Introduction

In the section on the principles of bow tuning it was mentioned that the tuning setup with respect to arrow group sizes was dependant on the wind and the compensating aim-off angle (windage adjustment) used when a wind was present. This section will expand on this idea and describe what I call a 'variable tuning' approach aimed at reducing group sizes compared with a conventional tuning approach. In the following discussion I am only going to consider what happens in the horizontal plane to the arrow.

 With a conventionally tuned bow, i.e. no arrow rotation with a perfect shot, you get a group pattern fairly symmetrical around the perfect shot (the 'x' that hits the center of the target). When shooting in a cross wind the archer adjusts the windage so that the perfect arrow again hits the middle but the arrow group is no longer symmetrical. The arrow group extends much further down wind than it does upwind (wind direction is from left to right in the above diagram). If we first understand why the arrow group gets stretched in the down wind direction then we can come up with a strategy, variable tuning, which will reduce this stretching effect hence overall reducing the arrow group size.

The photo (courtesy of Rick McKinney) illustrates the downwind stretching that occurs with arrow groups even with top archers. For the average archer the resulting groups would be nowhere near as compact.

Conventional Tuning Behavior

The section on Fletched Arrow Flight describes how arrow groups are created by the horizontal rotation that the arrow has when leaving the bow changing the direction of flight of the arrow. If the variation in rotation the arrow has around the perfect shot is much the same in the clockwise/anticlockwise directions then the arrow group distribution, with no wind, will be more or less symmetrical around the perfectly shot arrow. Once you have a cross wind this symmetrical behavior disappears. The following diagram illustrates the basic difference.

 Strictly speaking the asymmetry comes from the change in the wind vector and how this interacts with respect to the arrow orientation. Though technically incorrect I will describe the effect by separating the horizontal drag effects from the wind and from the arrow velocity. The drag force on the arrow from the wind always acts in the same direction (left to right in the diagram). The drag force on the arrow is in the same direction as the wind drag if the arrow comes off the bow rotating clockwise and in the opposite direction if the arrow leaves the bow rotating anticlockwise. The total sideways drag force is the 'sum' of the drag from wind and from arrow velocity. i.e. the total sideways drag force, and hence sideways arrow acceleration, will either be the sum or the difference between the wind and arrow velocity drag effects. There is a big difference in the arrow's sideways acceleration between the arrow offset angle being in one direction or the other. The drag force not only moves the arrow sideways it also rotates the arrow. Again as the drag force varies on the fletching area the angular acceleration of the arrow will also vary. This variation in sideways drag not only happens when the arrow leaves the bow but during the the flight of the arrow. As the arrow fishtails about the wind and arrow velocity drag forces will, depending on the orientation of the arrow, reinforce or oppose each other at different points in the arrow's flight. The following three graphs illustrate the behavior of an arrow when having to aim off in a cross wind. In all three graphs the cross wind direction is upwards i.e. right to left. The example archer normally groups within the blue with no wind at 90 meters and is shooting in moderate wind of around 10 mph.

The graph represents the 'perfect' shot which hits the center of the 10 at 90 meters. When the arrow leaves the bow ('straight' in the aim off direction) the wind rotates the arrow in a fletching downwind direction (negative angle) and so initiates the fishtailing of the arrow. At no point during the flight of the arrow does the arrow angle go sufficiently positive (fletching upwind) so that the wind drag reinforces the arrow velocity drag in the horizontal direction.

This graph represents one extreme of the archers variability. In this case the arrow leaves the bow with the fletching downwind and the fletching end of the arrow rotating in the downwind direction. Because the fletching is already rotating downwind the arrow gets minimal, zero or even negative rotational net push on the fletching in the downwind direction. As a consequence the initial arrow rotation is less than for the perfectly shot arrow. At no point during the flight of the arrow does the arrow angle go sufficiently positive (fletching upwind) so that the wind drag reinforces the arrow velocity drag in the horizontal direction. The arrow ends up hitting upwind of the center of the target much the same as for the no wind condition.

This graph represents the other extreme of the archer's variability. In this case the arrow leaves the bow with the fletching in the upwind direction and with the fletching end of the arrow rotating into the wind. In the initial part of the flight the horizontal drag forces from wind and from the arrow's velocity reinforce each other so you have a high downwind acceleration (first green bar). This acceleration basically cancels out any benefit from aiming off. The combined wind and arrow drag also give the fletching a larger initial push so the amount the arrow swings about is higher than the two previous cases. The period between distances around 10 to 40 meters works for the archer because due to the high rotation in the fletching downwind direction and corresponding shaft angle there is a considerable arrow acceleration in the upwind direction which starts to move the arrow back towards the target center. What does the damage to where the arrow hits is when the arrow swings back (second green bar) so that the horizontal drag forces again combine to accelerate the arrow in the downwind direction. In this case the arrow hits the target at 90 meters before the upwind shaft drag acceleration can recover any of the lost ground.

The relevant points relating to group sizes when shooting in a wind (and appropriate to this discussion) are:-

Aim Off Angle:- The more we rotate into the cross wind so that the perfect shot hits the center of the target then the lower the horizontal drag force from the wind on the arrow will be. The aim off angle will increase if the wind strength increases or if the target distance increases.

Initial Arrow Rotation:- We get an initial  high downwind arrow acceleration and a lot of arrow rotation if the arrow leaves the bow with the nock end rotating in the up wind direction.

Arrow Rotation Period:- If the arrow rotates through a full cycle during its flight combined with an adverse initial arrow rotation then the result can be a large downwind impact. The degree the arrow hits downwind also depends on the target distance with respect to the arrow rotation period. The deviation of the arrow from the target center increases/decreases with distance as it is the combination of distance and rotation period that determines how far away from the center the arrow is at any distance.

