HORSESHOES — credits, sources, and everything this app reconstructed ==================================================================== This is an INDEPENDENT REIMPLEMENTATION of the sport of horseshoe pitching, written from the published rules. It is not published by, endorsed by, or affiliated with the National Horseshoe Pitchers Association of America, or with any Charter, League or manufacturer. The rules of the sport are the NHPA's work. THE SOURCE ---------- Every rule, dimension and scoring case in this app comes from one document: National Horseshoe Pitchers Association of America, "THE OFFICIAL RULES / REGULATIONS / GUIDELINES / SPECIFICATIONS FOR THE SPORT OF HORSESHOE PITCHING", adopted 16 July 2006, revised 1 January 2024. https://www.horseshoepitching.com/wp-content/uploads/2025/10/RGS2024revjan2024.pdf linked from https://www.horseshoepitching.com/rules/ Cited below as "RGS 2024" with the book's own structure: RULE n, Section X for the playing rules; GUIDELINE n for the guidelines; and "SPECIFICATIONS I" (equipment) or "SPECIFICATIONS II" (court layout) for the specification part. The book has no "Articles"; a court dimension cited to an NHPA "Article" is being cited to the Bylaws, which is a different document and contains no dimensions at all. Two of the numbers this app needs are in the book's DRAWINGS rather than its text, and were read off the rendered pages: "Stake Detail", printed p.49 — the stake at 78 degrees to the horizontal against a 15 in height, i.e. 12 degrees off vertical, with 6 in of clay over a 4 in slab. "Anatomy of a pitching shoe", printed p.49 — the five features the rules name: the toe calk, the body, the hook, the heel calk and the point. Technique and flight material, none of which is in the rulebook, came from the NHPA's own "How to Pitch Horseshoes" page and, through it, Roy W. Smith, "Science at the Stake" (1946), the sport's standard textbook; and from the NHPA's "Care of Clay & Other Pit Material" page and its World Tournament records. WHAT IS FAITHFUL — every one of these is the NHPA's number, not ours ------------------------------------------------------------------- THE SHOE (SPECIFICATIONS I, Section A) weight ceiling 2 lb 10 oz, and there is NO minimum weight maximum width 7-1/4 in maximum length 7-5/8 in maximum height 1 in, placed with the calks down on a level surface maximum opening 3-1/2 in new, 3-5/8 in on used shoes (a 1/8 in wear tolerance), "measured from a parallel line three-fourths of an inch (3/4") inward from a straightedge touching the tips of the shoe points" Note what that last rule does and does not say. It constrains the shoe's THROAT, three quarters of an inch back from the mouth. It says NOTHING about the gap between the tips. THE STAKE (SPECIFICATIONS II, Section B.6) diameter 1 in height above the platform 14 in to 15 in lean "a three inch (3") lean toward the opposite end", drawn at 78 degrees to the horizontal. Each stake leans toward the far end of the court, so the two stakes lean TOWARD EACH OTHER and the stake a pitcher is aiming at leans toward that pitcher. spacing 40 ft, "measured from the front of each stake, level with the pitching platform" — so the CENTRES are 40 ft 1 in apart clay clearance at least 21 in of pit substance in front of and behind the stake THE COURT (SPECIFICATIONS II, Section B) playing area 6 ft x 46 ft; 10 ft x 50 ft with the recommended buffer pitcher's box 6 ft x 6 ft at each end pit 43-72 in long, 31-36 in wide (this app builds the largest legal pit) platforms 18 to 20-1/2 in wide, at least 6 ft long, extended a further 10 ft imaginary stakes painted at 30 ft and 23 ft from the opposite stake foul lines 37 ft, 27 ft and 20 ft, measured from the front of the OPPOSITE stake. The stakes are always 40 ft apart; the FOUL LINE is what changes by division, and "women pitch 30 feet" is not a rule — 30 ft is where a short-distance pitcher STANDS, behind a 27 ft foul line. backboard at least 3 ft behind the stake, at least 1 ft high pit substance clay, sand, dirt or an approved synthetic, at least 4 in deep overhead clearance at least 12 ft divisions Open Men and Senior Men at 37 ft; Open Women, Senior Women, Elder Men and Junior Girls at 27 ft; Cadets at 20 ft (RULE 1) THE RINGER (RULE 3, Section B.2a; Glossary "Ringer" and "Straightedge") "A ringer is a live shoe that comes to rest while encircling the stake. A straightedge touching either the points or any part of the heel calks of the shoe must clear (not touch) the stake in order for it to be declared a ringer. A ringer has a value of three (3) points." The straightedge is "usually a metal bar tool ... about eight inches (8") in length". The app implements the test as three separate conjuncts and reports which one failed: the stake's axis inside the shoe's cavity; the straightedge, taken as the SUPPORTING LINE of the shoe's open end (so a proud calk moves it, as the rule's "or any part of the heel calks" requires), clearing