One of the areas for recurve archers which seems to result in sleepless nights and hair loss is arrow selection. i.e which arrow shaft should I get and what pile weight should I put in it. The following is a suggested method for selecting arrows using a systematic approach. As usual there is no better method than trying different arrows for real and seeing how they group, but in general this is not a feasible option. I'm assuming up front that you know your arrow length and draw weight
Use an arrow selection chart/program to get a set of alternative arrow/pile combinations which are recommended as likely to work well with your bow.
The arrow selection charts are 2D, from your arrow length and weight you get a recommended set of alternative shafts. If you use Bloggs Corp. chart they are obviously only going to recommend Bloggs' arrows so using a multi-manufacturer chart is better. If you only have Bloggs' chart then you can use the suggested Bloggs spine range of the recommended arrows to include other manufacturers arrows in the initial pool of arrow shafts.
Arrow selection programs are 3D, from the information you put in you get a recommended set of shafts and associated pile weights deemed to work well with the bow. If the program vendor is commercially neutral than you get recommended arrows from different vendors and the arrow database is hopefully regularly updated.
Note that arrow selection charts/programs only try to give you a set of alternative arrows that will work well with the bow, they do not tell you the 'best arrow' for you to shoot.
If an arrow shaft is too weak then the arrow will hit the bow on the way past, you will have a clearance problem. If the arrow is too stiff then you won't be able to tune the setup. With an arrow selection chart/program you are identifying arrow shafts that fit into the 'window' between these two limits i.e. arrows that will have good clearance and be tuneable. Different shafts in the window will vary in how forgiving they are to archer variability in terms of sensitivity to the angular momentum the arrow has leaving the bow but this effect is far outweighed by the requirement to have an arrow with good (flight) grouping properties. Because of this arrow selection programs do not have to be particularly accurate - just identify shafts that are somewhere around the middle of the window.
The fact that arrow selection programs do not have to be very precise is lucky because there is currently no available method for an archer to accurately match an arrow to a specific bow. (People who create mathematical models of arrow behaviour on the bow have I think some optimism that this might at some time be feasible, but I would put this into the 'blue sky' category). A major factor in selecting a good arrow match are the properties of the bow (limb geometry, mass properties, elastic properties etc. etc. etc.). With the arrow selection charts for a recurve the matching arrows are defined against the arrow length and draw weight. The basic assumption is that at any given time all the current recurve bow properties are much the same, so all bows with the same draw weight will have more or less the same properties. On the whole this works pretty well though in some cases, if say the limb design is radically different, the standard selection charts fall over to some extent. If on the other hand you tried an arrow match with a 25" bow 40# draw then the tables wouldn't work. The same applies to some extent to the arrow properties (material density, elasticity etc.), all arrows are assumed to have similar characteristics. It is because the selection tables are based on the typical properties of archery kit at a given time that the selection tables have to be periodically revised (or in the case of an arrow selection program a recalibration has to be carried out). Bow/arrow design does change, if slowly, over time. As long as there have been bows there has probably been an empirical approach to arrow selection which in principle hasn't changed much, even though these days it gets wrapped up in fancy looking computer programs. For an overview of the methodologies suggested for arrow selection procedures see The Archers Paradox & Modelling A Review
Whittle down our initial pool of arrows on the basis of the specific archer's requirements. These are to some extent unpredictable but I'll mention a few of the obvious ones.
How much you're prepared to spend is the first one. If you only want to spend X on a dozen arrows then any arrow set costing move then X can be removed from the pool.
If you want arrows for indoor shooting only and you are a 'fat arrow line cutter' enthusiast then only the maximum diameter aluminium arrows are of interest. The selection will probably be influenced by having enough shaft wall thickness so you're not replacing damaged arrows every week.
If you have a low poundage bow and want to shoot 90 metres then the overall arrow weight (i.e. arrow speed) becomes important. There are a number of tools around for calculating arrow speed and relating this to arrow range. (e.g. pin tape programs). You may end up with a requirement that the all up weight of the arrow has to be less than X and so all heavier arrows can be removed from the pool.
Try to determine which of the arrows remaining in the pool will give the best result in terms of having the smallest arrow groups i.e overall the most forgiving arrow.
Most of the work in having a good flying arrow has already been done by the arrow designer. There would not be much point in selling an arrow which works fantastically well on the bow and flies like a pig.
Modern bows are very tunable so the differences between the arrows left in the pool with respect to how they behave on the bow are far outweighed by how they fly. What moves the arrow off the target centre is drag so we need to choose the arrow from the pool with the best drag characteristics. Basically were looking for the arrow with the best combination of minimum diameter, maximum fletching effect and rotation speed.
Unfortunately there is no quick fix method of assessing how well an arrow will group. Arrows will vary in how they group at different distances and in different wind conditions. FOC is a reasonable guide, the higher the FOC probably the better the arrow flight performance. However overall flight performance depends on more than just the FOC so the highest FOC arrow may not be the best. For a downloadable program aimed at trying to identify, "which of the possible arrows may be the best" see the Program downloads page
Having purchased a new set of arrows the final part of the selection process is selecting from the set the subset of arrows to be the 'competition set'. There will be physical differences between arrows in a nominally identically set which will result in the arrows hitting at different points contibuting to increased group sizes. Is it possible to select the best subset of arrows i.e. identify arrows which are physically the closest match in terms of how they behave in flight?
