Braking Generates Propulsion: Integrating Inertia in Walking and Throwing (The Kuriyama Protocol, Chapter 9)

Part 14 of a series; the ninth of fifteen chapter-by-chapter articles. Part 1: 10.5281/zenodo.23587879 · Part 2: 10.5281/zenodo.23587670 · Part 3 (v2): 10.5281/zenodo.23723510 · Part 4: 10.5281/zenodo.23609857 · Part 5: 10.5281/zenodo.23610607 · Part 6: 10.5281/zenodo.23682055 · Part 7: 10.5281/zenodo.23684537 · Part 8: 10.5281/zenodo.23684996 · Part 9: 10.5281/zenodo.23685960 · Part 10: 10.5281/zenodo.23686289 · Part 11: 10.5281/zenodo.23720048 · Part 12: 10.5281/zenodo.23723725 · Part 13: 10.5281/zenodo.23834848 Chapter 9 of The Kuriyama Protocol integrates the preceding layers into walking and throwing, treating throwing as walking compressed into one cycle. Braking is a means of transmission, not intrinsically a loss: proximal deceleration speeds distal segments, and braking is lost only when it occurs far in front of the centre of mass without being converted to rotation. Walking is an inverted pendulum; the trailing limb angle contributes about twice as much as ankle moment to raising propulsion when speed increases (Hsiao et al., 2015), and first-MTP dorsiflexion margin is the room for it. Elastic return requires short coupling time. Pelvic rotation contributes little to step length. Shoe mass tunes the leg's natural frequency. Throwing follows the same sequence once. Five gaps found while writing, mostly by calculation: - Parametric excitation by vertical centre-of-mass motion cannot by itself sustain arm swing: the arm's natural frequency (about 0.75 Hz) is detuned 26–28% from stride frequency (about 0.95 Hz), outside the first instability tongue (about ±4.5%). Fore–aft shoulder motion from trunk twist is the main driver. - The arms' centrifugal contribution to ground reaction force is about 1.3% of body weight, negligible; the claim extending "only pushing exists" on that basis is withdrawn. - A predicted braking/propulsive impulse ratio is identically about 1 at steady speed; magnitude must be used instead. - "Smaller vertical excursion means less loss" contradicts evidence that flattening the centre-of-mass path raises metabolic cost (Ortega & Farley, 2005; Gordon et al., 2009); rockers smooth the step-to-step collision instead. - In normal gait the swing-side pelvis drops slightly rather than lifting, and the book used leg length instead of inter-hip distance as the radius (about 6.4°, not 1.3°, to lift 2 cm). With minimum toe clearance about 1.3 cm (Winter, 1992), a few degrees of excess drop erase it: stumbling stems from failure to prevent excess pelvic drop. Five falsifiable predictions are registered (numbered 62–66, continuing the series): - P62. Restricting trunk twist reduces arm swing more than suppressing vertical centre-of-mass motion. - P63. At equal speed, larger body-weight-normalized braking impulse predicts higher cost of transport; the cue "body forward, legs behind" lowers both without changing speed. - P64. Frequent stumblers show greater swing-side pelvic drop; stance-side hip abductor training increases toe clearance more than ankle dorsiflexion training. - P65. Smaller loaded first-MTP dorsiflexion predicts smaller trailing limb angle; increasing dorsiflexion increases it. - P66. Equal added shoe mass lowers cadence more in shorter-legged people and more when placed at the toe. Refutations are welcome. The author has no formal research training. Corrections will be issued as new versions, with earlier versions kept retrievable. The article body is in Japanese. An English summary, the registered predictions and the reference list are included in the document. Contact: [email protected]