Archery - credits, sources and every reconstructed figure ========================================================= WHAT THIS IS An independent reimplementation of the World Archery recurve target round, written from scratch for the browser. It is not a port of any existing game, and no code, art, audio or data from any other archery game is used in it. The renderer is hand-written WebGL2 with no third-party libraries of any kind; the engine, the geometry, the icons and the social card are all original. WHAT IT REPLICATES, AND WHO GOVERNS IT Sport Target archery, recurve division Governing body World Archery Federation (WA) Founded 1931, as the Federation Internationale de Tir a l'Arc (FITA), at Lwow, Poland Renamed World Archery Federation, 2011 Olympic status On the programme in 1900, 1904, 1908 and 1920, and continuously since 1972 Format replicated the outdoor qualification round and individual set-play match play Rulebook edition the version effective 2026-08-15 This app is NOT affiliated with, endorsed by, or connected to World Archery or any of its member associations. "World Archery" and the federation's marks belong to World Archery. The rules and dimensions implemented here are quoted from its published rulebook, which is a technical standard, by article. 1. THE PRIMARY SOURCE --------------------- World Archery Rulebook, version effective 2026-08-15, English edition. Retrieved as PDF from the World Archery Documents Manager and extracted with pdftotext: Book 2 (Events) https://documents.worldarchery.sport/Rules/Rule_Book_versions/ 2026-08-15/EN/EN-Book_2_-_2026-08-15_Version.pdf Book 3 (Target Archery) https://documents.worldarchery.sport/Rules/Rule_Book_versions/ 2026-08-15/EN/EN-Book_3_-_2026-08_15_Version.pdf Directory browser https://extranet.worldarchery.org/documents/?dir=1 -> Rules (?dir=47) -> Rule_Book_versions (?dir=761) -> 2026-08-15 (?dir=1418) -> EN (?dir=1419) A NOTE ON ARTICLE NUMBERING, because secondary sources get it wrong. In the current rulebook the TARGET FACES AND THE FIELD OF PLAY ARE IN BOOK 2, CHAPTER 7. Book 3 begins at Chapter 9 and covers equipment, shooting and conduct, timing, scoring and penalties. Sources that cite "Book 3 Art. 7.2" for target faces are using superseded numbering. The HTML rulebook viewer at worldarchery.sport/rulebook is a client-rendered application and returns no article text to a plain fetch; the Documents Manager PDFs are the working route. 2. EVERY RULE AND DIMENSION, BY ARTICLE --------------------------------------- THE TARGET FACE Book 2 Art. 7.2.2.1 Ten scoring zones "of equal width when measured from the centre of the gold": 6.1 cm on the 122 cm face, 4 cm on the 80 cm, 3 cm on the 60 cm, 2 cm on the 40 cm. Five concentric colour zones, each split in two by a thin line. An inner 10-ring of 6.1 cm (122 cm face) or 4 cm (80 cm face) "is required to help determine ties in ranking". Dividing lines and the outermost line at most 2 mm and drawn "entirely within the higher-scoring zone in each case". "There are no dividing lines between light blue and black, nor between black and white." A centre cross at most 1 mm wide and 4 mm long. The 80 cm 6-ring face is the 80 cm face "with the 1 to 4 scoring zones removed", its lowest scoring zone the light blue 5. Book 2 Art. 7.2.2.2 Scoring value by colour, with Pantone references: 10 and 9 Yellow 107U, 8 and 7 Red 032U, 6 and 5 Light Blue 306U, 4 and 3 Process Black, 2 and 1 White. NO RGB VALUES APPEAR ANYWHERE IN THE RULEBOOK. Book 2 Art. 7.2.2.3 The full boundary-diameter table, in cm. 122 cm face: inner 10 at 6.1, then 12.2, 24.4, 36.6, 48.8, 61, 73.2, 85.4, 97.6, 109.8, 122. 