Matching the arrows in a set by weight and nominal spine is not enough

The summary today

Two independent bodies of evidence say the same thing, and neither has archers shooting. The first comes from the test bench: within one nominal spine group the real stiffness varies a great deal, to the point that in a dynamic identification two neighbouring carbon spines, 500 and 600, come out indistinguishable, 34.5 against 35.3 Hz, while the factory figures predicted a clear difference. The second comes from the shooting machine: on fifty-nine Easton X10 shafts of the same spine, measured one by one and shot at seventy metres, out of two hundred and fifty-five combinations of parameters the closeness of the arrows on the target is best explained by mass, mean spine and the frequency with which stiffness varies around the shaft, that is by something more than weight and spine alone. The same measurement shows that the weight already varies in the shafts and the points, with ranges three to five times the declared tolerance, while nocks and vanes weigh almost the same, and that in the assembled arrows the range reaches 0.282 g: matching heavy points with light shafts would bring the range down to 0.027 g. The counterweight has to be stated. Those same fifty-nine arrows, not matched for weight, still held a vertical spread of 8.8 cm at seventy metres, that is inside the ten ring, which measures 12.2 cm. A calculation by the same group, on twenty-six dozen X10s that did not meet the declared weight tolerance, points the same way: within each dozen the arrows would stay in the ten, and points would be lost only by mixing different dozens. Matching matters, but it is not what separates a ten from a nine, and the step into practice, with archers and a set selected two different ways, has not yet been taken.

Also phrased as: "how to match a set of arrows"; "is weighing arrows worth it"; "arrows of the same spine differ"; "the arrow that always flies out"; "selecting competition arrows"

Evidence

• 2012
  For Model Published later

  A recurve model calibrated against bench measurements: an X10 550 tunes at 175.5 N and a ProTour 570 at 180 N, even though the X10 is four per cent stiffer, and the clearance needed at the button goes from eleven to nine millimetres. In the same model one extra percentage point of elastic modulus shifts the impact twenty-five millimetres to the right at seventy metres. It says the nominal spine does not identify the arrow, but it is a calculation on a single bow.

  Arrow behaviour in the lateral plane during and immediately following the power stroke of a recurve archery bow · James L Park

• 2012
  Context Equipment tests Published later

  Three new specimens of each of three Easton ProTour carbon arrow models, 380, 420 and 470, cut to 710 mm and measured with a laser vibrometer under free conditions: within one model the first bending frequency barely varies, 83.3, 80.2 and 78.3 Hz with a standard deviation of 0.4 Hz for all three, while at the eighth mode the standard deviation rises to 16.5 Hz for the 380 and 12.5 Hz for the 420. On the fundamental bending mode, the one closest to what spine sums up, specimens of the same model are very much alike, and the differences appear at the higher frequencies. Three shafts per model and no shooting, so it does not put a set to the test.

  Modelling the three-dimensional vibration of composite archery arrows under free–free boundary conditions · Marianne Rieckmann, James L Park, John Codrington, Ben Cazzolato

• 2014
  For Equipment tests Published later

  Seventy-nine arrows from the same production run, three shots each at twenty-five metres with the nock turned a hundred and twenty degrees: the index derived from the triangle runs from 1.53 to 10.8 mm, and within the batch the measured spine and the straightness vary over a wide range, with the ranking of the spread following the measured spine. In the rows reported, the lower spine values give spreads of 1.53 to 1.75 mm and the higher ones from 6.68 to 10.8 mm. The units of the two measures are not made clear in the text and there are no statistical tests. A correction has to be made on that index, because it does not measure the group's size: it is the mean absolute deviation between the lengths of the triangle's sides, and the article itself writes that it is zero both when the three impacts coincide and when they form an equilateral triangle of any size. It rewards regularity, not precision. The English abstract calls it mean absolute distance and the body mean absolute deviation, two different measures, and the declared property identifies the second. The neural network gives a test error between 1.51 and 1.71 millimetres, but the output's dispersion across the seventy-nine cases is not reported, so that error cannot be judged.

  A Study of Arrow Performance using Artificial Neural Network · Yeongsang Jeong, Sungshin Kim

• 2015
  Context Equipment tests Published later

  A sample carbon arrow declared as spine 500, taken apart and weighed piece by piece: total mass 20.62 g, of which shaft 11.70 g, point 6.20 g, vanes 1.41 g and nock 1.24 g, with the centre of mass at 0.414 m and an FOC of 0.093. The measured spine is 492 with an uncertainty of 3, which is to say it matches the declared figure. The author also recalls that the stiffness of a tubular shaft depends on the cube of the radius and only linearly on the wall thickness, which explains how much tiny differences in diameter weigh.

