# Calculated FOC FORMULA



## archerm3 (Jan 4, 2007)

Sorry, no equation writer handy so the formatting will be hard to read..

Assumptions: 
1. Center of gravity/mass of points, inserts, nocks, and fletches occur exactly in the middle. If you know the center of gravity of these items, adjust the Lp, Li, Lf and add another term for Lncg.
2. Base of shaft to nock interface is used as the COM baseline to simplify the formula by one variable under assumption 1 relating to the center of mass of the nock is close to exactly in the middle.
3. All weights in grains and distances in inches. If other units are desired, you must convert your shafts GPI (grains per inch) into the required units.

Wp = Weight of point
Wi= Weight of insert
Wn = weight of nock (plus unibushing if installed)
Wf = weight on one fletch
G = gpi of shaft

Lp = distance from base of nock-to-shaft interface to the center of Point
Li= distance from base of nock-to-shaft interface to center of nock
Lf= distance from BONTS interface to center of fletch
Lncg= distance from BONTS interface to center of gravity of nock
N = number of fletches
Ls= length of shaft
Lt= length of arrow overall from tip of point to tip of nock
Ln= length of exposed nock when inserted into shaft


(((((Wp*Lp + Wi*Li + .5*G*Ls^2 + N*Wf*Lf) / (Wp + Wi + G*Ls + N*Wf + Wn)) + Ln) * (1 / .5 * Lt)) - 1) * 100 = FOC in percent.


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## LightmanSA (Jan 21, 2008)

OUTSTANDING...! 

Thanks Very Much, archerm3..

I'll throw that into my shaft selection spreadsheet..

This is what I really like about this Forum.. Brilliant people willing to help..!

Jeff


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## SonnyThomas (Sep 10, 2006)

I took one look at the Calcuation Chart and said: "@#*#@ that!"

And then there is the other FOC formula that uses the full length of the arrow and then the glue for the insert, the glue for the fletchings.
So there is science and doing it for real two different ways - see example at bottom of page and then go to the listed link within http://www.archerytalk.com/vb/showthread.php?t=453845


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## BeachBow (Jan 6, 2008)

*I'm with you!!*



SonnyThomas said:


> I took one look at the Calcuation Chart and said: "@#*#@ that!"
> 
> And then there is the other FOC formula that uses the full length of the arrow and then the glue for the insert, the glue for the fletchings.
> So there is science and doing it for real two different ways - see example at bottom of page and then go to the listed link within http://www.archerytalk.com/vb/showthread.php?t=453845


Just give me something simple like a chart I can scan thru. Just reading that formula gave me a headache!!


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## SonnyThomas (Sep 10, 2006)

BeachBow said:


> Just give me something simple like a chart I can scan thru. Just reading that formula gave me a headache!!


Run a unknown component built arrow through the calculation chart and see what kind of headache you'll get. 

Someone posed a question of the two formulas; One formula uses the measurement of the cut shaft length and the other uses the measurement of the entire length of the arrow. "Why use only the cut shaft length when you are in all actuality balancing the entire arrow?" Just things to think about.


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