MINIGOLF - credits, sources, and every figure this app had to choose ==================================================================== WHAT THIS IS An independent reimplementation of COMPETITION MINIGOLF - the codified sport ("Bahnengolf"), not a novelty crazy-golf course - played on the concrete ("Beton") lane system patented by the Swiss garden architect PAUL BONGNI in 1950 (patent granted 1953). The first standardised course to his plans opened at Ascona on Lake Maggiore on 19 March 1954; the second at Locarno at Easter the same year; by the end of 1954 there were eighteen, all in Switzerland. The sport is governed today by the WORLD MINIGOLFSPORT FEDERATION (WMF) and its member federations. This app is NOT affiliated with, endorsed by or connected to the WMF or any member federation. It implements a published technical standard; it does not reproduce anyone's creative work. WHY THIS SYSTEM AND NOT ANOTHER Bahnengolf has several standardised systems. Only ONE has a fixed eighteen-lane list in a fixed order: "the lanes must always be arranged in the same order, 1 to 18" (WMF Rulebook 2.4, rule 2). That is the concrete system, and it is what this app ships. The other well-known system, MINIATURGOLF (Eternit, 6.25 m x 0.90 m), is an 18-of-30 catalogue in any order, and it is where the familiar lane NAMES live - Pyramiden, Salto, Doppelwellen, Rohr, Labyrinth, Vulkan, Winkel, Blitz and the rest are the official names of the Miniaturgolf thirty. The concrete system's lanes carry NO official names at all: every source - the current WMF chapter 2.4, the OeBGV 2015 German edition and the DMV German S11 - labels them "Lane 1" to "Lane 18" and nothing else. The single exception is lane 7, universally called the WEITSCHLAG (long drive). This app therefore names the lanes by number, as the standard does, and describes each obstacle in the standard's own words. PRIMARY SOURCES WMF Rulebook, chapter 2.4 "System-specific rules concrete", update 260101 (in force from 1 January 2026). https://gov.minigolfsport.com/structures/official-wmf-rulebook - the eighteen lanes, their obstacles, their border lines and their repositioning lines; "Length: 12.00 m Width: 1.25 m Target circle diameter: 2.50 m"; the 30/40/8 cm tee marking; the +/- 2 % construction tolerance; mirror-image versions permitted on lanes 4, 5, 9, 11, 12, 13, 14 and 16; the hole labelled 10 cm on every lane's drawing. WMF Rulebook, chapter 2.3 "Worldwide international sport rules" (ISPR), update 260101. - rule 2.11, the hole diameter ceiling of 120 mm; rule 2.2, the marking colours (border line RED, helping lines dotted BLACK, repositioning markings BLACK); rule 2.6, "every obstacle must be different from the others in the same course, not only outwardly but also from a playing point of view"; rule 2.7, the definition of the border line; rule 3, the putter (no aiming devices, striking face at most 40 cm^2); rule 4.2, the ball; rule 8, the stroke, the border line, repositioning and holing out; rule 9.1, the stroke cap. DMV (Deutscher Minigolfsport Verband) S1 "Internationale Spielregeln" and S11 "Normungsbestimmungen fuer Beton", Stand 01/2026, https://www.minigolfsport.de/ - the German editions of chapters 2.3 and 2.4, read as an independent second rendering of every figure. DMV S12 "Normungsbestimmungen fuer Miniaturgolf", Stand 01/2026 - used for ONE figure about the concrete system, which chapter 2.4 never states: lane 28 of the Miniaturgolf catalogue says "die Hoehe des Zielhuegels entspricht der Ausfuehrung bei Bahn 8 Beton: 5-15 cm", which is where this app's lane 8 cone height comes from. OeBGV (Oesterreichischer Bahnengolfverband) Regelwerk 2.3 "MINIGOLF (Concrete) (WMF-2.4) (Mi)", 2015, https://www.oebgv.at/uploads/pdf/regelwerk/ - the same standard, in German, eleven years older, and it agrees with the current chapter 2.4 on every lane. WMF Rulebook chapters 2.8 "Homologation rules for courses" and 2.9 "Tournament approval" - the boundary MATERIALS for concrete lanes ("metal tubes, flat iron") and the approval