Boomerang - credits, sources, and what is different =================================================== WHAT THIS IS ------------ An independent reimplementation of the sport of boomerang throwing, written from published rules and published aerodynamics. It is not affiliated with, endorsed by, licensed by or derived from any boomerang association, tournament, maker or product. No code, art, text or data was taken from any existing boomerang game or simulator. Everything here - the flight model, the renderer, the art and the scoring - was written for this app. THE ORIGINAL ------------ The boomerang is a traditional Aboriginal Australian returning throwing tool. The oldest surviving Australian example, found in the Wyrie Swamp of South Australia in 1973 and held by the South Australian Museum in Adelaide, is dated to 10,000 BC. The word entered English from a language of the Sydney region and was recorded as "bou-mar-rang" in Dharawal in 1822. The modern sport - the events, the marked circles and the scoring - is a twentieth-century codification on top of that. THE RULES --------- Scoring follows the United States Boomerang Association's rulebook, whose own title inside the document is: Boomerang Competition Regulations, Revision 2007 United States Boomerang Association read at https://usba.org/rules/ (the live host serves a Cloudflare interstitial to scripted clients; the copy used here was read through the Internet Archive) The rulebook is NOT called "the WBA rules" anywhere in it, and I could not source a separate World Boomerang Association rulebook: worldboomerang.org does not resolve and the Internet Archive has no capture of it, and the international body Wikipedia links (ifba-online.com) is also dead. The USBA book is the live, citable codification, and it is the one the sport's own world-record clause points at: Sec.13.2.1 recognises a world record as a performance that equals or exceeds the USBA record and was set under rules "equivalent to USBA rules or more restrictive". Clause numbers used in the app and in this file are that document's own decimal numbering: Sec.3 definitions - "Boomerang", "Range", "Throw, Legal", "Catch, Legal", "Bull's-Eye" Sec.14.1 Accuracy 50 Sec.14.2 Accuracy 100 Sec.14.3 Australian Round Sec.14.5 Fast Catch Sec.14.6 Endurance Sec.14.7 MTA 100 Every scoring rule in this app is sourced. None is reconstructed. THE AERODYNAMICS ---------------- Hugh Hunt, "Unspinning the boomerang", Plus Magazine issue 7, January 1999 (Millennium Mathematics Project, University of Cambridge). https://plus.maths.org/content/unspinning-boomerang That article's closed-form treatment - the couple C = J w Omega, the tangency condition V = R Omega, and the result that the flight radius R = 4J/(rho C_L pi a^4) is independent of both spin speed and forward velocity - is what this app's own blade-element algebra is checked against. The two agree after the change of lift normalisation, and the app's engine harness asserts that identity. Cited as the literature this sits in, but not quoted (paywalled): Hess, F. "The Aerodynamics of Boomerangs." Scientific American 219(5), Nov 1968. doi:10.1038/scientificamerican1168-124 Azuma, A., Beppu, G., Ishikawa, H. and Yasuda, K. "Flight Dynamics of the Boomerang, Part 1: Fundamental Analysis." J. Guidance, Control, and Dynamics, Jul 2004. doi:10.2514/1.11157 (Part 2: doi:10.2514/1.11158; Erratum: doi:10.2514/1.22411) Vassberg, J. C. "Boomerang Flight Dynamics." 30th AIAA Applied Aerodynamics Conference, 2012. doi:10.2514/6.2012-2650 Lorenz, R. D. "The Boomerang", ch.11 of Spinning Flight, Springer. doi:10.1007/978-0-387-47289-8_11 OTHER SOURCES ------------- Wikipedia, "Boomerang" (https://en.wikipedia.org/wiki/Boomerang) for the equipment envelopes (70-110 g, 250-300 mm wingspan, 20-40 m range; MTA boomerangs often under 25 g), the throwing technique (tilt "from a nearly vertical position to 20 deg or 30 deg", aim to the right of the oncoming wind, light winds up to 3-5 knots manageable), the discipline list, and the world-record table. That record table carries the article's own {{citation needed}} tag dated May 2025 and an "updated September 2017" banner; the app quotes it as a benchmark and says so, rather than treating it as a fact. WHAT