Squash - credits, sources and provenance ======================================== https://squash.skillsafe.ai/ WHAT THIS IS ------------ An independent browser reimplementation of squash, the racket sport played in a four-walled court. The sport is not anyone's product: it descends from "rackets", played in the Fleet and King's Bench debtors' prisons in London in the 18th century, and the softer-ball game was being played at Harrow School by about 1830. It has no author, no publisher and no year of publication, and nothing here is copied from any commercial squash video game, television graphic or broadcast package. What IS someone's: the Rules of Singles Squash, the Court Specifications and the Specifications for Squash Balls are documents of World Squash (the World Squash Federation). This app quotes numbers and rule text from them, with the rule number, as a description of the sport - it is not endorsed by, affiliated with or connected to World Squash or the PSA. No accounts, no network calls, no analytics, no model. Everything runs in the page. HOW THE PROVENANCE TAGS WORK ---------------------------- [DOCUMENTED] a governing body's own published document, named, with the clause. [DOCUMENTED qualified] documented, but of something ADJACENT: a different body, a laboratory measurement rather than a rule, a generic material rather than this ball's compound. Counted apart, because folding these into DOCUMENTED would flatter the tally. [MEASURED] measured here, by running the model or the engine. [DERIVED] follows from other entries by arithmetic or by a physical argument. [CALIBRATED] chosen so the model reproduces a stated observable. The target is named. [RECONSTRUCTED] chosen, with a reason. Nothing here is a documented constant. DOCUMENTED 55 DOCUMENTED-qualified 16 MEASURED 11 DERIVED 12 CALIBRATED 9 RECONSTRUCTED 20 SOURCES ------- S1 World Squash, "Rules of Singles Squash 2025", version 1.2.2, in force from 1 September 2025. https://www.worldsquash.sport/wp-content/uploads/2025/07/250901_World-Squash-Rules-of-Singles-Squash-2025-V1.2.2.pdf S2 World Squash, "List of all the changes in the new 2025 version" (the 2024-to-2025 diff). https://www.worldsquash.sport/wp-content/uploads/2025/08/WSF-Singles-Rules-changes-2025-version.pdf S3 World Squash, "Court Specifications", November 2017 edition - still the document Appendix 5 of the 2025 rules points to. https://www.worldsquash.sport/wp-content/uploads/2021/08/171128_Court-Specifications.pdf S4 World Squash, "Specifications for Squash Balls", (c) WSF February 2013, updated at the 2021 AGM, rebranded 2025. https://www.worldsquash.sport/wp-content/uploads/2025/07/211127_Ball-Specifications.pdf S5 Lewis, G. J., Arnold, J. C. and Griffiths, I. W., "The dynamic behavior of squash balls", American Journal of Physics 79(3), 291-296 (2011). doi:10.1119/1.3531971 S6 Berencsi, B. F. and Kossa, A., "Analyzing the Effect of Temperature on Squash Ball Impacts Using High-Speed Camera Recordings", Periodica Polytechnica Mechanical Engineering 65(4), 354-362 (2021). doi:10.3311/PPme.18381 (open access) S7 Tadrist, L. and Texier, B. D., "Open questions on the impact of an inflated ball", arXiv:1708.01282. S8 Wikipedia, "Squash (sport)". https://en.wikipedia.org/wiki/Squash_(sport) S9 Wikipedia, "Squash court". https://en.wikipedia.org/wiki/Squash_court S10 Guinness World Records, "Fastest speed of a squash ball". https://www.guinnessworldrecords.com/ (checked 15 September 2026) S11 Williams, M. L., Landel, R. F. and Ferry, J. D., the WLF equation and its universal constants - standard polymer-physics textbook material, used here for the shift factor. SOURCES I COULD NOT OPEN ------------------------ X1 England Squash's rules page, https://www.englandsquash.com/resources/rules-of-squash/ - returns 403 Forbidden to every request made. It would have been a second, national-federation reading of the interference rule; the app quotes only World Squash's own text instead. X2 The WSF's ball TEST PROCEDURE. Note 1 of S4 says "The full procedure for testing balls to the above specifications is available from World Squash" - so it is NOT published. S4 gives the pass bands and the drop height and nothing else: not what the ball is dropped onto, not how long it is conditioned