Arrow FOC (front of center) is an important concept that all archers should understand. Whether bowhunting, target or 3d shooting, the FOC of an arrow will affect the flight of the arrow. FOC becomes especially important the farther downrange the target is, and also if a broadhead (most notably a fixed blade broadhead) is used.
The basic definition of FOC is the percent difference between the physical midpoint of the arrow and the center of gravity (balance point) of the arrow as compared to the total length.
When an arrow is shot, the fletchings immediately begin working to correct the flight of the arrow. Any little imperfection in the initial launch of the arrow, either from shooting with fingers, imperfect release, improperly tuned bow, torquing the handle of the bow, etc. will cause the arrow to flex as it leaves the bow and/or come out crooked. The job of the fletchings is to correct this imperfect flight by straightening the arrow as air flows over the fletchings during flight.
In order for the fletchings to correct the flight of the arrow, they must move the arrow into a straighter flight path by rotating the shaft about the center of pressure. The center of pressure is the point along the shaft where the aerodynamic forces are balanced. Just like with a weather vane, the fletchings on the back of the arrow provide more surface area on which the air can act upon the arrow.
Fletchings are best able to steer the arrow when the center of pressure is farther behind the center of gravity. This is more easily done the longer the distance from the fletchings to the center of gravity. Therefore the farther the center of gravity is from the back of the arrow, the easier it is for the fletchings to correct the arrow flight.
If the center of gravity and center of pressure are too close together, or worse if the center of gravity is behind the center of pressure, the arrow will become unstable. To witness this, take an arrow or a dart and try to throw it backwards! What happens?
For penetration purposes, the opposite phenomenon occurs. A larger FOC will prevent and arrow from flexing as much when coming into contact with the intended target. Hunters will want a higher FOC so that as the broadhead enters the the game, the distance from the front of the arrow to the center of gravity is lower, making it more difficult for the arrow to flex or deflect. Any flex or deflection of the shaft upon entry means that energy is being lost somewhere other than directly along the center of the shaft, lessening the overall penetration.
A larger FOC is necessary for shooting long distances where crosswinds tend to have a large effect on arrow flight. The same applies to shooting broadheads because the larger surface area of a broadhead is more greatly affected by launch imperfections as well as crosswinds. Broadheads effectively move the center of pressure closer to the point and tend to steer an arrow which can often have a negative affect that the fletchings must overcome.
There are two main ways of calculating FOC. Both use similar formulas; the difference being that one takes into account the length of the point and insert while the other does not.
Calculating arrow FOC
AMO Method:
1) Measure the length of the shaft from the throat of the nock to the end of the shaft, excluding the insert; this is length “L”
2) Using a sharp edge, balance the arrow (including the point) and mark the balance point
3) Measure the distance from the throat of the nock to the balance point; this is length “B”
4) Input B and L into the following formula:
The second method replaces the total length of the arrow, including the point, for the “L” value.
Arrow FOC calculator
This site has a calculator that will do the calculations for you once the measurements have been taken: ArcheryCalculator.com
Comparing arrow FOC values
When comparing FOC values, it is important that both values be calculated with the same formula. The second method will generally result in a lower FOC value.
Recommended values for FOC (using the AMO method) vary depending on the application, target arrows (field points) should generally be in the 8-11% range and broadhead tipped arrows in the 10-15% range. FITA and longer distance shooters will often go for a 12%+ FOC, even though they are using field points, because of the long distances involved. Some traditional hunters have used FOCs of over 30% because with the right setup it can enhance penetration on animals.
Calculating arrow FOC example
Here is an example of how to calculate FOC and how a field point and broadhead with identical weights can have different FOC values on the same arrow. This first image shows a Carbon Express Mayhem arrow with a 100 grain field point. The finished arrow is balanced on a triangular piece of wood and the balance point marked with a silver Sharpie:
Here the field point is changed out for a 100 grain NAP HellRazor and the balance point is marked with a thin piece of green painter’s tape:
Now a close up of the different marks:
As can be seen, the broadhead has a slightly higher FOC if using the AMO method, though just barely, with 10.45% vs. 10.35% of the field point. If using the second method stated above, the FOC difference is significantly more, and in the opposite direction, broadhead 7.48% and field point 8.68%. I have found that using the AMO method is a better overall method of comparing values and is the method that I consistently use.
