HuntingNet.com Forums - FOC Technical article

I can't remember where I found this but someone may be interested

FORWARD OF CENTRE (F.O.C.)
The FOC value for an arrow indicates how far forward of the centre of the shaft the centre of gravity (COG) is located, expressed as a percentage.
If 'L' is the length of the shaft and 'D' is the distance from the centre of the shaft to the COG then the FOC = 100 x D/L.
e.g if the arrow is 80 cm long and the FOC = 12% then the COG is 12*80/100 = 9.6 cm in front of the shaft centre.
Different types of arrow shaft have, based on experience, different recommended values for the FOC e.g an FOC of 7-9% for aluminium shafts, 11-16% for ACE carbon shafts.
The FOC relates to two different aspects of shooting arrows, how the arrow behaves on the bow when being shot and how the shot arrow flies through the air.
In order to hit what you are aiming at the arrow needs to come off the bow straight and with no rotation. One of the principal factors which affects how the arrow comes off the bow is how much it bends when being shot ("weak/stiff arrow"). For a given stiffness and length of arrow shaft the main way the amount of bending is controlled is by varying the pile weight. The heavier the pile weight then the more the arrow will bend. The shaft stiffness and associated weight depend on the shaft construction e.g. carbon arrow shafts are stiffer for the same weight then aluminium shafts. For the way the arrow behaves on the bow then the FOC is a guide to what the pile weight should be for the arrow to 'match' the bow in terms of coming off straight i.e. have the right amount of arrow bending.
The reason the recommended FOC values are higher for ACE then for aluminium shafts is because the carbon shaft is much lighter then the aluminium for the same shaft stiffness. As the shaft is lighter the COG is further forward & the FOC is larger. Because the FOC is expressed as a percentage of the total length of the arrow it is to a large extent independant of the length of the arrow.
While the FOC value is limited by how the arrow behaves on the bow it also affects how the arrow flies through the air. This is related to the arrow drag and the fletching action.
The principle drag effect on the arrow which makes you 'miss' with a bad shot or a gust of wind is the drag on the shaft. The drag area of the shaft with respect to moving the arrow about depends on the arrow FOC. If 'L' is the length of the arrow shaft and 'A' its diameter then the shaft area Fa which relates to drag movement of the arrow is approximately given by:-
Fa = LA(1-FOC/50)
This is only an approximation because any rotation (fishtailing) of the arrow will affect the value of the shaft drag area.
e.g if the arrow is 80 cm long and has a 0.5 cm diameter then:-
with an FOC of 8% the shaft drag area is around 80 x 0.5(1-8/50) = 33.6 square cm
with an FOC of 16% the shaft drag area is around 80 x 0.5(1-16/50) = 27.2 square cm
or to put it another way each 1% increase in FOC reduces the shaft drag by about 2%.
The overall fletching area with respect to how the arrow flies comprises three elements:
- the effective area of the fletchings (Fe)
- the shaft fletching area (Fs)
- vortex shedding torque (expressed as an area Fv)
The total fletching area = Fe + Fs - Fv
The shaft fletching area is determined by the position of the COG i.e. the value of the FOC for the arrow. The shaft fletching area = 2 x D x A = 2 x FOC x L x A / 100. ( A, D and L as defined above). In other words the higher the FOC value the higher the shaft fletching area.
For example suppose you have a 80 cm long arrow with 0.5 cm diameter with typical values of Fe = 5 cm squ. and Fv = 1.5 cm squ.
with a 7% FOC the total fletching area = 5 + 5.6 - 1.5 = 9.1 square cms
with a 11% FOC the total fletching area = 5 + 8.8 - 1.5 = 12.3 square cms
In practice the higher the arrow FOC the smaller the diameter is likely to be and also the size of the fletchings will probably be smaller (compare the typical fletching size/diameter of aluminium arrows to carbon arrows).
The FOC value also effects where the axis of rotation of the arrow is located as it fishtails etc. about. The arrow rotation point is always in front of the COG and as the COG moves forward increasing the FOC the axis of rotation moves forward. The overall speed of response of the arrow to fletching torque (its angular acceleration), i.e. how fast it straightens up, depends not only on the area of the fletchings but on the fletching torque and the 'rotatability' of the arrow, its moment of inertia. As the FOC increases the effective fletching area increases and the 'lever arm' increases. At the same time the 'rotatibility' of the shaft decreases (higher moment of inertia). Overall the arrow response increases with FOC. A calculator illustrating the variation in arrow response with FOC is included.
A recent example of how FOC affects flight comes from throwing the javelin. Javelins don't have any fletchings and because of the tapered end don't have any vortex shedding torque. Javelin rotation relies solely on shaft drag. The problem was that there was insufficient 'fletching' and javelins were often landing flat and skidding. A couple of years ago the regulations were changed increasing the required FOC value. Now javelins rotate and stick in the ground nicely. The downside is that the increased rotation reduces drag in the vertical plane and the distances being thrown have been reduced by several metres.

Andrew
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Edited by - ACLakey on 10/11/2002 09:57:30