80 cm face: inner 10 at 4, then 8, 16, 24, 32, 40, 48, 56, 64, 72, 80. Tolerance plus or minus 1 mm on zones 10, 9 and 8, and 2 mm on the rest. Book 2 Art. 7.2.2 The sixteen defined faces, and that only faces from a World Archery licensed manufacturer are used. Book 2 Art. 7.2.2.4 Paper or other suitable material, uniform within a category. This app draws the rings from the same boundary list the scorer uses, and tools-normals.js asserts that every one of the engine's boundaries is a ring the renderer draws. SCORING Book 3 Art. 12.2 "An arrow will be scored according to the position of the shaft in the target face. If the shaft of an arrow touches two colours or any dividing lines between two scoring zones, that arrow will score the higher value of the two zones involved." Both halves of that sentence are implemented: the arrow is scored by its shaft's inner edge, and every boundary is inclusive of the higher value. Book 3 Art. 12.2.1 Nothing on a butt is touched until every arrow on it has been recorded. Book 3 Art. 12.2.2 With too many arrows in the butt, only the lowest three (or four or six) in value are scored. Book 3 Art. 12.1.3 Arrow values are called in descending order. Book 3 Art. 12.1.4 "Recurve and Barebow will score using the set system, and Compound will be scored using a cumulative score." Book 3 Art. 12.1.4.1 Individual set-play: two set points for the higher score of a set, one each for a tie, and "as soon as an athlete reaches 6 set points, the athlete is declared the winner". Book 3 Art. 12.1.4.2 Team set-play: the same, with a threshold of FIVE set points. Book 3 Art. 12.1.4.3 Compound individual: five ends, the higher total wins. Book 3 Art. 12.1.4.4 Compound team: four ends. Book 3 Art. 12.5.1 Ranking ties: at long distances the greatest number of inner 10s FIRST and then of 10s; at short distances 10s and then 9s; after that the athletes are declared equal and a disk toss decides the chart position. Book 3 Art. 12.5.2 Shoot-offs for ties deciding entry to the eliminations, in matches, or entry to the top 8; "the system of Xs/10s and 10s/9s will not be used". Book 3 Art. 12.5.2.2 Individual shoot-off: a single arrow for score; on equal values the arrow closest to the centre; on equal distances successive single arrows; if both miss the scoring area, both shoot an additional arrow. Book 3 Art. 12.5.2.3 Team shoot-off: three arrows (two for a mixed team), then the closest, then the second and third closest. Book 3 Art. 12.6 Eliminated athletes are ranked by their arrow average, to three decimals. FORMATS AND DISTANCES Book 2 Art. 4.5.1.1 The qualification distances: 70 m / 122 cm / 72 arrows for Recurve; 60 m / 122 cm for Recurve U18 and 50+; 40 m / 122 cm for Recurve U15; 50 m / 122 cm for Barebow; 50 m / 80 cm for Compound, where the 6-ring face is mandatory at International Events; 30 m / 122 cm for Barebow U15; 18 m indoors and outdoors on triple faces for 60 arrows. Book 2 Art. 4.5.1.2 Elimination and final formats: Recurve individual at 70 m is FIVE SETS of THREE arrows on the 122 cm face; teams four sets of six arrows, three athletes shooting two each; mixed teams four sets of four arrows. Compound rows say "ends" where Recurve rows say "sets", which is the rulebook's own way of encoding cumulative against set scoring. Elimination matches are shot simultaneously and finals alternately. Brackets of 8, 16, 24, 32, 64 or 104. Book 2 Art. 5.2-5.5 The world-record framework. A NOTE ON "6-6". It is very widely written that a tied recurve match goes to a shoot-off at 6-6 set points. It cannot. Five sets distribute exactly ten set points, two per set, and Art. 12.1.4.1 ends the match the moment either athlete reaches six - so the only state a completed match can be unresolved in is 5-5. tools-harness.js enumerates all 243 sequences of set outcomes and all 81 for a team match, searches the state space breadth-first, and asserts that 6-6 never occurs and that 5-5 is the unique unresolved state. THE FIELD OF PLAY Book 2 Art. 7.2.3 The centre of a 122 cm face stands 130 cm above the ground, plus or minus 5 cm, for every 122 cm round including match play and the finals. Book 2 Art. 7.1.1.4 At 30 to 70 m the butts lean back between 10 and 15 degrees from vertical; at short distances between 0 and 10; a line of butts is set all at one angle. Book 2 Art. 7.2.1 The butt front, round or square, "will be large enough to ensure that any arrow hitting the butt and just missing the outermost edge of the scoring zone remains in the butt". NO NUMERIC BUTT DIMENSION IS GIVEN. Book 2 Art. 7.2.1.1 Butts secured against being blown or pulled over. Book 2 Art. 7.2.1.2 Target numbers at least 30 cm tall at long distances. Book 2 Art. 7.1.1.2 Distances measured from a point vertically