F.O.C. - Arrow center of gravity


From: 15821tmt@msu.edu (Terry Trier)
Subject: F.O.C.
Date: 6 Mar 1995 13:09:28 GMT

I would appreciate some information on calculating F.O.C.  I have some
2312 superslam arrows, 31 7/16 long.  I have 99 gr nibbs in them which
are supposed to give 8% F.O.C.  However, when I calculate actual F.O.C. 
(balance point-midpoint/length) it comes out to 6.3% F.O.C.

Easton says that the 8% is calculated using the most commonly used length
and fletching arrangement but they don't say WHAT that is. I should know
more about that today after I call them.  What I want to know is how much
should I chop off the arrow to get at least 8%.  I know I can go to a 
heavier point but I would have to use different points and not nibbs.  The
8% nibb is the only one made for 2312s.

Any info at all on F.O.C. would be helpful.

Also, I've used the F.O.C. formula published by Larry Wise in two different
books he wrote, one on bow tuning and one on broadhead tuning, and the 
results I get with that formula don't make sense to me.

I put this formula in a spreadsheet and the results come out to a decimal
value that is around 0.2.  Then when I make changes to the values in the
spreadsheet, the result is little affected.  Either I'm doing something
wrong or I'm not interpreting the results correctly.  Has anyone else used
this formula?

Thanks,

Terry Trier                     
Entomology Dept.                
Michigan State University               
15821tmt@msu.edu
trier@pilot.msu.edu
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From: ldiehr@eth233.eld.ford.com (L S Diehr (Lawrence))
Newsgroups: alt.archery
Subject: Re: F.O.C.
Date: 7 Mar 1995 21:23:27 GMT
Organization: ECC at Ford Motor Company, Dearborn Michigan

Terry Trier (15821tmt@msu.edu) wrote:

: Here is the spreadsheet formula:
: ((((0.5*D2)+(2*C2)+(0.5*B2*F2)+((B2-1)*E2))/(D2+C2+F2+P2))-(0.5*B2))/B2
: Here is the spreadsheet data:
:    B       C      D       E         F       G
:  31.44   21.52   24.6    99      294.88  0.218626
: B = arrow length
: C = nock wt (includes supernock bushing wt)
: D = wt of vanes
: E = wt of nibb
: F = wt of shaft 
: G = calculated F.O.C.
: Here is the formula in Larry Wise's book:
:         --                                      --
:        |.5xN + 2xF + .5xAxW + (A-1) x P           | 
:  R =   | ------------------------------  - (.5*A) |  /  A
:        |         N + F + W + P                    | 
:         --                                      --


: Variables:
: A = total arrow length including nock and point
: F = total weight of fletching
: N = weight of nock
: P = total point weight
: R = F.O.C. percent in decimal form
: W = shaft weight without nock, fletching or point

: I did find out from Chris at Easton that the "most common length" is
: considered to be 28 inches.  He couldn't tell me what the most
: common fletching used is.  Chris said that target arrows should have a 
: F.O.C. of 7 to 10% and hunting arrows 10 to 15%.

: Also, I'm working on the earwig thing. 8-)

And the answer is ---
(snip here)
Length  31.44
Nock       21.52
Fletch  24.6
Point   99
Shaft   294.88
FOC        =((Nock/2+2*Fletch+Length*Shaft/2+(Length-1)*Point)/(Nock+Fletch+Shaft+Point)-Length/2)/Length
(snip here)

Your data yields a 5.73% FOC

You are shooting very long 2312's or so.  Maybe you could consider 3/39 ACCs
with 100 gr points and Spin Wings (~12%FOC)

Concerning programming practices:

Estract the part between the (snip here)s, import that to the spreadsheet, 
create the lables, and the formula will work for you too.  This was 
extracted from an Excel spreadsheet.

Use lables whenever possible in your spreadsheets - they make it possible to 
understand your work a week or two after you finished it, and help when you
try to explain it to anyone else.

Your actual problem with the formula is the P2 that evaluates to 0.

Larry Diehr

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From: Culverhouse_S_R@BT-WEB.BT.Co.UK (Steve Culverhouse)
Subject: Re: F.O.C.
Date: 8 Mar 1995 17:56:19 GMT
Organization: BT Labs

To somewhat broaden this thread .... 

Does anyone know what the theoretical or practical effect of changing arrow
balance is? It strikes me that provided the centre of mass is in front of
the centre of drag that an arrow is (at least theoretically) stable. Has
anyone in Hoyt/Easton, for example, modelled arrow flight with different
FOCs or did they just do lots of pratical measurements. If the latter has
anyone ever seen this data ?.