  Applications of Physics to Archery · H. O. Meyer

• 2016
  Context Equipment tests Published later

  Three models of hunting arrows from the same maker, twelve arrows each, all 30 inches long, shot by a machine with a 51 lb bow at about 40 m, three times per arrow with the nock turned 120 degrees each time: within the same model the factory measurements differ in weight (15.49 to 15.60 g in the lightest model, 18.98 to 19.14 in the heaviest), diameter, straightness and spine, and the mean distance of the three impacts from their centre ranges from 1.81 to 20.07 mm. The lightest model has the lowest mean dispersion, 6.85 mm against 7.53 and 8.76, but with no statistical test, and the study does not relate the factory parameters to the group of each arrow: it shows how much arrows of the same model vary, not that measured weight and spine are not enough to match them.

  Position coordinate representation of flying arrow and analysis of its performance indicator · Yeongsang Jeong, Suryo Adhi Wibowo, Moonjae Song, Sungshin Kim

• 2019
  For Equipment tests Published later

  Dynamic identification by stochastic perturbation on carbon, aluminium and cedar shafts: within one nominal spine group the estimated stiffness varies widely, for instance 853.6 N/m with a range of 175.3 between minimum and maximum for carbon 300, that is 21 per cent, and 490.8 N/m with 109.7 for carbon 600. Two neighbouring spines come out indistinguishable, the 500 at 34.5 Hz and 486.2 N/m against the 600 at 35.3 Hz and 490.8 N/m, while the factory figures led them to expect 679.7 against 566.4. Damping also varies widely between arrows of the same model. The authors write that they cannot separate production variability from the clamping error of the rig. Two cautions about the rig that the register should carry with it. The shaft is clamped at both ends and shaken at the centre, with no longitudinal load, so it is no closer to the condition of a shot than the static test the work means to get past. And the estimated damping, from 0.32 to 0.67, describes clamps and actuator rather than the shaft: at 0.32 the amplitude falls to 12 per cent in one cycle, while an arrow in flight flexes for many cycles. The comparison with «manufacturers' values» is moreover a comparison with a prediction of the authors' own, and it holds for carbon, within 4 per cent, while on aluminium 2219 the discrepancy is 28.

  Dynamic Characterization of Arrows through Stochastic Perturbation · Ryan Fish, Youzhi Liang, Kyle Saleeby, Jonathan Spirnak, Mingxiu Sun, Xiang Zhang

• 2019
  Context Equipment tests Published later

  One thing that does not count, in the same measurement: in cedar, grain orientation changes neither stiffness nor damping. In cedar 405 the stiffness is 891.6 N/m with vertical grain and 967.7 N/m with horizontal grain, in cedar 520 it is 592.2 against 525.5, and the damping ratios are equivalent. It helps bound the claim: what varies within a set is the stiffness itself, not the way the shaft is turned.

  Dynamic Characterization of Arrows through Stochastic Perturbation · Ryan Fish, Youzhi Liang, Kyle Saleeby, Jonathan Spirnak, Mingxiu Sun, Xiang Zhang

• 2019
  Context Equipment tests Published later

  Twenty-six dozen Easton X10 shafts belonging to the French federation, in seven different spines, weighed one by one on a scale reading to a thousandth of a gram: no dozen stayed within the manufacturer's declared tolerance of half a grain between two shafts from the same pack, and mixing dozens of the same spine the range ran from 1.96 to 3.69 grains, up to 11.64 for spine 380. A ballistic calculation at constant bow energy, with no shaft flexing, says however that the arrows of each dozen, shot separately under identical conditions, would all stay in the ten at seventy metres, which requires them to sit between 3.35 grains under and 3.37 over the reference weight; losses appear only when dozens are mixed, from 7 to 10 with the 380s and at least 9 with the 350s and 550s. It shows that the declared weight is not enough and has to be measured, not that measured weight and spine are not enough. It is a conference abstract with a simple model.

  A study of the influence of arrow mass on ballistics · A. Kuch, J.-F. Debril, J.-M. Tizzoni, P. Laguillaumie, T. Monnet

• 2025
  For Equipment tests Published later

  Fifty-nine Easton X10 arrows in spine 325, assembled by a national-level archer with tungsten points, Spin Wing vanes and Beiter nocks, measured one by one and shot by machine at seventy metres indoors: out of two hundred and fifty-five combinations of eight parameters, the one that best explains the closeness of the arrows on the target is mass plus mean spine plus the frequency of the spine variation around the shaft, with a root-mean-square error of 0.195 over a range from 0.195 to 0.365. The mass of the assembled arrows varies by 0.282 g, against a declared matching tolerance below 0.032 g per dozen, and the variability comes from the shaft, 18.672 g with a standard deviation of 0.056 g, and from the point, 7.775 g with 0.032 g, not from the nock, 0.547 g with 0.001 g, nor from the vanes, 0.243 g with 0.004 g. Matching heavy points with light shafts would bring the range down to 0.027 g. Taken on their own, weight and spine account for about half of the vertical spread (R² 0.467, with weight at beta -0.525 and mean spine at 0.248) and less than a fifth of the horizontal spread (R² 0.186), where the amplitude of the stiffness variation around the shaft also comes in (beta 0.325, p = 0.012).

