long broadhead and measure a significant difference in the balance point along the shaft. That’s because, at the lower ‘AMO measured’ FOC’s you’re getting a ‘meaningfully’ longer forward leaver arm by moving some of the weight a bit farther forward. Because this will change the relationship between the Gravitational Center (GC) and the Center of Pressure (CP) of the arrow in flight it is going to cause a change in the TRUE FOC. It has nothing to do with the overall length of the arrow, merely the change in the relationship between the GC and the CP.

At the higher amounts of (AMO measured) FOC’s changing from a field point to even a very long broadhead makes less than a 1mm change in the location of the balance point (extremely hard to measure accurately). That’s because the forward lever arm is already extremely short and it takes a lot of weight change to make a significant difference. Using a hooter shooter, at those higher FOC’s there is no flight difference between field points and broadhead. (I know that you already understand all this, but the explanation is for those that don’t know.)

In a nutshell, the higher the arrow’s (AMO) measured FOC the less difference there will be between the GC and CP as one changes between a field point and a BH.

All that notwithstanding, since it does not reflect the true FOC I still see our relative FOC as merely a reference point for duplicating arrow setups. As you noted, without some pretty sophisticated measuring equipment we’ll never be able to accurately state the true FOC. As long as one states the measuring methiod used to determin the realtive FOC it really makes no difference which method we use. Since the true FOC depends on the relationship between and GC and the CP, and the fletching we use CAN have a large effect on the location of the CP it’s likely that we SHOULD be stating the fletching used in every setup too.

Ed

[david Keech]

#38294

😳

[mhay]

#61522

I just found and read this entire thread . Many thanks to all .

Having a more clear understanding now , along with using the BOP measurement , my arrows FOC is up 4.61% , to 19.11% .

Thanks.

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