HIGH JUMP — credits, sources and provenance =========================================== WHAT THIS IS ------------ An independent, unofficial browser simulation of the athletics high jump. It is not affiliated with, endorsed by, or connected to World Athletics, any Area Association or any national federation. No World Athletics material is redistributed here beyond rule text quoted for reference and identification. There is no "original game" being replicated: the reference is the SPORT, as codified by World Athletics in Book C — C2.1 Technical Rules, and as measured by the published biomechanics literature. Everything below says which document each number came from. THE EVENT --------- High jump has been contested in its modern form since the 19th century. The technique now used universally, the Fosbury flop, is named after Dick Fosbury, who won the 1968 Mexico City Olympic gold with it; Debbie Brill developed the same technique independently and called it the Brill Bend. The men's world record is 2.45 m (Javier Sotomayor, CUB, 1993) and the women's is 2.10 m (Yaroslava Mahuchikh, UKR, 2024). SOURCES, ALL OPENED ------------------- S1 World Athletics, Book C — C2.1 TECHNICAL RULES. Official PDF, 124 pages, amendment table running to 22 December 2021, in force 1 January 2022. worldathletics.org download "C2.1 Technical Rules". Rules used: TR25 (general field events, including the trial clock and ties), TR26 (vertical jumps: trials, height measurement, the crossbar, placings, the jump-off, extraneous forces) and TR27 (high jump: competition, runway, apparatus, landing area). S2 Wikipedia: "High jump", "Fosbury flop", "Straddle technique", "Scissors jump", fetched 2026-09-12 through the MediaWiki API. Used for the history of technique, the world records, and the descriptions of how each style crosses the bar. S3 de Leva, P. (1996). "Adjustments to Zatsiorsky-Seluyanov's segment inertia parameters." Journal of Biomechanics 29(9): 1223-1230. Tables 1, 3 and 4 supply every segment mass, length, centre-of-mass position and radius of gyration in this app, for both sexes. S4 Dapena, J. (2002). "The evolution of high jumping technique: biomechanical analysis." ISBS 2002, Cáceres, Spain, pp. 3-10. The source for the framing ("clear a bar set as close as possible to the peak height reached by the c.m."), for the 5-7 cm flop advantage over the dive straddle, and for the finding that almost all the flop's angular momentum is generated at take-off. S5 World Athletics, "Biomechanical Report for the World Indoor Championships 2018: High Jump Men" (Birmingham). Official PDF, 49 pages. The measured H1/H2/H3, velocities, take-off angles, contact times, step lengths and take-off distances for all eleven finalists, including Mutaz Barshim and Danil Lysenko. This is the dataset that decides the app's headline question. THE HEADLINE RESULT ------------------- It is widely said that the Fosbury flop works because it lets the jumper's centre of mass pass UNDER the bar. This app does not assume that; it computes it. * The engine's optimised flop clears a bar 4.6 cm ABOVE the peak of its own centre of mass. So the centre of mass really can pass under the bar, and this model says by about five centimetres. * But NOT ONE of the eleven finalists World Athletics measured in 2018 did it. Every one carried the centre of mass ABOVE the bar: +2 cm (Wang) to +12 cm (Thomas), mean +7.0 cm. The folklore describes a geometric possibility, not what elite high jumping actually does. The ~12 cm between the two is headroom the technique still has on paper. * The mechanism is real all the same. At the bar plane the modelled flop carries its centre of mass 77 mm OUTSIDE the body, in the hollow under the arch. The dive straddle keeps it 33 mm inside the body, the Eastern cut-off 16 mm inside, the scissors 8 mm inside. * Whole comparison, from an identical centre-of-mass arc peaking at 2.317 m (the 2018 finalists' mean H3), bar height minus centre-of-mass peak: Fosbury flop +4.6 cm Eastern cut-off −5.8 cm Dive straddle −6.6 cm Scissors −46.8 cm Legs-up (1797) −65.0 cm Flop over dive straddle: 11.2 cm. Dapena (S4) documents "about 5-7 cm", so this model overstates the gap by roughly 5 cm. Said plainly: the ordering reproduces, the magnitude does not. * The model cannot explain why the flop displaced the Eastern cut-off at all — it puts them only 10.7 cm apart on geometry, and the documented reason the flop won is that deep foam landing areas arrived (S2), which is a property of the facility and not of the flight. The model has no landing dynamics and says so. CALIBRATION FOLLOWS THAT FINDING ------------------------------- A perfect jump in the app leaves the ground at Vv = 4.362 m/s, which is the vertical velocity implied by the finalists' own measured centre-of-mass rise (H3 − H2 = 0.970 m mean). It is NOT the 4.64 m/s the same report prints for Vv at toe-off, because — as the section below shows — those two numbers cannot both be right. Calibrating to the rise keeps the app internally consistent and puts a flawless jump at 2.36 m, below the world record. A PUBLISHED TABLE THAT DOES NOT CLOSE ------------------------------------- S5's derived columns all check out exactly: H3 diff = H3 − mark, PPH diff = peak pelvis − mark, resultant velocity = hypot(Vh, Vv), and the take-off angle, for