There are two aspects to distance tuning, the bow setup and the arrow setup. These two aspects are not independent so as with any form of tuning it's a case of going round the loop on an iterative basis until no further improvement can be detected.

The basic concepts behind bow and arrow tuning with distance have already been covered in previous sections so here the various relevant bits are just pulled together as a package without repeating all the details.

Bow Setup

Minimum group size for a specific distance is dependant on the rotation in the vertical plane that the arrow has when it leaves the string. If there was no gravity then the optimum set up would be zero rotation in the vertical plane for all distances. With gravity the optimum bow exit rotation for a specific arrow and arrow speed with respect to minimizing groups is a function of target distance.

You can basically split "tuning" into coarse adjustment (limb angle, Center shot, bracing height) and fine adjustment (nocking point position and plunger button spring). Only fine tuning adjustment is being considered. Unfortunately arrow exit rotation in the vertical plane is affected by both nocking point position and button spring tension (it's assumed the bow setup is such that the arrow rest has no effect on arrow rotation). The assumed process is to set the nocking point and then adjust the button spring for zero arrow rotation in the horizontal plane (the more important of the two rotations) and live with the consequent change in vertical arrow rotation, going round this loop as required. Adjustment is made on an incremental trial and error basis looking for the optimum.

Tuning for distance is a bit of a "black art" with no defined procedure that I know of. There are (at least) two possible processes that seem to be used. One is to measure how the arrow group size varies directly at specific distance as the nocking point is changed, the other is to look at the variation in hit height difference between fletched and bareshaft arrows. Which ever process is used what distance is it done at?

Using an arrow flight simulator an assessment is made of the two processes and they are compared to the basic tuning 'zero vertical rotation' situation. Arrows are assumed always to have zero rotation in the horizontal plane so the groups used are the two dimensional vertical arrow spreads. 'Typical' values for the bow/arrow system are assumed and for the archer's skill level. As the 'best' tuning process will depend on both these factors the following table should be regarded as indicative only. To allow for the change in face size the group sizes at 50m and 30m have been weighted by a factor of 122/80 so that group sizes can be correlated to scored points value.

In the above table, each column represents a different bow (nocking point position) setup. e.g. for the 90m column under Minimum Group Size the bow is tuned to minimize the group size at 90m (0.78) and the consequent groups at 70m, 50m and 30m presented in the same column. The Bareshaft/Fletched Hit columns work on the same principle except that in this case the nocking point is adjusted so that the fletched and bareshaft arrows hit at the same vertical height for the specific distance, specified at the top of the column . The Basic Tune column gives the group sizes at the different distances assuming zero vertical arrow rotation on bow exit. Total Size is the overall (weighted) group size for all distances combined for that setup. Each Total size is normalized to the Total Size for the Minimum Group Size at 70m.

The best setup overall is obtained by minimizing groups at 70m. Using the bareshaft method at the longer distances also performs very well (bareshaft at 90m comes second overall). Tuning by whatever means at 30m does better then at 50m - don't ask me why! There was an anomaly at 50m in that it was not possible to bring the bareshaft down to the same height as the fletched shaft, possibly a combination of the bow angle and the rotation properties of the arrow. The 'basic tune' on the whole did not work as well as the group size or bareshaft methods. This is anyway a bit artificial as it more or less corresponds to the 'bullet hole' tear in a paper tune approach. In practice a basic tune is going to be more like the 30m bareshaft column which works well.

When actually tuning for distance it may practically be a case of first determining the best strategy for a particular archer's skill and equipment and then actually doing the tuning. An approach something like the above table is required for real rather than a simulation. Using a bareshaft approach at long distance (again limited by archer's skill) is a fast method of getting into the right area followed up by tuning on a group size basis.

A clever idea that archers report using is that once a tuning setup is established it is referenced by recording the relative hit positions of fletched and bareshaft arrow group centers at a specific distance. If say the bow is disassembled/reassembled instead of repeating the whole group tuning process the setup is adjusted to recreate the reference value. e.g. for the 70m group tune in the table above at 30m the bareshaft would hit around 20cms vertically above the fletched shaft.

Arrow Setup

The arrow has essentially already been selected before the distance tuning procedure begins for its tuneability, FOC, speed etc. The factor which has a secondary influence on group size is the arrow fishtailing amplitude and period as it relates to the target distance. A less then perfectly shot arrow ends up traveling in a different direction to that shot, the main source of groups. Superimposed on this is the side to side movement of the arrow resulting from fishtailing (up and down movement from porpoising is difficult to identify and is assumed to be incorporated in the nocking point tuning process). Using very 'ball-park' numbers, with an average/poor skill archer the fishtailing amplitude can be around 25% of the total group size and for a reasonable/good skill archer around 35%. Taking the fishtailing wavelength as the travel distance for the arrow to complete a side to side movement cycle the associated wavelengths are around 60m and 100m.

This graph illustrates what happens for the poorly shot arrow. The black line is the nominal post stabilization arrow direction. The actual arrow path (blue line) oscillates around the nominal arrow direction. The archer loses out badly at 30m, gains slightly at 50m, no gain/loss at 70m and loses out to some extent at 90m.

This graph illustrates what happens for the well shot arrow. The fishtailing wavelength is much longer so the archer loses out at all distances apart from 90m where some benefit is gained.

The only practical way the fishtailing effect can be modified (in the archer's favor) is by playing around with the fletching size and position (which is mainly limited by the wind sensitivity of the arrow). This graph illustrates the effect of increasing the fletching size for the good archer by varying amounts. The larger fletching result in more rapid stabilization and smaller groups anyway but the effect on the arrow fishtailing is to reduce both the amplitude and wavelength.

For the 44%,67% and 89% increased size over the standard for example the groups at 90m remain much the same while getting an improvement with a reduced 70m group size. Increasing fletching size shows diminishing returns but the main penalty is incurred if the fletching size is too small.

In practice it's difficult (short of an archery equivalent of Hawkeye) to determine fishtailing behavior. The only approach would be to measure group width variation by moving forward and backwards around a specific distance.

It is unlikely, but possible that arrow fishtailing can give a false indication of a tuned button. With a badly tuned bow both the bareshaft and fletched arrow will fishtail and its possible that the two arrows could coincidentally hit at the same horizontal position. A walk back/up approach clarifies such a situation

The attached graph illustrates how this 'false tune' can occur. In such a situation there is always going to be a significant lateral displacement of the arrow. When tuning getting the eye, plane of bow and sight pin in line will always reduce any problems.

Summary

Distance tuning is as stated previously a bit of black art and requires understanding what you're doing combined with experience of doing it. While the above comments don't supply any answers they hopefully cover some of the considerations.