PRINCIPLES OF BOW/ARROW TUNING

Rick McKinney's book "The Simple Art of Winning" published in 1996 is the earliest reference I know of which made the correct connection between the alignment and rotation the arrow has when leaving the bow and the consequent effect on it's subsequent flight direction (called in the book "nodal planing"). The following pages attempt to put some technical substance to this topic hopefully leading on to a basic understanding of how the various tuning methods work and why the optimum "tuning" setup for a given archer/arrow/bow combination is dependant on target distance and wind conditions.

There is no "how to tune" guide contained here. There are lots of these around - some good, some not so good and some just plain silly. For what it's worth, in my view, the two best bow setup and tuning guides around currently are contained in "The Simple Art of Winning" - Rick McKinney and "The Heretic Archer" - Vittorio Frangilli.
As of 2008 now also have the Fita Recurve Tuning Manual- has to be currently the best overall bow set up and tuning reference.

All archers indulge in some form of bow tuning (or setup). The bow and arrows we buy have some degree of tuning built into the design and the archer usually carries out additional modifications to the setup to improve the tuning. This discussion presents an overview of what tuning is, why it makes a difference and looks in particular at what archers generally mean by 'bow tuning', the control of the rotation the arrow has when leaving the bow.

The following diagram is a schematic representing the elements resulting in an arrow hit on the target.

ARCHER ---> BOW/ARROW---> INITIAL FLIGHT PROPERTIES----->ARROW HIT

What determines where the arrow hits the target are the initial arrow flight properties (direction of travel, speed etc.) and the physical properties of the arrow (mass, length etc). If we replace the archer with a shooting machine which operates the bow/arrow system exactly the same way on each shot and the bow/arrow system responds exactly the same way on each shot then the initial arrow flight properties would be exactly the same on each shot. If all the arrows had exactly the same physical properties then every arrow would hit in exacly the same spot. In this case there would be no benefit to be gained from bow tuning.You adjust the shooting machine so the bow is pointing in the right direction to hit the target centre and then you get a perfect score.

Archers are not shooting machines (though some seem to get pretty close to it). The way the archer operates the bow each time will in some way be slightly different. As a consequence the operation of the bow/arrow system will be slightly different. The resulting initial arrow flight characteristics will be slightly different and as a result where the arrow hits will be slightly different. The following diagrams summarise what happens. In each graph the vertical axis represents the proportion of arrows shot.

Shot Properties

The archer tries to make each shot exactly the same (like the shooting machine represented by the vertical orange line). The archer will vary round this perfect shot represented by the blue line in the 'Archers Shot' graph. Most arrows will be shot at or near the peak of the blue curve. The further away you get from the perfect shot than the lower proportion of shot arrows (you hope) you will get. The variation in the archers shot will feed through to a variation in the initial flight characteristics the arrow has leaving the bow (the middle graph) and a consequent variation in by how much the arrow misses the centre of the target (represented by the third graph). Strictly speaking the shape of the curve in the third graph should be like a letter 'M' rather than the bell shape illustrated. The probability of making a perfect shot and hitting the 'x' is actually very small (otherwise 'Robin Hoods' would be a daily ocurrence).

At the end of the day what we want is to produce the lowest variation in where the arrow hits (minimise group size). There are four mechanisms utilised to do this.

The first mechanism is designing the bow/arrow system to minimise archer's variability in the first place.(It is this area which many of the archery regulations are aimed to cover). Installing a mechanism to check draw length (a clicker or a draw stop) will reduce variation in draw length and hence variation in arrow speed. Using a back (peep) sight or a bubble level will reduce variablity in aiming. Installing a set of pressure sensors in the bow grip so that an LED lights up when you have the correct bowhand pressure would reduce bowhand torque.

The second mechanism is designing the bow/arrow system so that the variations in the archer's shot produce the minimum variation in the initial arrow flight characteristics. (This is why there are two curves in the middle graph above. The archer's shot variation can produce different distributions of the initial flight characteristics). What is usually termed 'arrow matching' is a prime example of this. Selecting the right spine/pile weight for a particular arrow length/draw force will result in less initial arrow rotation with a poor shot then selecting the 'wrong' arrow. Another example is using a long sight sidebar. The longer the sidebar then the less error there is in the arrow direction for a given archer misalignment of anchor point, head position etc.