My guess, for what it's worth, is that increasing the FOC would only change
the sensitivity to porpoising, fishtailing etc. and that if that is the
case that the further FOC you get the better from a stability point of view
that you are. The tradeoff would be that the heavier points to get further
FOC would drop your arrow speed too much.

If my assumption is true then why the big deal about whether it is 6% or
15% FOC? there is only 1.25 inches different in position (0.09*14") between
the 6 and 15% and if the centre of drag is near the fletchings (flaw in my
argument?) this is only a difference of around 10% in separation of centre
of mass and centre of drag. this seems unlikely to have a major effect on
the arrow flight.

Any opinions?

Steve
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From: 15821tmt@msu.edu (Terry Trier)
Subject: Re: F.O.C.
Date: 8 Mar 1995 20:42:47 GMT
Organization: Michigan State University

>Your actual problem with the formula is the P2 that evaluates to 0.
>
>Larry Diehr
>

I have the spreadsheet formula working now.  As you know I mixed my
spreadsheet letters with the formula letters.

But it works great and it's nice to be able to make subtle changes in arrow
length or point mass and see the change in FOC.  If you put the shaft weight
in as a formula of grains/inch x length (e.g., 9 grains per ince), then
every time you change the length, the shaft weight is automatically updated.
When I tried this, I found that changing shaft length does not have a very 
great effect on FOC.  Point wt, though has the greatest effect.

For the combination I use, the formula underestimates the FOC determined by
direct measurement, but it's close. 

Thanks for the help.


Terry Trier                     
Entomology Dept.                
Michigan State University               
15821tmt@msu.edu
trier@pilot.msu.edu
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From: Claes Colmeus (Claes.Colmeus@farm.lu.se)
Subject: Re: F.O.C.
Organization: Dept of Pharmacology, Lund
Date: Wed, 15 Mar 1995 09:59:43 GMT

In article Culverhouse_S_R-080395174351@132.146.229.212 Steve Culverhouse,
 Culverhouse_S_R@BT-WEB.BT.Co.UK writes:

>Does anyone know what the theoretical or practical effect of changing arrow
>balance is? 

snip

>My guess, for what it's worth, is that increasing the FOC would only change
>the sensitivity to porpoising, fishtailing etc. and that if that is the
>case that the further FOC you get the better from a stability point of view
>that you are. The tradeoff would be that the heavier points to get further
>FOC would drop your arrow speed too much.

snip

IMHO, based on (somewhat limited) experience, the main effect of increasing 
the point weight will be a change in the (dynamic) spine of your arrow. You 
will simply get a softer arrow. This is of course much more significant for
finger shooting. It is easy to make your arrows stiffer by shortening them,
however, stretching a too stiff shaft could be more difficult. This is where
increased point weight may solve the problem. 

You don't have to buy new nibbs, they are hollow. Just put a brass weight in 
it and glue it to the shaft again. Make sure the weight is well fixed, using 
the same thermal adhesive. A loose piece of metal inside an arrow will do 
nasty things to both ends of the shaft (don't ask how I found out, if you 
really must know, I will answer that by private email). Hold the nibb 
vertically, heat it, using a flame or a hot air gun, and let a couple of drops 
of glue run down the center hole. Then drop the (heated) weight into the hole 
and push it hard to make the glue flow up along it's sides. I made my weights 
slightly thinner than the hole diameter and with a threaded hole in the rear 
end, to be able to remove them again. When putting the nibb back on the arrow,
don't hold it upside down or the weight may come loose.

Claes
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Sorry to be so late, but I just read the question about calculating F.O.C. 
(meaning the % forward of center balance point of an arrow) and the answer with 
all the mathematics. It is of course correct, although slightly simplified, not 
taking into account the exact center of gravity of the fletching, the nock and 
the point. Especially points with long balance weights will upset the 
calculations, indicating a c. of g. too far forward. 

Also, it's a little like going birdhunting with an AA cannon, and further it
gives you ample opportunities to make mistakes. 

Why not visit your local archery dealer and ask for an FOCB% tool from Saunders,
costing a few dollars. It will give you the percentage value of any arrow in 
less than half a minute and you just can't get it wrong. 

Try it, unless of course you honor the old saying: Why make things simple 
when you can make them so wonderfully complicated.

Bertil

ideswede@algonet.se

Bow Pro. Meeting point for Scandinavian archers on the move.

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