There are three factors which contribute to where the arrow hits, the arrow's physical properties, systematic errors and random errors. Systematic errors result from the equipment setup (including tuning) and from how the archer shoots (i.e. an archer may have a tendancy towards a repetitive error e.g. arrows tend to go high right or whatever). Random errors result from each shot the archer makes being slightly different with no systematic structure to the variations.
Although these three factors to some degree interact with each other in terms of where the arrow hits the up front hypothesis is that the effects of systematic errors are relatively consistent between physically different arrows and that random errors are treatable using a statistical approach. The following diagram illustrates this assumption.
The 'nominal position' is where a 'physically standard' arrow would hit
with no systematic or random errors. The relative positions between the
centres of the groups for the individual arrows is determined principally
by the physical differences between the arrows,
As a quick test of the above hypothesis the behaviour of three physically different arrows is looked at using the arrow flight simulator for where the arrows hit and the Arowmaster program (Ref 1) to analyse the hit patterns. The physical difference used is the shaft weight; there is a 'standard' arrow, one with a shaft 3 grains heavier and one with a shaft 5 grains lighter. The systematic error used is a slightly mistuned bow.
The following diagrams illustrate the effect of the systematic error. The arrows are assumed to be perfectly shot with no random error.
The arrows in this case are bareshaft. The vertical arrow hits (black
dots) down the target centre are for the case with no random or systematic
error. The hit near the middle is the standard arrow, the hit above it the
light shaft and the one below it the heavier shaft. The three hits to right
and down are the same three arrows with the added effect of the systematic
error.
With no systematic error the distance between the standard shaft and the plus 3 grain shaft is less than the diference between the standard and minus 5 grain shaft. The differences between the arrow hits is proportional to the physical differences between them.
With a systematic error introduced the relative positions between the arrow hits remains proportional to the physical differences between the arrows. In fact the effect of the arrow physical differences appear to be somewhat exaggerated presumably due to the interaction between the physical difference and the systematic error.
This diagram represents exactly the same case as the previous one except
that the arrows are now fletched. The fletchings unsurprisingly greatly reduce
the effect of the systematic error. A consequence of this is that the differences
between where the arrows hit with respect to their physical differences
are also reduced. This suggests that using bareshaft arrows for arrow selection
is likely to be a more sensitive approach than using fletched arrows.
To the situation described above is now added the random error resulting
from the archers variablility. The basis for selecting the archer's skill
level is that the archer will put all the bareshaft arrows shot on the target.
Note that the arrow flight simulator assigns 'random' variations in a systematic
way so three arrow hit distibutions do follow a pattern. The centres of
the individual arrow hit distributions are calculated with Arrowmaster.
In this figure the black dots represent the arrow hits for the three arrows.resulting
from physical difference, systematic error and random error. The 'sight
pin' has been adjusted to get all the arrow hits on the target. The green
dots are the calculated centres of the individual arrow groups for the three
arrows. Again the relative positions of the individual arrow group centres
proportionally relate to the physical differences between the arrows.
This result seems to support the origional hypothesis that it is possible to select a best set of arrows from an overall set by analysing the arrow hit patterns.
This figure represents the same case as the one above except that the
arrows are fletched. The actual individual arrow hit positions are illustrative
only as the resulting groups were so compact. Again the relative positions
of the individual arrow group centres are proportional to the physical differences
between the arrows.
On a practical note if an archer's skill is such that that the groups when shooting the test set of fletched arrows is such that arrows are hitting each other then this is a fairly pointless exercise as you may end up damaging the arrows in the process of selecting them.
Another consideration that needs to made during the arrow selection process is the group size of the individual arrows. The physical arrow difference plus any systematic and random errors may result in significant differences between the group sizes of individual arrows. At the end of the day what you are looking for is a minimum overall group size for the set. The best set selection would be made on selecting arrows where the arrow group centres best 'group' but possibly excluding arrows which show a proportionally large individual group size.
A detailed description of a process for arrow selection has been given by Vittorio Frangilli (Ref 2). The procedure described here differs from the above approach in that selecting the best set is based on overall group sizes of the set rather than biased towards arrow group centres. When selecting arrows on a 'manual'. basis I think using group sizes is the only realistic approach. To work with group centres sensibly requires a number cruncher like Arrowmaster. Intuitively I feel that using group centres rather than overall group size is a preferable approach for a couple of reasons. The group centre positions relate more directly to the relative physical characteristics of the arrow than the group sizes as the effect of archer's variability is largely eliminated. Arrow selection is done under a particular set of environmental conditions. Tournaments will be shot is different conditions (e.g. wind). The relative behaviour of arrows will more closely match to the group centres than to the arrow hit distributions. Frangilli also points out correctly that arrow selection based on group sizes is only for the better archer (he suggests around 1200 Fita minimum for a recurve archer). This limitation results from the archer's variability being an integral part of the selection process. Using a group centre approach the average archer can use and benefit to some degree from an arrow selection procedure.
Recent update (2015) on the arrow selection process from Vittorio Frangilli.
Description of process on Archery Talk
Ref 1: Arrowmaster
Ref 2: Vittorio Frangilli, Arrow Selection, Archery Focus, Jan/Feb 2002
Last Revision 1 July 2009