at temperature, not whether the rebound is read to the bottom or the centre of the ball, not how many balls, not the tolerance on the drop. Every one of those changes the number. This is the single largest hole under the whole calibration and it is a hole in the published specification, not in the search for it. X3 "Beware the frozen squash ball", a 1994 note in an AIP journal, named in later bibliographies. The AIP page is behind a Cloudflare bot wall and no open mirror was found. Its subject is exactly this app's headline, so the cold-ball claim is tested here rather than quoted from it. X4 Pre-2024 editions of the WSF rules. Only the 2025 text and the 2024-to-2025 diff were reachable, so this app cannot say what the interference rule was numbered before 2024. X5 WebSearch was unavailable for the whole of this build (the session's quota was already spent), so every source above was found by fetching a URL and following links from it, not by searching. A broader search might have found more; that limitation is stated rather than hidden. THE REGISTER, LINE BY LINE -------------------------- THE COURT (all from S3, Appendix 1, "Description & Dimensions of an International Singles Squash Court", whose table is quoted verbatim) [DOCUMENTED] Length of court between playing surfaces: 9750 mm. S3 Appendix 1. [DOCUMENTED] Width of court between playing surfaces: 6400 mm. S3 Appendix 1. [DOCUMENTED] Diagonal: 11665 mm. S3 Appendix 1. Stated separately in the same table. [DOCUMENTED] Height to the lower edge of the Front Wall Line: 4570 mm. S3 Appendix 1. [DOCUMENTED] Height to the lower edge of the Back Wall Line: 2130 mm. S3 Appendix 1. [DOCUMENTED] Height to the lower edge of the Service Line on the front wall: 1780 mm. S3 App 1. [DOCUMENTED] Height to the top of the Tin: 480 mm. S3 Appendix 1. [DOCUMENTED] The PSA-preferred professional tin: 430 mm. S3, twice - the Configuration table ("A lowered tin height of 430mm is preferred for all PSA sanctioned tournaments") and Appendix 1's Construction Note. Selectable in the options. [DOCUMENTED] Distance to the nearest edge of the Short Line from the BACK wall: 4260 mm. S3 App 1. The document measures it from the back, not the front. [DOCUMENTED] Internal dimension of the Service Boxes: 1600 mm. S3 Appendix 1. [DOCUMENTED] Width of all lines and of the upper section of the Tin: 50 mm. S3 Appendix 1. [DOCUMENTED] Minimum clear height above the floor: 5640 mm. S3 Appendix 1. [DOCUMENTED] The Side Wall line "is angled between the Front Wall Line and the Back Wall Line". S3 Appendix 1, Note 1 - so it is a straight ramp, which is how it is drawn. [DOCUMENTED] The bevelled top of the tin may not project more than 45 mm from the front wall. S3 Appendix 1, Note 5. [DOCUMENTED] The court's length, width and diagonal are measured 1000 mm above the floor. S3 Note 3. [DERIVED] Short line at 5490 mm from the front wall: 9750 - 4260. S3 never prints this number. [DERIVED] The court table is internally inconsistent by 2.13 mm. S3 prints the length (9750 mm), the width (6400 mm) AND the diagonal (11665 mm), so the three can be checked against one another: sqrt(9750^2 + 6400^2) = 11662.87 mm. The printed diagonal is the larger by 2.13 mm. The engine uses the length and the width and treats the diagonal as a stated figure rather than a constraint. [DERIVED] A service box is 1600 x 1600 mm. S3 gives ONE dimension, 1600 mm, for a shape that S1 Appendix 1 separately calls "a square area". Square plus one dimension gives two, but the source prints one, so this is an inference and is tagged as one. THE RULES (all from S1 unless noted) [DOCUMENTED] Scoring: point-a-rally, each game to 11, and at 10-all until a player leads by 2. Rule 2.1-2.2. [DOCUMENTED] A match is normally the best of 5 games, but may be the best of 3. Rule 2.3. [DOCUMENTED] The winner of a rally scores a point and serves next. Rule 2.1. [DOCUMENTED] The server chooses a box at the start of a game and after each change of server, and while retaining the serve must alternate boxes. Rule 5.2. [DOCUMENTED] After a let, the server serves again from the same box. Rule 5.3. [DOCUMENTED] The whole definition of a good serve. Rule 5.7.1-5.7.5. [DOCUMENTED] A serve that does not comply is a fault and the RECEIVER WINS