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In a nutshell
- Researchers discovered that when urine hits a surface at less than 30 degrees, splashback is reduced by 95% compared to perpendicular impact.
- Two new urinal designs—the “Cornucopia” and “Nautilus”—use this critical angle principle to virtually eliminate splashing while improving accessibility.
- Widespread adoption could prevent about one million liters of urine from splashing onto floors daily in the US alone, saving substantial cleaning water and resources.
WATERLOO, Ontario — For over a century, men’s public restrooms worldwide have featured essentially the same urinal design. Despite their universal presence, these fixtures have a notorious flaw that anyone who’s used them knows all too well—they splash. A team of engineers from the University of Waterloo in Canada and Weber State University in Utah has finally solved this problem using basic physics principles and some clever mathematics.
In a research paper published in PNAS Nexus, the scientists demonstrate how relatively simple changes to urinal geometry can dramatically reduce splashback, improving hygiene and potentially saving millions of liters of cleaning water daily.
The Battle Against Tinkle Sprinkle
The urinal hasn’t changed much since Marcel Duchamp featured one in his provocative 1917 artwork “La Fontaine.” This design stagnation has perpetuated a messy problem: microscopic droplets spraying beyond the fixture onto floors, walls, and sometimes users themselves.
These seemingly minor splashes add up to major issues. With approximately 56 million urinals in non-residential settings across the United States, researchers estimate more than 350,000 liters of urine splashes onto floors daily. Once settled, these droplets become breeding grounds for bacteria and contribute to the characteristic odors of poorly maintained restrooms.
Cleaning this mess requires chemicals, water, and labor. The Toronto subway system spends over $122,000 Canadian dollars annually per bathroom on cleaning costs alone.
Previous solutions have mostly involved add-ons like absorbent mats or aiming targets. Amsterdam’s Schiphol Airport painted small fly images near urinal drains, reportedly cutting spillage by 50-80% and reducing cleaning costs by 8%. But these workarounds never addressed the fundamental physics of the problem.
The Physics Breakthrough: The Critical Angle
Dr. Zhao Pan and colleagues took a fresh approach by examining why splashback occurs in the first place. They found that the key factor was the “impinging angle”—the angle at which the liquid stream hits the urinal surface.
Through mathematical modeling and controlled experiments, the researchers discovered that when a stream hits a surface below a critical angle of approximately 30 degrees, splashback drops dramatically—by about 95% compared to a perpendicular impact.
This principle exists in nature too: when dogs urinate against vertical surfaces, they naturally create a shallow angle that minimizes splash onto their fur—a fortunate side effect of territorial marking behavior.
With this critical angle identified, the team used mathematical equations to design urinal surfaces that would ensure all impacts occurred at or below 30 degrees, regardless of user height or aim. Two distinct designs emerged from this work: the “Cornucopia” and the “Nautilus.”
Revolutionary Results and Real-World Impact
To test their designs, the researchers built prototypes and compared them against a replica of Duchamp’s “La Fontaine” and a modern commercial model. Using a custom apparatus that simulated human urination, they measured splash under various conditions.
The results were striking. While conventional designs created splatter extending up to one meter away, the new designs produced almost no visible splash. Measurements confirmed that under high-splash conditions, the Nautilus design reduced splashback by 85-95% compared to commercial urinals.
Beyond eliminating splash, the Nautilus design offers practical advantages. Its relatively low profile makes it accessible to users of all heights, including children and wheelchair users—solving another common problem with conventional urinals that require uncomfortable compromises in installation height.
The impact of widespread adoption would be substantial. If these designs replaced existing urinals in U.S. non-residential settings alone, approximately one million liters of urine would stop splashing onto floors daily. Assuming ten times that volume of water is currently used for cleaning, this could save up to ten million liters of water daily—particularly valuable in water-stressed urban areas.
What makes this solution especially elegant is its simplicity. The improved performance comes solely from reshaping the urinal’s geometry, requiring no expensive materials or complex systems. The designs can be manufactured using conventional porcelain and standard techniques, making them immediately practical for widespread adoption.