The third mechanism, which relates to the arrow design only, is minimising the spread of arrow hits on the target for a given distribution in the intial arrow flight characteristics. (This is why there are two curves on the right hand graph. A given distribution of the initial flight characteristics can produce different arrow hit distributions (groups) on the target depending on the arrow physical properties). The obvious example of this was the change over from aluminium to carbon arrows with their smaller diameter, higher FOC etc. Everybodies scores went up (unfortunately not due to everybody suddenly shooting better). Playing about with the physical properties of the arrow to reduce groups is a form of tuning though that is not what is generally understood by the term.

The fourth mechanism is what is generally understood to be 'bow tuning'. The archer's perfect shot will result in a specific set of initial arrow flight characteristics and variations from the perfect shot will result in variations in the values of these flight characteristics. The question is 'are there specific values of the initial flight characteristics associated with the perfect shot that minimise the arrow hit distribution (group size) resulting from the archer's shot variability'. Let's take each of the initial flight characteristics in turn:

Direction

Divorcing direction from arrow speed, there is clearly an optimum direction in which the arrow should be travelling when it leaves the bow to hit the centre of the target. This direction will depend on target distance, an uphill or downhill target and the effect of wind. Direction however is defined by the archer at the time of the shot. Anything one can do to minimise the effects of variation in direction are covered by mechanisms 1 and 2 above.

Vibration

I don't see any mechanism (other then the physical bending of the arrow at short distances) by which the amount of vibration the arrow has will significantly effect the arrow hit variation with archer's variability outside what is covered by the arrow matching process of mechanism 2 above. The optimum is presumed to be the minimum amount of vibration amplitude in flight (hence minimising vibrational drag effects) compatible with good arrow clearance during the arrow launch.
There have been a number of reports that on completion of a fine (group) tuning process at 70m the bare shaft ends up hitting to the left of the fletched shafts (RH archer). Arrow vibration amplitude/associated drag effects possibly coupled with the arrow rotation characteristics is put forward as a totally speculative suggestion as to the cause of this phenomenon and therefore vibration may have some small influence on group sizes.

Speed

Don't know the answer to this one. The problem here is that as you change the arrow speed you have to change the properties of the bow and the arrow and other factors like the archer's physique enter into it. At short distances I don't think speed matters. At longer distances my guess is that a 'higher' arrow speed will reduce group sizes for a given archer's shot variability compared with a 'lower' arrow speed. Whether there is an 'optimum' speed I have no idea.

Alignment

By alignment I mean the angle between the direction the arrow is travelling and the direction the arrow is pointing (sometimes called Nodal Alignment). As discussed elswhere the arrow misalignment can only be a small value and it does not have a significant effect on where the arrow hits. Having said that, the arrow leaving the bow straight is preferable.

Rotation

Arrow rotation is usually split between horizontal rotation (pressure button tuning) and vertical rotation (nocking point tuning) so I will do the same. In practice an arrow only has rotation (the combination of the horizontal and vertical components) and as a bow is always shot at angle the horizontal component is not horizontal but lets keep things simple.

Horizontal Rotation (Pressure Button Tuning)

Suppose we have an archer who shoots lots of arrows with a specific bow/arrow combination. We mount a camera above him and record how much horizontal rotation each arrow he shoots has when it leaves the bow. If we then plot a graph of the number of arrows that came out against the amount of rotation the arrow has then we get something like the following.

The arrow rotation with the highest number of arrows (the high point of the graph) represents the archers average (perfect) shot and the spread around it represents how much the archer varies around his average. The shape of the distribution indicates how good, i.e. how consistent on the shot, the archer is. For our imaginary archer the amount of rotation of the average shot (maximum number of arrows counted) is at value 'A' and the archer's variation in the shot goes from values A-2 to A+2.

The variation in arrow rotation is dependant on the archer, the bow and the arrow. For a given archer/bow combination different arrows will result in differing variations in rotation e.g. one arrow might give a variation of A+5, A-5 while another might give a variation of A+2, A-2. A part of the tuning process is the selection of the best arrow match giving the lowest variation in arrow rotation (mechanism 2 above). This is usually done by using an arrow selection chart.