beneath the gold to the shooting line, to 30 cm at 90/70/60 m and 15 cm at 50/40/30 m; the field oriented so athletes do not shoot into the sun, North plus or minus 20 degrees in the Northern Hemisphere. Book 2 Art. 7.1.1.3 A line 3 m in front of the shooting line, 3 cm wide, inside the 3 m area; for team rounds a 1 m line behind the shooting line, 3 cm wide; a waiting line at least 3 m behind. Book 2 Art. 7.1.1.5 The line of face centres should look straight at all times. Book 2 Art. 7.1.1.7 Three athletes per butt where possible, four at most. Book 2 Art. 7.1.1.8 At least 70 cm of shooting line per athlete at short distances and 90 cm at long; a target number 4 m in front of the shooting line. Book 2 Art. 7.1.1.9 The field divided into lanes of one to four butts. Book 2 Art. 7.1.1.10 The overshoot zone at least 50 m behind the longest target, 120 m for 70 m targets; side barriers 18 m out at 70 m downrange. Book 2 Art. 7.1.1.11 Butts arranged in pairs for the elimination rounds. Book 2 Art. 7.1.1.1 Venues capped at 1800 m above sea level. Book 2 Art. 7.2.4 The director of shooting controls time with a whistle or other audible indicator and digital clocks, lights, flags or plates. TIMING Book 3 Art. 11.2.1 "The total time allowed to shoot an end will be determined by the total number of arrows to shoot in the end" - the rulebook now states time PER ARROW, not per end. Book 3 Art. 11.2.1.1 At World Ranking Events and announced international events: 20 seconds an arrow for individual alternate shooting and all team and mixed team rounds, including shoot-offs; 30 seconds an arrow for individual shooting in qualifications and match play where alternate shooting does not apply. Book 3 Art. 11.2.1.2 At all other events: 20 seconds an arrow as above, and 40 seconds an arrow for individual non-alternating shooting, which organisers may reduce to 30. The familiar 2 minutes for 3 arrows and 4 minutes for 6 is the 40-second rate - the non-World-Ranking default, not the elite one. Book 3 Art. 11.2.3.1 Ten seconds to change details on the line. Book 3 Art. 11.2.3.2 In alternating shooting the opponent's 20-second clock starts "as soon as the first arrow is shot or the time runs out"; an athlete sure of the loss may vacate the line. Book 3 Art. 11.3.1 Two sound signals to occupy the line, one to begin ten seconds later, a YELLOW warning 30 seconds before time expires except in the finals with alternate shooting, two to stop, three to open scoring; the digital clock takes precedence over the lights. Book 3 Art. 11.3.3 At least five sound signals stop all shooting; one resumes it. Book 3 Art. 11.4.1 Make-up arrows for equipment failure, and none at the world championships. Book 3 Art. 11.4.3 Late arrival make-up capped at 12 arrows. Book 3 Art. 13.3 An arrow shot before the start signal, after the stop signal, or out of sequence in alternating shooting costs the HIGHEST-SCORING ARROW OF THAT END, scored as a miss - not the offending arrow. Book 3 Art. 13.6.1 The team-round yellow card. EQUIPMENT - AND WHAT THE RULES DELIBERATELY DO NOT FIX Book 3 Art. 9.1.1 A bow "held in one hand by its handle (grip) while the fingers of the other hand draw and release the string"; two flexible limbs, a single string, a no-shoot-through riser. This is what forbids a release aid. Book 3 Art. 9.1.2 The bowstring "will not in any way assist aiming through the use of a peephole, marking, or any other means". Compound (Art. 9.2.2) may have one. Book 3 Art. 9.1.3 The pressure point no further back than 4 cm from the pivot point. Book 3 Art. 9.1.4 Exactly ONE draw-check indicator - a clicker - audible, tactile or visual, and not electric or electronic. Book 3 Art. 9.1.5 ONE bow sight, with "no prism, magnifying lens/lenses, or any magnifying device, level, electric or electronic devices", providing "only one sighting point", its sighting element no more than 2 cm in the line of vision; windage and elevation adjustment permitted; an extension permitted; "a scale and/or tape with distance markings may be mounted on the sight as a guide for distance markings, but will not in any way offer additional aid". This is what makes a sight-mark mechanic faithful. Book 3 Art. 