procedure. de.wikipedia.org/wiki/Bahnengolf and /wiki/Minigolf - used only where the federation documents are silent, and flagged below wherever it is: the history, the ~25 m length of the Weitschlag, the name "Weitschlag" itself, the observation that a "dead" ball rolls considerably shorter than a fast one, and the statement that a perfect eighteen-stroke round had been achieved by the late 1970s "wenn auch nicht auf Betonbahnen" - though not on concrete lanes. PHYSICS SOURCES B. W. Holmes, "Putting: How a golf ball and hole interact", American Journal of Physics 59 (1991) 129, doi:10.1119/1.16592 - the critical capture speed, 1.626 m/s for a 108 mm hole. This app derives the same criterion from the geometry (the ball is unsupported across the chord it crosses and is captured if its centre falls to the lip plane by the far side, so V <= c*sqrt(2g/r)), which returns 1.637 m/s at the same dimensions, 0.7 % from Holmes. R. Cross, measured golf-ball friction on a putting surface: sliding about 0.33, rolling 0.044-0.051. These are the two friction coefficients this app uses. THEY WERE MEASURED ON A PUTTING GREEN, NOT ON A MINIGOLF LANE - see the reconstructed list below. D. G. Alciatore ("Dr. Dave"), Illustrated Principles of Pool and Billiards technical proofs, TP 4.1 (the sliding-to-rolling transition, independently derived) and TP 6.3 (the rail rebound: scale the normal component by the restitution, keep the tangential component but for friction, so the rebound is always shallower than a mirror). USGA Stimpmeter instructions - the ramp that releases a ball at 1.83 m/s, used here only to express the rolling resistance as a Stimpmeter reading a reader can judge. Classical rigid-body mechanics for the rest: I = (2/5) m r^2, a struck sphere rolls at 5/7 of the speed it was struck after sliding 12 v0^2 / (49 mu_k g), and a rolling sphere accelerates down a slope at 5/7 g sin(theta). WHAT IS FAITHFUL The eighteen lanes in the standard's order, at 12.00 m x 1.25 m, with a 2.50 m target circle and a 100 mm hole at its centre; the 30 cm tee circle 40 cm from the lane start with an 8 cm mark; the border line placed where each lane's own rule places it; the marking colours; the eight mirror-eligible lanes labelled as such; lane 7 as a fan defined by tangent lines with 2 m boundary markers on an optional 50 cm hill and protective structures at least 50 cm high; lane 15's tunnel, plateau, centre exit gate and its secondary teeing-off point 30 cm from the tunnel end and 8 cm across; lane 18 with no target circle and no hole at all, completed only when the ball stays in the collecting box; lane 2's four stones with their own 7 cm relief; lane 10's three hills and its rule that the ball must touch the lane between them; lane 6's bunker, which must be carried and which costs the stroke if it is touched. The rules: every stroke one point; six strokes and then a seventh point, seven the highest score on a lane; the border line passed by the ball's point of contact; from the tee again if it was not passed; replaced where it left the lane if it was; 20 cm relief off a rail on every system; 30 cm off an obstacle already passed; a ball rolling back over the border line stopped at the crossing; holed only when at rest such that it cannot leave the target under its own power. The ball: 37-43 mm across, under 120 g, rebounding at most 85 cm from a 1 m drop onto concrete at 25 C. The restitution used at a rail is the square root of that rebound ratio, so it comes out of the sport's own homologation test rather than being tuned. WHAT THIS APP CHOSE - the reconstructed list, in full Chapter 2.4 says "the construction-drawing set signed by Paul Bongni counts as the normative specification". That drawing set is not public, and the chapter's per-lane text gives obstacle POSITIONS and RULES but almost no obstacle DIMENSIONS. Everything below is therefore this app's and is labelled as such in the app itself, lane by lane. Across every lane: - rail height 0.06 m. No rule document states one; chapter 