If an arrow leaves the bow with horizontal rotation it ends up hitting the target horizontally displaced by some amount. This displacement mainly results from the initial arrow rotation (angular momentum) and offset angle with a small contribution from the arrow fishtailing about. We do another test, this time measuring the amount the arrow is displaced sideways for a particular amount of initial rotation. The thing we would notice is the amount the arrow is displaced increases faster than the increase in the value of the arrow rotation. In other words the distance between the arrows shot with rotations of 3 and 2 is bigger then the distance between the arrows shot with rotations 2 and 1, and this is bigger than the distance between arrows with rotations 0 and 1 (The vaules 0-3 are just numbers to represent the relative amounts of rotation)

Suppose we give the archer a bow and some arrows and he shoots them. By accident the average rotation value "A" for this setup is 2. The rotations of the archer's arrows will vary between 2 + 2 = 4 and 2 - 2 = 0 (using the variations from the average that were measured in the first test). We then give the archer another bow/arrow combination to shoot with. This time by coincidence the average rotation value 'A' is 0. The arrow rotations for this setup vary from 0 + 2 = 2 to 0 - 2 = -2. The attached diagram illustrates the arrow spreads obtained with the two setups. As can be seen the smallest spread, or group size, is obtained when the average arrow rotation value 'A' is zero.

The minimum arrow spread (group size) is obtained when the average arrow leaves the bow with zero offset angle and no rotation. The purpose of basic bow tuning is to get the setup so that the archers most frequent (i.e. perfect) shot meets this criteria. The fact that it is a statistical process does impact on the merits of the various tuning approaches that have been proposed. You can speculatively take the argument one step further. If the distribution of arrow hits produced by the archer is consistent and has a bias in one direction or another then tuning to match the arrow hit distribution, i.e. tuning to fit the archer's variability, would in theory produce higher scores then the conventional zero rotation approach. (Otherwise known as group tuning).

The fact that tuning relates to the archer's average and variation from it in shooting means that a statistical approach has to be applied to any tuning system. If you shoot one arrow though a paper sheet and it happens to be dead straight you can't just go off to celebrate. That arrow might be your 'A-4' arrow. A tuning approach either has to be based on looking at the same time at a lot of shot arrows like the test archer above or if the approach practically can only use a few arrows at a time, e.g. bare shaft tuning, it needs to be repeated lots of times and a composite picture built up.

A second consideration is the properties of the arrow itself. Sideways arrow movement type tuning approaches like bare shaft and walk-back relate to the variation of sideways drag force on the arrow with offset angle. The arrow weight, speed, rotational characteristics and diameter will affect how sensitive the tuning process is to the offset angle. For example compare bare shaft tuning with an ACC carbon arrow and an aluminium arrow. If we shoot the bareshaft carbon and aluminium arrow with the same initial offset angle and rotation, all other things being equal, the gap between the fletched and bare shaft arrows will be much larger for the aluminium then for the carbon arrow. The carbon arrow will probably have a higher FOC then the aluminium arrow resulting in faster arrow rotation. The sideways drag on the aluminium arrow will probably be greater than for carbon arrow because of the larger arrow diameter. It will be much easier to fine tune the aluminium arrow than the carbon.

There are two additional points to be made with respect to pressure button tuning which to some extent invalidate what has just been said.

The first point is arrow stabilisation. When an arrow is shot with horizontal rotation it initially 'swerves' until the effects of ths initial rotation are taken out by the fletching action. It obviously 'depends' but for your typical arrow (unless you are one of those archers who fit windmill sails on the back) it takes somwhere around 15-20 metres for the arrow flight to stabilize. At longer distances this doesn't matter but if you are shooting only 18 metres indoor the arrow is basically 'swerving' right up to hitting the target. The optimum tuning set up for short distances may be found to be different from the optimum tuning set up at longer distances.

The second point is that the assertion that the perfect shot should have zero rotation is based on the assumption that there is no external influence which affects arrow rotation between leaving the bow and hitting the target. Suppose as per the following diagram there is some 'magic gizzmo' located in front of the bow which adds angular momentum (rotation) to the arrow.

gizzmo If the arrow leaves the bow with no rotation then it leaves the gizzmo with rotation and hence the group size increases. If instead we adjust the bow so that the arrow leaves with just the right amount and direction of rotation to balance the gizzmo then it leaves the gizzmo with zero rotation and we get the minimum group size again. The general principle is that if there is something acting to change the arrow rotation between leaving the bow and hitting the target then the optimum tuning setup for the bow will not be zero arrow rotation. The optimum rotation of the arrow from the bow will be that which best counteracts the external influence to provide minimum group size. As any 'gizzmo' will in reality act over the whole arrow flight it is not possible to completely compensate for it, only minimise the increase in the sizes of groups.