the stake's section by a positive margin; and the shoe's own metal clear of the stake. THE REST OF THE SCORING (RULE 3, Section B; RULE 6, Section A; GUIDELINE 2, Section A) point a live shoe six inches or closer, INCLUDING a leaner: 1 point leaner "a live shoe that comes to rest vertically while touching the stake. This shoe has a scoring value of one (1) point." A leaner is worth ONE. "A leaner is two" is a backyard rule and is not the NHPA's; neither is any win-by-two. out of count more than six inches from the stake: no value how the six inches is measured — the rules never say in words, but the Glossary's "Scoring Area" builds a 31 in circle out of "the one inch (1") stake, plus the six inch (6") 'Shoe in Count' area surrounding the stake, plus an additional distance of approximately nine inches (9")". That arithmetic only closes if the six inches runs from the stake's SURFACE to the NEAREST POINT OF THE SHOE, which is what this app measures. The words are RECONSTRUCTED; the intent is the book's. cancellation RULE 6, A.1, clause by clause, including A.1.b.4's rule that opposing shoes TOUCHING the stake, or at an EQUAL distance from it, cancel each other and the next closest scores. the catch TWO DEAD ringers allow the closest shoe ONE point (A.1.b.1), where an inning with no ringers at all allows TWO (A.1.b.2). count-all RULE 6, A.2: each contestant scores what their own shoes are worth, 0, 1, 2, 3, 4 or 6 an inning — never 5. ringers only RULE 6, A.2b: one point a ringer, singles do not count. the ten calls GUIDELINE 2, Section A, verbatim, and the app calls each inning by its own name. fouls RULE 5: a shoe that "contacts the backboard, platform, court frame, or any ground outside the pit area before it comes to rest" is foul, scores as out of count wherever it lies, and is REMOVED from the pit before the next shoe is pitched. innings and delivery RULE 3, Sections A and C: four shoes an inning, two each; the contestant pitching first delivers BOTH shoes, then the other delivers both; both from the same platform; underhanded; thirty seconds for the pair. rotation RULE 7, A.1: in cancellation the contestant who SCORED pitches first in the next inning, and if neither scored, whoever pitched LAST goes first. RULE 7, B: count-all must use an alternate-first format, and A.2a's is the one the book calls fairest — first in innings 1, 4-5, 8-9, 12-13, 16-17 and so on. walking ends RULE 4, A.1: after four shoes the contestants walk to the opposite pit, score it and retrieve their shoes, so the next inning is pitched from the other end into an empty pit. length of game RULE 8, A: 40 points (reach OR EXCEED), or 40 shoes, or either. ties RULE 8, B: a two-inning tiebreaker, repeated until it breaks — not sudden death; or the game may simply stand drawn. ringer percentage RULE 11, C: ringers divided by shoes pitched. WHAT IS RECONSTRUCTED — none of this is fixed by the NHPA --------------------------------------------------------- The rulebook fixes a bounding box, a weight ceiling, one throat width and the court. It fixes nothing else about the shoe, and nothing whatever about the materials, the air or the pitcher. Every item below is this app's own choice. None of it is presented in the app as a rule. R1 THE SHOE'S OUTLINE inside its legal box: a toe arc of outer radius 3.50 in and inner radius 2.70 in over 236 degrees, and two prongs converging to square-cut tips, sized so the shoe is 7.00 in wide and 7.50 in long — both inside the NHPA's maxima. The prong convergence is SOLVED, not chosen: the app asks for an NHPA opening and computes the angle that produces it, so the opening is the input and the shape is the output. At the legal maximum of 3.50 in the convergence is 17.73 degrees and the TIP-TO-TIP gap comes out at 3.02 in. That tip gap is reconstructed; the NHPA publishes no figure for it. The prongs converge because the rulebook's own Glossary calls the hooks "a portion of the heel calk, designed to secure ringers" and its anatomy drawing shows them turned inward. R2 THE SHOE'S MASS AND MASS DISTRIBUTION: 2 lb 8 oz, inside the 2 lb 10 oz ceiling and inside the 2 lb 5 oz to 2 lb 9.3 oz range commercial shoes are sold at. The inertia tensor is integrated from the app's own outline at uniform density and a 3/8 in plate thickness; the NHPA publishes no moment of inertia for a pitching shoe and nobody else does either. R3 EVERY MATERIAL PROPERTY. The clay's stiffness and damping, the shoe-clay friction and the furrow it ploughs, the shoe-stake and shoe-shoe contact stiffness and restitution. The rulebook's only statement about the clay is that it is kept "in a soft, putty-like condition" (RULE 2, Section B) and that a shoe can become "buried" in it; the NHPA's own pit-care page adds that the fill is there "to cushion and hold the shoe when it lands instead of letting it bounce or slide", and that pitches which would slide on for a ringer in sand "will not slide on