IS RECONSTRUCTED --------------------- Boomerang equipment is not standardised. Mass, blade section, chord, hub size, blade pitch and moment of inertia vary by maker and no governing body publishes them, so EVERY equipment number in this app is a choice of mine, made inside the sourced envelopes where one exists. The full list, item by item, is printed in the app's own Help sheet and generated directly from the engine's constants so the two can never drift apart. In summary, RECONSTRUCTED: the four boomerangs' span, chord, hub radius, mass, arm count, blade pitch and arm-mass fraction; the section's camber coefficient, stall angle, profile drag and induced-drag factor; the post-stall blend width; the release height and catch point; the catch reach and the closing speed above which a catch cannot be held; the marked-line half width; the thrower's running speed. SOURCED and not reconstructed: every circle radius, every point value, every time limit, every legality condition, the definition of range, air density (ISA sea level, ISO 2533), standard gravity (CGPM 1901), the knot (0.514444 m/s exactly), and the lift-curve slope of 2 pi per radian (classical thin-airfoil theory). WHAT DIFFERS FROM THE REAL SPORT -------------------------------- 1. One thrower, no tournament. Sec.12's placing-point system, tandem throwing, re-throws, protests, range challenges and the judging apparatus are not implemented. 2. Endurance (Sec.14.6) and Trick Catch / Doubling (Sec.14.4), Long Distance (Sec.14.12), Juggling and the team and super-novice events are not offered as playable sessions. Endurance IS scored by the engine and is exercised by the harness; the rest are out of scope. 3. The catch is a single deterministic test - inside a reach of 1.05 m of the hands, not having touched the ground, and slower than 22 m/s in the hand frame. The rulebook's taxonomy of legal catches (one-hand-clean, behind the back, under the leg, hackey, foot/leg, tunnel...) is not modelled, because none of those distinctions matter in the events implemented. 4. A boomerang that lands is treated as coming to rest where it lands: no skid, no bounce. The rulebook's requirement that it "come to rest without touching or hitting anything except the ground" is enforced, but the ground is flat, level and unobstructed everywhere. 5. The four boomerangs are fixed per event rather than chosen by the thrower, and they cannot be tuned (real throwers bend and weight their sticks between throws). 6. The wind is a steady vector plus one slow deterministic gust, seeded from the session number. Real gusting is far nastier. 7. The thrower runs at a flat 6.5 m/s in any direction and never trips. 8. The boomerang is modelled as N identical straight arms through a common hub, all at the same pitch, with no twist, no dihedral and no turbulators. A real V-shaped stick has its arms at about 100 degrees, and MTA sticks deliberately have one arm longer than the other. 9. The drawn boomerang is FIVE TIMES its true size. A 30 cm stick is a couple of pixels at 20 m and the game is unplayable without it. This is a rendering exaggeration only: the engine's boomerang is 30 cm and nothing physical uses the drawing scale. 10. MTA 100 sessions draw their wind from a narrower band (0.1 to 1.1 knots) than the other events (0.4 to 4.8 knots). Both bands are reconstructed. The reason is physical: a 33-second flight in a two-knot breeze is carried more than 60 m downwind, clean out of the 50 m circle Sec.14.7 requires the catch to be made in, so an MTA event in an ordinary wind is simply unwinnable. Real MTA is contested in the calmest conditions a tournament can find, and MTA Unlimited exists for the rest. 11. In Fast Catch the clock carries the flights plus the deterministic run back to the 2 m circle after each catch, at the thrower's 6.5 m/s. Sec.14.5 times the whole turn, so the run must be on the clock; what is not on it is the real time a player spends deciding, which would make the score depend on how fast someone reads a slider. LICENCE ------- This reimplementation is released under the MIT Licence; see LICENSE.txt. The rulebook, the Plus Magazine article and the Wikipedia article remain the property of their respective authors and are cited, not reproduced.