9.1.6 Stabilisers permitted. NO LENGTH OR WEIGHT LIMIT IS STATED. Book 3 Art. 9.1.7 "The maximum diameter of arrow shafts will not exceed 9.3 mm" and "the tips/points of the arrows will not exceed 9.4 mm in diameter"; a wrap no further than 22 cm from the nock groove; arrows marked with the athlete's name; arrows in an end identical; tracer nocks NOT allowed. THERE IS NO ARROW LENGTH LIMIT AND NO ARROW MASS LIMIT. Book 3 Art. 9.1.8 Finger protection may not incorporate a device that assists the draw or the release. Book 3 Art. 9.1 NO DRAW-WEIGHT LIMIT EXISTS FOR RECURVE. A full reading of Art. 9.1 finds no poundage, peak-weight, bow-length or brace-height clause anywhere. Book 3 Art. 9.2.1 By contrast, compound "peak draw weight must not exceed 60 lbs". The existence of an explicit cap for compound and none for recurve is the evidence that the recurve omission is deliberate. Book 3 Art. 9.4.1 Physiological monitors permitted; no eye-tracking or head-mounted EEG. Book 3 Art. 9.4.2 No electronic or electrical device attachable to equipment; no software that aids sight adjustment anywhere on the field. Book 3 Art. 9.4.2.1 Camouflage patterns forbidden. Book 3 Art. 9.5 A scope for spotting arrows only, not ranging, below the armpit at full draw; no micro-hole lenses or aiming marks on glasses. Book 3 Art. 9.6 No electronic communication device on the Olympic competition field. Book 3 Art. 9.7 Equipment inspected the day before competition. 3. WHAT NO RULEBOOK FIXES, AND WHO MEASURED IT ---------------------------------------------- The rules cap arrow shaft diameter at 9.3 mm and point diameter at 9.4 mm and say nothing else about the arrow: no mass, no length, no speed, no drag - and no draw weight for recurve at all. So the flight model cannot be quoted from a rulebook. It is taken from published measurements instead, and each figure below names the measurement it came from. [M1] H. O. Meyer (Physics Department, Indiana University), "Applications of Physics to Archery", 6 November 2015. arXiv:1511.02250. Open access. https://arxiv.org/pdf/1511.02250 Settles the reference-area question by DEFINITION, his Eq. 22: "One expects the drag force to be proportional to the cross sectional area pi.R^2 of the arrow shaft and to the air density rho_air ... kappa = (pi.R^2.rho_air / 2M) . C_D". So an arrow's Cd is normalised on the SHAFT CROSS-SECTION, and this app's dragK() is that formula, asserted against it in tools-harness.js section 6. MEASURED, with a shooting machine and acoustic timing between two microphones at 4.6 m and 36.6 m from the bow, 25 shots at each of seven distances from 27.4 m to 82.3 m: velocity decay rate kappa = (2.31 +/- 0.16) x 10^-3 per metre drag coefficient C_D = 1.94 +/- 0.14 85.1 per cent of launch speed retained over 70 m air density at the measurement 1.19 +/- 0.01 kg/m^3 at 23 C Reynolds number at launch about 35,000 and the citable literature band, "C_D is typically between 1.5 and 2.5" around Re 25,000. Also: drag is quadratic in v above about 10 m/s; there is "no evidence" of aerodynamic lift on a well-tuned arrow, so a point mass with drag and gravity is the right physics and this app adds no lift term; fletching is about 35 to 40 per cent of the drag, first measured in the 1930s; and wind-tunnel Cd runs "consistently lower than those with arrows shot by archers, because the wind tunnel conditions do not replicate those of a real, rotating and oscillating arrow in flight". His Table 1 is a fully weighed arrow: length 0.696 m, shaft radius 3.63 mm, total mass 20.62 g, split 57 per cent shaft, 30 per cent tip, 7 per cent fletching, 6 per cent nock. His Eq. 23 gives the launch angle in closed form and Eq. 24 its sensitivities: at 70 m, one metre of shooting distance is worth about 7 cm of impact height, one metre per second of launch speed about 13 cm, and twenty per cent of kappa about 7 cm. The model was validated against sight positions found empirically with a shooting machine. tools-harness.js section 13 reproduces all of these from the trajectory: the app gives 85.11 per cent retained against his 85.1, 12.79 cm per m/s against his 13, and 7.86 cm per metre against his 7. Its figure for the kappa sensitivity