Splash-free urinals for global sustainability and accessibility: Design through physics and differential equations
Bibliographic record
Abstract
Abstract Urinals are a staple of public spaces yet their designs have remained essentially stagnant for over a century. The use of urinals often results in significant splatter (splashback) as urine splashes upon impact with the urinal generating droplets which travel back onto the floor and user, which generates unhygienic environments, high cleaning costs, and adds unpleasant workload for custodial staff. Impinging stream angle is one of many factors that affect splashback. We theoretically predict and experimentally validate that when the impinging angle is below an invariant critical value of ∼30∘, the flow rate of splashback under human urination conditions can be significantly suppressed. We propose novel urinal designs that were generated by solving differential equations derived from the isogonal curve problem to ensure the urine stream impacts at or below this critical angle. Experiments validate that these designs can substantially reduce splashback to only 1.4% of the splash of a common contemporary commercial urinal. The widespread adoption of the urinal designs described in this work would result in considerable conservation of human resources, cost, cleaning chemicals, and water usage, rendering large-scale impacts on modern society by improving sustainability, hygiene, and accessibility.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".