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.

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 it bends when being shot ("weak/stiff arrow"). For a given draw weight, shaft weight, shaft stiffness and length of arrow shaft the main way the amount of bending is affected is by varying the pile and nock weights. The heavier the pile weight or the lighter the nock 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.

Manufacturers publish recommended values for the FOC e.g an FOC of 7-9% for aluminium shafts, 11-16% for ACE carbon shafts. These values are largely based on the standard pile weights available for the shaft. In practice recurve archers often use higher FOCs by e.g. using specially made heavier tungsten points.

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.

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 total drag and the fletching action. As covered in the section on drag, the drag force on an arrow is split between two separate forces; one which acts through the arrow centre of gravity which acts to move the arrow and one which acts somewhere else, roughly around where the fletchings are which acts to rotate the arrow.

If you don't want to plod through the section on drag then A Rough Guide to FOC tries to give an idea of why FOC is so important to the drag properties of an arrow. The ideal FOC value for arrow flight performance is 50% i.e. the arrow balance point is at the front of the arrow. In reality for OR archery the maximum practicable FOC is in the low 20's. The limiting factor is arrow speed. For a given arrow shaft/nock/fletching all up weight the only way to increase FOC is to increase the point weight. Problem is increasing point weight increases overall arrow weight and hence reduces arrrow speed. For best arrow performance you need the best combination of FOC and arrow speed. For example the reason for the low recommended FOC of 7-9% for aluminium arrows is not that this is a good FOC value in itself just that if you try to increase the FOC value to a higher value the arrow speed drops to an unacceptable level.Overall arrow performance is lower.

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. You can break the total drag force on the arrow shaft into two components, a component that acts through the arrow centre of gravity which acts only to move the arrow (no rotation) and a second component located to the rear of the COG cog which acts like a fletching to rotate the arrow. The relative size of these two forces depends on the arrow FOC. If 'L' is the length of the arrow shaft and 'A' its diameter then the total shaft drag area is LA. The shaft area Fa which relates to the shaft drag force acting through the cog is approximately given by:-

Fa = LA(1-FOC/50)

This is only an approximation because any rotation (fishtailing) of the arrow will affect arrow lateral movement and also 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% this shaft drag area is around 80 x 0.5(1-8/50) = 33.6 square cm

with an FOC of 16% this 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 this shaft drag area by about 2%.

The overall fletching area with respect to how the arrow flies comprises three elements:

- the effective area of the fletchings
- the shaft fletching area
- vortex shedding torque (expressed as an area)

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 a 7% FOC the shaft fletching area = 5.6 square cms
with a 11% FOC the shaft fletching area = 8.8 square cms

As what is important physically is the turning moment generated on the shaft from the fletching areas let's look at this from this viewpoint taking moments with respect the shaft centre of mass

The shaft fletching effect drag Fs = FOC x KLA/50 (where K is the area to drag force constant).

The turning moment on the arrow from the shaft drag is FOC x KL2A/100

Assume we have fletchings with the centre of pressure at distance P behind the shaft centre with a fletching effect drag of Ff. Then the turning moment on the arrow from the fletchings is Ff (P + FOC x L/100).

The total turning moment on the arrow T = FOC x KL2A/100 + Ff (P + FOC x L/100).The equation for T illustrates how the arrow length, area, FOC and fletching position affect the turning moment on the arrow. This combined with the arrow rotational moment of intertia determine the stability of the arrow.

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 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. The FOC value effects the torque on the arrow from the fletching area and defines the area of the shaft that acts like a fletching. 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 fletching response increases with FOC.

Having a high FOC for an arrow provides two principal benefits - better arrow groups and reduced wind sensitivity. When you aim at the gold but the arrow ends up in the black something must have changed the direction of the arrow. An arrow mechanically has to leave a bow going in the direction it was pointed and with its axis very closely aligned with the direction it's going. The arrow changes direction after it leaves the bow and the cause is arrow rotational energy (cartwheeling). The arrow flies in a curved path until this kinetic energy is removed by fletching drag (the stabilisation distance). Having a higher FOC results in faster energy dissipation (more fletching action) and because the overall drag force (net momentum) moving the arrow sideways is smaller the amount the arrow direction is changed is reduced. The result is more forgiving arrow to bad tuning or a poor shot leading to reduced group sizes. In a wind the faster arrow rotation rate results in reduced wind drift.

The downside to a higher FOC is because the offset angle between the arrow axis and the direction it's going will in general be smaller, the drag on the pile will increase; lift from shaft drag will be reduced and probably the arrow will be heavier and hence going at a lower speed. All these factors result in 'loss of sight mark'.

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. Also because of the low FOC a lot of drag lift was being generated. Competitors were throwing javelins over 100m which was too for far safety at most stadiums. A couple of years ago the regulations were changed increasing the required FOC value. Now javelins rotate and stick in the ground nicely. The increased rotation rate has reduced the vertical drag component and the distances being thrown have been reduced to within safety acceptable distances.

An FOC calculator is available if required.

FOC is a key consideration of the arrow selection process. The attached spreadsheet illustrates a an arrow selection process incorporating FOC. FOC for arrow selection

Fletchings Versus FOC

Shoot an arrow with no fletchings and a large enough FOC and the arrow will fly straight. Shoot an arrow with zero FOC and large enough fletchings and the arrow will fly straight. Both fletchings and FOC will create arrow flight stability. Both fletchings and FOC have pluses and minuses associated with their use. In practice we use both together. Which of the two is more useful and what limits are their on the two approaches.

Fletchings:

The larger the fletching area the larger the drag torque on the arrow. The first limit on fletching size is that the arrow must pass the riser cleanly so there is a height restriction. The second limit on fletching size is balance between the fletching torque and overall lateral drag. Too large a fletching area and the overall "wind drift" drag effect exceeds the benefit of the higher drag torque. This is particularly true shooting outdoors as you have the external wind lateral drag effect as well as the internal lateral drag effect from fishtailing/porpoising. Larger fletchings weigh more so increasing the area reduces the arrow speed and reduces the arrow FOC.

FOC

Increasing the FOC increases the drag torque on the arrow from both the fletchings and from the arrow shaft areas. It does this without any increase in the overall "wind drift" drag area. Increasing FOC is done by increasing the point weight and the increased mass reduces the overall arrow "wind drift" acceleration. The two practical limitations on FOC are the increase in point weight which reduces the arrow speed to the point where it impedes the use of a bow sight and, as there is a restriction on the diameter, the increase in point/insert length results in an unacceptable strength for the point as regards target impact.

Last Revision 8 April 2014