Like dogs being able to avoid their own spray, now humans can benefit from the same physics principles, through intentional design rather than evolutionary coincidence. From public health to sustainability to accessibility, this reimagining of the humble urinal shows how science can solve everyday problems hiding in plain sight.
Paper Summary
Methodology
The researchers approached this problem systematically, combining theoretical modeling with experimental validation. They first developed a mathematical model to predict how splash generation relates to the angle at which a liquid stream hits a surface. This model extended previous research on droplet impact dynamics, introducing a “modified Weber number” to account for how the normal velocity component affects splash generation. After predicting that a critical impinging angle of approximately 30 degrees would dramatically reduce splash, they tested this theory using an experimental setup. This involved a custom apparatus with an anatomically accurate urethral nozzle that delivered controlled water flows onto surfaces at various angles. By precisely measuring the mass of liquid that splashed versus the total volume delivered, they quantified a “splash ratio” for different angles and confirmed their theoretical predictions. With this critical angle established, they solved differential equations to design urinal surfaces that would ensure all liquid impacts occurred below this threshold angle, regardless of user height or aim direction. The resulting designs were then prototyped and subjected to comparative testing against conventional urinals.
Results
The experimental results showed remarkable splash reduction with the new designs. When testing traditional urinals, researchers found extensive splatter patterns extending up to one meter from Duchamp’s “La Fontaine” design and about half a meter from a modern commercial urinal. In contrast, the novel Cornucopia and Nautilus designs produced virtually no visible splash on surrounding floors. Quantitative measurements revealed the Nautilus design reduced splash by 24% compared to commercial urinals under moderate conditions, and by 85-95% under high-splash conditions. The Cornucopia design performed even better in some tests. The team mapped impinging angles across each urinal’s surface, confirming that conventional designs had significant areas where impacts occurred at high angles (60-90 degrees), while the new designs maintained angles consistently below 30 degrees across their entire surfaces. They also noted that the prototypes were made from coated foam with a contact angle of about 60 degrees, which is actually less favorable for splash reduction than the porcelain typically used in commercial urinals, suggesting even better performance could be achieved with standard materials.
Limitations
The researchers acknowledge several limitations in their study. The experimental setup, while using an anatomically accurate nozzle, cannot perfectly simulate all variables in human urination, such as varying stream cohesion and natural variations in flow rate throughout the voiding process. The prototypes were constructed from foam coated with resin rather than the porcelain used in commercial urinals, which may affect wettability and splash characteristics. Additionally, the study focused primarily on physical splash reduction and did not extensively evaluate other practical considerations such as manufacturing feasibility, cleaning ease, or user experience factors beyond splash reduction. The research also did not include field testing in actual public restroom settings, which would provide data on real-world performance and user acceptance. Finally, while the team calculated potential water and resource savings based on their laboratory findings, these projections would need validation through larger-scale implementation studies.
Funding and Disclosures
This research was supported by the University of Waterloo, Weber State University, and the Natural Sciences and Engineering Research Council of Canada (NSERC) through Undergraduate Student Research Awards (USRA). The authors declared no competing interests that might influence their work or its interpretation. The study was conducted as part of academic research with the stated goal of improving sustainability, hygiene, and accessibility in public facilities.
Publication Information
The study, titled “Splash-free urinals for global sustainability and accessibility: Design through physics and differential equations,” was published in PNAS Nexus (2025, Volume 4, Issue 4, pgaf087) on April 8, 2025. The paper was authored by Kaveeshan Thurairajah, Xianyu (Mabel) Song, JD Zhu, and Mia Shi from the Department of Mechanical and Mechatronics Engineering at the University of Waterloo, along with Ethan A. Barlow and Randy C. Hurd from the Department of Mechanical Engineering at Weber State University, with Dr. Zhao Pan as the corresponding author. The research was accepted for publication on February 13, 2025, after being initially submitted on August 2, 2024. It was published as an open-access article under the Creative Commons Attribution License, making the findings freely available to the public and other researchers.
