Toilets and geometry
Toilets and geometry intersect in a fascinating way, particularly through the analysis of modern toilet design and efficiency. This relationship is underscored by the fact that the proper disposal of human waste is a critical health concern across all societies, with a significant volume of bodily waste produced daily. Historically, human beings have formalized waste disposal through various systems, evolving from early dry toilets to the sophisticated flush toilets we see today. The geometry of these toilets is vital for their operation, which typically involves a tank, bowl, and an S-shaped siphon that works together to facilitate waste removal through gravitational and siphon action.
With increasing awareness of resource conservation, there has been a push for low-flush and water-saving designs, such as dual flush toilets and composting options that require no water. Additionally, advancements have led to features aimed at enhancing user comfort and health monitoring, including heated seats and built-in analysis tools. Understanding the geometry and operation of toilets is not just a matter of design but also one of public health, as adequate restroom facilities and equitable access are essential considerations in planning for urban spaces. These aspects underscore the importance of toilets in both historical and contemporary contexts, highlighting their role in maintaining sanitation and health globally.
Toilets and geometry
SUMMARY: The geometry of modern toilets has been analyzed by engineers using a variety of mathematical and statistical methods.
In all human societies, the disposal of bodily waste has been a primary health concern. It has been estimated that the average human being produces one to two liters of urine and one-quarter to one-half kilogram of feces each day. Fecal matter, in particular, can contribute to the spread of a wide range of diseases, as bacteria and other pathogens can enter food and water when waste is not treated properly. Such problems are especially prevalent in areas of high population density and limited water resources. Over time, a range of toilets and treatment systems have been developed to deal with sewage. Because of the lack of resources and infrastructure, many places in the world in the twenty-first century still contend with waterborne diseases that originate in human waste.
History
Given that many mammals, including most primates, choose to defecate in selected areas in their habitat, it is likely that humans have had specific defecation sites throughout history. Dry toilets, such as pit latrines and outhouses, are ways communities formalized the locations in which humans defecate and are still used in many parts of the world in the twenty-first century. In these systems, waste is concentrated in one place, ideally where it will not infect drinking water. The earliest sitting toilets that used running water to carry waste away date to at least 2500 BCE in the civilizations of the Indus Valley, in what is now India and Pakistan. In 1596, Queen Elizabeth I’s godson, Sir John Harrington, invented the first indoor flushing toilet. In 1775, Alexander Cummings, a Scottish watchmaker who studied mathematics, filed a patent for a flush toilet. However, it was not until the late 1700s in Europe and 1800s in America that further modifications and inventions ushered in an age of modern plumbing.
Design and Operation
The geometry of modern toilets is essential to their efficiency and is extensively analyzed by design engineers using a variety of mathematical and statistical methods. The modern home tank toilet consists of a storage tank, a bowl, and an S-shaped siphon. Water is stored in the tank. When the toilet is flushed, this water is released into the bowl through rim jets on the underside of the toilet’s rim and through a tube called the “siphon jet” that allows most of the water to flow directly into the bowl. The bowl is attached to an S-shaped tube, and the influx of water from the tank into the bowl pushes the waste and water over the lip of the “S” and down to an attached waste system. The bowl clears because of the siphon action created. When the toilet finishes flushing, air enters the siphon tube and stops the siphon. Meanwhile, a flapper valve in the toilet tank closes the connection between the tank and the bowl and allows the tank to refill.
New Developments
The flush toilet takes a large volume of water to operate. In an era of increasingly limited resources, there has been a movement to create low-flush, no-flush, and water-saving toilets. For example, toilets manufactured in the United States prior to 1994 used 13 liters (3.5 gallons) of water per flush. The US Environmental Protection Agency issues regulations concerning toilet specifications. The Energy Policy Act of 1992 required that toilets use 6 liters (1.6 gallons) or less per flush. Modern high-efficiency WaterSense-labeled toilets use 4.8 liters (1.2 gallons) per flush. The WaterSense Specification for Tank–Type Toilets (Version 2.0) officially limits the maximum water usage per flush to 4.8 liters (1.28 gallons) for toilets that have the WaterSense label.
In Europe, dual flush toilets are common, allowing the user to choose how much water to use depending on whether urine or feces is being flushed. Other technologies, including composting toilets that require no water and allow waste to biodegrade for use as fertilizer, have been developed for use by ecologically conscious consumers and people in areas of the world where water or sewage treatment facilities are limited. In addition, a number of toilets have been developed that include warmed seats, water and air jets for cleaning and drying the user, and built-in stool and urine analysis for health assessments.
Modeling Toilet Use
Many modern homes have multiple toilets and ensuring adequate toilet facilities in public places requires planning and calculation. Two statistical studies of public restroom use in the late 1980s are still referenced in the twenty-first century. They focused on the amount of time men and women spent in the restroom, and they provided some of the first quantitative evidence that women take longer and thus require more toilets. This equity principle, known as “potty parity," has been enacted into law in many places.
Bibliography
George, Rose. The Big Necessity: The Unmentionable Subject of Human Waste and Why It Matters. Henry Holt and Co., 2008.
Raum, Elizabeth. The Story Behind Toilets. Heinemann Library, 2009.
"Residential Toilets." U.S. Environmental Protection Agency, 3 June 2024, www.epa.gov/watersense/residential-toilets. Accessed 1 Oct. 2024.