Any wind acts like a gizzmo changing the arrow rotation. When shooting in a wind therefore it follows that the optimum initial arrow rotation (the button tuning) in terms of group size becomes dependant on wind strength, wind direction and the distance to the target.

The diagram illustrates the affect of a cross wind on arrow group sizes. The red lines indicate the flight paths and resultant group size for a representative archer with a perfectly tuned bow with no wind present. The blue lines indicates what happens in a cross wind to the same conventionally 'zero rotation tuned' archer/bow setup. The group size increases significantly. Most of the increase comes from the arrow (the zig-zag blue line) that comes off the bow with the nock end rotating into the wind. In this case the sideways drag force from the arrow's forward motion reinforces the sideways drag from the wind at a number of points during the arrow's flight and as a consequence the arrow ends up with a high downwind lateral displacement. The green lines show the flight paths and group size for a bow optimally tuned for the wind conditions and target distance. In practice you cannot optimally tune the bow for the current conditions. As a general guideline a good setup when shooting in a cross wind will require the arrow to leave the bow with the nock end rotating in the downwind direction. The key to having good groups in a crosswind is to avoid the sideways drag on the arrow from its velocity reinforcing the sideways drag on the arrow from wind. This topic is discussed in more detail in the section on Variable Tuning

Vertical Rotation (Nocking Point Tuning)

Much of the discussion relating to horizontal rotation applies equally to vertical rotation. There is one key difference in that in the vertical plane there is always an external force affecting arrow rotation - Gravity. Because the gravitational acceleration results in the rotatation of the arrow there is no optimum value for the initial vertical rotation of the arrow, it becomes a function of distance (time of flight and launch angle) as well as the arrow rotational properties. The basic tuning setting of zero vertical rotation for the arrow leaving the bow, although it works well for short distances will probably become increasingly unstuck as the target distances increase. In the case of wind the bow tuning is adjusted so that the arrow leaves the bow rotating in the same sense as will result from the action of the wind on the arrow.If you regard gravity as acting like a wind that always comes from one direction then gravity always rotates the arrow in the sense of pile down and fletching up so that should be the rotation direction of the arrow at launch resulting from the nocking point position. (Effectively a paper tune should show the fletching going through the paper slightly higher than the point). This makes the relative positions of the bare shaft and the fletched shaft somewhat unclear as far as nocking point tuning using the bare shaft method goes. At longer distances the bare shaft will hit higher than the fletched shaft (higher launch speed and higher initial lift force). At short distances as the arrows are launched rotating pile down the bare shaft will get less lift than the fletched shaft so it's maybe possible for the bare shaft arrow to hit lower than the fletched shaft. It will depend on a combination of factors.

It is not possible, short of having a height adjustable button/arrow rest assembly, to adjust vertical arrow rotation on the fly and any adjustment is limited by the arrow interaction with the arrow rest. So the general nocking point tuning guidlines (assuming you don't group tune) runs something like a) at short distances go for a zero rotation tune (bare shaft impacts same height as fletched shaft) and b) at long distances have the bare shaft impacting slightly above the fletched shaft. This of course assumes that there is no headwind/tailwind component which will also effect arrow rotation in the vertical plane. Short of having a set of strings with different nocking points for different distances and wind conditions then you end up with a some compromise nocking point setting. I'm told (before my time) that it was once fairly common practice for archers to use different strings with different nocking points at different distances. The practice seems to have died out.I suppose this is because arrows these days are faster/more forgiving and competition distances have essentially reduced to 70m and 18m.

The sections on Variable Tuning - Distance and Flight Instability relate to the nocking point tuning subject.The following graphs illustrate how the effects of gravity affect the basic principle of tuning as described above.

nocking point The graph represents the vertical displacement from the target centre (vertical axis) as a function of the amount and direction of rotation in the vertical plane of the arrow leaving the bow (the horizontal axis) at a target distance of 18 metres.. The data is produced using the arrow flight simulator for a specific set of arrow properties. A negative rotation represents a high nocking point (bareshaft impacts below fletched shaft) and a positive rotation a low nocking point. The red and turquoise horizontal bars represent the arrow rotation for the 'perfect' shot (rotation 0 and 6) and the width of the bar represents the variation in rotation from how much the archer varies from the perfect shot. The corresponding vertical coloured bars indicate the vertical spread (group size) of where the arrows hit resulting from the archer's variation. I have ignored the fact that the turquoise archer will adjust his bowsight so that his perfect shot has zero displacement from the target centre which will have some effect on his group size.