clay and will remain a short shoe". The app's clay is set from the shoe's own statics — the weight sinks it about 3 mm, and the damping is 1.7 times critical, so it does not bounce — and the numbers are ours. R4 AERODYNAMICS. Air density, two drag coefficients and the shoe's silhouette areas. No lift and no aerodynamic torque are modelled, so free-flight spin is constant. R5 THE RELEASE. Hand height, forward reach past the foul line, and the ranges the sliders offer. The rulebook says only that delivery is underhanded. The ARC, though, is not ours: the coaching literature publishes an apex of 7 to 10 ft, typically about 8 ft, and it is the only flight figure published anywhere — no time of flight, no release speed, no release angle exists in print. So the app SOLVES its release to hit that apex rather than picking one, which puts it at about 10.2 m/s at 35 degrees with a flight of 1.29 s. R6 THE OPPONENT. Four levels, each one three standard deviations on the speed, the line and the spin. Measured over 900 simulated shoes each: Novice 10.4%, Club 28.7%, A class 50.2%, Champion 80.6% ringers. The NHPA publishes NO ringer-percentage class boundaries — a Class is a relative seeding bucket of usually six to twelve pitchers, re-cut for each tournament (RULE 11, Sections D and E) — so the levels are labelled with their own measured figure and compared against ACHIEVED ones: Alan Francis won the 2026 world title at 89.37%, holds the tournament record at 90.26%, and the men's national top 100 begins at 48.48%. R7 THE SIMPLIFICATIONS. The shoe never breaks (RULE 9 is not modelled). There is no judge, no time limit, no doubles play, no handicap and no pacer. A foul is detected from where the shoe goes, not from where the pitcher's feet are. R8 ALL COLOUR, ART, SOUND AND CAMERA WORK. WHAT DIFFERS FROM THE REAL SPORT -------------------------------- * Singles only, against a simulated opponent. No doubles, no handicap, no pacer, no judge. * The pitcher does not walk, stand or step: the app checks a foul from where the SHOE goes (RULE 5, B.2c), not from a foot on a line. * Shoes never break, and no shoe is ever re-pitched. * The 30-second delivery limit is not enforced. * The clay is never re-prepared between games. * The stake is never repainted, and there is no wind, weather or sun. HOW IT WAS CHECKED ------------------ The engine is a pure, deterministic, DOM-free module with a seeded generator, and it is checked by four oracles that share no code with it: the ringing region in CLOSED FORM. The cavity is bounded by four curves — the straightedge, two prong edges and the toe arc — and a stake rings when its section is inside all four by more than its own radius. Every distance is a closed form, so membership is exact with no sampling. The engine was asked at 21,091 stake placements and agreed at every one, and at each of six boundary types the verdict was probed a MICRON either side and flipped exactly there. Sweeping the shoe's opening across the NHPA's legal range grows the region from 16.14 to 19.75 square inches, and shows that below an opening of 2.03 in the shoe's mouth is narrower than the stake and cannot get onto it at all, however well thrown. GUIDELINE 2's own enumeration of every legal inning, written as a decision table keyed on the ten calls. 1,048,576 four-shoe combinations were scored three ways against it, plus 65,536 more with shoes touching the stake and at equal distances, with no disagreement; the per-inning score set came out as exactly {0,1,2,3,4,6}, which is what RULE 6, A.2a states independently. an INDEPENDENT FLIGHT INTEGRATOR: an eighteen-state adaptive Cash-Karp 4(5) carrying a 3x3 rotation matrix rather than a quaternion, with the equations written out again from scratch. It agrees with the engine to 1e-9 m of position and 3e-8 rad of orientation over random flights with off-axis spin, and both conserve angular momentum and rotational energy. and the TURNS, measured rather than asserted: the arrival-yaw window is 23.5 degrees wide, the spin windows for the 1-1/4, 1-3/4, 2-1/4 and 2-3/4 turns are each about 0.077 rev/s wide and separated by 0.314 rev/s, and holding the spin fixed while changing the elevation moves the turn count by 0.8 turns — which is what "a consequence, not a preset" means. THE ORIGINAL ------------ Horseshoe pitching is a folk sport with no author. The National Horseshoe Pitchers Association of America was founded on 10 May 1921, with a predecessor body dating to 16 May 1914, and it standardised the 40 ft distance on 1 January 1925 — it had been 38-1/2 ft in 1909. The rules this app implements are the NHPA's and remain their work. THIS APP -------- Written for horseshoes.skillsafe.ai. Hand-written WebGL2, no libraries, no CDN, no external font, image, script or stylesheet: everything it needs ships in the bundle. It makes no network requests of any kind and stores nothing but your own settings, in your own browser. See LICENSE.txt.