is larger than his, 11.25 cm against 7, because Eq. 24 linearises exactly the term that carries the kappa dependence - and the app's launch angle sits 2 to 3 per cent above his closed form, growing with kappa.Z, which is the signature of a truncated series. With the drag switched off, the two agree to machine precision. [M2] "Experimental and Computational Study of Archery Arrows Fletched with Straight Vanes", Proceedings (MDPI) 2020, 49(1), 56. doi:10.3390/proceedings2020049056. Gold open access. Measured in JAXA's 60 x 60 cm Magnetic Suspension and Balance System - no support interference: C_D = 1.56 for SHORT straight vanes at Re 1.2 x 10^4 C_D = 2.05 for LARGE straight vanes at Re 1.2 x 10^4 about 8 per cent of velocity lost in free flight, measured with an accelerometer inside the shaft, from an initial velocity of about 56.4 m/s and a turbulent-to-laminar transition observed DURING free flight at Re 1.8 x 10^4. The two coefficients are why this app offers a fletching choice: the vanes select the coefficient. [M3] K. Okawa, Y. Komori, T. Miyazaki, S. Taguchi, H. Sugiura, "Free Flight and Wind Tunnel Measurements of the Drag Exerted on an Archery Arrow", Procedia Engineering 60 (2013), 67-72. doi:10.1016/j.proeng.2013.07.017. Measured Cd about 1.6 laminar and 2.6 turbulent in the same JAXA facility, and about 2.65 on a real shot by an elite female recurve archer at 58 m/s "indicating that the oscillation of the arrow induces the boundary layer transition"; with Gas Pro vanes "the boundary layer remains laminar at any Re considered". The 58 m/s is one of the two published recurve launch speeds this app is calibrated to. [M4] S. Dall and J. L. Park, "Shot distribution in target archery, with application to arrow selection", Proc. IMechE Part P: Journal of Sports Engineering and Technology, 2022. doi:10.1177/17543371221130537. On a very large sample, the radial distance from the centre to the point of impact follows a RAYLEIGH distribution very closely, and "only varying the scale, this holds for subpopulations of interest: compound, recurve, male, female, indoors and outdoors and from intermediate to elite skill level". So this app's accuracy model is one parameter because the measurement says one parameter is enough, and tools-harness.js checks the simulated groups against the Rayleigh mean, mean square and CDF. The same paper finds "substantial benefits in selecting the maximum permitted arrow shaft diameter, for indoor archery" - which is the line-breaking rule paying for width. [M5] J. L. Park, "The dynamic behaviour of an arrow in wind", Proc. IMechE Part P, 2020. doi:10.1177/1754337120910015. "Even for the best arrows, the drift for a 3-m/s side wind is greater than four score rings for a recurve bow at a target distance of 70 m with a 1220-mm diameter target face" - more than 24.4 cm on the 6.1 cm rings of Art. 7.2.2.3 - and the equipment conclusion that "archers should use small diameter arrow shafts with a high density in order to minimise wind drift". Note that this pulls the opposite way from [M4]'s indoor conclusion, and both fall out of this app's model without being coded. [M6] "Numerical Simulation of Wind Drift of Arrows on the Olympic Venue for Tokyo 2020", Athens Journal of Sports, 2020. doi:10.30958/ajspo.7-1-1. On the venue's own wind data from JAMSTEC, a 70 m range gave about 0.11 m of lateral deviation for a heavier arrow and about 0.15 m for a lighter one. [M7] J. L. Park and D. Larven, "Analysis of scores and arrow grouping at major international archery competitions", Proc. IMechE Part P, 2014. doi:10.1177/1754337113519760. Score loss grows faster than linearly with distance, and "many archers lose score through incorrectly adjusting their sights". [M8] J. L. Park, S. Aitchison, R. Bielby, "Effect of arrow shaft straightness on arrow grouping", Proc. IMechE Part P, 2017. doi:10.1177/1754337117736705. Fletches set at an angle, so the arrow spins, reduce group size. [M9] J. L. Park, "The impact of the atmosphere on target archery", Proc. IMechE Part P, 2019. doi:10.1177/1754337118823967. And T. Wright, K. Sherab, J. L. Park, "Effects of diurnal air-density variation on arrow range in Bhutanese