The overall shape of the curve through the zero displacement point is 'S' shaped. If the curve was a straight line then whatever the arrow rotation was for the perfect shot the group size would always be the same. In fact the group size for the archer with zero rotation for the the perfect shot is smaller than for the archer with perfect shot rotation of 6.

If there was no influence on arrow rotation after the arrow had left the bow then the curve would be symmetric about the zero displacement point and there would be a clear optimum setting for the nocking point position. The effect of gravity results in the curve being assymetric. At 18 metres the effect of gravity is small but you can see from the simulation that the curve risers faster with a positive rotation (low nocking point) than it does with a high one. The arrow (vertical) groups will for an average archer (wide-ish bar) be smaller if the nocking point is slightly high (bare shaft maybe impacts below fletched shaft).

nock 70 The 70 metres distance graph is generated in similar way to the 18m graph except it uses the Drift simulator. The curve still shows the arrow displacement rising faster with a positive arrow launch rotation. In this case the bare shaft arrow will invariably hit higher than the fletched arrow.

The model produces an interesting dog leg (in this case at a -1.6 rads/sec launch angular velocity) which occurs at a very clear "magic" point regarding the arrow flight parameters. Any suggestions about this point any whether it might relate to the "optimum" tuning setup would be welcome.


When it comes to setting a nocking point where you are going to be shooting different distances, e.g. a Fita round, then the only option is to look at the group sizes at the different distances and come up with the best overall compromise setting.

Tuning Principles - The Bow Aspects

It has been pretty much an 'open season' in recent years about inventing explanations for bow tuning. We've had arrow alignment, nodes, purple elephants, arrow vibration etc. None of these 'explanations' have agreed with known factual data or complied with Newtonian mechanics.

The above discussion shows that bow tuning is all about controlling the angular momentum (rotation) that the arrow has when it leaves the bow. For 'basic tuning' the bow is adjusted so that for the average shot the arrow leaves the bow with zero angular momentum. For 'group tuning' the bow is adjusted so that the amount and direction of arrow rotation for the average shot is that which results in the tightest groups. Arrow angular momentum on leaving the bow results from the overall torque generated on the arrow during the power stroke. What is termed 'bow tuning' is therefore all about adjusting the torque input into the arrow from the bow.

The archer has two basic arrow torque controls at his disposal the nocking point position (torque in the vertical plane) and the plunger button settings (torque in the horizontal plane).There are alternative methods of torque adjustment e.g changing draw weight but nock and button are the conventionally used controls.

How the nocking point position affects torque input into the arrow is fairly obvious, the higher the nocking point the more torque is generated by the string re rotation in the vertical plane in the point going down direction and vice versa. Torque adjustment is made by moving the nocking point up and down in response to the arrow behaviour in whatever tuning method you are using.

How the button effects arrow torque is more complex (and as yet not undersood in detail). Looking down on the bow and assuming a right handed archer then the following torques act on an arrow during the power stroke;

These torques are interdependant but fortunately the archer doesn't have to be concerned with the detail only the end result of having zero arrow rotation on bow exit. Centreshot position is a coarse adjuster of arrow torque. Increasing centreshot increases the overall anticlockwise torque on the arrow decreasing centreshot decreases overall anticlockwise torque. The required centreshot position is defined as reducing overall torque on the arrow to the point where arrow torque control becomes within the control of the pressure button spring adjustment. Centreshot position has nothing to do with 'arrow alignment' as is often quoted. Alignment of a bent stick doesn't mean anything anyway. The pressure button spring is the fine arrow torque controller. Increasing spring pressure increases anticlockwise torque on the arrow and vice versa. The final test that a correct setup has been attained whatever tuning methodology is used is that the button spring is in control of the arrow torque. e.g. with bareshaft tuning you must be able to move the bareshaft hit position from left to right of the fletched arrow with button spring adustment. If you cannot do this then the centreshot position is incorrect

Summary

The sources of angular momentum into the arrow comprise:

Horizontal rotation

Vertical rotation

The items above for the effects of the bow and string hands really relate to the archer's technique and the bow parameters are adjusted to include the effects of 'form'. The normal controls used to vary the net arrow angular momentum are the nocking point position and the plunger button spring tension. These are adjusted using some systematic process (the tuning method) to obtain zero angular momentum or minimum arrow groups. By selecting the correct arrow specification for the bow in the first place the arrow will leave with near zero angular momentum and only fine adjustment is required.

Last Revision 1 July 2009