Bear in mind that the above items are not independent of each other.

Variable Tuning Strategy

Aim off and arrow rotation properties can only be changed by modifying the bow or arrow setup with wind strength and distance. Serious convention tuning involves looking at the variation of group size with distance caused by fishtailing and selecting optimum sets of arrows for each distance. The majority of archers will stick with one set of arrows. For example the graph illustrates the effect of increasing the fletching size for the same case as above where the arrow leaves the bow with the fletching rotating upwind. In this case the shorter arrow fishtailing period acts in the archer's favor.

The one thing the archer can easily control by adjustment of the plunger button pre-tension is the variation in angle/rotation of the arrows that the archer shoots. The key is to prevent any arrows coming out of the bow rotating nock upwind. Increasing spring tension will result in the arrow leaving the bow with the nock of the arrow having more rotation towards the bow (RH archer) and decreasing spring tension the opposite effect.

In the diagram the green circle represents the archer's typical group (no wind). If the button spring tension is increased to move the group to the left until the right hand side of the group is near the middle then all the arrows are leaving the bow with the fletching rotating towards the bow to some degree. The 'worst' shot has the arrow leaving the bow straight.. The spring adjustment from the green group to the red group represents the maximum spring adjustment required for a variable tuning approach  for a left to right wind. The blue group represents doing the same for a right to left wind by decreasing the button spring tension. These variations in spring tension my be limited by requiring good arrow clearance.

When shooting in say a right to left wind by decreasing button spring tension you can avoid most if not all arrows having the horizontal wind plus arrow drag situation which in theory can reduce group sizes. (The headache as with conventional tuning is that group size goes up and down as shooting distance increases). It should be pointed out that spring tension adjustment is not a substitute for aiming off, the spring tension should be tweaked and then the required aim off determined.

What all the above boils down to is that the optimum tuning set up as regards button spring tension is not  fixed but is dependant on wind conditions. The actual optimum setup is a complex interaction of the arrow and wind properties. Using the flight simulator you can determine for a given situation this optimum setup which can produce significant group sizes over a conventional tuning approach. (See the graph in the section on bow tuning). In practice of course you can never get this optimum setup but the simulator indicates that a button spring adjustment in the right direction (towards the optimum tuning setup) can reap appreciable benefits over a conventionally tuned bow.

Practical Experience

Theory is fine but its where the arrows go that counts. As far as I know no serious testing of the above concept has been carried out. When I first came up with the idea of variable tuning a few years ago I tested it using a standard button modified so that I could easily manually adjust the button spring tension. The problem with this was that I kept losing the zero (the conventially tuned) spring setting. In order to implement a variable tuning strategy you need a plunger button with a calibrated spring pre-tension system so that you always know where you are and can always reset to zero. In practice this means you need a Beiter button. My subjective views based on trying out the idea are as follows:

At distances up to around 40/50 yards tweaking the button spring appear to have no effect on group sizes. (this is what you would expect as the arrows would not have completed a full rotational cycle and the groups are small anyway)

At distances 60 to 80 yards there was a subjective reduction in group sizes. On occasion the group sizes seemed to be significantly reduced. (This may be me just having a good day or possible getting the spring setting right on the button (pun intended)).

At 100 yards adjusting the button spring  seemed to make no difference to the group size.

The following two graphs (generated using the arrow flight simulator) shed some light on the subjective results obtained above from using the variable tuning approach. Both graphs plot how far the arrow hits horizontally from the target center in cms (the vertical axis) as a function of the amount and direction of horizontal arrow rotation off  the bow (negative rotation = nock end of arrow rotating downwind). A comparison is made between where the arrow hits with a wind and with no wind. In both wind and no wind cases the perfect arrow hits the target center. The comparison is made at target distances of 90 meters and 60 meters.

The main point from the this curve is that you only start to suffer from the downwind stretching of the arrow groups when the arrow rotation goes over the value of around 4.5 (the point where the wind curve starts to lift above the no wind curve). This point corresponds on the target to around the blue 6 ring. So if your arrows go mainly in the gold and red you will see no benefit in general from a variable tuning approach at 90 meters. However using variable tuning will not make any significant change to the group size (the two curves are very similar with negative rotation) and could reduce the consequences of the occasional howler.

At 60 meters distance the wind curve starts to lift above the no wind curve when the arrow rotation goes over the value of around 0.5. This corresponds on the target to around the gold 9 ring. So unless all your arrows go in the 10 ring at 60 meters there will be a significant reduction in group sizes from using a variable tuning approach.

It should be noted that the above curves are based on the physical properties of my arrows and evaluation of the possible benefits are based on my typical arrow groups. While the general shape of the curves will be generally applicable any individual archer needs to run the above simulation based on their specific arrows and evaluated with respect to their specific arrow groups. (Of course there is no real substitute for actual shooting).

Conclusion

The idea of a variable tuning as a practicable strategy is currently an untested idea but may be worth looking at. One problem is that many archers tend to regard a tuned bow as a fixed thing. Having spent a lot of time and effort tuning the bow for a no wind condition hearing that as soon as a wind blows the bow is not tuned anymore is not going to be popular.

A second problem is that currently there is probably not a plunger button on the market useable by elite archers to implement a variable tuning approach. If one takes a Beiter button as an example, this button has 10 click stops for one rotation of the spring tension adjustment knob. At 70 meters let's say one click stop moves the arrow group sideways by 5 cms. If your horizontal group width at 70 meters is 30 cms. (average archer) then a variable tuning strategy will require a maximum spring adjustment of 3 click stops. If on the other hand your group width at 70 meters is 8 cms (elite archer) then the maximum spring adjustment required is less than 1 click - you can't do it, there is insufficiently fine adjustment of the spring tension. (This comment is not of course a criticism of the Beiter button).