THE RALLY - there is no second serve. Rule 5.8. [DOCUMENTED] A serve that hits the service-line, the short-line, the half-court line or any line bounding the top of the court is a fault. Rule 5.8, Note. [DOCUMENTED] A good return: struck before the ball has bounced twice, reaching the front wall above the tin and below the out-line without first bouncing, and not out. Rule 6.2. [DOCUMENTED] DOWN, OUT and NOT UP, verbatim definitions. S1 Appendix 1. [DOCUMENTED] The four requirements a player must leave the opponent: a fair view, access, the space for a reasonable swing, and the freedom to strike the ball to any part of the front wall. Rule 8.1.1-8.1.4. [DOCUMENTED] The general let/stroke/no-let provisions. Rule 8.6.1-8.6.7. [DOCUMENTED] Fair View means "enough time to view the ball and prepare to strike it as it returns from the front wall". Rule 8.7. [DOCUMENTED] Access: the three sub-cases. Rule 8.8.1-8.8.3. [DOCUMENTED] Racket swing: a let if the swing was affected, a stroke if it was prevented. Rule 8.9.1-8.9.2. [DOCUMENTED] Excessive swing. Rule 8.10.1-8.10.3. [DOCUMENTED] Freedom to strike the ball to any part of the front wall. Rule 8.11.1-8.11.4. [DOCUMENTED] Further attempt. Rule 8.12.1. [DOCUMENTED] Turning, including its definition: "the ball passes behind their body from one side to the other". Rule 8.13 and 8.13.1-8.13.4. [DOCUMENTED] Ball hitting a player. Rule 9.1.1-9.1.5 and 9.2.1-9.2.3. [DOCUMENTED] "No let is allowed for any unusual bounce." Rule 11.10 - so a ball that dies because it is cold is never a let. [DOCUMENTED] A let is allowed if the ball breaks during a rally. Rule 11.1. [DOCUMENTED] The players may warm up the ball for a maximum of 4 minutes, changing sides after 2. Rule 4.1. This is the sport's own answer to how long warming a ball takes. [DOCUMENTED] The Referee's decision is final. Rule 3.6. [DOCUMENTED qualified] Point-a-rally to 11 was adopted by the PSA in 2004 and ratified by the WSF in 2009. S8, not a WSF document. [DOCUMENTED] Hand-in/hand-out scoring to 9, and point-a-rally to 15, survived in the rulebook as Appendix 3 "Alternative Scoring Systems" until they were ERASED with effect from 1 September 2025. S2, the rows for Rule 2.4 and Appendix 3, rationale "No longer applicable". So the old scoring left the rules this year, not in 2004 or 2009. THE BALL (all from S4 unless noted) [DOCUMENTED] Diameter: 40.0 +/- 0.5 mm. S4, all three specified categories. [DOCUMENTED] Weight: 24.0 +/- 1.0 g. S4, all three specified categories. [DOCUMENTED] Stiffness: 3.2 +/- 0.4 N/mm at 23 degrees C. S4. [DOCUMENTED] Seam strength: 6.0 N/mm minimum. S4. [DOCUMENTED] The rebound-resilience test is a drop "from 254 centimetres". S4. [DOCUMENTED] Double yellow dot (Competition): 12% minimum at 23 C, 25%-30% at 45 C. S4 clause 1. [DOCUMENTED] Single yellow dot (Club): 15% minimum at 23 C, 30%-35% at 45 C. S4 clause 2. [DOCUMENTED] Green dot (High Altitude): 9% minimum at 23 C, 25%-30% at 45 C. S4 clause 3. [DOCUMENTED] Beginner, RECOMMENDED not specified: not less than 17% at 23 C, 36%-38% at 45 C. S4 Note 2. [DOCUMENTED] Improver, RECOMMENDED not specified: not less than 15% at 23 C, 33%-36% at 45 C. S4 Note 2. [DOCUMENTED] "No specifications are set for faster or slower speeds of ball" - so the red (Medium) and blue (Fast) dots have NO WSF specification at all. S4 Note 2. [DOCUMENTED] Red and blue dot balls "can be larger than 40mm diameter" - S4 Note 2 says only that, and gives no figure. The widely repeated "6% larger" and "12% larger" are not WSF. [DOCUMENTED] The speed names: Super slow = double yellow and green; Slow = single yellow; Medium = red; Fast = blue. S4 Note 2. There is no orange tier in the document. [DOCUMENTED] Yellow-dot balls larger than 40.0 mm may be authorised for tournaments. S4 Note 4. THE BALL'S PHYSICS [DOCUMENTED qualified] Coefficient of restitution 0.45 to 0.65 over roughly 30-55 C, rising with temperature. S5, Fig. 1 - a laboratory measurement, not a rule. [DOCUMENTED qualified] Hysteresis at bounce timescale for a double-yellow ball: 79.5% at 35 C, 74.7% at 40 C, 72.9% at 45 C, 70.5% at 50 C, 67.5% at 55 C. S5 Table I. Held OUT of this app's calibration and used to test it. [DOCUMENTED qualified] Hysteresis% = (1 - COR^2) x 100. S5 - the conversion