archery", Proc. IMechE Part P, 2026. doi:10.1177/17543371261450305: a 0.05 kg/m^3 air-density change moves range 0.11 to 0.25 m at 145 m, and archers overestimate the effect by three to four times. At 70 m it is second-order, which is why this app fixes the air density. [M10] World Archery, "Top Performers in 2025", the federation's own statistics: https://documents.worldarchery.sport/Statistics/TOP_SCORES/2025/TOP_2025_PERFORMERS_RM.pdf and .../TOP_2025_PERFORMERS_RW.pdf. The 72-arrow qualification totals the opponent ladder is pinned to: 709 the highest of 2025 (KIM Woojin, KOR), 688 at rank ten, 679 at fifty, 667 at one hundred and fifty. The ratified men's world record is 702 (Brady Ellison, USA, 2019 Pan American Games) and the women's 694 (Lim Sihyeon, KOR, Paris 2024). Standards: standard gravity 9.80665 m/s^2 exactly, CGPM 1901 Resolution 2 and NIST/CODATA; International Standard Atmosphere sea-level density 1.225 kg/m^3, ISO 2533; the grain as exactly 64.79891 mg and the inch as exactly 25.4 mm. Manufacturer geometry: Easton X10 shaft outside diameters, 0.182 to 0.221 inches (4.62 to 5.61 mm), and Easton A/C/E, 0.205 to 0.230 inches, with grains-per-inch, from eastonarchery.com/arrows_/x10/ and /a-c-e/. Manufacturer data, cited as such. Upstream literature the above cites, for the record: G. J. Higgins, "The aerodynamics of an arrow", Journal of the Franklin Institute 216, 91-101 (1933), the first study of the subject; C. N. Hickman, "The dynamics of a bow and arrow", J. Appl. Phys. 8, 404 (1937); P. E. Klopsteg, "Physics of bows and arrows", Am. J. Phys. 11, 175 (1943); B. W. Kooi, "Bow-arrow interaction in archery", J. Sports Sciences (1998), doi:10.1080/026404198366353; T. Miyazaki et al., "Aerodynamic properties of an archery arrow", Sports Engineering 16, 43-45 (2013). 4. EVERY RECONSTRUCTED FIGURE ----------------------------- Nobody has published these. They are this app's, and they are listed here in full so that no reader has to guess which numbers are the sport's and which are the author's. THE BOW * Storage factor 0.50 - the area under a recurve's force-draw curve as a fraction of peak force times power stroke, taken as linear. * Dynamic efficiency 0.77 - the share of stored energy the arrow leaves with. NOT FREE: it is the value that puts the middle bow's arrow at 56.9 m/s, inside the 56.4 to 58.0 m/s band that [M2] and [M3] measured, and tools-harness.js asserts it stays there. * The three bows: 34 lbs at 27.5 inches over an 8.75 inch brace, 42 at 28.5 over 9.0, and 48 at 29.5 over 9.25. Art. 9.1 fixes none of these for recurve. They produce 50.2, 56.9 and 62.0 m/s with the reference arrow; only the middle one is inside the measured band, and the fastest is labelled in the app as an extrapolation because no source gives a men's elite recurve launch speed. * Arrow masses of 330, 340, 344 and 470 grains. Easton publish grains-per-inch for the bare shaft only, so a finished mass is an estimate; [M1]'s fully weighed 20.62 g (318 grains) brackets it. THE ARCHER * A nocking point 1.52 m above the ground and an aiming eye at 1.62 m, for a 1.78 m archer at full draw. They enter the physics only through the angle between the line of sight and the horizontal, a fifth of a degree at 70 m. * A sight extension of 0.86 m from eye to aperture. A pure scale factor on the whole sight tape; the app prints it. * The draw taking 1.15 s to reach full draw and the clicker; the calmest moment 0.55 s after it, over a window of 0.85 s; and the hold going sour after 3.2 s. No steadiness curve for an archer at full draw appears in any source found. * The aim wander at full draw: four sinusoids at incommensurable frequencies with phases drawn from the arrow's own seed, amplitude 1.1 milliradians times the steadiness factor, plus a release error of 0.45 milliradians. * ENDSHARE = 0.45, the fraction of a group's VARIANCE that is common to an end rather than independent per arrow. [M4] measured the total Rayleigh scale and nothing decomposes it, but the split is what decides whether a three-arrow set is volatile. It is named and isolated for that reason, and constrained two ways: variances add, so the ranking-round average is unchanged at any partition, which