all eleven athletes. Each athlete's stature can be recovered four independent ways from the percentage columns and the four agree to within 12 mm. The flight, however, does not close. A free centre of mass must rise exactly Vv²/2g. The measured rise (H3 − H2) is 90.2 % of that on average, and the horizontal flight distance is 93.6 % of Vh·Vv/g. One explanation fits both: Vv at toe-off is reported about 5-7 % high (rise scales as Vv², range as Vv), which is the classic signature of endpoint bias when digitised centre-of-mass data is low-pass filtered and differentiated at the last frame of ground contact. It is a measurement artefact, not anything unphysical in the jumps — but it means the table's own numbers cannot all be right at once. This app's engine closes both identities to machine precision. A PUBLISHED TABLE THAT DISAGREES WITH ITSELF -------------------------------------------- de Leva (S3) Table 4 gives the trunk twice: as one segment and as three. For females the two agree exactly — mass-weighting the three sub-segments puts the trunk centre of mass 219.71 mm below the suprasternale, and so does the one-segment row. For MALES they differ: 241.554 mm from the three-part decomposition against 238.610 mm from the one-segment row, a 2.944 mm gap, 0.55 % of trunk length. This app uses the three-part trunk, because it needs a spine that can arch, and reports the residual rather than hiding it. WHERE THE RULES DO NOT DECIDE ----------------------------- G1 TR26.9 never states that a jump-off athlete who fails while another clears is out. The rule only moves the bar; the elimination is established solely by the rule's own worked example, where C fails at 1.89 and is placed third. This app follows the example. G2 TR26.9.4 lowers the jump-off bar 2 cm whenever everybody fails, with no floor. Repeated failures can legally put the bar below a height every athlete in the jump-off has already cleared. The app lets that happen and flags it on the board. G3 TR26.8.3 shares a non-first place, but neither TR26 nor TR25 says whether the athlete after two shared seconds is third or fourth. The app skips by the group size, which is universal practice and not a rule. G4 If the announced progression runs out, TR26 does not say what the next height is. The app extends by the competition's own last increment and marks the jump-off extrapolated. G5 TR26.9.2 says "Each athlete shall have one jump at each height", which read literally forbids ever returning to a height — yet the rule's own worked example sends A and B back to 1.91 after the bar was lowered to 1.89. It has to mean one jump per height per round. Related, and not a gap but a trap: TR26.2 counts three consecutive FAILURES, and a pass taken between two failures does not reset the count. The published example demonstrates it — athlete A fails at 1.91, passes, fails twice at 1.94, and is out. The first version of this app's test suite asserted the opposite. The engine was right. PROVENANCE TALLY ---------------- This build declares 77 constants and modelling choices: DOCUMENTED 51 66.2 % DERIVED 8 10.4 % MEASURED 5 6.5 % CALIBRATED 2 2.6 % RECONSTRUCTED 11 14.3 % The full list, item by item with its source, is in js/provenance.js and is rendered in the app's Lab panel. The page harness recounts it from the shipped file and fails the build if the number printed on the page disagrees. WHAT IS RECONSTRUCTED --------------------- Every joint-angle trajectory: the arch timing, the pike, the lead-leg drive, the arm carriage. Published biomechanics gives postures at instants, never angle-by-angle paths. The five techniques' shapes were found by the same bounded numerical search against the same objective, so no technique is hand-tuned to win. Also reconstructed: the segment capsule radii (de Leva publishes no surface geometry at all), the joint ranges of motion that bound the search, the definitional test for each technique, the 2 mm rattle tolerance before a graze counts as dislodging the bar, the rival jumpers, and the three-input control scheme. WHAT THE MODEL IS NOT --------------------- The flight is solved in the plane perpendicular to the bar; rotation is constrained to the bar axis, so the model cannot twist. The run-up and take-off are not simulated — the jump begins at toe-off. Air resistance is ignored. The landing is not simulated. Limb motion is planar apart from one abduction angle per segment. VERIFICATION ------------ The engine harness runs 109,553 assertions with four independent oracles: a point-cloud centre of mass that integrates mass over 57,600 sampled point masses instead of using the published fractions; a pairwise count-back rebuilt from the rule text and diffed against the engine over 400 randomised competitions; a dense-surface clearance test that samples segment surfaces instead of doing capsule algebra; and a post-hoc angular momentum check that recomputes L from the finished trajectory. The three renderer meshes are checked for outward normals face by face, each against a deliberately reversed control that proves the check can fail. The World Athletics worked example is reproduced move for move. THANKS ------ To Dick Fosbury and Debbie Brill, who both worked out that you could go over backwards. Built as an independent reimplementation. MIT licensed — see LICENSE.txt.