that makes the WSF's rebound percentages and a restitution the same statement. [DOCUMENTED qualified] Cold compression: hysteresis rises from 28.3% at 23 C to 47.9% at 0 C for a double-yellow ball. S5. [DOCUMENTED qualified] Bleeding the enclosed air out through a drilled hole barely changes the hysteresis loop: at 20 mm compression the force falls from 82 N to 50 N, so the air carries about 39% of the FORCE, but "almost all of the energy lost during a compression comes from deformation of the rubber". S5. [DOCUMENTED qualified] "The normal warming up process at the start of a squash game is important to raise the temperature of the rubber rather than to increase the internal air pressure." S5, in those words. [DOCUMENTED qualified] Coefficient of restitution falls from about 0.33 to about 0.17 as the impact speed rises from about 25 m/s to about 72 m/s, and at any speed a hotter ball is bouncier - EXCEPT above about 61 m/s, where the ordering reverses. S6, Fig. 6. [DOCUMENTED qualified] "The ball's overall stiffness grows as the temperature increases", and a heated ball deforms MORE for the same impact speed: +12% for a 10 C rise, +18% for a 25 C rise. S6. [DOCUMENTED qualified] Squash at game-maximum conditions: contact time 4 ms, e = 0.37, maximum game speed 78 m/s, kinetic energy 73 J, dissipated energy 63 J per impact - about 86% of the kinetic energy gone in one bounce. S7 Table 2. [DOCUMENTED qualified] S7 also prints e_rules = 0.346 for squash, which is the square root of the WSF's 12% - two unrelated documents agreeing. [DOCUMENTED qualified] A squash ball is dominated by its shell, not its gas: S7's "storage number" for squash is 0.61. [DOCUMENTED qualified] Fastest squash ball: 267.151 km/h (166 mph), David Hilton III, 11 June 2021. S10. A record attempt, not a game shot. [DOCUMENTED qualified] Specific heat of rubber about 2.01 kJ/(kg K); thermal conductivity of natural rubber about 0.13 W/(m K). Generic engineering tables, NOT a squash-ball measurement. [DOCUMENTED qualified] The WLF shift factor with the universal constants C1 = 17.44 and C2 = 51.6, referenced to the glass transition, stated as usable from Tg to about Tg + 100 K. S11. [CALIBRATED] Master curve position LOGF0 = 3.714028 and width LOGW = 0.905069. Target: the WSF bounce test at BOTH its temperatures, 12% at 23 C and the 27.5% midpoint of the 25-30% band at 45 C. tools-calibrate.js. [CALIBRATED] Amplitude-loss constants KAPPA = 11.043273 and QEXP = 1.781186. Target: S6's cannon measurements at 25 m/s and 72 m/s at 41.5 C. tools-calibrate.js. [CALIBRATED] Reference contact time TC0 = 1.25 ms at the bounce-test impact speed. [CALIBRATED] Contact-time speed exponent PV = 0.20. [CALIBRATED] Butyl glass transition taken as -65 C for the shift factor. [CALIBRATED] Rubbery-plateau loss TD_LO = 0.055 and transition-flank loss TD_HI = 1.10, the two ends the logistic master curve runs between. [CALIBRATED] Compound density 1550 kg/m^3, which with the specified mass and diameter fixes the wall. [CALIBRATED] Compound specific heat 1600 J/(kg K) and conductivity 0.20 W/(m K) - a filled compound, so both differ from the unfilled-rubber table values above. [DERIVED] Shell wall thickness 3.73 mm. The specification fixes the mass and the diameter, so it fixes the PRODUCT of wall thickness and density: quoting one commits you to the other. The commonly repeated "about 3 mm" wall would need a density near 1900 kg/m^3. [DERIVED] Heat capacity of the whole ball: 38.4 J/K. Raising it by 22 K therefore takes 845 J. [DERIVED] Enclosed air volume 18.03 cm^3. [DERIVED] Outer surface area 50.27 cm^2. [DERIVED] The shift factor between the bounce test's two temperatures is 0.878 decades of frequency, i.e. 7.54x, and 0.046 decades per kelvin near 23 C. [DERIVED] Dynamic stiffness at bounce-test speed: 151.6 N/mm, which is 47 times the 3.2 N/mm the specification measures quasi-statically. A rubber sitting on the low-frequency flank of its glass transition is expected to stiffen by about that much, so the two numbers are consistent rather than contradictory. [DERIVED] Biot number at 20 m/s: 0.75. Of order one, which is why the shell is carried as two nodes and not one. [DERIVED] Peak compression at 25 m/s: 7.4 mm, 37% of the ball's radius. [MEASURED] Restitution