the harness asserts by measuring it at four values; and the resulting spread of a set score is measured and asserted to widen with it. The MATCH win rate turns out to move within sampling noise, which the harness reports rather than hides. * The opponent's wind-reading error, from 0.80 of the wind for a novice down to 0.10 for a world-class archer. Nobody has published a distribution of wind-reading error. THE WIND * The wind field itself: a slowly varying crosswind plus a smaller head or tail component, deterministic from the round's seed, capped at 6 m/s. A wind is a field, not a rule. * A KNOWN LIMITATION, stated as a number. This app's crosswind drift at 70 m for a 3 m/s wind is 17.1 cm, which sits between [M5]'s "greater than 24.4 cm" for exactly that case and [M6]'s 11 to 15 cm on real venue wind. A point mass cannot weathervane into the resultant airflow and develop lateral lift on its fletching, which is what [M5]'s flexible-beam model adds, so the figure here is a LOWER BOUND. tools-harness.js asserts it stays between 55 and 105 per cent of [M5]'s figure, so a future change that quietly widened the gap would fail. THE PICTURE * The sRGB values standing in for Pantone 107U, 032U, 306U and Process Black. The rulebook specifies colour by Pantone and contains no RGB anywhere, so this is the one place a cited figure had to be turned into something the rulebook does not state. * The butt at 1.32 m square and 10 cm thick - the smallest square satisfying Art. 7.2.1's sentence for a 122 cm face with a margin, since the article gives no dimension. * The target stand, the wind flags, the treeline, the mown stripes, the lighting, and the three cameras and their fields of view. The fields of view are chosen against real angles: a 122 cm face at 70 m subtends 1.0 degrees and a 2 cm aperture at 0.86 m subtends 1.3, so the sight view is 7 degrees wide and the scope 2.2. * That an arrow with the low-drag fletching still flies laminar on a real shot. [M3]'s wind tunnel found Gas Pro vanes laminar at every Reynolds number tested; nobody has shot one past a camera to check, so extending the tunnel result to a real shot is this app's extrapolation. DELIBERATE SIMPLIFICATIONS * The arrow is a point mass. It does not flex off the bow (the archer's paradox), does not oscillate, and carries no lift or pitching-moment term. [M1] found no evidence of net lift on a well-tuned arrow, which licenses the first two; the third is the cause of the wind shortfall above. * Timing is not enforced. The rulebook's per-arrow allowances are shown and cited, but the app does not stop you shooting after 20 seconds, and it does not implement Art. 13.3's penalty. * Only the individual formats are playable. The team and mixed-team set thresholds and shoot-off procedures are implemented in the engine and tested, but there is no team UI. * One archer shoots per butt, and the neighbouring butts are scenery. 5. HOW IT WAS TESTED -------------------- tools-harness.js 554 assertions over the engine, including four independent oracles tools-oracle.js a scorer built from the rulebook's published diameter table in cm, sharing no code with the engine; a second integrator for the same equations (an implicit trapezoid at a fraction of the step, a different order); a first-principles skin-friction estimate of the drag area; and the set-play state machine re-derived from the article text tools-normals.js every triangle the renderer emits, checked against an outward direction rebuilt from the primitive's own parameters, with zero exclusions tools-harness-page.js the shipped bundle: assets, CSP hygiene, wiring, and that every figure the page prints is the constant it claims to quote tools-smoke.js headless Chrome against a local server and against the live host The scoring geometry was diffed over 6,000,000 random landing points on three faces with no mismatches, plus 37,440 probes a micron either side of every ring boundary on every face with every shaft the app ships. 6. THANKS --------- To World Archery for publishing a rulebook precise enough that a target face can be rebuilt from it exactly, and to the researchers above for measuring the things the rulebook does not fix.