  Improving the arrow selection process in archery: the stiffness variation pattern matters · A. Kuch, P. Laguillaumie, F. Durand, J.-F. Debril, T. Monnet

• 2025
  Context Equipment tests Published later

  The same study also measures how much matching really weighs: those fifty-nine arrows, unmatched for weight, held a vertical spread of 8.8 cm at seventy metres, against the 12.2 cm of the ten ring and the 6.1 cm of the X. Within the same spine category the real arrow departs from the nominal value by a few hundredths of a millimetre, on average towards the weaker side, 8.290 mm measured with a standard deviation of 0.070 mm against the 8.255 mm expected, and the assembled arrow weighs 27.250 g with a standard deviation of 0.057 g.

  Improving the arrow selection process in archery: the stiffness variation pattern matters · A. Kuch, P. Laguillaumie, F. Durand, J.-F. Debril, T. Monnet

Status history

1. 2012 Transferred A recurve model puts figures on something archers say on the field: two shafts of different models with the same nominal spine need different draw weights to tune, 175.5 against 180 N, and one percentage point of difference in the elastic modulus shifts the impact by twenty-five millimetres at seventy metres. In the same year a laser vibrometer measurement on three specimens per model of carbon shafts finds that within one model the first bending frequency barely varies, with a standard deviation of 0.4 Hz, while the differences grow at the higher frequencies: arrows of the same model are alike on the main bending mode, and the figures do not compare the arrows of a set with each other. In that year the claim therefore rests on a calculation alone: transferred.
2. 2014 Reported The first direct test arrives and the status rises. Seventy-nine arrows from the same production run, each shot three times from a launcher at twenty-five metres, give a spread index for the triangle of the three impacts running from 1.53 to 10.8, and within the same batch the measured spine and the straightness vary a great deal, with the ranking of that index following each arrow's measured spine. The index, though, rewards the regularity of the triangle more than its size, and the units are not made clear. It is a bench test on the equipment, so direct evidence in this domain, but on one batch, in a regional journal and with no statistical tests: reported.
3. 2015 Reported On a single arrow the measured spine matches the declared one almost exactly, 492 against 500, and the arithmetic recalls that stiffness depends on the cube of the shaft's radius, which is to say that tiny differences in diameter count for a lot. Nobody is yet comparing the arrows of one set with each other, though, so the question is not put to the test and the status does not move.
4. 2016 Reported A Korean study of hunting arrows shot by machine at 40 m confirms that within a single model the factory measurements of weight, diameter, straightness and spine vary, and that the spread of the three impacts of an arrow turned through 120 degrees ranges from under two millimetres to two centimetres. It does not link those parameters to the group of each arrow, though, and has no statistical tests: it is context, and the status stays reported.
5. 2019 Reported An independent dynamic measurement reaches the same conclusion by another route: within one nominal spine group the identified stiffness varies widely, in carbon as in aluminium and cedar, and two neighbouring carbon spines come out indistinguishable to the measurement while the factory figures predicted a clear difference. Damping varies widely too between arrows of the same model. In the same year a conference abstract weighs twenty-six dozen X10s and none stays within the declared weight tolerance, but its calculation says that within each dozen the arrows would still stay in the ten at seventy metres: it confirms that the declared weight has to be measured, not that measured weight and spine are not enough, and it stays context. The authors of the dynamic measurement admit they cannot separate production variability from clamping error, so two coherent bodies of evidence but none on archers: reported.
6. 2025 Reported An independent and much finer test: fifty-nine Easton X10 arrows of the same spine, measured one by one and then shot by machine at seventy metres. Out of two hundred and fifty-five combinations of parameters, the closeness of the arrows on the target is best explained by mass, mean spine and the frequency of the stiffness variation around the shaft, that is not by weight and spine alone. The picture gets stronger, but the evidence is still entirely without archers shooting, and those same arrows, unmatched for weight, stayed inside the ten ring anyway: the status does not move.

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Research lines

• 29 studiesThe archer's paradox in research: from 1987 to today
• 32 studiesArrow aerodynamics: drag, boundary layer, vanes

Other claims in this domain

• CorroboratedAlong its flight the arrow loses an appreciable part of its launch speed12 studiesStatus since 2011
• CorroboratedAs it leaves the bow, the arrow flexes and snakes around the riser instead of leaving straight19 studies · 47 archers measuredStatus since 2012
• ReportedA camera-based scoring system misreads some arrows: the ones barely sticking out and the ones that shift the target face7 studies · 2 archers measuredStatus since 2017
• ReportedA chest band with fibre optic sensors measures breathing and mean heart rate with small errors, and an archer can wear it while shooting2 studiesStatus since 2019
• ReportedA compound bow stores between 70 and 100 joules and sheds about two thirds of the force at full draw4 studiesStatus since 2015

See all claims on equipment and tuning