Loading ...
{ 12 comments… read them below or add one }
Something that virtually everyone overlooks is the placement of the fletchings. The roughly 1 inch forward spacing of the fletching was traditionally there for finger clearance, but if your using a release aid, there is no need for that offset. By moving the fletching back to the nock, you decrease your FOC slightly, but effectively increase the lever arm by an inch. I have experimented on my own arrows with this. Leaving the fletchings alone, I would have to add something like 50 grains to the tip of my arrow to move my FOC forward 1 inch, by moving the fletching I get the additional inch without adding weight.
The dramatic change happens when you remove any wraps, change to light weight feathers and move them to the back of the arrow. Now add a stiffer splined arrow with more tip weight (FOC = 19%) and you have one mean flying object.
Greg,
I have always liked keeping my fletchings back as far as possible for that very reason. As long as they have good clearance, I’ll push them all the way back I can. Thanks for bringing up this important point!
Suggest you correct the formula for FOC else you will cause confusion. You can find it in lots of places e.g. Easton tuning guide.
You need to do some reading around the topic of arrow (fletching) rotation and centre of pressure.
Don’t worry, I’ve done plenty of reading on FOC
To clarify – I don’t mean that your equation is incorrect just that the normal format emphasises the “Front of Centre” aspect.
Joe, I’m a bit confused about what you mean by the “normal format” and how my formula does not emphasize the FOC seeing as it’s a direct calculation of FOC?
OK am being somewhat nit picking here. Only because this is a great site so a little constructive criticism is maybe permissible
Front of Centre is an arbitrary definition of centre of mass location (e.g. you wouldn’t actually use FOC in a flight calculation). i.e. its the distance the balance point is in Front of the Centre of the arrow divided by the arrow length x 100. It’s helpful to readers to clearly work through from the definition to the calculation. Not so obvious what the ratio B/L has to do with Front of Centre. Not doing this – been there and got the T shirt and confused people.
“The job of the fletchings is to correct this imperfect flight by straightening the arrow as air flows over the fletchings during flight. In order for the fletchings to correct the flight of the arrow, they must move the arrow into a straighter flight path by rotating the shaft about the center of pressure. The center of pressure is the point along the shaft where the force that flexes the shaft is greatest”
I have a of problems with the above
It’s been a while since this article was first written and as I did a review of it, I agree that what I originally said about the center of pressure was confusing. Sometimes when you first write something you have it so ingrained in you head that what you wrote is what you meant. However, as time passes and you can step back and see it from a different angle, you can see a different view! The article has been updated to better clarify “center of pressure” and “center of gravity” and how they relate.
[...] LONGBOWS, and ARCHERY ACCESSORIES BY: O.L. ADCOCK And here is a good link for figuring FOC:Arrow FOC Basics and How to Calculate FOC | Archery Report: bows, arrows, physics and more! Personally in my quest to build light woodies for competion I have found an FOC of 6% to be [...]
Thanks for this description and calculation of FOC. Been wrestling with the correct way to do this. I see there are actually two methods. I think I’ll choose the AMO method as well. My arrows ( Gold TIP 3555) are cut to 26.25 inches and shoot out of my Mathews at 60 lbs. Use a G5 100 gr broadhead and this calculated out to 13.5% FOC. In my 3D shoots I shoot 27 inch arrows with 100 gr field tips or my 26.25 arrows with 85 gr field tips. Seem to get good straight flight with a smaller value FOC
Bill, higher FOC is not always better, depending on how the bow is tuned as you have noticed. I have found that higher FOC is more stable in most cases if you tune your bow to each individual arrow setup. However, it won’t be the same for everyone and the real key is to experiment with your own equipment and find what works best for you.
Thanks for information and FOC is not always better but i reading on Foc….