The coefficient of restitution of pressurized balls: a mechanistic model
Bibliographic record
Abstract
Pressurized, inflated balls used in professional sports are regulated so that their behaviour upon impact can be anticipated and allow the game to have its distinctive character. However, the dynamics governing the impacts of such balls, even on stationary hard surfaces, can be extremely complex. The energy transformations, which arise from the compression of the gas within the ball and from the shear forces associated with the deformation of the wall, are examined in this paper. We develop a simple mechanistic model of the dependence of the coefficient of restitution, e, upon both the gauge pressure, PG, of the gas and the shear modulus, G, of the wall. The model is validated using the results from a simple series of experiments using three different sports balls. The fits to the data are extremely good for PG > 25 kPa and consistent values are obtained for the value of G for the wall material. As far as the authors can tell, this simple, mechanistic model of the pressure dependence of the coefficient of restitution is the first in the literature.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".