at the bounce test: e = 0.3536 at 23 C and 0.5369 at 45 C - a factor of 1.52 in speed and 2.31 in energy. [MEASURED] Restitution at a drive speed of 25 m/s: 0.2221 at 23 C, 0.3455 at 45 C. [MEASURED] Of the rise in e^2 from 23 C to 45 C, 98.2% is the rubber getting less lossy and 2.4% is the enclosed air getting stiffer, with a -0.6% cross term. The folk explanation names the smaller of the two. [MEASURED] Against S5 Table I, which was held out of the calibration: the model is within 3.2% on every one of the five temperatures, worst at 40 C. [MEASURED] A length drive that just carries to the back wall needs 29.1 m/s (105 km/h) at 45 C and 59.4 m/s (214 km/h) at 23 C. The second is most of the way to the world record. [MEASURED] A 4-minute knock-up at 20 m/s in an 18 C court takes the ball from 18 C to 26.1 C. [MEASURED] At knock-up pace the ball does not reach 45 C at all - it levels out around 31 C after ten minutes. Match play, which is harder and more continuous, reaches about 36 C. [MEASURED] The ball's CORE runs hotter than its SURFACE during a knock-up, by up to 1.5 K, because the dissipation is spread through the shell and only the outside is cooled. An infrared thermometer therefore UNDER-reads the temperature the bounce follows. [MEASURED] Turning the convective loss off entirely changes the 4-minute figure from 26.1 C to 28.9 C, but the 10-minute figure from 30.8 C to 43.6 C. Early on the ball is simply short of energy; only later is cooling the thing holding it back. [MEASURED] The conclusion "a knock-up does not reach 45 C" survives a fourfold change in the convective coefficient and a +/-25% change in the share of impact energy that stays in the ball: the 4-minute figure moves only between 22.8 C and 28.7 C. WHAT THIS APP CHOSE, BECAUSE NOTHING PUBLISHED DECIDES IT [RECONSTRUCTED] Player body radius 0.30 m, racket reach 1.45 m, acceleration 13.5 m/s^2, top speed 6.2 m/s. No rule describes a player's body at all. [RECONSTRUCTED] The space a "reasonable swing" needs: 0.95 m. Rule 8.9 defines a reasonable swing as one with a reasonable backswing and a reasonable follow-through. There is no number anywhere in the rules. [RECONSTRUCTED] The half-width of the sight corridor for "a fair view": 0.30 m. Not in the rules. [RECONSTRUCTED] The clearance the path to the ball needs for "access": 0.30 m. Not in the rules. [RECONSTRUCTED] The clearance the intended shot line needs for "freedom to strike the ball to any part of the front wall": 0.26 m. Not in the rules. [RECONSTRUCTED] "Reasonable fear of injury" (Rule 8.6.1) is taken as the opponent being within 0.45 m of the ball. Not in the rules. [RECONSTRUCTED] A swing is "prevented" rather than "affected" (Rule 8.9.2 against 8.9.1) when the opponent is within 0.62 m. Not in the rules. [RECONSTRUCTED] The six shots - straight drive, cross-court drive, kill, drop, lob, boast - and the speed and height band of each. [RECONSTRUCTED] Execution scatter: the aim point is jittered, with a spread that is 1.35 m at zero skill, so that a player can tin a drop or hit a drive out. [RECONSTRUCTED] Default skill 0.93, which gives about 5 shots a rally and a tin on about 13% of them. [RECONSTRUCTED] A player asks for a let at 0.25 requests per second while a let is worth asking for. Expressed per SECOND, not per frame - see the bugs list. [RECONSTRUCTED] The share of each impact's lost energy that stays in the BALL: 0.92 off a wall, 0.88 off the floor, 0.55 off the racket. S5 and S7 both treat the wall as rigid and undissipative, which supports a high share, but no source gives a number. [RECONSTRUCTED] Ball-on-plaster friction coefficient 0.30, and aerodynamic spin damping 0.28 /s. [RECONSTRUCTED] Drag coefficient 0.47 and Magnus lift slope 0.22 for a smooth sphere. [RECONSTRUCTED] The spin each shot is given. No source gives squash spin rates. [RECONSTRUCTED] The reference "length drive" used to define playability: 26 m/s meeting the front wall 1.60 m up. Playability is not defined by any rule. [RECONSTRUCTED] Court air at 18 C by default, and the ball starting at court temperature. [RECONSTRUCTED] The AI clears to the T after striking, and fails to clear 14% of the time. [RECONSTRUCTED] The camera positions, the colours, and the player figures.