2.8 gives only the material. - hole depth 0.10 m. Not published anywhere checked; the rules give only the capture condition. - surface friction: sliding 0.33 and rolling 0.047 (a Stimpmeter reading of 11.9 ft for the medium ball). No federation document publishes anything about how fast a concrete lane runs, so these come from Cross's measurements on a PUTTING GREEN. - the ball's rolling resistance is made to fall with its restitution, spanning about a factor of two across the four balls. The sport says a dead ball "rolls considerably shorter" and attaches no number; deriving the link from hysteresis directly gives a factor of five, which no player would recognise and which makes half the lanes impossible to ace. - the four balls' exact bounce, diameter and mass inside the legal ranges. - the reading of "length 12.00 m" as the centreline from the back rail to the far edge of the target circle, so the path to the circle's centre is 10.75 m. - the hole at the exact centre of the target circle: that is how every lane's drawing shows it, but no clause states it. Per lane, the obstacle sizes and their positions along the lane - the turn radii on lanes 4, 9, 12 and 14 and the right-angle CORNER radius on 16, the curve radii on 5, 11 and 13, the 5 % bank that stands in for the INCLINE ("Schraege") the standard names on lanes 5 and 13, the stone sizes and the 0.30 m passages, the hill heights on lane 10, the bunker's 0.55 m gap and its ramp on lane 6, the slope and passage on lane 8, the tunnel bore and plateau on lane 15, the wedge gate on lane 17, and the slope and box on lane 18. Lane 8's cone height is the ONE exception: 5-15 cm is sourced, via the Miniaturgolf chapter's cross-reference, and this app uses 8 cm. Lane 7's target circle is drawn as 2.25 m RADIUS because the WMF drawing labels "2.25 m" with a single arrow from the centre, unlike lane 1 where "2.5 m" spans the whole circle; the app says so in the lane panel because the text does not settle it. Lane 7's fan is modelled as a 5.20 m wide field rather than a true trapezium, and its 50 cm protective height is applied all the way round rather than only behind the circle. Lane 9's two bars were 0.69 m wide in the first draft, with a 0.13 m overlap on the centre line. The ace search proved that lane UNPLAYABLE - a rail rebound can only make a crossing angle shallower, so no stroke that passed the first bar could reach past the second - and they are 0.525 m wide here. That is a reconstruction being corrected by a test, not a sourced change. Colours, lighting, the surrounding ground, the camera, and the four balls' names. The rules colour the MARKINGS and nothing else. Not modelled: the referee, the penalty cards, the twenty centimetre placement as a CHOICE the player makes (the app applies it automatically when the ball lies within 20 cm of a rail), the seven centimetre stone relief on lane 2 as an interactive choice, warming or cooling a ball, and the tunnel roof on lane 15 as anything other than a ceiling the ball cannot pass through. VERIFICATION Every lane in this app has been proved ACEABLE by searching over aim, stroke strength and ball choice on the real engine - which is the standard's own design principle: "through the standardisation it should theoretically be possible to master every lane with an ace". The ace found for each lane, and how wide the window around it is, is in the deploy record. The physics is checked against closed forms rather than tuned by eye: the 5/7 law, the slide distance and time, the total roll-out, energy that never increases, a control with a restitution above 1 that must gain energy, and the hole's capture threshold measured as a RESULT and compared with Holmes. An independent oracle solves the same motion in closed form and finds every rail contact by root-finding, sharing no dynamics code with the engine. THANKS To Paul Bongni, who standardised a game so that players in different towns could compete at all, and to the federations who publish the standard rather than keeping it.